1. EIS Spectrum Analyser

EIS Spectrum Analyser is a standalone program for analysis and simulation of impedance spectra. The analyser routine is based on algorithms of the PDEIS spectrometer. In the original (potentiodynamic) version the impedance data analysis is applied on a 3D spectrum and gives dependences of the ac response components on electrode potential.

This standalone program has been adapted to solve a wide range of tasks in the common (stationary) impedance spectroscopy. In addition to data fitting to equivalent circuits with resistors, capacitors, inductors, constant phase, Warburg (3 types), user-defined and Gerischer elements, the EIS Spectrum Analyser provides various tests for data consistency and quality of fit. It has also a built-in impedance spectra simulation routine, tools for impedance data processing (subtraction of circuit elements and subcircuits, normalisation for electrode surface area) and plotting in various formats. The program is free for noncommercial use.

See: http://www.abc.chemistry.bsu.by/vi/analyser/

2. ZsimpWin

ZSimpWin is a EIS Data Analysis program that does not require user-input on initial values. ZSimpWin is an Electrochemical Impedance Spectroscopy (EIS) Data Analysis Software integrated with the 
VersaStudio software to provide straightforward and versatile equivalent circuit model fitting.  Innovative concepts have been implemented to achieve the following performance:

• Minimal user input: The user specifies a job by selecting a model for an impedance data set, and simply requests execution to ZSimpWin.  
• Automatic analysis: Parameters associated with the selected model are determined automatically. ZSimpWin assigns an initial guess of these parameters (default = Auto Setup option), starts computation using the initial guess, finds results, improves these results a number of times until desired results are obtained, and then saves the final results. 
• Batch Analysis: Setup a batch by including multiple jobs and process in sequence.  
• Output results in various forms: Results consist of plots, estimated parameters, and historical records of computation process.  Each or several combinations can be printed or copied to Windows clipboard. 
  
• Requires only mouse button clicks:  The whole process requires no entry of numbers or character strings.                                                                
• Compatible with Windows 10, 8 , 7 and XP.

See: https://www.ameteksi.com/products/software/zsimpwin

3. Zview

ZView software from Scribner Associates offers best-in-class equivalent circuit modeling. Fit common circuits instantly, generate publication-quality graphs quickly. ZView integrates easily with SAI measurement softwares, and supports testing hardware from Solartron, PAR, and others. Increase your data processing efficiency quickly and easily with ZView.

See: https://sai-zview1.software.informer.com/3.4/

Introduction of EIS

Electrochemical impedance spectroscopy (EIS) is one of the most powerful methods in the study of corrosion. The EIS method can be used to measure the rate or rate of corrosion, monitor corrosion, determine coating integrity, and study the mechanism of reactions. In this article, which is a compilation, translation and purification of references [1] and [2], the applications, limitations and benefits of this method are introduced. EIS is usually performed by applying an AC current signal to a state-steady electrochemical system and then measuring the current response. Because the amount of disturbance applied, the AC signal, is a small excitation signal, EIS is essentially a non-destructive technique. To apply this method requires a geometrically corroded cell that includes a reference electrode, as well as equipment capable of measuring and recording the electrical response of an electrochemical cell over a wide range of applied AC frequencies. When a small sine voltage is applied to an electrochemical system according to Equation 9, a sine current response in the form of Equation 2 will be observed. Due to the lack of rapid response of relaxation processes or the release of dipoles, the rotation of bipolar components in response to the applied alternating electric field results in a phase change.

Typical measurements in EIS are usually made in a three-electrode system, as shown in Figure 9. The entire set includes an electrochemical cell, a frequency generator, a frequency response analyzer (FRA), and a computer that is used to control experiments and store information. A potentiostat is used to control the electrode potential. The FRA is the heart of the system that calculates the imaginary and real parts of impedance. The frequency studied is usually in the cell range. 0.01–100,000 Hz (cycles / s) Electrochemical, the test material is embedded as an electrode working. Electrode counters, which must be neutral and not involved in the electrochemical reaction, are usually made of Pt, gold, or graphite. Reference electrodes are usually conventional saturated calomel electrodes (SCE) or AgCl / Ag electrodes. However, in many applications, such as thin electrolyte layers or in high temperature environments, conventional reference electrodes do not work properly. In these cases, systems without conventional reference electrodes should be used. As an example, we can refer to the two-electrode system, which usually consists of two identical electrodes consisting of test materials (Figure 2-a) and is widely used in atmospheric corrosion monitoring [5. [Figure 2-b) Indicates that it is used to monitor high-corrosion corrosion. , Multi-electrode array (Figure 2-c) can be used for EIS monitoring.

An uncompensated electrolyte resistance (Rs), a specific capacitance value related to the coating applied to the metal surface (Cc), a hole resistance in the coating of resistance pathways (pore solution resistance) (Rcp) in the coating where ions are transported, a The specific capacitance corresponding to the double layer in the solution / metal (Cdl) and a resistance (Rp) which is the resistance of the charge transfer process (ie corrosion), and in other words, the resistance to polarization at the solution / metal interface. In Beaunier rectified circuits, usually other additional components, such as the constant phase element (CPE), the phase component of the inductance or induction coefficient (L) and the resistor (W (Warburg,) replace the resistor or capacitor. Special capacitance, accuracy and quality of experimental data fitting with these circuits are improved, but the physical interpretation of the results will be ambiguous, this is because the CPE module can not be easily obtained with capacitor capacitance, and the capacity power calculation is calculated. Capacitor from CPE parameters requires accurate knowledge of the physical reasons for CPE behavior [7.] An example of a Nyquist diagram and its equivalent wind diagram in doubt ل 4 is given. The position of the equivalent circuit components in these diagrams is given on each diagram. In addition to common, simple equivalent circuit models, more complex physical models are sometimes used to interpret EIS data obtained from more complex systems. An example is the line transmission model (TML), which was first used by Levie de in his research on porous electrodes [11] [TML model and its modified models for analyzing EIS data on atmospheric corrosion under electrolyte layers Thin [5] as well as stress corrosion [12] have been used.

Atmospheric corrosion is an electrochemical process that usually occurs beneath a thin electrolyte surface layer, in the presence or absence of salt contaminants and dissolved gases in these layers. It has been shown that the atmospheric corrosion rate of metals depends on the thickness of the electrolyte thin film. The thickness of the electrolyte layer affects the rate of oxygen transfer through the electrolyte layer and the dissolution of corrosion products. The rate of oxygen transfer determines the rate of cathodic reaction (in neutral and alkaline solutions) and the dissolution of corrosion products determines the anodic process. Monitoring or corrosion of thin electrolytic films using conventional electrochemical methods is challenging The electrolyte is thin, very high, leading to a sharp drop in ohmic potential and a non-uniform current distribution that makes it difficult to measure the corrosion rate [5. The solution resistance is estimated from the impedance measured in the high frequency range of the EIS spectrum, and the sum of the resistivity (Rp) and the solution resistance (RS) from the impedance in the low frequency range. Figure 4b: The calculated resistive palliation is then converted to the corrosion rate of the metal. To study atmospheric corrosion of the metal surface under thin electrolytic layers (100010-1000 ~) by EIS, it is possible to expose the corrosion cell to the atmosphere. weather Use outside or use laboratory-drier simulation cycles [19–13,10,9,5. Used in epoxy resin (Figure 2-A) to make cells. The study can be done in two ways: either the impedance spectrum is recorded over a wide range of applied frequencies or the impedance value is checked continuously at two constant frequencies. The study of EIS spectrum in a wide frequency range has shown that a one-dimensional equivalent circuit model called TML can be used to model the corrosion rate in these systems [5. Palrization is calculated from the impedance difference measured at the above two frequencies. The corrosion rate is then calculated using the polarization resistance [5]. Nishikata et al. [5] also used shoulder-shaped electrodes to study atmospheric corrosion to EIS. Impedance information was monitored at 10 mHz and 10 kHz. The results showed that the inverse of the mean impedance at low frequency completely corresponds to the corrosion rate obtained by gravimetry. Wetting of Time also occurs when the amount of solution conductivity or high frequency impedance image (Rs image) exceeds a threshold value. One of the disadvantages of this method in the study of atmospheric corrosion is that if the metal surface is covered with a thick layer of corrosion products, the low frequency impedance can not be equated to the polarization resistance. Finally, Ma et al. [20] used a complex multi-electrode system to study atmospheric corrosion and found the results to be more accurate than two-electrode systems. 3.2 Corrosion of reinforced concrete Rebar (in concrete is the main reason for reducing the life of reinforced concrete structures that are exposed to strong corrosive environments) such as marine environment. Therefore, reinforcement corrosion monitoring is very important to assess the health status of reinforced concrete. Various methods are used to evaluate corrosion in reinforced concrete, and electrochemical methods are among the most common. Among these, EIS is an attractive technique because, as mentioned earlier, it is almost a non-destructive method. In addition, EIS is suitable for environments with very high strength, such as concrete, because it is essentially a transient method and does not require the system to be in a stable state [21. [In steel systems (reinforcement) / Concrete, information Various parameters such as the presence of surface films, concrete properties, joint joint corrosion and mass transfer phenomena can be obtained from the EIS method [21. [22] [In addition, the high-frequency impedance of information in Moore Provides dielectric properties of concrete, and low-frequency impedance information on the properties of passive films (surface oxide layers) on steel. Studies that began three decades ago have proven the validity of EIS as a technique for studying rebar corrosion in concrete, both experimentally and theoretically. John et al. (9189) monitored corrosion of rebar in high porosity concrete using EIS. They obtained both the corrosion rate of the steel rebars and the information on the steel surface layers. Later, more fundamental work was done by McDonald et al. To establish the application of EIS in the detection of rebar corrosion in concrete [3]. In this work, the rebar was simulated as a one-dimensional electrical transmission line. Their results show that imaginary and real components of impedance and phase angle can be used to detect corrosion of rebar embedded in concrete, but this is only possible at very low frequencies (for example, 1 mHz). It was also found that monitoring the peak voltage at the concrete surface just above the rebar helps to fully detect corrosion.

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Nuclear Magnetic Resonance (NMR) spectroscopy is an incredibly powerful tool for characterizing molecular structures. When submitting to the FDA or other regulatory agencies, full structural characterization by NMR provides crucial evidence of compound identity. A combination of 1-dimensional and 2-dimensional NMR experiments are necessary for complete confidence in chemical structure.

This post will walk you through the steps to fully characterize a molecule by 1- and 2-dimensional NMR, including on how to perform NMR interpretation.

Step 1: ¹H-NMR

The first step in structural characterization is 1-dimensional proton ¹H-NMR. The chemical shift, multiplicity, coupling constants, and integration are all factors to consider when assigning protons. In this example, only three protons can be assigned by the proton spectrum alone: protons 3, 4, and 6.

To begin, let’s start with proton 3. Proton 3 is the only methyl group in the structure, and therefore must integrate to 3 protons. The only peak with an integration of 3 is the doublet at 1.770 ppm. The high field chemical shift supports this assignment. The peak is split into a doublet with a coupling constant of 1.2 Hz, reflecting the long-range coupling between protons 3 and 4, which also supports this assignment.

Protons that are coupled to each other should exhibit the same coupling constant. The long-range coupling constant observed for proton 3 (J=1.2 Hz, split into a doublet by proton 4) is reflected in the coupling constant for proton 4 (J=1.2 Hz, split into a quartet by proton 3). Therefore, the peak at 7.690 ppm must represent proton 4! The integration and chemical shift support the assignment, as proton 4 is the only aromatic proton in the structure.

There is only one singlet in the ¹H-NMR spectrum. The only proton that should show up as a singlet is proton 6, as it has no neighboring protons that would split the peak (the nearest proton is 5 bonds away!). The chemical shift of 11.256 ppm supports this assignment, as imide protons often show up far downfield. The peak also integrates to 1 proton, supporting the assignment.

The remaining protons are doublets, triplets, and multiplets that can be assigned by 2-dimensional COSY.

Step 2: ¹H-¹H COSY

¹H-¹H Correlation Spectroscopy (COSY) shows the correlation between hydrogens which are coupled to each other in the ¹H NMR spectrum. The ¹H spectrum is plotted on both 2D axes. While 2-bond and 3-bond ¹H-¹H coupling is easily visible by COSY, long range coupling can also be observed with long acquisition times. The cross-peaks (not on the diagonal) that are symmetric to the diagonal show the COSY correlations. For example, protons 3 and 4 are coupled to each other, since they form a box pattern symmetric to the diagonal. This confirms assignments 3 and 4 made from the proton spectrum alone.

Two types of COSY coupling: 3-bond short range coupling between protons 7 and 8 (red) and 4-bond long range coupling between protons 3 and 4 (blue).

My favorite way to analyze a COSY spectrum with many unassigned protons is to make a table of correlations, like the one seen here. Look at the table for any clear differences in correlation and begin there! In this example, all unassigned protons show one or two COSY correlations-except the proton at 4.233 ppm, which correlates to threeother protons by COSY. The only proton expected to correlate with three nonequivalent protons is proton 9!

Now that proton 9 has been assigned, the fun really begins. Thymidine’s structure suggests that proton 9 should couple protons 8, 10, and 11. Based on the COSY, proton 9 couples protons at 2.068 ppm (2H), 3.754 ppm (1H), and 5.209 ppm (1H). From this list, we can easily assign proton 8 as the peak at 2.068 ppm based on its integration of 2 protons. To differentiate protons 10 and 11, take a look at our COSY table; 3.754 ppm shows two COSY correlations, while 5.209 ppm only shows one. Therefore, we can assign proton 10 as 5.209 ppm and proton 11 as 3.754 ppm.

Once proton 8 has been assigned, we can easily assign proton 7 based on the remaining COSY correlation for proton 8. Proton 7’s peak at 6.163 ppm is split into a triplet by the two 8 protons, confirming the assignment.

All that remains are protons 12 and 13. We can assign proton 12 (3.564 ppm) based on its integration of 2H and its COSY correlation to proton 11. The last remaining peak at 4.999 ppm must be proton 13; this is confirmed by COSY correlation with proton 12, triplet multiplicity based on splitting by proton 12, and integration of one proton.

Now we have a fully assigned ¹H-NMR spectrum! This spectrum will help us assign our carbons using HSQC and HMBC NMR spectroscopy.

Step 3: ¹³C-NMR

Carbon NMR is a necessary step in full structural characterization. However, ¹³C-NMR alone does not provide enough information to assign the carbons in the molecule. The NMR spectrum below does confirm the number of carbons in the molecule; however, HSQC and HMBC (we will get to these soon!) are necessary to assign the carbons with confidence. Note that one of the carbons is hidden beneath the solvent signal but is clearly visible after zooming into that region.

Step 4: DEPT-45, 90, and 135

Distortionless Enhancement of Polarization Transfer (DEPT) experiments help assign carbon peaks by determining the number of protons attached to each carbon. For very simple molecules, DEPT may be enough to partially or fully assign all carbons. In complex molecules, DEPT and HSQC together are useful for confirming both carbon and proton assignments. For example, the DEPT experiments below can only identify carbon 3-it is the only CH₃ peak. I always go back and use DEPT to confirm the carbons I assigned by HSQC.

• DEPT-45 shows CH, CH₂, and CH₃ carbons as positive peaks. Carbons with no protons are not visible.
• DEPT-90 shows only CH peaks as positive peaks. Carbons with no protons, CH₂, and CH₃ carbons are not visible.
• DEPT-135 shows CH and CH₃ carbons as positive peaks and CH₂ carbons as negative peaks. Carbons with no protons are not visible.

Step 5: ¹H-¹³C HSQC

¹H-¹³C Heteronuclear Single Quantum Coherence Spectroscopy (HSQC) shows which hydrogens are directly attached to which carbon atoms. The ¹H spectrum is shown on the horizontal axis and the ¹³C spectrum is shown on the vertical axis. The HSQC spectrum is most valuable when protons have already been assigned.

For example, HSQC shows a correlation between proton 4 and the carbon at 136.113 ppm; this carbon is now assigned as carbon 4. Carbons 3, 4, 7, 8, 9, 11, and 12 are assigned by HSQC. Only 1-bond correlations are observed, so HSQC assignments are relatively straightforward. The DEPT experiments also confirm these assignments. HSQC is also useful in confirming proton assignments of nitrogen or oxygen-bound protons; they show no signal by HSQC. This further supports the assignments of protons 6, 10, and 13.

An example correlation between proton and carbon 4 is observed by HSQC.

Step 6: ¹H-¹³C HMBC

¹H-¹³C Heteronuclear Multiple Bond Correlation Spectroscopy (HMBC) shows the correlations between protons and carbons that are separated by multiple bonds. The ¹H spectrum is shown on the horizontal axis and the ¹³C spectrum is shown on the vertical axis. Correlated atoms are shown in blue and the connecting atoms are shown in red. Note that direct hydrogen-carbon bonds (1-bond correlations) are generally not seen. For example, hydrogen 4 shows correlations with carbons 1, 2, 3, 5, and 7, but not carbon 4.

HMBC interactions between proton 4 and carbons 1, 2, 3, 5, and 7.

HMBC is incredibly useful for assigning carbons that have no protons attached. In this example, carbons 1, 2, and 5 have no protons attached. Carbon 1 is assigned by HMBC interactions with protons 3, 4, and 6; carbon 2 by interaction with protons 3, 4, 6, and 7; and carbon 5 by interactions with protons 4 and 7 only. The chemical environment of carbon 5 suggests it would appear more downfield than carbon 1, which confirms these assignments.

HMBC also confirms assignments that were based solely on the proton and COSY spectrum. For example, protons 10 and 13 are differentiated by HMBC; proton 10 is confirmed by interactions with carbons 8, 9, and 11, while proton 13 is confirmed by interactions with 11 and 12. HMBC supports all proton and all carbon assignments, unambiguously confirming both the structure and analysis of thymidine.

At Emery Pharma, we are experts in 1D and 2D NMR characterization and structure elucidation; in fact, 2D NMR projects are some of our favorites! We have supported numerous pharmaceutical companies in full NMR characterization for API submissions to regulatory agencies, as well as complete structure elucidation of impurities. We provide a fully annotated report with images similar to those seen here and support our results with high resolution mass spectrometry and elemental analysis. 

Some nuclei rotate around their axis like electrons. In the presence of an external magnetic field, a rotating nucleus has only a small number of stable orientations. Nuclear magnetic resonance (NMR) occurs when a spinning core is excited from a lower energy orientation to a higher energy orientation in the presence of a magnetic field by absorbing enough electromagnetic radiation. Nuclear magnetic resonance spectroscopy involves measuring the amount of energy required to change spin nuclei from a stable orientation to a more unstable orientation in a magnetic field. Because spin-core nuclei change direction in a magnetic field at different frequencies, different frequencies of absorbing radiation are needed to change the orientation of spin-core nuclei. The frequency at which the absorption takes place is used for analysis and spectroscopy [1].

Nuclear magnetic resonance was first discovered independently in 1946 by Felix Bloch of Stanford University and Edward Parcel of Harvard University. They were able to show the absorption of electromagnetic radiation as a result of the transfer of the energy level of the nucleus in a strong magnetic field. The two physicists won the Nobel Prize in 1952 for their work. In the first five years after the discovery of the nuclear magnetic resonance method, chemists discovered that the molecular environment of objects affects the absorption of radiation by nuclei in the presence of a magnetic field, and this effect could be related to the structure of the molecule. Since then, the growth of magnetic resonance spectroscopy has been explosive and this method has had a significant effect on the development of organic chemistry, inorganic chemistry and biochemistry [2]. In 1999, a team of Canadian physicists developed a new method using the Beta Nuclear Magnetic Resonance Method, which is capable of demonstrating the magnetic and electrical properties of very thin layers and surfaces. BetaNMR methods are used in nanoscience. Be [3].

The magnitude of the spin angle motion in the nuclei is determined by the quantum number of the nucleus spin. Quantum number The core spin of any number can be integer or semi-integer. In 16 O and 12C non-spin nuclei, the quantum spin number of the nucleus is zero. Cores that are not spin and therefore do not have the magnitude of the spin angle motion can not be detected by NMR spectroscopy. Spin-core cores with spherical charge distribution have a spin quantum number of 1/2. Examples of these nuclei include 13C, 19F, 3H, 15N, 31P and 1H, which have a quantum number of 1/2 and a magnetic moment. In order for a nucleus in a magnetic field to absorb a large amount of electromagnetic radiation, it must have a high frequency in the sample and also have a relatively large magnetic moment (µ). Cores that have both properties in question include 1H, 19F, 21P. Most NMR measurements are usually performed for 1 h. Measurements of other nuclei are often performed using signal amplification methods to observe the spectrum. Usually, among the nuclei with low relative frequency that show the magnetic resonance of the nucleus, 12 C, 15N, 16O are the most important for chemists. The magnetic resonance method of the hydrogen nucleus (1H), which is used more than other nuclei, has a magnetic torque of about 79.2 برای. It will be magnetic. For other cores used for nuclear magnetic resonance spectroscopy, the magnetic torque for 21P, 19F 12C is 6873.2, 1305.1 and 0.7022, respectively [4]. In most cases, the sensitivity of non-proton core magnetic resonance devices, such as 12C, etc., is lower than that of HNMR. Also, in most compounds, the natural abundance of non-proton magnetic nuclei is significantly lower than that of protons. This factor causes the NMR spectra of non-proton nuclei to have a relatively low noise signal. The peaks of these spectra are small, and often the spectrum cannot be determined if the same device used for proton nucleus (PMR) NMR is used. Due to the low signal-to-noise ratio in these cases, most devices designed to record the NMR spectra of non-proton nuclei use multiple traverses with signal averaging techniques. The most common devices for spectral peak extraction use the Fourier transform. Fourier transformers are also used to prepare PMR spectra of dilute solutions and complex molecules, such as proteins, in which the amount of a particular proton in the molecule is small. The difference between PMR spectra and other NMR spectra is in the range of chemical displacement. The chemical displacement range for PMR is 10PPM in most cases. While for the 12C core the chemical displacement is up to about 200PPM, for the 19F and 21P spectra it is 300 and 400PPM, respectively. In NMR methods, the units used are usually time (seconds), angle (degrees or radians), temperature (Kelvin), magnetic field strength (Tesla, T), energy (joules), vibration (rpm) and power ( Watts) is. [5] Components of the NMR Device The important components of an NMR spectrometer are shown schematically in Figure (1). A brief description of each component is given below.

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Over the past fifty years nuclear magnetic resonance spectroscopy, commonly referred to as nmr, has become the preeminent technique for determining the structure of organic compounds. Of all the spectroscopic methods, it is the only one for which a complete analysis and interpretation of the entire spectrum is normally expected. Although larger amounts of sample are needed than for mass spectroscopy, nmr is non-destructive, and with modern instruments good data may be obtained from samples weighing less than a milligram. To be successful in using nmr as an analytical tool, it is necessary to understand the physical principles on which the methods are based.

The nuclei of many elemental isotopes have a characteristic spin (I). Some nuclei have integral spins (e.g. I = 1, 2, 3 ….), some have fractional spins (e.g. I = 1/2, 3/2, 5/2 ….), and a few have no spin, I = 0 (e.g. ¹²C, ¹⁶O, ³²S, ….). Isotopes of particular interest and use to organic chemists are ¹H, ¹³C, ¹⁹F and ³¹P, all of which have I = 1/2. Since the analysis of this spin state is fairly straightforward, our discussion of nmr will be limited to these and other I = 1/2 nuclei.

The following features lead to the nmr phenomenon:

1. A spinning charge generates a magnetic field, as shown by the animation on the right. The resulting spin-magnet has a magnetic moment (μ) proportional to the spin.
2. In the presence of an external magnetic field (B0), two spin states exist, +1/2 and -1/2. The magnetic moment of the lower energy +1/2 state is aligned with the external field, but that of the higher energy -1/2 spin state is opposed to the external field. Note that the arrow representing the external field points North.
3. The difference in energy between the two spin states is dependent on the external magnetic field strength, and is always very small. The following diagram illustrates that the two spin states have the same energy when the external field is zero, but diverge as the field increases. At a field equal to Bx a formula for the energy difference is given (remember I = 1/2 and μ is the magnetic moment of the nucleus in the field).
Strong magnetic fields are necessary for nmr spectroscopy. The international unit for magnetic flux is the tesla (T). The earth’s magnetic field is not constant, but is approximately 10-4 T at ground level. Modern nmr spectrometers use powerful magnets having fields of 1 to 20 T. Even with these high fields, the energy difference between the two spin states is less than 0.1 cal/mole. To put this in perspective, recall that infrared transitions involve 1 to 10 kcal/mole and electronic transitions are nearly 100 time greater. For nmr purposes, this small energy difference (ΔE) is usually given as a frequency in units of MHz (106 Hz), ranging from 20 to 900 Mz, depending on the magnetic field strength and the specific nucleus being studied. Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2 spin state. Note that this electromagnetic radiation falls in the radio and television broadcast spectrum. Nmr spectroscopy is therefore the energetically mildest probe used to examine the structure of molecules.  The nucleus of a hydrogen atom (the proton) has a magnetic moment μ = 2.7927, and has been studied more than any other nucleus. The previous diagram may be changed to display energy differences for the proton spin states (as frequencies) by mouse clicking anywhere within it.
4. For spin 1/2 nuclei the energy difference between the two spin states at a given magnetic field strength will be proportional to their magnetic moments. For the four common nuclei noted above, the magnetic moments are: 1H μ = 2.7927, 19F μ = 2.6273, 31P μ = 1.1305 & 13C μ = 0.7022. These moments are in nuclear magnetons, which are 5.05078•10-27 JT-1. The following diagram gives the approximate frequencies that correspond to the spin state energy separations for each of these nuclei in an external magnetic field of 2.35 T. The formula in the colored box shows the direct correlation of frequency (energy difference) with magnetic moment (h = Planck’s constant = 6.626069•10-34 Js).

      2. Proton NMR Spectroscopy
This important and well-established application of nuclear magnetic resonance will serve to illustrate some of the novel aspects of this method. To begin with, the nmr spectrometer must be tuned to a specific nucleus, in this case the proton. The actual procedure for obtaining the spectrum varies, but the simplest is referred to as the continuous wave (CW) method. A typical CW-spectrometer is shown in the following diagram. A solution of the sample in a uniform 5 mm glass tube is oriented between the poles of a powerful magnet, and is spun to average any magnetic field variations, as well as tube imperfections. Radio frequency radiation of appropriate energy is broadcast into the sample from an antenna coil (colored red). A receiver coil surrounds the sample tube, and emission of absorbed rf energy is monitored by dedicated electronic devices and a computer. An nmr spectrum is acquired by varying or sweeping the magnetic field over a small range while observing the rf signal from the sample. An equally effective technique is to vary the frequency of the rf radiation while holding the external field constant.

As an example, consider a sample of water in a 2.3487 T external magnetic field, irradiated by 100 MHz radiation. If the magnetic field is smoothly increased to 2.3488 T, the hydrogen nuclei of the water molecules will at some point absorb rf energy and a resonance signal will appear. An animation showing this may be activated by clicking the Show Field Sweep button. The field sweep will be repeated three times, and the resulting resonance trace is colored red. For visibility, the water proton signal displayed in the animation is much broader than it would be in an actual experiment.

Since protons all have the same magnetic moment, we might expect all hydrogen atoms to give resonance signals at the same field / frequency values. Fortunately for chemistry applications, this is not true. By clicking the Show Different Protons button under the diagram, a number of representative proton signals will be displayed over the same magnetic field range. It is not possible, of course, to examine isolated protons in the spectrometer described above; but from independent measurement and calculation it has been determined that a naked proton would resonate at a lower field strength than the nuclei of covalently bonded hydrogens. With the exception of water, chloroform and sulfuric acid, which are examined as liquids, all the other compounds are measured as gases.

Why should the proton nuclei in different compounds behave differently in the nmr experiment ? 
The answer to this question lies with the electron(s) surrounding the proton in covalent compounds and ions. Since electrons are charged particles, they move in response to the external magnetic field (B_o) so as to generate a secondary field that opposes the much stronger applied field. This secondary field shields the nucleus from the applied field, so B_o must be increased in order to achieve resonance (absorption of rf energy). As illustrated in the drawing on the right, B_o must be increased to compensate for the induced shielding field. In the upper diagram, those compounds that give resonance signals at the higher field side of the diagram (CH₄, HCl, HBr and HI) have proton nuclei that are more shielded than those on the lower field (left) side of the diagram. 
The magnetic field range displayed in the above diagram is very small compared with the actual field strength (only about 0.0042%). It is customary to refer to small increments such as this in units of parts per million (ppm). The difference between 2.3487 T and 2.3488 T is therefore about 42 ppm. Instead of designating a range of nmr signals in terms of magnetic field differences (as above), it is more common to use a frequency scale, even though the spectrometer may operate by sweeping the magnetic field. Using this terminology, we would find that at 2.34 T the proton signals shown above extend over a 4,200 Hz range (for a 100 MHz rf frequency, 42 ppm is 4,200 Hz). Most organic compounds exhibit proton resonances that fall within a 12 ppm range (the shaded area), and it is therefore necessary to use very sensitive and precise spectrometers to resolve structurally distinct sets of hydrogen atoms within this narrow range. In this respect it might be noted that the detection of a part-per-million difference is equivalent to detecting a 1 millimeter difference in distances of 1 kilometer.

Chemical Shift

Unlike infrared and uv-visible spectroscopy, where absorption peaks are uniquely located by a frequency or wavelength, the location of different nmr resonance signals is dependent on both the external magnetic field strength and the rf frequency. Since no two magnets will have exactly the same field, resonance frequencies will vary accordingly and an alternative method for characterizing and specifying the location of nmr signals is needed. This problem is illustrated by the eleven different compounds shown in the following diagram. Although the eleven resonance signals are distinct and well separated, an unambiguous numerical locator cannot be directly assigned to each.

One method of solving this problem is to report the location of an nmr signal in a spectrum relative to a reference signal from a standard compound added to the sample. Such a reference standard should be chemically unreactive, and easily removed from the sample after the measurement. Also, it should give a single sharp nmr signal that does not interfere with the resonances normally observed for organic compounds. Tetramethylsilane, (CH₃)₄Si, usually referred to as TMS, meets all these characteristics, and has become the reference compound of choice for proton and carbon nmr.
Since the separation (or dispersion) of nmr signals is magnetic field dependent, one additional step must be taken in order to provide an unambiguous location unit. This is illustrated for the acetone, methylene chloride and benzene signals by clicking on the previous diagram. To correct these frequency differences for their field dependence, we divide them by the spectrometer frequency (100 or 500 MHz in the example), as shown in a new display by again clicking on the diagram. The resulting number would be very small, since we are dividing Hz by MHz, so it is multiplied by a million, as shown by the formula in the blue shaded box. Note that ν_ref is the resonant frequency of the reference signal and ν_samp is the frequency of the sample signal. This operation gives a locator number called the Chemical Shift, having units of parts-per-million (ppm), and designated by the symbol δ   Chemical shifts for all the compounds in the original display will be presented by a third click on the diagram.

The compounds referred to above share two common characteristics:

• The hydrogen atoms in a given molecule are all structurally equivalent, averaged for fast conformational equilibria. 
• The compounds are all liquids, save for neopentane which boils at 9 °C and is a liquid in an ice bath.

The first feature assures that each compound gives a single sharp resonance signal. The second allows the pure (neat) substance to be poured into a sample tube and examined in a nmr spectrometer. In order to take the nmr spectra of a solid, it is usually necessary to dissolve it in a suitable solvent. Early studies used carbon tetrachloride for this purpose, since it has no hydrogen that could introduce an interfering signal. Unfortunately, CCl₄ is a poor solvent for many polar compounds and is also toxic. Deuterium labeled compounds, such as deuterium oxide (D₂O), chloroform-d (DCCl₃), benzene-d₆(C₆D₆), acetone-d₆ (CD₃COCD₃) and DMSO-d₆ (CD₃SOCD₃) are now widely used as nmr solvents. Since the deuterium isotope of hydrogen has a different magnetic moment and spin, it is invisible in a spectrometer tuned to protons.

From the previous discussion and examples we may deduce that one factor contributing to chemical shift differences in proton resonance is the inductive effect. If the electron density about a proton nucleus is relatively high, the induced field due to electron motions will be stronger than if the electron density is relatively low. The shielding effect in such high electron density cases will therefore be larger, and a higher external field (B_o) will be needed for the rf energy to excite the nuclear spin. Since silicon is less electronegative than carbon, the electron density about the methyl hydrogens in tetramethylsilane is expected to be greater than the electron density about the methyl hydrogens in neopentane (2,2-dimethylpropane), and the characteristic resonance signal from the silane derivative does indeed lie at a higher magnetic field. Such nuclei are said to be shielded. Elements that are more electronegative than carbon should exert an opposite effect (reduce the electron density); and, as the data in the following tables show, methyl groups bonded to such elements display lower field signals (they are deshielded). The deshielding effect of electron withdrawing groups is roughly proportional to their electronegativity, as shown by the left table. Furthermore, if more than one such group is present, the deshielding is additive (table on the right), and proton resonance is shifted even further downfield.

The general distribution of proton chemical shifts associated with different functional groups is summarized in the following chart. Bear in mind that these ranges are approximate, and may not encompass all compounds of a given class. Note also that the ranges specified for OH and NH protons (colored orange) are wider than those for most CH protons. This is due to hydrogen bonding variations at different sample concentrations.

Proton Chemical Shift Ranges*
Low Field Region		High Field Region
	* For samples in CDCl3 solution. The δ scale is relative to TMS at δ = 0.

To make use of a calculator that predicts aliphatic proton chemical shifts Click Here. This application was developed at Colby College.

Signal Strength

The magnitude or intensity of nmr resonance signals is displayed along the vertical axis of a spectrum, and is proportional to the molar concentration of the sample. Thus, a small or dilute sample will give a weak signal, and doubling or tripling the sample concentration increases the signal strength proportionally. If we take the nmr spectrum of equal molar amounts of benzene and cyclohexane in carbon tetrachloride solution, the resonance signal from cyclohexane will be twice as intense as that from benzene because cyclohexane has twice as many hydrogens per molecule. This is an important relationship when samples incorporating two or more different sets of hydrogen atoms are examined, since it allows the ratio of hydrogen atoms in each distinct set to be determined. To this end it is necessary to measure the relative strength as well as the chemical shift of the resonance signals that comprise an nmr spectrum. Two common methods of displaying the integrated intensities associated with a spectrum are illustrated by the following examples. In the three spectra in the top row, a horizontal integrator trace (light green) rises as it crosses each signal by a distance proportional to the signal strength. Alternatively, an arbitrary number, selected by the instrument’s computer to reflect the signal strength, is printed below each resonance peak, as shown in the three spectra in the lower row. From the relative intensities shown here, together with the previously noted chemical shift correlations, the reader should be able to assign the signals in these spectra to the set of hydrogens that generates each. If you click on one of the spectrum signals (colored red) or on hydrogen atom(s) in the structural formulas the spectrum will be enlarged and the relationship will be colored blue.
Hint: When evaluating relative signal strengths, it is useful to set the smallest integration to unity and convert the other values proportionally.

Hydroxyl Proton Exchange and the Influence of Hydrogen Bonding

The last two compounds in the lower row are alcohols. The OH proton signal is seen at 2.37 δ in 2-methyl-3-butyne-2-ol, and at 3.87 δ in 4-hydroxy-4-methyl-2-pentanone, illustrating the wide range over which this chemical shift may be found. A six-membered ring intramolecular hydrogen bond in the latter compound is in part responsible for its low field shift, and will be shown by clicking on the hydroxyl proton. We can take advantage of rapid OH exchange with the deuterium of heavy water to assign hydroxyl proton resonance signals . As shown in the following equation, this removes the hydroxyl proton from the sample and its resonance signal in the nmr spectrum disappears. Experimentally, one simply adds a drop of heavy water to a chloroform-d solution of the compound and runs the spectrum again. The result of this exchange is displayed below.

R-O-H   +   D2O      R-O-D   +   D-O-H

Hydrogen bonding shifts the resonance signal of a proton to lower field ( higher frequency ). Numerous experimental observations support this statement, and a few of these will be described here.

i)   The chemical shift of the hydroxyl hydrogen of an alcohol varies with concentration. Very dilute solutions of 2-methyl-2-propanol, (CH3)3COH, in carbon tetrachloride solution display a hydroxyl resonance signal having a relatively high-field chemical shift (< 1.0 δ ). In concentrated solution this signal shifts to a lower field, usually near 2.5 δ.
ii)   The more acidic hydroxyl group of phenol generates a lower-field resonance signal, which shows a similar concentration dependence to that of alcohols. OH resonance signals for different percent concentrations of phenol in chloroform-d are shown in the following diagram (C-H signals are not shown).
iii)   Because of their favored hydrogen-bonded dimeric association, the hydroxyl proton of carboxylic acids displays a resonance signal significantly down-field of other functions. For a typical acid it appears from 10.0 to 13.0 δ and is often broader than other signals. The spectra shown below for chloroacetic acid (left) and 3,5-dimethylbenzoic acid (right) are examples.
iv)   Intramolecular hydrogen bonds, especially those defining a six-membered ring, generally display a very low-field proton resonance. The case of 4-hydroxypent-3-ene-2-one (the enol tautomer of 2,4-pentanedione) not only illustrates this characteristic, but also provides an instructive example of the sensitivity of the nmr experiment to dynamic change. In the nmr spectrum of the pure liquid, sharp signals from both the keto and enol tautomers are seen, their mole ratio being 4 : 21 (keto tautomer signals are colored purple). Chemical shift assignments for these signals are shown in the shaded box above the spectrum. The chemical shift of the hydrogen-bonded hydroxyl proton is δ 14.5, exceptionally downfield. We conclude, therefore, that the rate at which these tautomers interconvert is slow compared with the inherent time scale of nmr spectroscopy.
Two structurally equivalent structures may be drawn for the enol tautomer (in magenta brackets). If these enols were slow to interconvert, we would expect to see two methyl resonance signals associated with each, one from the allylic methyl and one from the methyl ketone. Since only one strong methyl signal is observed, we must conclude that the interconversion of the enols is very fast-so fast that the nmr experiment detects only a single time-averaged methyl group (50% α-keto and 50% allyl).

Although hydroxyl protons have been the focus of this discussion, it should be noted that corresponding N-H groups in amines and amides also exhibit hydrogen bonding nmr shifts, although to a lesser degree. Furthermore, OH and NH groups can undergo rapid proton exchange with each other; so if two or more such groups are present in a molecule, the nmr spectrum will show a single signal at an average chemical shift. For example, 2-hydroxy-2-methylpropanoic acid, (CH₃)₂C(OH)CO₂H, displays a strong methyl signal at δ 1.5 and a 1/3 weaker and broader OH signal at δ 7.3 ppm. Note that the average of the expected carboxylic acid signal (ca. 12 ) and the alcohol signal (ca. 2 ) is 7. Rapid exchange of these hydrogens with heavy water, as noted above, would cause the low field signal to disappear.

π-Electron Functions

An examination of the proton chemical shift chart (above) makes it clear that the inductive effect of substituents cannot account for all the differences in proton signals. In particular the low field resonance of hydrogens bonded to double bond or aromatic ring carbons is puzzling, as is the very low field signal from aldehyde hydrogens. The hydrogen atom of a terminal alkyne, in contrast, appears at a relatively higher field. All these anomalous cases seem to involve hydrogens bonded to pi-electron systems, and an explanation may be found in the way these pi-electrons interact with the applied magnetic field.
Pi-electrons are more polarizable than are sigma-bond electrons, as addition reactions of electrophilic reagents to alkenes testify. Therefore, we should not be surprised to find that field induced pi-electron movement produces strong secondary fields that perturb nearby nuclei. The pi-electrons associated with a benzene ring provide a striking example of this phenomenon, as shown below. The electron cloud above and below the plane of the ring circulates in reaction to the external field so as to generate an opposing field at the center of the ring and a supporting field at the edge of the ring. This kind of spatial variation is called anisotropy, and it is common to nonspherical distributions of electrons, as are found in all the functions mentioned above. Regions in which the induced field supports or adds to the external field are said to be deshielded, because a slightly weaker external field will bring about resonance for nuclei in such areas. However, regions in which the induced field opposes the external field are termed shielded because an increase in the applied field is needed for resonance. Shielded regions are designated by a plus sign, and deshielded regions by a negative sign. 
The anisotropy of some important unsaturated functions will be displayed by clicking on the benzene diagram below. Note that the anisotropy about the triple bond nicely accounts for the relatively high field chemical shift of ethynyl hydrogens. The shielding & deshielding regions about the carbonyl group have been described in two ways, which alternate in the display.

Sigma bonding electrons also have a less pronounced, but observable, anisotropic influence on nearby nuclei. This is seen in the small deshielding shift that occurs in the series CH₃–R, R–CH₂–R, R₃CH; as well as the deshielding of equatorial versus axial protons on a fixed cyclohexane ring.

Solvent Effects

Chloroform-d (CDCl₃) is the most common solvent for nmr measurements, thanks to its good solubilizing character and relative unreactive nature ( except for 1º and 2º-amines). As noted earlier, other deuterium labeled compounds, such as deuterium oxide (D₂O), benzene-d6 (C₆D₆), acetone-d6 (CD₃COCD₃) and DMSO-d6 (CD₃SOCD₃) are also available for use as nmr solvents. Because some of these solvents have π-electron functions and/or may serve as hydrogen bonding partners, the chemical shifts of different groups of protons may change depending on the solvent being used. The following table gives a few examples, obtained with dilute solutions at 300 MHz.

For most of the above resonance signals and solvents the changes are minor, being on the order of ±0.1 ppm. However, two cases result in more extreme changes and these have provided useful applications in structure determination. First, spectra taken in benzene-d₆ generally show small upfield shifts of most C–H signals, but in the case of acetone this shift is about five times larger than normal. Further study has shown that carbonyl groups form weak π–π collision complexes with benzene rings, that persist long enough to exert a significant shielding influence on nearby groups. In the case of substituted cyclohexanones, axial α-methyl groups are shifted upfield by 0.2 to 0.3 ppm; whereas equatorial methyls are slightly deshielded (shift downfield by about 0.05 ppm). These changes are all relative to the corresponding chloroform spectra.
The second noteworthy change is seen in the spectrum of tert-butanol in DMSO, where the hydroxyl proton is shifted 2.5 ppm down-field from where it is found in dilute chloroform solution. This is due to strong hydrogen bonding of the alcohol O–H to the sulfoxide oxygen, which not only de-shields the hydroxyl proton, but secures it from very rapid exchange reactions that prevent the display of spin-spin splitting. Similar but weaker hydrogen bonds are formed to the carbonyl oxygen of acetone and the nitrogen of acetonitrile. A useful application of this phenomenon is described elsewhere in this text.

Spin-Spin Interactions

The nmr spectrum of 1,1-dichloroethane (below right) is more complicated than we might have expected from the previous examples. Unlike its 1,2-dichloro-isomer (below left), which displays a single resonance signal from the four structurally equivalent hydrogens, the two signals from the different hydrogens are split into close groupings of two or more resonances. This is a common feature in the spectra of compounds having different sets of hydrogen atoms bonded to adjacent carbon atoms. The signal splitting in proton spectra is usually small, ranging from fractions of a Hz to as much as 18 Hz, and is designated as J (referred to as the coupling constant). In the 1,1-dichloroethane example all the coupling constants are 6.0 Hz, as illustrated by clicking on the spectrum.

1,2-dichloroethane		1,1-dichloroethane

The splitting patterns found in various spectra are easily recognized, provided the chemical shifts of the different sets of hydrogen that generate the signals differ by two or more ppm. The patterns are symmetrically distributed on both sides of the proton chemical shift, and the central lines are always stronger than the outer lines. The most commonly observed patterns have been given descriptive names, such as doublet (two equal intensity signals), triplet (three signals with an intensity ratio of 1:2:1) and quartet (a set of four signals with intensities of 1:3:3:1). Four such patterns are displayed in the following illustration. The line separation is always constant within a given multiplet, and is called the coupling constant (J). The magnitude of J, usually given in units of Hz, is magnetic field independent.

The splitting patterns shown above display the ideal or “First-Order” arrangement of lines. This is usually observed if the spin-coupled nuclei have very different chemical shifts (i.e. Δν is large compared to J). If the coupled nuclei have similar chemical shifts, the splitting patterns are distorted (second order behavior). In fact, signal splitting disappears if the chemical shifts are the same. Two examples that exhibit minor 2nd order distortion are shown below (both are taken at a frequency of 90 MHz). The ethyl acetate spectrum on the left displays the typical quartet and triplet of a substituted ethyl group. The spectrum of 1,3-dichloropropane on the right demonstrates that equivalent sets of hydrogens may combine their influence on a second, symmetrically located set. 
Even though the chemical shift difference between the A and B protons in the 1,3-dichloroethane spectrum is fairly large (140 Hz) compared with the coupling constant (6.2 Hz), some distortion of the splitting patterns is evident. The line intensities closest to the chemical shift of the coupled partner are enhanced. Thus the B set triplet lines closest to A are increased, and the A quintet lines nearest B are likewise stronger. A smaller distortion of this kind is visible for the A and C couplings in the ethyl acetate spectrum.

What causes this signal splitting, and what useful information can be obtained from it ? 
If an atom under examination is perturbed or influenced by a nearby nuclear spin (or set of spins), the observed nucleus responds to such influences, and its response is manifested in its resonance signal. This spin-coupling is transmitted through the connecting bonds, and it functions in both directions. Thus, when the perturbing nucleus becomes the observed nucleus, it also exhibits signal splitting with the same J. For spin-coupling to be observed, the sets of interacting nuclei must be bonded in relatively close proximity (e.g. vicinal and geminal locations), or be oriented in certain optimal and rigid configurations. Some spectroscopists place a number before the symbol J to designate the number of bonds linking the coupled nuclei (colored orange below). Using this terminology, a vicinal coupling constant is ³J and a geminal constant is ²J.

The following general rules summarize important requirements and characteristics for spin 1/2 nuclei :

1)   Nuclei having the same chemical shift (called isochronous) do not exhibit spin-splitting. They may actually be spin-coupled, but the splitting cannot be observed directly.
2)   Nuclei separated by three or fewer bonds (e.g. vicinal and geminal nuclei ) will usually be spin-coupled and will show mutual spin-splitting of the resonance signals (same J’s), provided they have different chemical shifts. Longer-range coupling may be observed in molecules having rigid configurations of atoms.
3)   The magnitude of the observed spin-splitting depends on many factors and is given by the coupling constant J (units of Hz). J is the same for both partners in a spin-splitting interaction and is independent of the external magnetic field strength.
4)   The splitting pattern of a given nucleus (or set of equivalent nuclei) can be predicted by the n+1 rule, where n is the number of neighboring spin-coupled nuclei with the same (or very similar) Js. If there are 2 neighboring, spin-coupled, nuclei the observed signal is a triplet ( 2+1=3 ); if there are three spin-coupled neighbors the signal is a quartet ( 3+1=4 ). In all cases the central line(s) of the splitting pattern are stronger than those on the periphery. The intensity ratio of these lines is given by the numbers in Pascal’s triangle. Thus a doublet has 1:1 or equal intensities, a triplet has an intensity ratio of 1:2:1, a quartet 1:3:3:1 etc. To see how the numbers in Pascal’s triangle are related to the Fibonacci series click on the diagram.

If a given nucleus is spin-coupled to two or more sets of neighboring nuclei by different J values, the n+1 rule does not predict the entire splitting pattern. Instead, the splitting due to one J set is added to that expected from the other J sets. Bear in mind that there may be fortuitous coincidence of some lines if a smaller J is a factor of a larger J.

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Spin 1/2 nuclei include ¹H, ¹³C, ¹⁹F & ³¹P. The spin-coupling interactions described above may occur between similar or dissimilar nuclei. If, for example, a ¹⁹F is spin-coupled to a ¹H, both nuclei will appear as doublets having the same J constant.  Spin coupling with nuclei having spin other than 1/2 is more complex and will not be discussed here.

To make use of a calculator that predicts first order splitting patterns Click Here. This application was developed at Colby College.

Some Examples

Test your ability to interpret ¹H nmr spectra by analyzing the seven examples presented below. The seven spectra may be examined in turn by clicking the “Toggle Spectra” button. Try to associate each spectrum with a plausible structural formula. 
Although the first four cases are relatively simple, keep in mind that the integration values provide ratios, not absolute numbers. In two cases additional information from infrared spectroscopy is provided. When you have made an assignment you may check your answer by clicking on the spectrum itself. In the sixth example, a similar constitutional isomer cannot be ruled out by the data given.

      3. Carbon NMR Spectroscopy
The power and usefulness of ¹H nmr spectroscopy as a tool for structural analysis should be evident from the past discussion. Unfortunately, when significant portions of a molecule lack C-H bonds, no information is forthcoming. Examples include polychlorinated compounds such as chlordane, polycarbonyl compounds such as croconic acid, and compounds incorporating triple bonds (structures below, orange colored carbons).

Even when numerous C-H groups are present, an unambiguous interpretation of a proton nmr spectrum may not be possible. The following diagram depicts three pairs of isomers (A & B) which display similar proton nmr spectra. Although a careful determination of chemical shifts should permit the first pair of compounds (blue box) to be distinguished, the second and third cases (red & green boxes) might be difficult to identify by proton nmr alone.

These difficulties would be largely resolved if the carbon atoms of a molecule could be probed by nmr in the same fashion as the hydrogen atoms. Since the major isotope of carbon (¹²C) has no spin, this option seems unrealistic. Fortunately, 1.1% of elemental carbon is the ¹³C isotope, which has a spin I = 1/2, so in principle it should be possible to conduct a carbon nmr experiment. It is worth noting here, that if much higher abundances of ¹³C were naturally present in all carbon compounds, proton nmr would become much more complicated due to large one-bond coupling of ¹³C and ¹H.

The most important operational technique that has led to successful and routine ¹³C nmr spectroscopy is the use of high-field pulse technology coupled with broad-band heteronuclear decoupling of all protons. The results of repeated pulse sequences are accumulated to provide improved signal strength. Also, for reasons that go beyond the present treatment, the decoupling irradiation enhances the sensitivity of carbon nuclei bonded to hydrogen. 
When acquired in this manner, the carbon nmr spectrum of a compound displays a single sharp signal for each structurally distinct carbon atom in a molecule (remember, the proton couplings have been removed). The spectrum of camphor, shown on the left below, is typical. Furthermore, a comparison with the ¹H nmr spectrum on the right illustrates some of the advantageous characteristics of carbon nmr. The dispersion of ¹³C chemical shifts is nearly twenty times greater than that for protons, and this together with the lack of signal splitting makes it more likely that every structurally distinct carbon atom will produce a separate signal. The only clearly identifiable signals in the proton spectrum are those from the methyl groups. The remaining protons have resonance signals between 1.0 and 2.8 ppm from TMS, and they overlap badly thanks to spin-spin splitting.

Unlike proton nmr spectroscopy, the relative strength of carbon nmr signals are not normally proportional to the number of atoms generating each one. Because of this, the number of discrete signals and their chemical shifts are the most important pieces of evidence delivered by a carbon spectrum. The general distribution of carbon chemical shifts associated with different functional groups is summarized in the following chart. Bear in mind that these ranges are approximate, and may not encompass all compounds of a given class. Note also that the over 200 ppm range of chemical shifts shown here is much greater than that observed for proton chemical shifts.

13C Chemical Shift Ranges*
Low Field Region		High Field Region
	* For samples in CDCl3 solution. The δ scale is relative to TMS at δ=0.

The isomeric pairs previously cited as giving very similar proton nmr spectra are now seen to be distinguished by carbon nmr. In the example on the left below (blue box), cyclohexane and 2,3-dimethyl-2-butene both give a single sharp resonance signal in the proton nmr spectrum (the former at δ 1.43 ppm and the latter at 1.64 ppm). However, in its carbon nmr spectrum cyclohexane displays a single signal at δ 27.1 ppm, generated by the equivalent ring carbon atoms (colored blue); whereas the isomeric alkene shows two signals, one at δ 20.4 ppm from the methyl carbons (colored brown), and the other at 123.5 ppm (typical of the green colored sp² hybrid carbon atoms).

The C₈H₁₀ isomers in the center (red) box have pairs of homotopic carbons and hydrogens, so symmetry should simplify their nmr spectra. The fulvene (isomer A) has five structurally different groups of carbon atoms (colored brown, magenta, orange, blue and green respectively) and should display five ¹³C nmr signals (one near 20 ppm and the other four greater than 100 ppm). Although ortho-xylene (isomer B) will have a proton nmr very similar to isomer A, it should only display four ¹³C nmr signals, originating from the four different groups of carbon atoms (colored brown, blue, orange and green). The methyl carbon signal will appear at high field (near 20 ppm), and the aromatic ring carbons will all give signals having δ > 100 ppm. Finally, the last isomeric pair, quinones A & B in the green box, are easily distinguished by carbon nmr. Isomer A displays only four carbon nmr signals (δ 15.4, 133.4, 145.8 & 187.9 ppm); whereas, isomer B displays five signals (δ 15.9, 133.3, 145.8, 187.5 & 188.1 ppm), the additional signal coming from the non-identity of the two carbonyl carbon atoms (one colored orange and the other magenta).

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1. NMRshiftdb

NMRshiftdb2 is a NMR database (web database) for organic structures and their nuclear magnetic resonance (nmr) spectra. It allows for spectrum prediction (¹³C, ¹H and other nuclei) as well as for searching spectra, structures and other properties. The nmrshiftdb2 software is open source, the data is published under an open content license. The core of nmrshitdb2 are fully assigned spectra with raw data and peak lists (we have pure peak lists as well). Those datasets are peer reviewed by a board of reviewers. The project is supported by a scientific advisory board.

nmrshiftdb2 is part of the NFDI4Chem initiative and will provide a component for a curated repository there. Please consult the documentation for more detailed information.

See: https://nmrshiftdb.nmr.uni-koeln.de/portal

2. ACD/NMR

ACD/NMR Workbook Suite is a comprehensive NMR software application with an intuitive interface. It features a full suite of advanced processing, analysis, and databasing functionalities for 1D and 2D NMR data from all major vendor formats. NMR Workbook Suite is built upon cutting-edge algorithms for the most reliable NMR data interpretation. It is designed to streamline routine NMR workflows, simplify structure characterization, and much more.

Powerful NMR Interpretation Software | Highlights

• Import and process 1D and 2D NMR data from all major instrument vendor formats in a single collaborative platform
• Process NMR data manually or automate routine processing workflows—Fourier transformation, calibration, peak picking, integration, multiplet analysis, etc.
• Synchronize peak picking and assignments across datasets within a project
• Confidently verify structures with 3 different verification levels
• Perform targeted analysis of known mixture components and optimize untargeted mixture analysis workflow
• Perform Conformational Analysis using NOESY/ROESY spectra
• Create comprehensive multiplet reports and publication-ready data
• Store, manage, and share live NMR spectra

Synchronize peak picking and assignments across NMR datasets using NMRSync—our game-changing technology. Plus, the associated peaks from NMRSync, NMR prediction, and connectivity-based algorithms are automatically used to only identify the assignments that match all data. This quick and accurate peak picking and assignment workflow helps you to maximize your productivity in the following ways:

• Use any peak in any spectrum to initiate NMRSync
• Integrate a peak in any spectrum and all related peaks in the 1D and 2D NMR spectra of that dataset will be identified and linked in real time
• Automatically resolve overlapping ¹H and ¹³C peaks from 2D NMR data
• Receive immediate color-coded feedback on the best assignment for instant decision-making purposes

NMR Workbook Suite includes three levels of structure verification that evaluate alternative structures to varying degrees for added flexibility in your NMR analysis. This ensures the best structure that matches the experimental NMR data is confirmed with much less time and effort than manual interpretation.

• Determine how well your proposed structure matches the datasets in your NMR project with single structure verification
• Generate a specified number of alternative structures, based on the user-defined proposed structure, and evaluate whether they are a better match to the NMR dataset using Combined and Concurrent Verification
• Generate and view every alternative structural and cis/trans isomer that matches the experimental data in real-time using Unbiased Verification for an absolute level of confidence. This workflow eliminates the user bias and ensures the assigned structure is indeed the best structure that fits the experimental data.

See: https://www.acdlabs.com/products/spectrus/workbooks/nmr/

3. See: http://www.cheminfo.org/Spectra/NMR/Predictions/1H_Prediction/index.html

4. See: https://www.nmrprocflow.org/

5. See: https://chem.washington.edu/facilities/data-processing

6. See: https://www.cgl.ucsf.edu/home/sparky/

7. See: http://www.nmrdb.org/about/

Only 15$ for interpretation of your NMR spectrum
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Nuclear Magnetic Resonance (NMR) interpretation plays a pivotal role in molecular identifications. As interpreting NMR spectra, the structure of an unknown compound, as well as known structures, can be assigned by several factors such as chemical shift, spin multiplicity, coupling constants, and integration. This Module focuses on the most important ¹H and ¹³C NMR spectra to find out structure even though there are various kinds of NMR spectra such as ¹⁴N, ¹⁹F, and ³¹P. NMR spectrum shows that x- axis is chemical shift in ppm. It also contains integral areas, splitting pattern, and coupling constant.

Strategy for Solving Structure

Here is the general strategy for solving structure with NMR:

1. Molecular formula is determined by chemical analysis such as elementary analysis
2. Double-bond equivalent (also known as Degree of Unsaturation) is calculated by a simple equation to estimate the number of the multiple bonds and rings. It assumes that oxygen (O) and sulfur (S) are ignored and halogen (Cl, Br) and nitrogen is replaced by CH. The resulting empirical formula is C_aH_b

3. Structure fragmentation is determined by chemical shift, spin multiplicity, integral (peak area), and coupling constants (1J1J, 2J2J)
4. Molecular skeleton is built up using 2-dimensional NMR spectroscopy.
5. Relative configuration is predicted by coupling constant (³J).

¹H NMR

Chemical Shift

Chemical shift is associated with the Larmor frequency of a nuclear spin to its chemical environment. Tetramethylsilane (TMS, (CH3)4Si(CH3)4Si) is generally used as an internal standard to determine chemical shift of compounds: δ_TMS=0 ppm. In other words, frequencies for chemicals are measured for a ¹H or ¹³C nucleus of a sample from the ¹H or ¹³C resonance of TMS. It is important to understand trend of chemical shift in terms of NMR interpretation. The proton NMR chemical shift is affect by nearness to electronegative atoms (O, N, halogen.) and unsaturated groups (C=C,C=O, aromatic). Electronegative groups move to the down field (left; increase in ppm). Unsaturated groups shift to downfield (left) when affecting nucleus is in the plane of the unsaturation, but reverse shift takes place in the regions above and below this plane. ¹H chemical shift play a role in identifying many functional groups. Figure 11. indicates important example to figure out the functional groups.

Chemical equivalence

Protons with Chemical equivalence has the same chemical shift due to symmetry within molecule (CH3COCH3CH3COCH3) or fast rotation around single bond (-CH₃; methyl groups).

Spin-Spin Splitting

Spin-Spin splitting means that an absorbing peak is split by more than one “neighbor” proton. Splitting signals are separated to J Hz, where is called the coupling constant. The spitting is a very essential part to obtain exact information about the number of the neighboring protons. The maximum of distance for splitting is three bonds. Chemical equivalent protons do not result in spin-spin splitting. When a proton splits, the proton’s chemical shift is determined in the center of the splitting lines.

Spin Multiplicity (Splitting pattern)

Spin Multiplicity plays a role in determining the number of neighboring protons. Here is a multiplicity rules: In case of AmBnAmBn system, the multiplicity rule is that Nuclei of BB element produce a splitting the AA signal into nB+1nB+1 lines. The general formula which applies to all nuclei is 2nI+12nI+1, where II is the spin quantum number of the coupled element. The relative intensities of the each lines are given by the coefficients of the Pascal’s triangle (Figure 22).

First-order splitting pattern

The chemical shift difference in Hertz between coupled protons in Hertz is much larger than the JJ coupling constant:ΔνJ≥8(1)(1)ΔνJ≥8

Where ΔνΔν is the difference of chemical shift. In other word, the proton is only coupled to other protons that are far away in chemical shift. The spectrum is called first-order spectrum. The splitting pattern depends on the magnetic field. The second-order splitting at the lower field can be resolved into first-order splitting pattern at the high field. The first-order splitting pattern is allowed to multiplicity rule (N+1) and Pascal’s triangle to determine splitting pattern and intensity distribution.

Example 11

The note is that structure system is A₃M₂X₂. H_a and H_x has the triplet pattern by Hm because of N+1 rule. The signal of Hm is split into six peaks by H_x and H_a(Figure3) The First order pattern easily is predicted due to separation with equal splitting pattern.

High-order splitting pattern

High-order splitting pattern takes place when chemical shift difference in Hertz is much less or the same that order of magnitude as the j coupling.ΔvJ≤10(2)(2)ΔvJ≤10

The second order pattern is observed as leaning of a classical pattern: the inner peaks are taller and the outer peaks are shorter in case of AB system (Figure 44). This is called the roof effect.

Here is other system as an example: A₂B₂ (Figure 55). The two triplet incline toward each other. Outer lines of the triplet are less than 1 in relative area and the inner lines are more than 1. The center lines have relative area 2.

Coupling constant (J Value)

Coupling constant is the strength of the spin-spin splitting interaction and the distance between the split lines. The value of distance is equal or different depending on the coupled nuclei. The coupling constants reflect the bonding environments of the coupled nuclei. Coupling constant is classified by the number of bonds:

Geminal proton-proton coupling (²J_HH)

Germinal coupling generates through two bonds (Figure 66). Two proton having geminal coupling are not chemically equivalent. This coupling ranges from -20 to 40 Hz. ²J_HHdepends on hybridization of carbon atom and the bond angle and the substituent such as electronegative atoms. When S-character is increased, Geminal coupling constant is increased: ²J_sp1>²J_sp2>²J_sp3 The bond angle(HCH) gives rise to change ²J_HH value and depend on the strain of the ring in the cyclic systems. Geminal coupling constant determines ring size. When bond angle is decreased, ring size is decreased so that geminal coupling constant is more positive. If a atom is replace to an electronegative atom, Geminal coupling constant move to positive value.

Vicinal proton-proton coupling (³J_HH)

Vicinal coupling occurs though three bonds (Figure 77.). The Vicinal coupling is the most useful information of dihedral angle, leading to stereochemistry and conformation of molecules. Vicinal coupling constant always has the positive value and is affected by the dihedral angle (?;HCCH), the valence angle (?; HCC), the bond length of carbon-carbon, and the effects of electronegative atoms. Vicinal coupling constant depending on the dihedral angle (Figure 88) is given by the Karplus equation.3J=7.0−0.5cosϕ+4.5cos2ϕ(3)(3)3J=7.0−0.5cos⁡ϕ+4.5cos2⁡ϕ

When ? is the 90^o, vicinal coupling constant is zero. In addition, vicinal coupling constant ranges from 8 to 10 Hz at the and ?=180^o, where ?=0^o and ?=180^o means that the coupled protons have cis and trans configuration, respectively.

The valence angle(?;Figure 88) also causes change of ³J_HH value. Valence angle is related with ring size. Typically, when the valence angle decreases, the coupling constant reduces. The distance between the carbons atoms gives influences to vicinal coupling constant

The coupling constant increases with the decrease of bond length. Electronegative atoms affect vicinal coupling constants so that electronegative atoms decrease the vicinal coupling constants.

Integral

Integral is referred to integrated peak area of 1H signals. The intensity is directly proportionally to the number of hydrogen.

¹³C NMR

Chemical Shift

Spin-Spin splitting

Comparing the ¹H NMR, there is a big difference thing in the ¹³C NMR. The ¹³C- ¹³ C spin-spin splitting rarely exit between adjacent carbons because ¹³C is naturally lower abundant (1.1%)

• ¹³C-¹H Spin coupling: ¹³C-¹H Spin coupling provides useful information about the number of protons attached a carbon atom. In case of one bond coupling (¹J_CH), -CH, -CH₂, and CH₃ have respectively doublet, triplet, quartets for the ¹³C resonances in the spectrum. However, ¹³C-¹H Spin coupling has an disadvantage for ¹³C spectrum interpretation. ¹³C-¹H Spin coupling is hard to analyze and reveal structure due to a forest of overlapping peaks that result from 100% abundance of ¹H.
• Decoupling: Decoupling is the process of removing ¹³C-¹H coupling interaction to simplify a spectrum and identify which pair of nuclei is involved in the J coupling. The decoupling ¹³C spectra shows only one peak(singlet) for each unique carbon in the molecule(Figure 1010.). Decoupling is performed by irradiating at the frequency of one proton with continuous low-power RF.

• Distortionless enhancement by polarization transfer (DEPT): DEPT is used for distinguishing between a CH₃ group, a CH₂ group, and a CH group. The proton pulse is set at 45^o, 90^o, or 135^o in the three separate experiments. The different pulses depend on the number of protons attached to a carbon atom. Figure 1111. is an example about DEPT spectrum.

2-dimensional NMR spectroscopy (COSY)

COSY stands for COrrelation SpectroscopY. COSY spectrum is more useful information about what is being correlated.

¹H-¹H COSY (COrrelation SpectroscopY)

¹H-¹H COSY is used for clearly indicate correlation with coupled protons. A point of entry into a COSY spectrum is one of the keys to predict information from it successfully. Relation of Coupling protons is determined by cross peaks(correlation peaks) and in the COSY spectrum. In other words, Diagonal peaks by lines ar e coupled to each other. Figure 1212 indicates that there are correlation peaks between proton H₁ and H₂ as well as between H₂ and H₄. This means the H₂ coupled to H₁ and H₄.

¹H-¹³C COSY (HETCOR)

¹H-¹³C COSY is the heteronuclear correlation spectroscopy. The HETCOR spectrum is correlated ¹³C nuclei with directly attached protons. ¹H-¹³C coupling is one bond. The cross peaks mean correlation between a proton and a carbon (Figure 1313). If a line does not have cross peak, this means that this carbon atoms has no attached proton (e.g. a quaternary carbon atom)

References

1. Balc*, M., Basic p1 sH- and p13 sC-NMR spectroscopy. 1st ed.; Elsevier: Amsterdam ; Boston, 2005; p xii, 427.
2. Breitmaier, E., Structure elucidation by NMR in organic chemistry : a practical guide. 3rd rev. ed.; Wiley: Chichester, West Sussex, England, 2002; p xii, 258.
3. Jacobsen, N. E., NMR spectroscopy explained : simplified theory, applications and examples for organic chemistry and structural biology. Wiley-Interscience: Hoboken, N.J., 2007; p xv, 668.
4. Silverstein, R. M.; Webster, F. X., Spectrometric identification of organic compounds. 6th ed.; Wiley: New York, 1998; p xiv, 482.

Outside Links

• NMRShiftDB: a Free web database for NMR data : nmrshiftdb.chemie.uni-mainz.de/nmrshiftdb
• NMR database from ACD/LAbs : www.acdlabs.com/products/spec_lab/exp_spectra/spec_libraries/aldrich.html
• NMR database from John Crerar Library : http://crerar.typepad.com/crerar_lib…h_ir_nmr_.html

Problems

Draw the 1H NMR spectrum for 2-Hydroxypropane in CDCl3. Assume sufficient resolution to provide a first-order spectrum and ignore vicinal proton-proton coupling(3JHH)

Solution

1) the structure of 2-hydoroxyporpane is drawn

Figure out which protons are chemically equivalent, i.e., two methyl (-CH₃) groups are chemical equivalent.

4) Splitting pattern is determined by (N+1) rule: Ha is split into two peaks by H_b(#of proton=1). H_b has the septet pattern by H_a (#of proton=6). H_c has one peak.(Note that H_c has doublet pattern by H_b due to vicinal proton-proton coupling.)

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This handout relates the basic theory of NMR described on the theory web handout with spectra of real molecules and how to deduce structure from the spectra. Before reading this handout, you need to be thoroughly familiar with all of theory concepts that were described.

1.0 The NMR spectrum.

1.1 Because different amounts of electron density are around different non-eqivalent nuclei, the different non-equivalent nuclei in a molecule are experiencing slightly different net magnetic fields in an NMR experiment (Review Section 5.2A of the theory handout). Recall also that the difference in energy between the two allowed spin states (+1/2 and -1/2 spin states) of a spin 1/2 nucleus (like in 1H and 13C nuclei) depends on the exact magnetic field felt by the nucleus (Review Section 2.3Cin the theory handout). Recall further that in the NMR experiment, when and only when nuclei are irradiated with electromagnetic radiation of energy that exactlycorresponds to the energy difference between the +1/2 and -1/2 spin states, the nuclei absorb the energy and the NMR spectrometer measures this absorbance (Review section 3.1 of the theory handout). The absorbance of energy to convert a nucleus from a +1/2 to a -1/2 spin state is referred to as “resonance” of that nucleus.1.1A The key conclusion is that nuclei with different electron densities have +1/2 and -1/2 spin states that differ in energy by differing amounts, so these nuclei will absorb electromagnetic radiation of different frequencies in the NMR experiment.

1.1B Nuclei surrounded by greater amounts of electron density will be more shielded from the external magnetic field, so they will absorb electromagnetic radiation of lower energy, that is, lower frequency (energy is proportional to frequency). You may want to review Section 5.2A of the theory handout again.

1.1C The converse is also true, namely that nuclei surrounded by lesser amounts of electron density will be less shielded (referred to as being “deshielded”) from the external magnetic field, so they will absorb electromagnetic radiation of higher energy, that is, higher frequency(energy is proportional to frequency).

1.1D The three most important factors influencing the electron density around a hydrogen nucleus are: (i) adjacent electronegative atoms remove electron density; (ii) hybridization of the attached carbon atom, increasing shielding is observed in the order sp2, sp, sp3; (iii) adjacent pi bonds are deshielding, which relates to (ii).1.2 An NMR spectrum is a plot of absorbance versus frequency.

1.2A To make different spectra directly comparable, a standard is used for all NMR spectra. For 1H NMR spectra, the standard is called tetramethylsilane (TMS) and a small amount of TMS is usually added to any 1H NMR sample.

1.2B Magnets of different strengths lead to absorbance of electromagnetic radiation at different frequencies for the same nucleus, meaning that if simple frequency were plotted in an NMR spectra, you could not compare spectra taken of the same sample on machines with different magnet strengths. To solve this problem, the frequency of absorption plotted on NMR spectra are corrected for the magnet strength. In addition, frequency is correlated to the reference compound TMS. The frequency at which TMS absorbs is defined as 0 frequency by convention. In the NMR spectrum, absorbance frequencies of electromagnetic radiation are plotted as chemical shift (d) listed in units called parts per million (ppm) that is defined by the following equation:

1.3 The bottom line to this entire section is that the hydrogen atoms of different functional groups (methyl groups, -CH2- groups, aldehyde -C(O)H, alkene C-H, etc.) have characteristic chemical shifts, i.e. absorbance frequencies. These characteristic chemical shifts are collected in tables such as Fgure 13.8 and Appendix 4 of your book. From the chemical shift information, you thus know what functional groups are present in a molecule.

1.4 Chemically equivalent hydrogen atoms will have the same chemical shift and therefore give rise to the same signal. This is why we defined equivalent atoms in Section6.1 of the theory handout. Non-equivalent groups of hydrogens will have different chemical shifts. Thus, you will have as many different signals in an NMR spectrum as there are chemically non-equivalent groups of hydrogen atoms.

2.0 The nuclear spin of hydrogen atoms creates a magnetic field that influences the chemical shift of nearby hydrogen atoms (Review Sections 5.1 and 5.2).

2.1 Nuclear spin magnetic fields will influence hydrogen atoms that are three or fewer bonds away from each other in the same molecule. Hydrogen atoms that are four or greater bonds away usually do not influence each other.

2.2 A hydrogen atom with a nuclecus in a spin state of +1/2 produces a slightly different magnetic field than a one in a –1/2 spin state.

2.3 Even in a strong magnetic field, across a population of molecules, there is only a very slight excess of nuclei in the +1/2 spin state.

2.4 Putting all of these ideas together means the following: Consider a hydrogen X adjacent (three bonds away) to another hydrogen Y in a molecule. In around half of the molecules in the NMR sample, hydrogen X feels the magnetic field from a Y with nuclear spin of +1/2. The other half feel from Y a nuclear spin of –1/2. Thus, when you look at the spectrum, there are actually two different, but closely spaced peaks as the signal for hydrogen X. This phenomenon is called “spin-spin” splitting, and the distance between the two signals for X is called the “coupling constant”, often denoted as “J”. Similarly, the signal for Y actually has two peaks because of spin-spin splitting by X.

2.5 Consider a –CH2- group adjacent to a hydrogen X. Both of the hydrogen atoms in the –CH2- are chemically equivalent and could be either in the +1/2 or –1/2 nuclear spin state. Thus, there are three situations possible: i) +1/2,+1/2; ii) +1/2,-1/2, which is the same as –1/2, +1/2 and iii) –1/2,-1/2. Thus, there are actually three different magnetic fields that are felt by X in molecules of the sample, in a 1:2:1 ratio. Thus, the signal for hydrogen X is split into three peaks in a 1:2:1 ratio.

2.6 The same holds for a –CH3 group, that will split an adjacent hydrogen signal into four peaks, with a 1:3:3:1 ratio. You should verify this for yourself by making all the possible combinations of nuclear spins for the three equivalent hydrogen atoms of a methyl group.

2.7 In the general case, N equivalent hydrogen atoms will split an adjacent signal into (N+1) peaks, with relative ratios that are predicted by Pascal’s triangle (Figure 13.16 in the book).

3.0 Following the same logic, the splitting should multiply if a single hydrogen atom is adjacent to hydrogen atoms on either side. Think about combining all the possible nuclear spin states for these nearby sets of hydrogen atoms. Thus, if you have a hydrogen atom X between one –CH2- and one –CH3 group, it should be split into an amazing (2+1) x (3 + 1) = 12 signals because there are that many different combinations of +1/2 and -1/2 spins possible.

3.1 Thus, if the coupling constants (J) from the –CH2- and –CH3 groups are significantly different from each other, then 12 peaks will be observed as the signal for hydrogen X.

3.2 However, in practice, coupling constants (J) are pretty close to the same value for almost all sets of hydrogen atoms in organic molecules, simplifying the splitting pattern, since now many of the twelve peaks will overlap with each other. What this means is that for almost all the spectra you will see, if a hydrogen X is surrounded by N hydrogen atoms, the signal for X will be split into only (N+1) peaks, no matter how those N hydrogen atoms are grouped in terms of sets of equivalent atoms. Thus, what is actually seen for the example above is that the signal for X would appear in the spectrum to be split into 2 + 3 + 1 = 6 peaks, not 12, peaks. This is the so-called “N+1” rule.

3.3 The diagram below shows these two different situations. When nuclei from hydrogen atoms Z and Y split the signal for hydrogen X with very different coupling constants (notice how the coupling constant J for the red Z hydrogen nuclei is larger than J for the blue Y hydrogen nuclei), all twelve peaks are spread out and identifiable. Below that is shown the situation in which the coupling constants are the same for nuclei of both Z and Y, so only 6 peaks are actually observed in the signal for hydrogen X due to extensive overlap. This latter case, with six peaks, is what you will almost always see in reality since coupling constants tend to be similar in organic molecules.

3.3 The above explanation of splitting can confuse students for a while. The important point is that in the example given, you see 6 different peaks in the spectrum (N+1 rule) even though there are really 12 peaks produced, it is just that several of them are on top of each other because the coupling constants are the same. For alkyl groups in organic molecules, the coupling constants are generally the same so you will almost always see the fewer peaks, corresponding to the simple N+1 rule, rather than the greater number of peaks derived from the multiplication rule.

3.4 The bottom line here is that by seeing how a given signal is split, you can figure out how many hydrogen atoms are adjacent on the molecule, namely the number of peaks in the signal minus 1. From this information you can piece together what a molecule looks like if you know how many atoms of each type are present (i.e. the molecular formula such as C4H10N2O). You get the molecular formula information from something called a mass spectrum, described later in the text. Molecular formulas will be provided to you in homework or test questions.

4.0 For a given signal, integrating the signal (include all splitting peaks for a given signal) gives you a relative value that is proportional to the number of equivalent hydrogen atoms that gave rise to the signal. Thus, by looking at the integration values, you can deduce how many of each type of equivalent hydrogen atoms are in the molecule. For example, a -CH3 group would have a signal that integrates to a relative value of 3 (no matter how the signal is split), and a -CH2- group would have a relative integration of 2, etc. Note that sometimes integrations are simply given as absolute numbers, and you must find the common factor to deduce how many hydrogen atoms are represented by each integration value.

5.0 Putting it all together: How to deduce a structure from an NMR spectrum. First, you must be given the molecular formula, so you know how many of each type of atom are present. Second, count the number of different signals and their relative integrations to see how many different sets of equivalent hydrogen atoms are in a molecule, and how many of each set are present. Compare the chemical shifts of each signal to tables to identify what functional groups are present. Finally, use the signal splittings to determine which hydrogen atoms must be no more than 3 bonds away from each other.

6.0 For alkenes, the pi bond prevents bond rotation so the different hydrogen atoms on an unsymmetrical alkene are not equivalent, so they all have different signals, and splitting follows the multiplicative rule (the coupling constants are usually significantly different for geminal vs. cis. vs. trans relationships).

7.0 For hydrogens in a -CH2- group adjacent to a chiral center, the two different H atoms are no longer equivalent, because even with bond rotation, the two hydrogens are never in the same environment with respect to the groups on the adjacent chiral center. Thus, each H of -CH2- group adjacent to a chiral center usually has its own signal in the NMR spectrum.

8.0 There is a great deal more to NMR than this, I am only trying to give you the basics here.

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In Figure 10.9 we examined Nessler’s original method for matching the color of a sample to the color of a standard. Matching the colors was a labor intensive process for the analyst. Not surprisingly, spectroscopic methods of analysis were slow to develop. The 1930s and 1940s saw the introduction of photoelectric transducers for ultraviolet and visible radiation, and thermocouples for infrared radiation. As a result, modern instrumentation for absorption spectroscopy became routinely available in the 1940s—progress has been rapid ever since.

10.3.1 Instrumentation

Frequently an analyst must select—from among several instruments of different design—the one instrument best suited for a particular analysis. In this section we examine several different instruments for molecular absorption spectroscopy, emphasizing their advantages and limitations. Methods of sample introduction are also covered in this section.

Instrument Designs for Molecular UV/Vis Absorption

Filter Photometer. The simplest instrument for molecular UV/Vis absorption is a filter photometer (Figure 10.25), which uses an absorption or interference filter to isolate a band of radiation. The filter is placed between the source and the sample to prevent the sample from decomposing when exposed to higher energy radiation. A filter photometer has a single optical path between the source and detector, and is called a single-beam instrument. The instrument is calibrated to 0% T while using a shutter to block the source radiation from the detector. After opening the shutter, the instrument is calibrated to 100% T using an appropriate blank. The blank is then replaced with the sample and its transmittance measured. Because the source’s incident power and the sensitivity of the detector vary with wavelength, the photometer must be recalibrated whenever the filter is changed. Photometers have the advantage of being relatively inexpensive, rugged, and easy to maintain. Another advantage of a photometer is its portability, making it easy to take into the field. Disadvantages of a photometer include the inability to record an absorption spectrum and the source’s relatively large effective bandwidth, which limits the calibration curve’s linearity.

Note

The percent transmittance varies between 0% and 100%. As we learned in Figure 10.21, we use a blank to determine P₀, which corresponds to 100% T. Even in the absence of light the detector records a signal. Closing the shutter allows us to assign 0% T to this signal. Together, setting 0% T and 100% T calibrates the instrument. The amount of light passing through a sample produces a signal that is greater than or equal to that for 0% T and smaller than or equal to that for 100%T.

Figure 10.25 Schematic diagram of a filter photometer. The analyst either inserts a removable filter or the filters are placed in a carousel, an example of which is shown in the photographic inset. The analyst selects a filter by rotating it into place.

Single-Beam Spectrophotometer. An instrument that uses a monochromator for wavelength selection is called a spectrophotometer. The simplest spectrophotometer is a single-beam instrument equipped with a fixed-wavelength monochromator (Figure 10.26). Single-beam spectrophotometers are calibrated and used in the same manner as a photometer. One example of a single-beam spectrophotometer is Thermo Scientific’s Spectronic 20D+, which is shown in the photographic insert to Figure 10.26. The Spectronic 20D+ has a range of 340–625 nm (950 nm when using a red-sensitive detector), and a fixed effective bandwidth of 20 nm. Battery-operated, hand-held single-beam spectrophotometers are available, which are easy to transport into the field. Other single-beam spectrophotometers also are available with effective bandwidths of 2–8 nm. Fixed wavelength single-beam spectrophotometers are not practical for recording spectra because manually adjusting the wavelength and recalibrating the spectrophotometer is awkward and time-consuming. The accuracy of a single-beam spectrophotometer is limited by the stability of its source and detector over time.

Figure 10.26 Schematic diagram of a fixed-wavelength single-beam spectrophotometer. The photographic inset shows a typical instrument. The shutter remains closed until the sample or blank is placed in the sample compartment. The analyst manually selects the wavelength by adjusting the wavelength dial. Inset photo modified from: Adi (www.commons.wikipedia.org).

Double-Beam Spectrophotometer. The limitations of fixed-wavelength, single-beam spectrophotometers are minimized by using a double-beamspectrophotometer (Figure 10.27). A chopper controls the radiation’s path, alternating it between the sample, the blank, and a shutter. The signal processor uses the chopper’s known speed of rotation to resolve the signal reaching the detector into the transmission of the blank, P₀, and the sample, P_T. By including an opaque surface as a shutter, it is possible to continuously adjust 0% T. The effective bandwidth of a double-beam spectrophotometer is controlled by adjusting the monochromator’s entrance and exit slits. Effective bandwidths of 0.2–3.0 nm are common. A scanning monochromator allows for the automated recording of spectra. Double-beam instruments are more versatile than single-beam instruments, being useful for both quantitative and qualitative analyses, but also are more expensive.

Figure 10.27 Schematic diagram of a scanning, double-beam spectrophotometer. A chopper directs the source’s radiation, using a transparent window to pass radiation to the sample and a mirror to reflect radiation to the blank. The chopper’s opaque surface serves as a shutter, which allows for a constant adjustment of the spectrophotometer’s 0% T. The photographic insert shows a typical instrument. The unit in the middle of the photo is a temperature control unit that allows the sample to be heated or cooled.

Diode Array Spectrometer. An instrument with a single detector can monitor only one wavelength at a time. If we replace a single photomultiplier with many photodiodes, we can use the resulting array of detectors to record an entire spectrum simultaneously in as little as 0.1 s. In a diode array spectrometer the source radiation passes through the sample and is dispersed by a grating (Figure 10.28). The photodiode array is situated at the grating’s focal plane, with each diode recording the radiant power over a narrow range of wavelengths. Because we replace a full monochromator with just a grating, a diode array spectrometer is small and compact.

Figure 10.28 Schematic diagram of a diode array spectrophotometer. The photographic insert shows a typical instrument. Note that the 50-mL beaker provides a sense of scale.

One advantage of a diode array spectrometer is the speed of data acquisition, which allows to collect several spectra for a single sample. Individual spectra are added and averaged to obtain the final spectrum. This signal averaging improves a spectrum’s signal-to-noise ratio. If we add together n spectra, the sum of the signal at any point, x, increases as nS_x, where S_x is the signal. The noise at any point, N_x, is a random event, which increases as √nN_x when we add together nspectra. The signal-to-noise ratio (S/N) after n scans isSN=nSxn−−√Nx=n−−√SxnNx(4.8.1)(4.8.1)SN=nSxnNx=nSxnNx

where S_x/N_x is the signal-to-noise ratio for a single scan. The impact of signal averaging is shown in Figure 10.29. The first spectrum shows the signal for a single scan, which consists of a single, noisy peak. Signal averaging using 4 scans and 16 scans decreases the noise and improves the signal-to-noise ratio. One disadvantage of a photodiode array is that the effective bandwidth per diode is roughly an order of magnitude larger than that for a high quality monochromator.

Figure 10.29 Effect of signal averaging on a spectrum’s signal-to-noise ratio. From top to bottom: spectrum for a single scan; average spectrum after four scans; and average spectrum after adding 16 scans.

Sample Cells. The sample compartment provides a light-tight environment that limits the addition of stray radiation. Samples are normally in the liquid or solution state, and are placed in cells constructed with UV/Vis transparent materials, such as quartz, glass, and plastic (Figure 10.30). A quartz or fused-silica cell is required when working at a wavelength <300 nm where other materials show a significant absorption. The most common pathlength is 1 cm (10 mm), although cells with shorter (as little as 0.1 cm) and longer pathlengths (up to 10 cm) are available. Longer pathlength cells are useful when analyzing a very dilute solution, or for gas samples. The highest quality cells allow the radiation to strike a flat surface at a 90^o angle, minimizing the loss of radiation to reflection. A test tube is often used as a sample cell with simple, single-beam instruments, although differences in the cell’s pathlength and optical properties add an additional source of error to the analysis.

Figure 10.30 Examples of sample cells for UV/Vis spectroscopy. From left to right (with path lengths in parentheses): rectangular plastic cuvette (10.0 mm), rectangular quartz cuvette (5.000 mm), rectangular quartz cuvette (1.000 mm), cylindrical quartz cuvette (10.00 mm), cylindrical quartz cuvette (100.0 mm). Cells often are available as a matched pair, which is important when using a double-beam instrument.

If we need to monitor an analyte’s concentration over time, it may not be possible to physically remove samples for analysis. This is often the case, for example, when monitoring industrial production lines or waste lines, when monitoring a patient’s blood, or when monitoring environmental systems. With a fiber-optic probe we can analyze samples in situ. An example of a remote sensing fiber-optic probe is shown in Figure 10.31. The probe consists of two bundles of fiber-optic cable. One bundle transmits radiation from the source to the probe’s tip, which is designed to allow the sample to flow through the sample cell. Radiation from the source passes through the solution and is reflected back by a mirror. The second bundle of fiber-optic cable transmits the nonabsorbed radiation to the wavelength selector. Another design replaces the flow cell shown in Figure 10.31 with a membrane containing a reagent that reacts with the analyte. When the analyte diffuses across the membrane it reacts with the reagent, producing a product that absorbs UV or visible radiation. The nonabsorbed radiation from the source is reflected or scattered back to the detector. Fiber optic probes that show chemical selectivity are called optrodes.⁶

Figure 10.31 Example of a fiber-optic probe. The inset photographs provide a close-up look at the probe’s flow cell and the reflecting mirror.

Instrument Designs for Infrared Absorption

Filter Photometer. The simplest instrument for IR absorption spectroscopy is a filter photometer similar to that shown in Figure 10.25 for UV/Vis absorption. These instruments have the advantage of portability, and typically are used as dedicated analyzers for gases such as HCN and CO.

Double-beam spectrophotometer. Infrared instruments using a monochromator for wavelength selection use double-beam optics similar to that shown in Figure 10.27. Double-beam optics are preferred over single-beam optics because the sources and detectors for infrared radiation are less stable than those for UV/Vis radiation. In addition, it is easier to correct for the absorption of infrared radiation by atmospheric CO₂ and H₂O vapor when using double-beam optics. Resolutions of 1–3 cm^–1 are typical for most instruments.

Fourier transform spectrometer. In a Fourier transform infrared spectrometer, or FT–IR, the monochromator is replaced with an interferometer (Figure 10.13). Because an FT-IR includes only a single optical path, it is necessary to collect a separate spectrum to compensate for the absorbance of atmospheric CO₂ and H₂O vapor. This is done by collecting a background spectrum without the sample and storing the result in the instrument’s computer memory. The background spectrum is removed from the sample’s spectrum by ratioing the two signals. In comparison to other instrument designs, an FT–IR provides for rapid data acquisition, allowing an enhancement in signal-to-noise ratio through signal-averaging.

Sample Cells. Infrared spectroscopy is routinely used to analyze gas, liquid, and solid samples. Sample cells are made from materials, such as NaCl and KBr, that are transparent to infrared radiation. Gases are analyzed using a cell with a pathlength of approximately 10 cm. Longer pathlengths are obtained by using mirrors to pass the beam of radiation through the sample several times.

A liquid samples may be analyzed using a variety of different sample cells (Figure 10.32). For non-volatile liquids a suitable sample can be prepared by placing a drop of the liquid between two NaCl plates, forming a thin film that typically is less than 0.01 mm thick. Volatile liquids must be placed in a sealed cell to prevent their evaporation.

Figure 10.32 Three examples of IR sample cells: (a) NaCl salts plates; (b) fixed pathlength (0.5 mm) sample cell with NaCl windows; (c) disposable card with a polyethylene window that is IR transparent with the exception of strong absorption bands at 2918 cm^–1 and 2849 cm^–1.

The analysis of solution samples is limited by the solvent’s IR absorbing properties, with CCl₄, CS₂, and CHCl₃ being the most common solvents. Solutions are placed in cells containing two NaCl windows separated by a Teflon spacer. By changing the Teflon spacer, pathlengths from 0.015–1.0 mm can be obtained.

Transparent solid samples can be analyzed directly by placing them in the IR beam. Most solid samples, however, are opaque, and must be dispersed in a more transparent medium before recording the IR spectrum. If a suitable solvent is available, then the solid can be analyzed by preparing a solution and analyzing as described above. When a suitable solvent is not available, solid samples may be analyzed by preparing a mull of the finely powdered sample with a suitable oil. Alternatively, the powdered sample can be mixed with KBr and pressed into an optically transparent pellet.

The analysis of an aqueous sample is complicated by the solubility of the NaCl cell window in water. One approach to obtaining infrared spectra on aqueous solutions is to use attenuated total reflectance instead of transmission. Figure 10.33 shows a diagram of a typical attenuated total reflectance (ATR) FT–IR instrument. The ATR cell consists of a high refractive index material, such as ZnSe or diamond, sandwiched between a low refractive index substrate and a lower refractive index sample. Radiation from the source enters the ATR crystal where it undergoes a series of total internal reflections before exiting the crystal. During each reflection the radiation penetrates into the sample to a depth of a few microns. The result is a selective attenuation of the radiation at those wavelengths where the sample absorbs. ATR spectra are similar, but not identical, to those obtained by measuring the transmission of radiation.

Figure 10.33 FT-IR spectrometer equipped with a diamond ATR sample cell. The inserts show a close-up photo of the sample platform, a sketch of the ATR’s sample slot, and a schematic showing how the source’s radiation interacts with the sample. The pressure tower is used to ensure the contact of solid samples with the ATR crystal.

Solid samples also can be analyzed using an ATR sample cell. After placing the solid in the sample slot, a compression tip ensures that it is in contact with the ATR crystal. Examples of solids that have been analyzed by ATR include polymers, fibers, fabrics, powders, and biological tissue samples. Another reflectance method is diffuse reflectance, in which radiation is reflected from a rough surface, such as a powder. Powdered samples are mixed with a non-absorbing material, such as powdered KBr, and the reflected light is collected and analyzed. As with ATR, the resulting spectrum is similar to that obtained by conventional transmission methods.

Note

Further details about these, and other methods for preparing solids for infrared analysis can be found in this chapter’s additional resources.

10.3.2 Quantitative Applications

The determination of an analyte’s concentration based on its absorption of ultraviolet or visible radiation is one of the most frequently encountered quantitative analytical methods. One reason for its popularity is that many organic and inorganic compounds have strong absorption bands in the UV/Vis region of the electromagnetic spectrum. In addition, if an analyte does not absorb UV/Vis radiation—or if its absorbance is too weak—we often can react it with another species that is strongly absorbing. For example, a dilute solution of Fe²⁺ does not absorb visible light. Reacting Fe²⁺ with o-phenanthroline, however, forms an orange–red complex of Fe(phen)₃²⁺ that has a strong, broad absorbance band near 500 nm. An additional advantage to UV/Vis absorption is that in most cases it is relatively easy to adjust experimental and instrumental conditions so that Beer’s law is obeyed.

Note

Figure 10.18 shows the visible spectrum for Fe(phen)₃²⁺.

A quantitative analysis based on the absorption of infrared radiation, although important, is less frequently encountered than those for UV/Vis absorption. One reason is the greater tendency for instrumental deviations from Beer’s law when using infrared radiation. Because an infrared absorption band is relatively narrow, any deviation due to the lack of monochromatic radiation is more pronounced. In addition, infrared sources are less intense than UV/Vis sources, making stray radiation more of a problem. Differences in pathlength for samples and standards when using thin liquid films or KBr pellets are a problem, although an internal standard can be used to correct for any difference in pathlength. Finally, establishing a 100% T (A = 0) baseline is often difficult because the optical properties of NaCl sample cells may change significantly with wavelength due to contamination and degradation. We can minimize this problem by measuring absorbance relative to a baseline established for the absorption band. Figure 10.34 shows how this is accomplished.

Note

Another approach is to use a cell with a fixed pathlength, such as that shown in Figure 10.32b.

Figure 10.34 Method for determining absorbance from an IR spectrum.

Environmental Applications

The analysis of waters and wastewaters often relies on the absorption of ultraviolet and visible radiation. Many of these methods are outlined in Table 10.6. Several of these methods are described here in more detail.

Although the quantitative analysis of metals in waters and wastewaters is accomplished primarily by atomic absorption or atomic emission spectroscopy, many metals also can be analyzed following the formation of a colored metal–ligand complex. One advantage to these spectroscopic methods is that they are easily adapted to the analysis of samples in the field using a filter photometer. One ligand that is used in the analysis of several metals is diphenylthiocarbazone, also known as dithizone. Dithizone is not soluble in water, but when a solution of dithizone in CHCl₃ is shaken with an aqueous solution containing an appropriate metal ion, a colored metal–dithizonate complex forms that is soluble in CHCl₃. The selectivity of dithizone is controlled by adjusting the sample’s pH. For example, Cd²⁺ is extracted from solutions that are made strongly basic with NaOH, Pb²⁺ from solutions that are made basic with an NH₃/NH₄⁺ buffer, and Hg²⁺ from solutions that are slightly acidic.

Note

Atomic absorption is the subject of Section 10.4 and atomic emission is the subject of Section 10.7.

The structure of dithizone is shown to the right. See Chapter 7 for a discussion of extracting metal ions using dithizone.

When chlorine is added to water the portion available for disinfection is called the chlorine residual. There are two forms of chlorine residual. The free chlorine residual includes Cl₂, HOCl, and OCl^–. The combined chlorine residual, which forms from the reaction of NH₃ with HOCl, consists of monochloramine, NH₂Cl, dichloramine, NHCl₂, and trichloramine, NCl₃. Because the free chlorine residual is more efficient at disinfection, there is an interest in methods that can distinguish between the different forms of the total chlorine residual. One such method is the leuco crystal violet method. The free residual chlorine is determined by adding leuco crystal violet to the sample, which instantaneously oxidizes to give a blue colored compound that is monitored at 592 nm. Completing the analysis in less than five minutes prevents a possible interference from the combined chlorine residual. The total chlorine residual (free + combined) is determined by reacting a separate sample with iodide, which reacts with both chlorine residuals to form HOI. When the reaction is complete, leuco crystal violet is added and oxidized by HOI, giving the same blue colored product. The combined chlorine residual is determined by difference.

Note

In Chapter 9 we explored how the total chlorine residual can be determined by a redox titration; see Representative Method 9.3 for further details. The method described here allows us to divide the total chlorine residual into its component parts.

The concentration of fluoride in drinking water may be determined indirectly by its ability to form a complex with zirconium. In the presence of the dye SPADNS, solutions of zirconium form a red colored compound, called a lake, that absorbs at 570 nm. When fluoride is added, the formation of the stable ZrF₆^2– complex causes a portion of the lake to dissociate, decreasing the absorbance. A plot of absorbance versus the concentration of fluoride, therefore, has a negative slope.

Note

SPADNS, which is shown below, is an abbreviation for the sodium salt of 2-(4-sulfophenylazo)-1,8-dihydroxy-3,6-napthalenedisulfonic acid, which is a mouthful to say.

Spectroscopic methods also are used to determine organic constituents in water. For example, the combined concentrations of phenol, and ortho- and meta- substituted phenols are determined by using steam distillation to separate the phenols from nonvolatile impurities. The distillate reacts with 4-aminoantipyrine at pH 7.9 ± 0.1 in the presence of K₃Fe(CN)₆, forming a yellow colored antipyrine dye. After extracting the dye into CHCl₃, its absorbance is monitored at 460 nm. A calibration curve is prepared using only the unsubstituted phenol, C₆H₅OH. Because the molar absorptivity of substituted phenols are generally less than that for phenol, the reported concentration represents the minimum concentration of phenolic compounds.

Molecular absorption also can be used for the analysis of environmentally significant airborne pollutants. In many cases the analysis is carried out by collecting the sample in water, converting the analyte to an aqueous form that can be analyzed by methods such as those described in Table 10.6. For example, the concentration of NO₂ can be determined by oxidizing NO₂ to NO₃^–. The concentration of NO₃^– is then determined by first reducing it to NO₂^– with Cd, and then reacting NO₂^– with sulfanilamide and N-(1-naphthyl)-ethylenediamine to form a red azo dye. Another important application is the analysis for SO₂, which is determined by collecting the sample in an aqueous solution of HgCl₄^2– where it reacts to form Hg(SO₃)₂^2–. Addition of p-rosaniline and formaldehyde produces a purple complex that is monitored at 569 nm. Infrared absorption is useful for the analysis of organic vapors, including HCN, SO₂, nitrobenzene, methyl mercaptan, and vinyl chloride. Frequently, these analyses are accomplished using portable, dedicated infrared photometers.

Clinical Applications

The analysis of clinical samples is often complicated by the complexity of the sample matrix, which may contribute a significant background absorption at the desired wavelength. The determination of serum barbiturates provides one example of how this problem is overcome. The barbiturates are first extracted from a sample of serum with CHCl₃ and then extracted from the CHCl₃ into 0.45 M NaOH (pH ≈ 13). The absorbance of the aqueous extract is measured at 260 nm, and includes contributions from the barbiturates as well as other components extracted from the serum sample. The pH of the sample is then lowered to approximately 10 by adding NH₄Cl and the absorbance remeasured. Because the barbiturates do not absorb at this pH, we can use the absorbance at pH 10, A_pH 10, to correct the absorbance at pH 13, A_pH 13Abarb=ApH 13−Vsamp+VNH4ClVsamp×ApH 10(4.8.2)(4.8.2)Abarb=ApH 13−Vsamp+VNH4ClVsamp×ApH 10

where A_barb is the absorbance due to the serum barbiturates, and V_samp and V_NH4Cl are the volumes of sample and NH₄Cl, respectively. Table 10.7 provides a summary of several other methods for analyzing clinical samples.

Industrial Analysis

UV/Vis molecular absorption is used for the analysis of a diverse array of industrial samples including pharmaceuticals, food, paint, glass, and metals. In many cases the methods are similar to those described in Table 10.6 and Table 10.7. For example, the amount of iron in food can be determined by bringing the iron into solution and analyzing using the o-phenanthroline method listed in Table 10.6.

Many pharmaceutical compounds contain chromophores that make them suitable for analysis by UV/Vis absorption. Products that have been analyzed in this fashion include antibiotics, hormones, vitamins, and analgesics. One example of the use of UV absorption is in determining the purity of aspirin tablets, for which the active ingredient is acetylsalicylic acid. Salicylic acid, which is produced by the hydrolysis of acetylsalicylic acid, is an undesirable impurity in aspirin tablets, and should not be present at more than 0.01% w/w. Samples can be screened for unacceptable levels of salicylic acid by monitoring the absorbance at a wavelength of 312 nm. Acetylsalicylic acid absorbs at 280 nm, but absorbs poorly at 312 nm. Conditions for preparing the sample are chosen such that an absorbance of greater than 0.02 signifies an unacceptable level of salicylic acid.

Forensic Applications

UV/Vis molecular absorption is routinely used for the analysis of narcotics and for drug testing. One interesting forensic application is the determination of blood alcohol using the Breathalyzer test. In this test a 52.5-mL breath sample is bubbled through an acidified solution of K₂Cr₂O₇, which oxidizes ethanol to acetic acid. The concentration of ethanol in the breath sample is determined by the decrease in absorbance at 440 nm where the dichromate ion absorbs. A blood alcohol content of 0.10%, which is above the legal limit, corresponds to 0.025 mg of ethanol in the breath sample.

Developing a Quantitative Method for a Single Component

In developing a quantitative analytical method, the conditions under which Beer’s law is obeyed must be established. First, the most appropriate wavelength for the analysis is determined from an absorption spectrum. In most cases the best wavelength corresponds to an absorption maximum because it provides greater sensitivity and is less susceptible to instrumental limitations. Second, if an instrument with adjustable slits is being used, then an appropriate slit width needs to be chosen. The absorption spectrum also aids in selecting a slit width. Usually we set the slits to be as wide as possible because this increases the throughput of source radiation, while also being narrow enough to avoid instrumental limitations to Beer’s law. Finally, a calibration curve is constructed to determine the range of concentrations for which Beer’s law is valid. Additional considerations that are important in any quantitative method are the effect of potential interferents and establishing an appropriate blank.

Note

The best way to appreciate the theoretical and practical details discussed in this section is to carefully examine a typical analytical method. Although each method is unique, the following description of the determination of iron in water and wastewater provides an instructive example of a typical procedure. The description here is based on Method 3500- Fe B as published in Standard Methods for the Examination of Water and Wastewater, 20th Ed., American Public Health Association: Washington, D. C., 1998.

Representative Method 10.1

Determination of Iron in Water and Wastewater

Description of Method

Iron in the +2 oxidation state reacts with o-phenanthroline to form the orange-red Fe(phen)₃²⁺ complex. The intensity of the complex’s color is independent of solution acidity between a pH of 3 and 9. Because the complex forms more rapidly at lower pH levels, the reaction is usually carried out within a pH range of 3.0–3.5. Any iron present in the +3 oxidation state is reduced with hydroxylamine before adding o-phenanthroline. The most important interferents are strong oxidizing agents, polyphosphates, and metal ions such as Cu²⁺, Zn²⁺, Ni²⁺, and Cd²⁺. An interference from oxidizing agents is minimized by adding an excess of hydroxylamine, and an interference from polyphosphate is minimized by boiling the sample in the presence of acid. The absorbance of samples and standards are measured at a wavelength of 510 nm using a 1-cm cell (longer pathlength cells also may be used). Beer’s law is obeyed for concentrations of within the range of 0.2–4.0 mg Fe/L.

(Figure 10.18 shows the visible spectrum for Fe(phen)₃²⁺.)

Procedure

For samples containing less than 2 mg Fe/L, directly transfer a 50-mL portion to a 125-mL Erlenmeyer flask. Samples containing more than 2 mg Fe/L must be diluted before acquiring the 50-mL portion. Add 2 mL of concentrated HCl and 1 mL of hydroxylamine to the sample. Heat the solution to boiling and continue boiling until the solution’s volume is reduced to between 15 and 20 mL. After cooling to room temperature, transfer the solution to a 50-mL volumetric flask, add 10 mL of an ammonium acetate buffer, 2 mL of a 1000 ppm solution of o-phenanthroline, and dilute to volume. Allow 10–15 minutes for color development before measuring the absorbance, using distilled water to set 100% T. Calibration standards, including a blank, are prepared by the same procedure using a stock solution containing a known concentration of Fe²⁺.

Questions

1. Explain why strong oxidizing agents are interferents, and why an excess of hydroxylamine prevents the interference.

A strong oxidizing agent oxidizes some Fe²⁺ to Fe³⁺. Because Fe(phen)₃³⁺ does not absorb as strongly as Fe(phen)₃²⁺, the absorbance decreases, producing a negative determinate error. The excess hydroxylamine reacts with the oxidizing agents, removing them from the solution.

2. The color of the complex is stable between pH levels of 3 and 9. What are some possible complications at more acidic or more basic pH’s?

Because o-phenanthroline is a weak base, its conditional formation constant for Fe(phen)₃²⁺ is less favorable at more acidic pH levels, where o-phenanthroline is protonated. The result is a decrease in absorbance and a less sensitive analytical method.

(In Chapter 9 we saw the same effect of pH on the complexation reactions between EDTA and metal ions.)

When the pH is greater than 9, competition between OH^– and o-phenanthroline for Fe²⁺ also decreased the absorbance. In addition, if the pH is sufficiently basic there is a risk that the iron will precipitate as Fe(OH)₂.

3. Cadmium is an interferent because it forms a precipitate with o-phenanthroline. What effect would the formation of precipitate have on the determination of iron?

Because o-phenanthroline is present in large excess (2000 μg of o-phenanthroline for 100 μg of Fe²⁺), it is not likely that the interference is due to an insufficient amount of o-phenanthroline being available to react with the Fe²⁺. The presence of a precipitate in the sample cell results in the scattering of radiation, which causes an apparent increase in absorbance. Because the measured absorbance increases, the reported concentration is too high.

(Although scattering is a problem here, it can serve as the basis of a useful analytical method. See Section 10.8 for further details.)

4. Even high quality ammonium acetate contains a significant amount of iron. Why is this source of iron not a problem?

Because all samples and standards are prepared using the same volume of ammonium acetate buffer, the contribution of this source of iron is accounted for by the calibration curve’s reagent blank.

Quantitative Analysis for a Single Analyte

To determine the concentration of a an analyte we measure its absorbance and apply Beer’s law using any of the standardization methods described in Chapter 5. The most common methods are a normal calibration curve using external standards and the method of standard additions. A single point standardization is also possible, although we must first verify that Beer’s law holds for the concentration of analyte in the samples and the standard.

Example 10.5

The determination of Fe in an industrial waste stream was carried out by the o‑phenanthroline described in Representative Method 10.1. Using the data in the following table, determine the mg Fe/L in the waste stream.

Solution

Linear regression of absorbance versus the concentration of Fe in the standards gives a calibration curve with the following equation.A=0.0006+0.1817×(mgFe/L)(4.8.3)(4.8.3)A=0.0006+0.1817×(mgFe/L)

Substituting the sample’s absorbance into the calibration expression gives the concentration of Fe in the waste stream as 1.48 mg Fe/L.

Practice Exercise 10.5

The concentration of Cu²⁺ in a sample can be determined by reacting it with the ligand cuprizone and measuring its absorbance at 606 nm in a 1.00-cm cell. When a 5.00-mL sample is treated with cuprizone and diluted to 10.00 mL, the resulting solution has an absorbance of 0.118. A second 5.00-mL sample is mixed with 1.00 mL of a 20.00 mg/L standard of Cu²⁺, treated with cuprizone and diluted to 10.00 mL, giving an absorbance of 0.162. Report the mg Cu²⁺/L in the sample.

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Quantitative Analysis of Mixtures

Suppose we need to determine the concentration of two analytes, X and Y, in a sample. If each analyte has a wavelength where the other analyte does not absorb, then we can proceed using the approach in Example 10.5. Unfortunately, UV/Vis absorption bands are so broad that it frequently is not possible to find suitable wavelengths. Because Beer’s law is additive the mixture’s absorbance, A_mix, is(Amix)λ1=(εX)λ1bCX+(εY)λ1bCY(10.11)(10.11)(Amix)λ1=(εX)λ1bCX+(εY)λ1bCY

where λ1 is the wavelength at which we measure the absorbance. Because equation 10.11 includes terms for the concentration of both X and Y, the absorbance at one wavelength does not provide enough information to determine either C_X or C_Y. If we measure the absorbance at a second wavelength(Amix)λ2=(εX)λ2bCX+(εY)λ2bCY(10.12)(10.12)(Amix)λ2=(εX)λ2bCX+(εY)λ2bCY

then C_X and C_Y can be determined by solving simultaneously equation10.11 and equation 10.12. Of course, we also must determine the value for ε_X and ε_Y at each wavelength. For a mixture of n components, we must measure the absorbance at n different wavelengths.

Example 10.6

The concentrations of Fe³⁺ and Cu²⁺ in a mixture can be determined following their reaction with hexacyanoruthenate (II), Ru(CN)₆^4–, which forms a purple-blue complex with Fe³⁺ (λ_max = 550 nm) and a pale-green complex with Cu²⁺ (λ_max = 396 nm).⁷ The molar absorptivities (M^–1 cm^–1) for the metal complexes at the two wavelengths are summarized in the following table.

When a sample containing Fe³⁺ and Cu²⁺ is analyzed in a cell with a pathlength of 1.00 cm, the absorbance at 550 nm is 0.183 and the absorbance at 396 nm is 0.109. What are the molar concentrations of Fe³⁺ and Cu²⁺ in the sample?

Solution

Substituting known values into equations 10.11 and 10.12 givesA550=0.183=9970CFe+34CCu(4.8.4)(4.8.4)A550=0.183=9970CFe+34CCuA396=0.109=84CFe+856CCu(4.8.5)(4.8.5)A396=0.109=84CFe+856CCu

To determine C_Fe and C_Cu we solve the first equation for C_CuCCu=0.183–9970CFe34(4.8.6)(4.8.6)CCu=0.183–9970CFe34

and substitute the result into the second equation.0.109=84CFe+856×0.183−9970CFe34=4.607–(2.51×105)CFe(4.8.7)(4.8.7)0.109=84CFe+856×0.183−9970CFe34=4.607–(2.51×105)CFe

Solving for C_Fe gives the concentration of Fe³⁺ as 1.79 × 10^–5 M. Substituting this concentration back into the equation for the mixture’s absorbance at 396 nm gives the concentration of Cu²⁺ as 1.26 × 10^–4 M.

(Another approach is to multiply the first equation by 856/34 giving4.607=251009CFe+856CCu(4.8.8)(4.8.8)4.607=251009CFe+856CCu

Subtracting the second equation from this equation4.607=251009CFe+856CCu−0.109=84CFe+856CCu–––––––––––––––––––––––––––––––4.498=250925CFe(4.8.9)(4.8.10)(4.8.11)(4.8.9)−4.607=251009CFe+856CCu(4.8.10)−0.109=84CFe+856CCu6CCu_(4.8.11)−4.498=250925CFe

we find that C_Fe is 1.79×10^–5. Having determined C_Fe we can substitute back into one of the other equations to solve for C_Cu, which is 1.26×10^–5.)

Practice Exercise 10.6

The absorbance spectra for Cr³⁺ and Co²⁺ overlap significantly. To determine the concentration of these analytes in a mixture, its absorbance was measured at 400 nm and at 505 nm, yielding values of 0.336 and 0.187, respectively. The individual molar absorptivities (M^–1 cm^–1) are

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To obtain results with good accuracy and precision the two wavelengths should be selected so that ε_X > ε_Y at one wavelength and ε_X < ε_Y at the other wavelength. It is easy to appreciate why this is true. Because the absorbance at each wavelength is dominated by one analyte, any uncertainty in the concentration of the other analyte has less of an impact. Figure 10.35 shows that the choice of wavelengths for Practice Exercise 10.6 are reasonable. When the choice of wavelengths is not obvious, one method for locating the optimum wavelengths is to plot ε_X/ε_Y as function of wavelength, and determine the wavelengths where ε_X/ε_Y reaches maximum and minimum values.⁸

Note

For example, in Example 10.6 the molar absorptivity for Fe³⁺ at 550 nm is 119× that for Cu²⁺, and the molar absorptivity for Cu²⁺ at 396 nm is 10.2× that for Fe³⁺.

Figure 10.35 Visible absorption spectra for 0.0250 M Cr³⁺, 0.0750 M Co²⁺, and for a mixture of Cr³⁺ and Co²⁺. The two wavelengths used for analyzing the mixture of Cr³⁺ and Co²⁺ are shown by the dashed lines. The data for the two standard solutions are from reference 7.

When the analyte’s spectra overlap severely, such that ε_X ≈ ε_Y at all wavelength, other computational methods may provide better accuracy and precision. In a multiwavelength linear regression analysis, for example, a mixture’s absorbance is compared to that for a set of standard solutions at several wavelengths.⁹ If A_SXand A_SY are the absorbance values for standard solutions of components X and Y at any wavelength, thenASX=εXbCSX(10.13)(10.13)ASX=εXbCSXASY=εYbCSY(10.14)(10.14)ASY=εYbCSY

where C_SX and C_SY are the known concentrations of X and Y in the standard solutions. Solving equation 10.13 and equation 10.14 for ε_X and ε_Y, substituting into equation 10.11, and rearranging, givesAmixASX=CXCSX+CYCSY×ASYASX(4.8.12)(4.8.12)AmixASX=CXCSX+CYCSY×ASYASX

To determine C_X and C_Y the mixture’s absorbance and the absorbances of the standard solutions are measured at several wavelengths. Graphing A_mix/A_SX versus A_SY/A_SX gives a straight line with a slope of C_Y/C_SY and a y-intercept of C_X/C_SX. This approach is particularly helpful when it is not possible to find wavelengths where ε_X > ε_Y and ε_X < ε_Y.

Note

The approach outlined here for a multiwavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of this data—what we call a multiple linear regression—is beyond the level of this text. For more details about multiple linear regression see Brereton, R. G. Chemometrics: Data Analysis for the Laboratory and Chemical Plant, Wiley: Chichester, England, 2003.

Example 10.7

Figure 10.35 shows visible absorbance spectra for a standard solution of 0.0250 M Cr³⁺, a standard solution of 0.0750 M Co²⁺, and a mixture containing unknown concentrations of each ion. The data for these spectra are shown here.¹⁰

Use a multiwavelength regression analysis to determine the composition of the unknown.

Solution

First we need to calculate values for A_mix/A_SX and for A_SY/A_SX. Let’s define X as Co²⁺ and Y as Cr³⁺. For example, at a wavelength of 375 nm A_mix/A_SX is 0.53/0.01, or 53 and A_SY/A_SX is 0.26/0.01, or 26. Completing the calculation for all wavelengths and graphing A_mix/A_SX versus A_SY/A_SXgives the result shown in Figure 10.36. Fitting a straight-line to the data gives a regression model ofAmixASX=0.636+2.01×ASYASX(4.8.13)(4.8.13)AmixASX=0.636+2.01×ASYASX

Using the y-intercept, the concentration of Co²⁺ isCXCSX=CCo0.0750M=0.636(4.8.14)(4.8.14)CXCSX=CCo0.0750M=0.636

or C_Co = 0.048 M, and using the slope the concentration of Cr³⁺ isCYCSY=CCr0.0250M=2.01(4.8.15)(4.8.15)CYCSY=CCr0.0250M=2.01

or C_Cr = 0.050 M.

Figure 10.36 Multiwavelength linear regression analysis for the data in Example 10.7.

Practice Exercise 10.7

A mixture of MnO₄^– and Cr₂O₇^2–, and standards of 0.10 mM KMnO₄ and of 0.10 mM K₂Cr₂O₇ gives the results shown in the following table. Determine the composition of the mixture. The data for this problem is from Blanco, M. C.; Iturriaga, H.; Maspoch, S.; Tarin, P. J. Chem. Educ. 1989, 66, 178–180.

(There are many additional ways to analyze mixtures spectrophotometrically, including generalized standard additions, H-point standard additions, principal component regression to name a few. Consult the chapter’s additional resources for further information.)

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10.3.3 Qualitative Applications

As discussed earlier in Section 10.2.1, ultraviolet, visible, and infrared absorption bands result from the absorption of electromagnetic radiation by specific valence electrons or bonds. The energy at which the absorption occurs, and its intensity is determined by the chemical environment of the absorbing moiety. For example, benzene has several ultraviolet absorption bands due to π → π* transitions. The position and intensity of two of these bands, 203.5 nm (ε = 7400 M^–1 cm^–1) and 254 nm (ε = 204 M^–1 cm^–1), are sensitive to substitution. For benzoic acid, in which a carboxylic acid group replaces one of the aromatic hydrogens, the two bands shift to 230 nm (ε = 11 600 M^–1 cm^–1) and 273 nm (ε = 970 M^–1 cm^–1). A variety of rules have been developed to aid in correlating UV/Vis absorption bands to chemical structure. Similar correlations have been developed for infrared absorption bands. For example a carbonyl’s C=O stretch is sensitive to adjacent functional groups, occurring at 1650 cm^–1 for acids, 1700 cm^–1 for ketones, and 1800 cm^–1 for acid chlorides. The interpretation of UV/Vis and IR spectra receives adequate coverage elsewhere in the chemistry curriculum, notably in organic chemistry, and is not considered further in this text.

With the availability of computerized data acquisition and storage it is possible to build digital libraries of standard reference spectra. The identity of an a unknown compound can often be determined by comparing its spectrum against a library of reference spectra, a process is known as spectral searching. Comparisons are made using an algorithm that calculates the cumulative difference between the sample’s spectrum and a reference spectrum. For example, one simple algorithm uses the following equationD=∑i=1n|(Asample)i−(Areference)i|(4.8.16)(4.8.16)D=∑i=1n|(Asample)i−(Areference)i|

where D is the cumulative difference, A_sample is the sample’s absorbance at wavelength or wavenumber i, A_reference is the absorbance of the reference compound at the same wavelength or wavenumber, and n is the number of digitized points in the spectra. The cumulative difference is calculated for each reference spectrum. The reference compound with the smallest value of D provides the closest match to the unknown compound. The accuracy of spectral searching is limited by the number and type of compounds included in the library, and by the effect of the sample’s matrix on the spectrum.

Another advantage of computerized data acquisition is the ability to subtract one spectrum from another. When coupled with spectral searching it may be possible, by repeatedly searching and subtracting reference spectra, to determine the identity of several components in a sample without the need of a prior separation step. An example is shown in Figure 10.37 in which the composition of a two-component mixture is determined by successive searching and subtraction. Figure 10.37a shows the spectrum of the mixture. A search of the spectral library selects cocaine ^. HCl (Figure 10.37b) as a likely component of the mixture. Subtracting the reference spectrum for cocaine ^. HCl from the mixture’s spectrum leaves a result (Figure 10.37c) that closely matches mannitol’s reference spectrum (Figure 10.37d). Subtracting the reference spectrum for leaves only a small residual signal (Figure 10.37e).

Figure 10.37 Identifying the components of a mixture by spectral searching and subtracting. (a) IR spectrum of the mixture; (b) Reference IR spectrum of cocaine^. HCl; (c) Result of subtracting the spectrum of cocaine ^. HCl from the mixture’s spectrum; (d) Reference IR spectrum of mannitol; and (e) The residual spectrum after removing mannitol’s contribution to the mixture’s spectrum.

Note

IR spectra traditionally are displayed using percent transmittance, %T, along the y-axis (for example, see Figure 10.16). Because absorbance—not percent transmittance—is a linear function of concentration, spectral searching and spectral subtraction, is easier to do when displaying absorbance on the y-axis.

10.3.4 Characterization Applications

Molecular absorption, particularly in the UV/Vis range, has been used for a variety of different characterization studies, including determining the stoichiometry of metal–ligand complexes and determining equilibrium constants. Both of these examples are examined in this section.

Stoichiometry of a Metal-Ligand Complex

We can determine the stoichiometry of a metal–ligand complexation reactionM+yL⇋MLy(4.8.17)(4.8.17)M+yL⇋MLy

using one of three methods: the method of continuous variations, the mole-ratio method, and the slope-ratio method. Of these approaches, the method of continuous variations, also called Job’s method, is the most popular. In this method a series of solutions is prepared such that the total moles of metal and ligand, n_total, in each solution is the same. If (n_M)_i and (n_L)_i are, respectively, the moles of metal and ligand in solution i, thenntotal=(nM)i+(nL)i(4.8.18)(4.8.18)ntotal=(nM)i+(nL)i

The relative amount of ligand and metal in each solution is expressed as the mole fraction of ligand, (X_L)_i, and the mole fraction of metal, (X_M)_i,(XL)i=(nL)intotal(4.8.19)(4.8.19)(XL)i=(nL)intotal(XM)i=1−(nL)intotal=(nM)intotal(4.8.20)(4.8.20)(XM)i=1−(nL)intotal=(nM)intotal

The concentration of the metal–ligand complex in any solution is determined by the limiting reagent, with the greatest concentration occurring when the metal and the ligand are mixed stoichiometrically. If we monitor the complexation reaction at a wavelength where only the metal–ligand complex absorbs, a graph of absorbance versus the mole fraction of ligand will have two linear branches—one when the ligand is the limiting reagent and a second when the metal is the limiting reagent. The intersection of these two branches represents a stoichiometric mixing of the metal and the ligand. We can use the mole fraction of ligand at the intersection to determine the value of y for the metal–ligand complex ML_y.y=nLnM=XLXM=XL1−XL(4.8.21)(4.8.21)y=nLnM=XLXM=XL1−XL

Note

You also can plot the data as absorbance versus the mole fraction of metal. In this case, y is equal to (1–X_M)/X_M.

Example 10.8

To determine the formula for the complex between Fe²⁺ and o-phenanthroline, a series of solutions is prepared in which the total concentration of metal and ligand is held constant at 3.15 × 10^–4 M. The absorbance of each solution is measured at a wavelength of 510 nm. Using the following data, determine the formula for the complex.

(To prepare the solutions for this example I first prepared a solution of 3.15 × 10^-4 M Fe²⁺ and a solution of 3.15 × 10^-4 M o-phenanthroline. Because the two stock solutions are of equal concentration, diluting a portion of one solution with the other solution gives a mixture in which the combined concentration of o-phenanthroline and Fe²⁺ is 3.15 × 10^-4 M. If each solution has the same volume, then each solution contains the same total moles of metal and ligand.)

Solution

A plot of absorbance versus the mole fraction of ligand is shown in Figure 10.38. To find the maximum absorbance, we extrapolate the two linear portions of the plot. The two lines intersect at a mole fraction of ligand of 0.75. Solving for y givesy=XL1–XL=0.751–0.75=3(4.8.22)(4.8.22)y=XL1–XL=0.751–0.75=3

The formula for the metal–ligand complex is Fe(o-phenanthroline)₃²⁺.

Figure 10.38 Continuous variations plot for Example 10.8. The photo shows the solutions used in gathering the data. Each solution is displayed directly below its corresponding point on the continuous variations plot.

Practice Exercise 10.8

Use the continuous variations data in the following table to determine the formula for the complex between Fe²⁺ and SCN^–. The data for this problem is adapted from Meloun, M.; Havel, J.; Högfeldt, E. Computation of Solution Equilibria, Ellis Horwood: Chichester, England, 1988, p. 236.

Click here to review your answer to this exercise.

Several precautions are necessary when using the method of continuous variations. First, the metal and the ligand must form only one metal–ligand complex. To determine if this condition is true, plots of absorbance versus X_L are constructed at several different wavelengths and for several different values of n_total. If the maximum absorbance does not occur at the same value of X_L for each set of conditions, then more than one metal–ligand complex must be present. A second precaution is that the metal–ligand complex’s absorbance must obey Beer’s law. Third, if the metal–ligand complex’s formation constant is relatively small, a plot of absorbance versus X_L may show significant curvature. In this case it is often difficult to determine the stoichiometry by extrapolation. Finally, because the stability of a metal–ligand complex may be influenced by solution conditions, the composition of the solutions must be carefully controlled. When the ligand is a weak base, for example, the solutions must be buffered to the same pH.

In the mole-ratio method the amount of one reactant, usually the moles of metal, is held constant, while the amount of the other reactant is varied. The absorbance is monitored at a wavelength where the metal–ligand complex absorbs. A plot of absorbance as a function of the ligand-to-metal mole ratio, n_L/n_M, has two linear branches, which intersect at a mole–ratio corresponding to the complex’s formula. Figure 10.39a shows a mole-ratio plot for the formation of a 1:1 complex in which the absorbance is monitored at a wavelength where only the complex absorbs. Figure 10.39b shows a mole-ratio plot for a 1:2 complex in which all three species—the metal, the ligand, and the complex—absorb at the selected wavelength. Unlike the method of continuous variations, the mole-ratio method can be used for complexation reactions that occur in a stepwise fashion if there is a difference in the molar absorptivities of the metal–ligand complexes, and if the formation constants are sufficiently different. A typical mole-ratio plot for the step-wise formation of ML and ML₂ is shown in Figure 10.39c.

Figure 10.39 Mole-ratio plots for: (a) a 1:1 metal–ligand complex in which only the complex absorbs; (b) a 1:2 metal–ligand complex in which the metal, the ligand, and the complex absorb; and (c) the stepwise formation of a 1:1 and a 1:2 metal–ligand complex.

In both the method of continuous variations and the mole-ratio method we determine the complex’s stoichiometry by extrapolating absorbance data from conditions in which there is a linear relationship between absorbance and the relative amounts of metal and ligand. If a metal–ligand complex is very weak, a plot of absorbance versus X_L or n_L/n_M may be so curved that it is impossible to determine the stoichiometry by extrapolation. In this case the slope-ratio may be used.

In the slope-ratio method two sets of solutions are prepared. The first set of solutions contains a constant amount of metal and a variable amount of ligand, chosen such that the total concentration of metal, C_M, is much larger than the total concentration of ligand, C_L. Under these conditions we may assume that essentially all the ligand reacts in forming the metal–ligand complex. The concentration of the complex, which has the general form M_xL_y, is[MxLy]=CLy(4.8.23)(4.8.23)[MxLy]=CLy

If we monitor the absorbance at a wavelength where only M_xL_y absorbs, thenA=εb[MxLy]=εbCLy(4.8.24)(4.8.24)A=εb[MxLy]=εbCLy

and a plot of absorbance versus C_L is linear with a slope, s_L, ofsL=εby(4.8.25)(4.8.25)sL=εby

A second set of solutions is prepared with a fixed concentration of ligand that is much greater than a variable concentration of metal; thus[MxLy]=CMx(4.8.26)(4.8.26)[MxLy]=CMxA=εb[MxLy]=εbCMx(4.8.27)(4.8.27)A=εb[MxLy]=εbCMxsM=εbx(4.8.28)(4.8.28)sM=εbx

A ratio of the slopes provides the relative values of x and y.sMsL=εb/xεb/y=yx(4.8.29)(4.8.29)sMsL=εb/xεb/y=yx

An important assumption in the slope-ratio method is that the complexation reaction continues to completion in the presence of a sufficiently large excess of metal or ligand. The slope-ratio method also is limited to systems in which only a single complex is formed and for which Beer’s law is obeyed.

Determination of Equilibrium Constants

Another important application of molecular absorption spectroscopy is the determination of equilibrium constants. Let’s consider, as a simple example, an acid–base reaction of the general formHIn(aq)+H2O(l)⇋H3O+(aq)+In−(aq)(4.8.30)(4.8.30)HIn(aq)+H2O(l)⇋H3O+(aq)+In−(aq)

where HIn and In^– are the conjugate weak acid and weak base forms of an acid–base indicator. The equilibrium constant for this reaction isKa=[H3O+][In−][HIn](4.8.31)(4.8.31)Ka=[H3O+][In−][HIn]

To determine the equilibrium constant’s value, we prepare a solution in which the reaction is in a state of equilibrium and determine the equilibrium concentration of H₃O⁺, HIn, and In^–. The concentration of H₃O⁺ is easy to determine by simply measuring the solution’s pH. To determine the concentration of HIn and In^– we can measure the solution’s absorbance.

If both HIn and In^– absorb at the selected wavelength, then, from equation 10.6, we know thatA=εHInb[HIn]+εInb[In−](10.15)(10.15)A=εHInb[HIn]+εInb[In−]

where ε_HIn and ε_In are the molar absorptivities for HIn and In^–. The total concentration of indicator, C, is given by a mass balance equationC=[HIn]+[In−](10.16)(10.16)C=[HIn]+[In−]

Solving equation 10.16 for [HIn] and substituting into equation 10.15 givesA=εHInb(C−[In−])+εInb[In−](4.8.32)(4.8.32)A=εHInb(C−[In−])+εInb[In−]

which we simplify toA=εHInbC−εHInb[In−]+εInb[In−](4.8.33)(4.8.33)A=εHInbC−εHInb[In−]+εInb[In−]A=AHIn+b[In−](εIn−εHIn)(10.17)(10.17)A=AHIn+b[In−](εIn−εHIn)

where A_HIn, which is equal to ε_HInbC, is the absorbance when the pH is acidic enough that essentially all the indicator is present as HIn. Solving equation 10.17 for the concentration of In^– gives[In−]=A−AHInb(εIn−εHIn)(10.18)(10.18)[In−]=A−AHInb(εIn−εHIn)

Proceeding in the same fashion, we can derive a similar equation for the concentration of HIn[HIn]=AIn−Ab(εIn−εHIn)(10.19)(10.19)[HIn]=AIn−Ab(εIn−εHIn)

where A_In, which is equal to ε_InbC, is the absorbance when the pH is basic enough that only In^– contributes to the absorbance. Substituting equation 10.18 and equation 10.19 into the equilibrium constant expression for HIn givesKa=[H3O+]A−AHInAIn−A(10.20)(10.20)Ka=[H3O+]A−AHInAIn−A

We can use equation 10.20 to determine the value of K_a in one of two ways. The simplest approach is to prepare three solutions, each of which contains the same amount, C, of indicator. The pH of one solution is made sufficiently acidic such that [HIn] >> [In⁻]. The absorbance of this solution gives A_HIn. The value of A_In is determined by adjusting the pH of the second solution such that [In⁻] >> [HIn]. Finally, the pH of the third solution is adjusted to an intermediate value, and the pH and absorbance, A, recorded. The value of K_a is calculated using equation 10.20.

Example 10.9

The acidity constant for an acid–base indicator is determined by preparing three solutions, each of which has a total indicator concentration of 5.00 × 10^–5 M. The first solution is made strongly acidic with HCl and has an absorbance of 0.250. The second solution was made strongly basic and has an absorbance of 1.40. The pH of the third solution is 2.91 and has an absorbance of 0.662. What is the value of K_a for the indicator?

Solution

The value of K_a is determined by making appropriate substitutions into 10.20; thusKa=(1.23×10−3)×0.662−0.2501.40−0.662=6.87×10−4(4.8.34)(4.8.34)Ka=(1.23×10−3)×0.662−0.2501.40−0.662=6.87×10−4

Practice Exercise 10.9

To determine the K_a of a merocyanine dye, the absorbance of a solution of 3.5×10^–4 M dye was measured at a pH of 2.00, a pH of 6.00, and a pH of 12.00, yielding absorbances of 0.000, 0.225, and 0.680, respectively. What is the value of K_a for this dye? The data for this problem is adapted from Lu, H.; Rutan, S. C. Anal. Chem., 1996, 68, 1381–1386.

Click here to review your answer to this exercise.

A second approach for determining K_a is to prepare a series of solutions, each containing the same amount of indicator. Two solutions are used to determine values for A_HIn and A_In. Taking the log of both sides of equation 10.20 and rearranging leave us with the following equation.logA−AHInAIn−A=pH−pKa(10.21)(10.21)log⁡A−AHInAIn−A=pH−pKa

A plot of log[(A – A_HIn)/(A_In – A)] versus pH is a straight-line with a slope of +1 and a y-intercept of –pK_a.

Practice Exercise 10.10

To determine the K_a of the indicator bromothymol blue, the absorbance of a series of solutions containing the same concentration of the indicator was measured at pH levels of 3.35, 3.65, 3.94, 4.30, and 4.64, yielding absorbances of 0.170, 0.287, 0.411, 0.562, and 0.670, respectively. Acidifying the first solution to a pH of 2 changes its absorbance to 0.006, and adjusting the pH of the last solution to 12 changes its absorbance to 0.818. What is the value of K_a for this day? The data for this problem is from Patterson, G. S. J. Chem. Educ., 1999, 76, 395–398.

Click here to review your answer to this exercise.

In developing these approaches for determining K_a we considered a relatively simple system in which the absorbance of HIn and In^– are easy to measure and for which it is easy to determine the concentration of H₃O⁺. In addition to acid–base reactions, we can adapt these approaches to any reaction of the general formX(aq)+Y(aq)⇋Z(aq)(4.8.35)(4.8.35)X(aq)+Y(aq)⇋Z(aq)

including metal–ligand complexation reactions and redox reactions, provided that we can determine spectrophotometrically the concentration of the product, Z, and one of the reactants, and that the concentration of the other reactant can be measured by another method. With appropriate modifications, more complicated systems, in which one or more of these parameters can not be measured, also can be treated.¹¹

10.3.5 Evaluation of UV/Vis and IR Spectroscopy

Scale of Operation

Molecular UV/Vis absorption is routinely used for the analysis of trace analytes in macro and meso samples. Major and minor analytes can be determined by diluting the sample before analysis, while concentrating a sample may allow for the analysis of ultratrace analytes. The scale of operations for infrared absorption is generally poorer than that for UV/Vis absorption.

Note

See Figure 3.5 to review the meaning of macro and meso for describing samples, and the meaning of major, minor, and ultratrace for describing analytes.

Accuracy

Under normal conditions a relative error of 1–5% is easy to obtained with UV/Vis absorption. Accuracy is usually limited by the quality of the blank. Examples of the type of problems that may be encountered include the presence of particulates in a sample that scatter radiation and interferents that react with analytical reagents. In the latter case the interferent may react to form an absorbing species, giving rise to a positive determinate error. Interferents also may prevent the analyte from reacting, leading to a negative determinate error. With care, it may be possible to improve the accuracy of an analysis by as much as an order of magnitude.

Precision

In absorption spectroscopy, precision is limited by indeterminate errors—primarily instrumental noise—introduced when measuring absorbance. Precision is generally worse for low absorbances where P₀ ≈ P_T, and for high absorbances when P_T approaches 0. We might expect, therefore, that precision will vary with transmittance.

We can derive an expression between precision and transmittance by applying the propagation of uncertainty as described in Chapter 4. To do so we rewrite Beer’s law asC=−1εblogT(10.22)(10.22)C=−1εblog⁡T

Table 4.10 in Chapter 4 helps us in completing the propagation of uncertainty for equation 10.22, giving the absolute uncertainty in the concentration, s_C, assC=−0.4343εb×sTT(10.23)(10.23)sC=−0.4343εb×sTT

where s_T is the absolute uncertainty in the transmittance. Dividing equation 10.23 by equation 10.22 gives the relative uncertainty in concentration, s_C/C, assCC=0.4343sTTlogT(4.8.36)(4.8.36)sCC=0.4343sTTlog⁡T

If we know the absolute uncertainty in transmittance, we can determine the relative uncertainty in concentration for any transmittance.

Determining the relative uncertainty in concentration is complicated because s_T may be a function of the transmittance. As shown in Table 10.8, three categories of indeterminate instrumental error have been observed.¹² A constant s_T is observed for the uncertainty associated with reading %T on a meter’s analog or digital scale. Typical values are ±0.2–0.3% (a k₁ of ±0.002–0.003) for an analog scale, and ±0.001% a (k₁ of ±0.000 01) for a digital scale. A constant s_T also is observed for the thermal transducers used in infrared spectrophotometers. The effect of a constant s_T on the relative uncertainty in concentration is shown by curve A in Figure 10.40. Note that the relative uncertainty is very large for both high and low absorbances, reaching a minimum when the absorbance is 0.4343. This source of indeterminate error is important for infrared spectrophotometers and for inexpensive UV/Vis spectrophotometers. To obtain a relative uncertainty in concentration of ±1–2%, the absorbance must be kept within the range 0.1–1.

Values of s_T are a complex function of transmittance when indeterminate errors are dominated by the noise associated with photon detectors. Curve B in Figure 10.40 shows that the relative uncertainty in concentration is very large for low absorbances, but is less at higher absorbances. Although the relative uncertainty reaches a minimum when the absorbance is 0.963, there is little change in the relative uncertainty for absorbances within the range 0.5–2. This source of indeterminate error generally limits the precision of high quality UV/Vis spectrophotometers for mid-to-high absorbances.

Figure 10.40 Percent relative uncertainty in concentration as a function of absorbance for the categories of indeterminate errors in Table 10.8. A: k₁ = ±0.0030; B: k₂ = ±0.0030; C:k₃ = ±0.0130. The dashed lines correspond to the minimum uncertainty for curve A (absorbance of 0.4343) and for curve B (absorbance of 0.963).

Finally, the value of s_T is directly proportional to transmittance for indeterminate errors resulting from fluctuations in the source’s intensity and from uncertainty in positioning the sample within the spectrometer. The latter is particularly important because the optical properties of any sample cell are not uniform. As a result, repositioning the sample cell may lead to a change in the intensity of transmitted radiation. As shown by curve C in Figure 10.40, the effect is only important at low absorbances. This source of indeterminate errors is usually the limiting factor for high quality UV/Vis spectrophotometers when the absorbance is relatively small.

When the relative uncertainty in concentration is limited by the %T readout resolution, the precision of the analysis can be improved by redefining 100% T and 0% T. Normally 100% T is established using a blank and 0% T is established while preventing the source’s radiation from reaching the detector. If the absorbance is too high, precision can be improved by resetting 100% T using a standard solution of the analyte whose concentration is less than that of the sample (Figure 10.41a). For a sample whose absorbance is too low, precision can be improved by redefining 0% T using a standard solution of the analyte whose concentration is greater than that of the analyte (Figure 10.41b). In this case a calibration curve is required because a linear relationship between absorbance and concentration no longer exists. Precision can be further increased by combining these two methods (Figure 10.41c). Again, a calibration curve is necessary since the relationship between absorbance and concentration is no longer linear.

Figure 10.41 Methods for improving the precision of absorption methods: (a) high-absorbance method; (b) low-absorbance method; (c) maximum precision method.

Sensitivity

The sensitivity of a molecular absorption method, which is the slope of a Beer’s law calibration curve, is the product of the analyte’s absorptivity and the pathlength of the sample cell (εb). You can improve a method’s sensitivity by selecting a wavelength where absorbance is at a maximum or by increasing the pathlength.

Note

See Figure 10.24 for an example of how the choice of wavelength affects a calibration curve’s sensitivity.

Selectivity

Selectivity is rarely a problem in molecular absorption spectrophotometry. In many cases it is possible to find a wavelength where only the analyte absorbs. When two or more species do contribute to the measured absorbance, a multicomponent analysis is still possible, as shown in Example 10.6 and Example 10.7.

Time, Cost, and Equipment

The analysis of a sample by molecular absorption spectroscopy is relatively rapid, although additional time may be required if we need to chemically convert a nonabsorbing analyte into an absorbing form. The cost of UV/Vis instrumentation ranges from several hundred dollars for a simple filter photometer, to more than $50,000 for a computer controlled high resolution, double-beam instrument equipped with variable slits, and operating over an extended range of wavelengths. Fourier transform infrared spectrometers can be obtained for as little as $15,000–$20,000, although more expensive models are available.

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While interaction with infrared light causes molecules to undergo vibrational transitions, the shorter wavelength, higher energy radiation in the UV (200-400 nm) and visible (400-700 nm) range of the electromagnetic spectrum causes many organic molecules to undergo electronic transitions. What this means is that when the energy from UV or visible light is absorbed by a molecule, one of its electrons jumps from a lower energy to a higher energy molecular orbital.

Electronic transitions

Let’s take as our first example the simple case of molecular hydrogen, H₂. As you may recall from section 2.1A, the molecular orbital picture for the hydrogen molecule consists of one bonding σ MO, and a higher energy antibonding σ* MO. When the molecule is in the ground state, both electrons are paired in the lower-energy bonding orbital – this is the Highest Occupied Molecular Orbital (HOMO). The antibonding σ* orbital, in turn, is the Lowest Unoccupied Molecular Orbital (LUMO).

If the molecule is exposed to light of a wavelength with energy equal to ΔE, the HOMO-LUMO energy gap, this wavelength will be absorbed and the energy used to bump one of the electrons from the HOMO to the LUMO – in other words, from the σ to the σ* orbital. This is referred to as a σ – σ* transition. ΔE for this electronic transition is 258 kcal/mol, corresponding to light with a wavelength of 111 nm.

When a double-bonded molecule such as ethene (common name ethylene) absorbs light, it undergoes a π – π* transition. Because π- π* energy gaps are narrower than σ – σ* gaps, ethene absorbs light at 165 nm – a longer wavelength than molecular hydrogen.

The electronic transitions of both molecular hydrogen and ethene are too energetic to be accurately recorded by standard UV spectrophotometers, which generally have a range of 220 – 700 nm. Where UV-vis spectroscopy becomes useful to most organic and biological chemists is in the study of molecules with conjugated ππsystems. In these groups, the energy gap for π -π* transitions is smaller than for isolated double bonds, and thus the wavelength absorbed is longer. Molecules or parts of molecules that absorb light strongly in the UV-vis region are called chromophores.

Let’s revisit the MO picture for 1,3-butadiene, the simplest conjugated system. Recall that we can draw a diagram showing the four pi MO’s that result from combining the four 2p_z atomic orbitals. The lower two orbitals are bonding, while the upper two are antibonding.

Comparing this MO picture to that of ethene, our isolated pi-bond example, we see that the HOMO-LUMO energy gap is indeed smaller for the conjugated system. 1,3-butadiene absorbs UV light with a wavelength of 217 nm.

As conjugated pi systems become larger, the energy gap for a π – π* transition becomes increasingly narrow, and the wavelength of light absorbed correspondingly becomes longer. The absorbance due to the π – π* transition in 1,3,5-hexatriene, for example, occurs at 258 nm, corresponding to a ΔE of 111 kcal/mol.

In molecules with extended pi systems, the HOMO-LUMO energy gap becomes so small that absorption occurs in the visible rather then the UV region of the electromagnetic spectrum. Beta-carotene, with its system of 11 conjugated double bonds, absorbs light with wavelengths in the blue region of the visible spectrum while allowing other visible wavelengths – mainly those in the red-yellow region – to be transmitted. This is why carrots are orange.

The conjugated pi system in 4-methyl-3-penten-2-one gives rise to a strong UV absorbance at 236 nm due to a π – π* transition. However, this molecule also absorbs at 314 nm. This second absorbance is due to the transition of a non-bonding (lone pair) electron on the oxygen up to a π* antibonding MO:

This is referred to as an n – π* transition. The nonbonding (n) MO’s are higher in energy than the highest bonding p orbitals, so the energy gap for an n→π∗n→π∗transition is smaller that that of a π – π* transition – and thus the n – π* peak is at a longer wavelength. In general, n – π* transitions are weaker (less light absorbed) than those due to π – π* transitions.

Exercise 4.9

What is the energy of the photons (in kJ/mol) of light with wavelength of 470 nm, the l_max of b-carotene?

Exercise 4.10

Which of the following molecules would you expect absorb at a longer wavelength in the UV region of the electromagnetic spectrum? Explain your answer.

Solutions

Protecting yourself from sunburn

Human skin can be damaged by exposure to ultraviolet light from the sun. We naturally produce a pigment, called melanin, which protects the skin by absorbing much of the ultraviolet radiation. Melanin is a complex polymer, two of the most common monomers units of which are shown below.

Overexposure to the sun is still dangerous, because there is a limit to how much radiation our melanin can absorb. Most commercial sunscreens claim to offer additional protection from both UV-A and UV-B radiation: UV-A refers to wavelengths between 315-400 nm, UV-B to shorter, more harmful wavelengths between 280-315 nm. PABA (para-aminobenzoic acid) was used in sunscreens in the past, but its relatively high polarity meant that it was not very soluble in oily lotions, and it tended to rinse away when swimming. Many sunscreens today contain, among other active ingredients, a more hydrophobic derivative of PABA called Padimate O.

Looking at UV-vis spectra

We have been talking in general terms about how molecules absorb UV and visible light – now let’s look at some actual examples of data from a UV-vis absorbance spectrophotometer. The basic setup is the same as for IR spectroscopy: radiation with a range of wavelengths is directed through a sample of interest, and a detector records which wavelengths were absorbed and to what extent the absorption occurred.

Schematic for a UV-Vis spectrophotometer

(Image from Wikipedia Commons)

Below is the absorbance spectrum of an important biological molecule called nicotinamide adenine dinucleotide, abbreviated NAD⁺. This compound absorbs light in the UV range due to the presence of conjugated pi-bonding systems.

You’ll notice that this UV spectrum is much simpler than the IR spectra we saw earlier: this one has only one peak, although many molecules have more than one. Notice also that the convention in UV-vis spectroscopy is to show the baseline at the bottom of the graph with the peaks pointing up. Wavelength values on the x-axis are generally measured in nanometers (nm) rather than in cm^-1 as is the convention in IR spectroscopy.

Peaks in UV spectra tend to be quite broad, often spanning well over 20 nm at half-maximal height. Typically, there are two things that we look for and record from a UV-Vis spectrum. The first is λmaxλmax, which is the wavelength at maximal light absorbance. As you can see, NAD⁺ has λmax=260nmλmax=260nm. We also want to record how much light is absorbed at λmaxλmax. Here we use a unitless number called absorbance, abbreviated ‘A’. This contains the same information as the ‘percent transmittance’ number used in IR spectroscopy, just expressed in slightly different terms. To calculate absorbance at a given wavelength, the computer in the spectrophotometer simply takes the intensity of light at that wavelength before it passes through the sample (I₀), divides this value by the intensity of the same wavelength after it passes through the sample (I), then takes the log₁₀ of that number:A=logI0I(4.3.1)(4.3.1)A=log⁡I0I

You can see that the absorbance value at 260 nm (A₂₆₀) is about 1.0 in this spectrum.

Exercise 4.11

Express A = 1.0 in terms of percent transmittance (%T, the unit usually used in IR spectroscopy (and sometimes in UV-vis as well).

Solutions

Here is the absorbance spectrum of the common food coloring Red #3:

Here, we see that the extended system of conjugated pi bonds causes the molecule to absorb light in the visible range. Because the λ_max of 524 nm falls within the green region of the spectrum, the compound appears red to our eyes. Now, take a look at the spectrum of another food coloring, Blue #1:

Here, maximum absorbance is at 630 nm, in the orange range of the visible spectrum, and the compound appears blue.

Applications of UV spectroscopy in organic and biological chemistry

UV-vis spectroscopy has many different applications in organic and biological chemistry. One of the most basic of these applications is the use of the Beer – Lambert Law to determine the concentration of a chromophore. You most likely have performed a Beer – Lambert experiment in a previous chemistry lab. The law is simply an application of the observation that, within certain ranges, the absorbance of a chromophore at a given wavelength varies in a linear fashion with its concentration: the higher the concentration of the molecule, the greater its absorbance.

If we divide the observed value of A at λ_max by the concentration of the sample (c, in mol/L), we obtain the molar absorptivity, or extinction coefficient (ε), which is a characteristic value for a given compound.ϵ=Ac(4.3.2)(4.3.2)ϵ=Ac

The absorbance will also depend, of course, on the path length – in other words, the distance that the beam of light travels though the sample. In most cases, sample holders are designed so that the path length is equal to 1 cm, so the units for molar absorptivity are L_* mol^-1_*cm^-1. If we look up the value of e for our compound at λ_max, and we measure absorbance at this wavelength, we can easily calculate the concentration of our sample. As an example, for NAD⁺ the literature value of ε at 260 nm is 18,000 L_* mol^-1_*cm^-1. In our NAD⁺ spectrum we observed A₂₆₀ = 1.0, so using equation 4.4 and solving for concentration we find that our sample is 5.6 x 10^-5 M.

The bases of DNA and RNA are good chromophores:

Biochemists and molecular biologists often determine the concentration of a DNA sample by assuming an average value of ε = 0.020 ng^-1×mL for double-stranded DNA at its λ_max of 260 nm (notice that concentration in this application is expressed in mass/volume rather than molarity: ng/mL is often a convenient unit for DNA concentration when doing molecular biology).Exercise 4.1250 microliters of an aqueous sample of double stranded DNA is dissolved in 950 microliters of water. This diluted solution has a maximal absorbance of 0.326 at 260 nm. What is the concentration of the original (more concentrated) DNA sample, expressed in micrograms per microliter?Solutions

Because the extinction coefficient of double stranded DNA is slightly lower than that of single stranded DNA, we can use UV spectroscopy to monitor a process known as DNA melting. If a short stretch of double stranded DNA is gradually heated up, it will begin to ‘melt’, or break apart, as the temperature increases (recall that two strands of DNA are held together by a specific pattern of hydrogen bonds formed by ‘base-pairing’).

As melting proceeds, the absorbance value for the sample increases, eventually reaching a high plateau as all of the double-stranded DNA breaks apart, or ‘melts’. The mid-point of this process, called the ‘melting temperature’, provides a good indication of how tightly the two strands of DNA are able to bind to each other.

Later we will see how the Beer – Lambert Law and UV spectroscopy provides us with a convenient way to follow the progress of many different enzymatic redox (oxidation-reduction) reactions. In biochemistry, oxidation of an organic molecule often occurs concurrently with reduction of nicotinamide adenine dinucleotide (NAD⁺, the compound whose spectrum we saw earlier in this section) to NADH:

Both NAD⁺ and NADH absorb at 260 nm. However NADH, unlike NAD⁺, has a second absorbance band with λ_max = 340 nm and ε = 6290 L_*mol^-1_*cm^-1. The figure below shows the spectra of both compounds superimposed, with the NADH spectrum offset slightly on the y-axis:

By monitoring the absorbance of a reaction mixture at 340 nm, we can ‘watch’ NADH being formed as the reaction proceeds, and calculate the rate of the reaction.

UV spectroscopy is also very useful in the study of proteins. Proteins absorb light in the UV range due to the presence of the aromatic amino acids tryptophan, phenylalanine, and tyrosine, all of which are chromophores.

Biochemists frequently use UV spectroscopy to study conformational changes in proteins – how they change shape in response to different conditions. When a protein undergoes a conformational shift (partial unfolding, for example), the resulting change in the environment around an aromatic amino acid chromophore can cause its UV spectrum to be altered.

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Light interacts with matter in different ways, transmitting through some materials, while reflecting or scattering off others. Both the material and the colour (wavelength) of the light affect this interaction. We call the study of this light ‘spectroscopy’. Which parts of the visible spectrum enter our eyes determines which colours we perceive.

A substance might appear blue, for example, if it absorbs the red parts of the spectrum of light falling upon it, only reflecting (or scattering) the blue parts into our eyes.

Raman spectroscopy looks at the scattered light

If you were to shine blue light—from just one part of the spectrum—onto the material, you might expect to just see blue light reflected from it, or no light at all if it is completely absorbed (i.e. a black material).

However, by using a Raman spectrometer, you can see that often a very tiny fraction of the scattered light has a different colour. It has changed frequency because, during the scattering process, its energy changed by interacting with molecular vibrations. This is the Raman scattering process, named after its discoverer, the famous Indian physicist C.V. Raman. He was awarded the 1930 physics Nobel Prize for this great discovery.

By studying the vibration of the atoms we can discover the chemical composition and other useful information about the material.

The Raman effect is very weak; only about 1 part in 10 million of the scattered light has a shifted colour. This is too weak to see with the naked eye, so we analyse the light with a highly sensitive spectrometer.

Raman spectrometers

These systems consist of:

• one or more single coloured light sources (lasers)
• lenses (both to focus the light onto the sample and to collect the scattered light)
• filters (to purify the reflected and scattered light so that only the Raman light is collected)
• a means of splitting the light into its constituent colours (normally a diffraction grating or prism)
• a very sensitive detector (to detect the weak light)
• a device such as a computer to control the whole system, display the spectrum and enable this information to be analysed

Raman scattering offers significant advantages for the investigation of materials over other analytical techniques, such as x-raying them or seeing how they absorb light (e.g. infrared absorption or ultraviolet absorption).

aman spectroscopy reveals the chemical and structural composition of samples. Generally, all materials produce Raman spectra, with the exception of pure metals.

Raman scattering

Raman scattering occurs when light interacts with molecular vibrations. This is similar to the more widely known infrared absorption spectroscopy, but different rules apply. A change in molecular polarisability is required during the vibration for the Raman effect to occur.

You will see some vibrations in the Raman spectrum that are not visible in the infrared spectrum, and vice-versa, because of the different selection rules. For example, Raman spectroscopy is superb for studying the carbon atoms that make up the structure of diamond, unlike infrared absorption spectroscopy.

Scattered light

The first step in producing a Raman spectrum is to illuminate your sample with a monochromatic light source, such as a laser.

Most of the light that scatters off is unchanged in energy (‘Rayleigh scattered’). A minute fraction—perhaps 1 part in 10 million—has lost or gained energy (‘Raman scattered’). This Raman shift occurs because photons (particles of light) exchange part of their energy with molecular vibrations in the material.

Where energy is lost the Raman scattering is designated as ‘Stokes’; where energy is gained the Raman scattering is designated as ‘anti-Stokes’. We rarely use anti-Stokes Raman light as it is less intense than the Stokes, however it does represent equivalent vibrational information of the molecule.

Vibrating atoms

The change in energy depends on the frequency of vibration of the molecule. If it is very fast (high frequency)—light atoms held together with strong bonds—the energy change is significant. If it is very slow (low frequency)—heavy atoms held together with weak bonds—the energy change is small.

Raman spectrometers

Renishaw inVia systems consist of:

• single or multiple lasers, from UV (244 nm) to IR (1064 nm) – switch with a single click
• high quality objective lenses, from high confocal 100× to long working distance and immersion options
• custom designed motorised spectrometer lenses­ – automatically align for each configuration
• laser-line-specific Rayleigh filters with a dual filter arrangement to optimise sensitivity
• highest quality master diffraction gratings provide exceptional dispersion and longevity
• thermoelectrically cooled (- 70 ºC) CCD detector – stable and sensitive
• high specification multi-core PC for data collection and analysis

Raman spectra

We graphically depict the results of our measurements as Raman spectra. We plot the intensity of the scattered light (y-axis) for each energy (frequency) of light (x-axis). The frequency is traditionally measured in a unit called the wavenumber (number of waves per cm, cm^-1).

We plot the x-axis frequencies relative to that of the laser as it is the shift in energy of the light that is of particular interest.

How do I get the information I want from my spectrum?

You can tell a great deal about a material from its Raman spectrum, with different features relating to different aspects of the material.

The key features are:

The Raman shifts and relative intensities of all of the Raman bands of the material
With this, we can identify the material.

Individual band changes
A band may shift, narrow or broaden, or vary in intensity. These changes can reveal information about stresses in the sample, variations in crystallinity, and the amount of material respectively.

Variations in spectra with position on the sample
This will reveal changes in the uniformity (homogeneity) of the material. You can analyse at several arbitrary points, or systematically measure an array of points (enabling the production of images of composition, stress, crystallinity, etc.)

What do the Raman bands represent?

It is easy to understand the Raman spectrum of crystals with a regular array of identical atoms, all in the same configuration (such as the carbon atoms in diamond). In these cases, you often see just one dominant Raman band (because there is just one molecular environment of the crystal).

The Raman spectrum of polystyrene, however, is much more complex because the molecule is less symmetric and has hydrogen atoms in addition to carbon atoms. There are also different bond types connecting the atoms.

Vibration frequencies

The frequencies of vibration depend on the masses of the atoms involved and the strength of the bonds between them. Heavy atoms and weak bonds have low Raman shifts. Light atoms and strong bonds have high Raman shifts.

We see the high frequency carbon-hydrogen (C-H) vibrations in the polystyrene spectrum at about 3000 cm^-1. The low frequency carbon-carbon (C-C) vibrations are at around 800 cm^-1. The C-H vibrations have a higher frequency than the C-C vibrations because hydrogen is lighter than carbon.

We see the vibrations of two carbon atoms linked by strong double bonds (C=C) at around 1600 cm^-1. This is at a higher frequency than two carbon atoms lined by a weaker single bond (C-C, 800 cm^-1).

You can use these simple rules to explain many of the features of Raman spectra.

Vibrations in detail

You can see more subtle effects if you inspect spectra closely. The strength of bonds also affects their vibration rates. For example, the C-H vibrations of polystyrene appear in two bands, at approximately 2900 cm^-1 and 3050 cm^-1. The carbons in the former are part of carbon chains (‘aliphatic’), whereas the carbons in the latter form part of carbon rings (‘aromatic’).

You can view the vibrations of a complex molecule as partly consisting of many simple diatomic vibrations. However the full richness of the Raman spectrum can only be understood by considering the vibrations of larger groups of atoms (such as the expanding/contracting ‘breathing mode’ of the aromatic carbon ring that appears at 1000 cm^-1 in polystyrene).

Low frequency vibrations

You can also study Raman bands with low Raman shifts, below 100 cm^-1. These originate from very heavy atoms or very large-scale vibrations, such as the whole crystal lattice vibrating. Renishaw’s Raman instruments enable you to study these modes and explore a wide range of materials and crystals, and distinguish between different crystalline forms (polymorphs).

The big picture

A Raman spectrum therefore consists of a range of features, each associated with a vibrational mode. The spectrum is unique to the material and enables you to identify it. It is important to note that, although a full understanding of the vibrational modes is of interest, you rarely need this as you can use a reference database for identification.

When a sample is illuminated by a laser, both Raman scattering and photoluminescence (PL) can occur. The latter can be many times stronger than the former and can prevent successful Raman analysis.

PL comprises both fluorescence and phosphorescence processes and originates from an absorption/emission process between different electronic energy levels in the material. The amount and type of PL depends on which material you are studying and which laser wavelength you are using. Unwanted fluorescence interference can normally be avoided by choosing an appropriate laser wavelength.

• Energy diagram showing absorption of light and the processes involved in the emission of light as fluorescence and phosphorescence.

What PL can tell us

In many cases photoluminescence carries useful information that can facilitate sample analysis and augment the Raman data. inVia confocal Raman microscopes are suited to the analysis of both Raman scattering and PL.

Fluorescence imaging (a type of PL) is often employed in the biological sciences, where fluorescent tags are used to reveal the presence and distribution of molecular species. However, this approach is more invasive than Raman analysis, which is typically tag-free. Renishaw’s inVia confocal Raman microscope can be used to generate images of fluorescent tags, but more commonly provides valuable tag-free chemical information.

You can also use PL to study crystal defects, such as atomic vacancies and substitutions. This is of particular importance for materials such as diamond and silicon carbide (SiC). Not only can you identify the defect, but you can also tell if the crystal has internal stresses.

• Stress image generated from the ruby R2 PL band position

How to avoid PL backgrounds

Occasionally PL bands are strong and broad, masking Raman information. You can counter this by using a different laser wavelength. This can move the Raman bands away from the peak emission of the PL band and may even avoid generation of the PL entirely.

Ideally, a Raman instrument should be able to switch rapidly and easily between different laser wavelengths, so that you can select or avoid PL features, depending on your requirements.

Raman images (sometimes referred to as maps) depict a variation in spectral information from different points on, or in your sample. They can take the form of one-dimensional profiles, two-dimensional images, or three-dimensional rendered volumes. With them, you can rapidly see how a Raman parameter alters with position.

The parameter could be as simple as the intensity of a particular Raman band, or you could derive it from a more complicated analysis of the whole Raman spectrum.

The two main methods of collecting the spectral data to generate these images are Raman mapping and Raman imaging.

• White light and Raman images of washing powder

Raman mapping

Raman mapping collects a spectral hypercube (a Raman spectrum from each position on the sample in a single file), rather than a simple intensity image. The hypercube is analysed to produce Raman images.

There are several Raman mapping methods, such as:

• Point-by-point mapping
  The laser is focused to a spot. A motorised stage moves the sample under the laser. Spectra are sequentially acquired from an array of sample points spanning the defined region of interest. Fast versions of this are Renishaw’s StreamHR™ and StreamHR Rapide.
• Line focus mapping
  This is similar to point-by-point mapping, but the laser illuminates a line on the sample, rather than a spot. This enables you to simultaneously collect spectra from multiple positions on the sample, saving time. With this method you can use higher laser powers without damaging the sample (reducing exposure times). Renishaw’s StreamLine™ is a sophisticated modern implementation of this concept.

It is important to consider the potentially undesirable effects of undersampling when mapping. This is most clearly illustrated when point-by-point mapping: parts of the sample will be ‘missed’ if the laser spot is smaller than the spacing between acquisition points. Renishaw has solved this problem through the use of the StreamLine™ Slalom mode.

Generating Raman images from map data

Once all the Raman spectra are collected from the mapping experiment, they can be analysed to produce profiles, images or rendered volumes. Analysis options in Renishaw’s WiRE software include:

• Intensity at one frequency in the spectrum
  This produces an equivalent image to that from Raman imaging. These are quick to generate but may be misleading because it is not possible to differentiate between intensities arising from a Raman band of interest and those associated with a broad background fluorescence.
• Curve fit parameters
  All the spectra in the set have a theoretical curve fitted to one of the Raman bands. Images are then made based on the theoretical curve parameters for each spectrum. Images are often made using the centre frequency of the curve (band), or the full width at half maximum (FWHM), as this is sensitive to stresses and crystallinity within the sample respectively.
• Multivariate parameters
  Images can be generated using chemometric tools, such as generic principal component analysis (PCA), or Renishaw’s Empty Modelling™, which is optimised for Raman data. The Empty Modelling method reveals systematic variations between the Raman spectra, and highlights the distribution of these variations across the sample as an image. This is achieved without the need for prior knowledge of what is present within the sample, which greatly simplifies the analysis process. Multivariate analysis is very powerful because it uses information from the entire spectrum, not just one part of it (intensity at one frequency) or one curve-fitted band. This typically results in higher quality Raman images.

Raman imaging

Raman imaging is analogous to taking a photograph; spectral intensity values are collected simultaneously from the entire area of interest. The laser illuminates a square or circular region on the sample. The light is filtered so that the intensity of just one narrow part of the spectrum is recorded on the detector.

The single image collected contains limited information, just the intensity of the light at that frequency. However, these images can be acquired rapidly. This is especially true if you have a high power laser; because the light is spread over an area, you can use all the power without damaging your samples, with correspondingly short exposure times.

Two-dimensional images are typically produced using this method. Renishaw’s True Raman Imaging is an example of Raman imaging.

Note that it is possible to collect intensity values covering multiple points of the spectrum by using multiple and/or tuneable filters.

Spatial resolution

Point-by-point Raman mapping

Spatial resolution is determined by a combination of the laser spot size and the spacing between acquisition points on the sample.

• Laser spot size
  This is a function of the objective magnification and the laser wavelength (higher magnification and shorter wavelengths produce smaller spot sizes)
• Spacing between acquisition points on the sample (sampling)
  This is a function of the sample stage (ideally stages should have a large travel range while still enabling a step size down to 100 nm, smaller than the smallest spot size)

Raman imaging

Spatial resolution is determined by the magnification of the optics in the system and the size of the elements in the detector. Ultimately this is limited, by the inherent wavelike nature of light, to a little under a micrometre.

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Driven by applications in chemical sensing, biological imaging and material characterisation, Raman spectroscopies are attracting growing interest from a variety of scientific disciplines. The Raman effect originates from the inelastic scattering of light, and it can directly probe vibration/rotational-vibration states in molecules and materials.

Despite numerous advantages over infrared spectroscopy, spontaneous Raman scattering is very weak, and consequently, a variety of enhanced Raman spectroscopic techniques have emerged. These techniques include stimulated Raman scattering and coherent anti-Stokes Raman scattering, as well as surface- and tip-enhanced Raman scattering spectroscopies. The present review provides the reader with an understanding of the fundamental physics that govern the Raman effect and its advantages, limitations and applications. The review also highlights the key experimental considerations for implementing the main experimental Raman spectroscopic techniques. The relevant data analysis methods and some of the most recent advances related to the Raman effect are finally presented. This review constitutes a practical introduction to the science of Raman spectroscopy; it also highlights recent and promising directions of future research developments.

Introduction

Raman Spectroscopy

There are numerous forms of light-matter interaction: fluorescence and phosphorescence are examples of absorption and subsequent emission of light by matter. Elastic scattering of light, such as Rayleigh scattering by atoms, molecules or phonons, and Mie/Tyndall scattering by dust particles are examples where the wavelength of the light is unchanged. Inelastic scattering such as Brillouin scattering by acoustic waves in crystals, Compton scattering by charged particles and Raman scattering by molecules or phonons are examples where the wavelength of the light does change [1]. Raman scattering of light by molecules was first predicted using classical quantum theory by Smekal in 1923 [2] and experimentally observed by Raman and Krishnan in 1928 [3, 4].

There are now more than 25 different types of known Raman spectroscopy techniques, such as spontaneous Raman, hyper-Raman scattering, Fourier transform Raman scattering [5], Raman-induced Kerr effect spectroscopy [6] and stimulated/coherent Raman scattering [1]. This review considers spontaneous and stimulated Raman scattering, coherent anti-Stokes Raman scattering (CARS), surface-enhanced Raman scattering (SERS) and tip-enhanced Raman scattering (TERS).

Fifty years after its first observation, Raman spectroscopy started to become a prominent analysis technique among other optical metrology techniques, such as those involving absorption of infrared light; particularly when water and other useful polar solvents were present, because these media typically strongly absorb light in the infrared region. For example, in 1974, Fleischmann et al. [7] used Raman spectroscopy to distinguish two types of adsorbed pyridine (a basic cyclic heterodyne compound molecule) on the surface of a silver electrode to mitigate absorption effects. This experiment was incidentally the first serendipitous observation of SERS.

Raman spectroscopy is now an eminent technique for the characterisation of 2D materials (e.g. graphene [8,9,10] and transition metal dichalcogenides [11,12,13]) and phonon modes in crystals [14,15,16]. Properties such as number of monolayers [9, 12, 17, 18], inter-layer breathing and shear modes [19], in-plane anisotropy [20], doping [21,22,23], disorder [10, 24,25,26], thermal conductivity [11], strain [27] and phonon modes [14, 16, 28] can be extracted using Raman spectroscopy.

The biological and medical fields of research are greatly impacted by the development of Raman spectroscopy as it is a label-free (does not require fluorescent marker molecules [29, 30]) chemically selective hyperspectral imaging technique [31]. For instance, studying the transdermal delivery of drugs into skin often ordains ex vivo and invasive analysis techniques. Ex vivo transdermal delivery studies are unfavourable because skin regeneration stops, the immune response ceases, and metabolic activity is usually lost. Hence, the performance of transdermal drug delivery ex vivo is not an accurate reflection of the in vivo situation [32]. However, non-invasive in vivo measurements can be performed using Raman spectroscopy to gain detailed information about the molecular composition and concentration gradients in the skin [33]. In many biological processes, living microorganisms such as bacteria act as biocatalysts. Raman spectroscopy can probe inhomogeneity in the properties and physiological status of individual cells in biocatalytic processes [34]. Raman spectroscopy has also been used to identify and differentiate benign and malignant breast cancer lesions by probing their unique chemical compositions [35].

For biological samples, approximately 90% of the peaks are found in the ‘fingerprint’ spectral region, covering (Δν∼Δν∼ ~ 500 cm⁻¹ to ~ 1800 cm⁻¹; Δν∼Δν∼ is the wavenumber shift defined in the “Analysis methods” section), with the remaining found in the higher energy CH/OH stretching vibrational modes covering (Δν∼Δν∼ ~ 2700 cm⁻¹ to ~ 3300 cm⁻¹) [36].

Coherent Raman Spectroscopy

Coherent light-scattering events involving multiple incident photons simultaneously interacting with the scattering material was not observed until laser sources became available in the 1960s, despite predictions being made as early as the 1930s [37, 38]. The first laser-based Raman scattering experiment was demonstrated in 1961 [39]. Stimulated Raman scattering (SRS) and CARS have become prominent four-wave mixing techniques and are of interest in this review.

SRS is a coherent process providing much stronger signals relative to spontaneous Raman spectroscopy as well as the ability to time-resolve the vibrational motions. SRS is relevant to numerous areas of research such as plasma physics [40], atomic interferometry [41], supercontinuum generation [42], imaging of biomolecules in food products [43], imaging chemistry inside living cells [44], bulk media and nanoscale specimens [45]. The exchange of photon orbital angular momentum by SRS in plasma is gaining interest, particularly in the context of inertial fusion research [40, 46,47,48]. Supercontinuum generation is a complex nonlinear phenomenon that is characterized by the dramatic spectral broadening of intense light pulses passing through a nonlinear material [49]. Knight et al. [42] demonstrated flat ultrabroadband octave-spanning white-light supercontinuum generation by SRS and parametric four-wave mixing with 60-ps pump pulses of sub-kilowatt peak power in a photonic crystal fibre. Kasevich and Chu [41] demonstrated a matter-wave interferometer with laser-cooled sodium atoms using the mechanical effects of stimulated Raman transitions. SRS has even been used to observe time-resolved vibrational spectra of the primary isomerisation of retinal in the visual pigment rhodopsin [50].

Since its resurgence in 1999, CARS has become a prominent vibrational mode imaging tool in biological medicine [51, 52]. As anti-Stokes photons are blue shifted from the pump and Stokes frequencies, they are more easily detected in the presence of single-photon fluorescence [53]. CARS microscopy has been successfully applied to live-cell imaging [51, 54], skeletal stem cells [55], tracing toxic nanomaterials in biological tissues [56], volumetric imaging of human somatic cell division [57], flow cytometry [58, 59], detection of brain tumours [60] and tracking organelle transport in living cells [61]. Zirak et al. [62] has developed a CARS endoscope for in vivo imaging and demonstrated the instrument with murine adipose tissue and human nervus suralis samples. Evans et al. [63] have combined CARS with video rate microscopy to chemically image tissue in vivo. Potma and Xie [64] have directly visualised lipid phase segregation in single lipid bilayers with CARS. CARS can even be used as a high temporal and spatial resolution thermography technique and has found applications in electronic and opto-electronic device characterisation [65] and even turbomachinery [66].

Orientational order is a salient feature of many soft matter systems. Detail in structural molecular organisation is a prevailing goal in the field of biology, biomedicine, material sciences and molecular physics [67]. Polarisation-resolved optical microscopy is becoming a powerful tool to address molecular orientational distributions into the focal volume of a microscope [68]. In coherent nonlinear optics, polarised second harmonic generation [69,70,71], polarised third harmonic generation [72] and polarised four-wave mixing [73, 74] have already been used to recover orientational information on endogeneous proteins and lipids in biological tissues. In addition to the orientational information, coherent Raman scattering (CRS) processes are sensitive to molecular bond vibrations, allowing chemical specificity without the need for fluorescence labelling/dyes [75,76,77]. CARS microscopy can be used to image chemical and orientational order of liquid crystalline (commonly used in display technology) samples [78]. Polarisation-resolved hyperspectral SRS microscopy has also been demonstrated as a label-free biomolecular imaging technique with teeth [79]. In addition, polarised-CARS has been used to study the molecular order of lipids in myelin at sub-diffraction scales in mice [80].

Enhanced Raman Spectroscopy

The sensitivity of Raman spectroscopy can be enhanced through various techniques such as resonance Raman spectroscopy [81], TERS [82, 83] or SERS [84]. SERS is particularly interesting since it allows an enhancement of several orders of magnitude of the Raman signal by modifying the surface upon which an analyte material is to be placed. The enhanced light-matter interaction in TERS and SERS is tuneable (to some extent) by modifying the surface nanostructure of metallic films on dielectric surfaces [85, 86]. The wavelength of charge density oscillations, known as plasmons, is dependent on these surface nanostructures and can enhance the light-matter interaction locally [87]. Plasmons are a prominent topic in physics and plasmonic devices such as filters [88], waveguides [88, 89], polarisers [90] and nanoscale light sources [91] have now been realised.

Fleischmann et al. [7] first observed SERS in 1974 when investigating pyridine on the rough surface of a silver electrode [92]. The sensitivity of SERS makes it well-suited to study electron transfer reactions, which lie at the heart of numerous fundamental processes: electro-catalysis, solar energy conversion, energy storage in batteries, and biological events such as photosynthesis [93]. SERS has also been identified as a valuable technique for the detection of explosives/chemical weapons [94], unmodified DNA [95], aerosol pollutants [96] and pathogens [97].

TERS is a technique that provides spectral information with a spatial resolution on the nanometre scale [98]. Since the first reports of TERS emerged in 2000 [99, 100], TERS has become a powerful technique for studying thin crystalline materials [101], carbon nanotubes[86, 102, 103], single strands of RNA/DNA [104, 105], redox reactions [106], mapping of individual molecules [83], semi-conductor nanostructures and microcavities [107].

In the following sections, the fundamental physics that underpins the spontaneous Raman effect, stimulated- and coherent Raman spectroscopy, SERS and TERS are detailed in the context of their applications. Experimental considerations are discussed, and examples of Raman spectroscopy instrumentation setups are presented. The conventions for presenting spectra are detailed and examples of analysis techniques are given for each of the applications of Raman spectroscopy. In the final sections, the recent advances that constitute the current frontiers of Raman spectroscopy are presented from various fields of research worldwide.

Fundamental Principles

When light interacts with matter, the oscillatory electro-magnetic (EM) field of the light perturbs the charge distribution in the matter which can lead to the exchange of energy and momentum leaving the matter in a modified state. Examples include electronic excitations and molecular vibrations or rotational-vibrations (ro-vibrations) in liquids and gases, electronic excitations and optical phonons in solids, and electron-plasma oscillations in plasmas [108].

Spontaneous Raman

When an incident photon interacts with a crystal lattice or molecule, it can be scattered either elastically or inelastically. Predominantly, light is elastically scattered (i.e. the energy of the scattered photon is equal to that of the incident photon). This type of scattering is often referred to as Rayleigh scattering. The inelastic scattering of light by matter (i.e. the energy of the scattered photon is not equal to that of the incident photon) is known as the Raman effect[1, 4, 6]. This inelastic process leaves the molecule in a modified (ro-)vibrational state. In the case of a crystal lattice, the energy transfer creates a quantum of vibration in the lattice known as a phonon (a quasi-particle). Raman scattering in crystals can also lead to paramagnetic ions, surface plasmons (which are discussed later in this review) and spin waves [15]. The shift in angular frequency of the scattered light can be described by the following equation:ωscat=ωp±ωosc,ωscat=ωp±ωosc,(1)

where subscripts osc denotes the lattice or molecule vibration, p denotes the incident photon (often referred to as the pump photon) and scat denotes the scattered light [1]. The binary operator (±) is determined by energy conservation. When the energy of the scattered photon is lower than that of the incident photon (i.e. red shifted), the process is referred to as Stokes Raman scattering. Conversely, when the energy of the scattered photon is higher than that of the incident photon (i.e. blue shifted), the process is referred to as anti-Stokes Raman scattering. The Raman process must also conserve momentum, which is expressed in wave vector form as:k⇀scat=k⇀p±q⇀,k⇀scat=k⇀p±q⇀,(2)

where k⇀scatk⇀scat, k⇀pk⇀p and q⇀q⇀ are the wave vectors of the scattered light, the incident light and the phonon or molecular (ro-)vibration, respectively.

In molecules and crystals, the charge distribution has an equilibrium state to which it tends. An externally applied field can modify or perturb the charge distribution but only in accordance with the molecule or crystal’s ability to form dipoles which may be anisotropic. This anisotropic property of molecules and crystals is called the polarisability and dielectric susceptibility, respectively. The classical approach theorises that the existence of the Raman effect is associated with the modulation of the polarisability (for molecular (ro-)vibrations) or dielectric susceptibility (for crystal lattice vibrations) due to the oscillatory nature of their interatomic displacement [6, 109]. For crystal lattice vibrations, consider the polarisation vector of the material, P⇀P⇀. If the suffixes j and k represent the vector components in the x, yand z directions, the j^th component of P⇀P⇀ (to first-order) is related to the oscillatory electric field vector E⇀E⇀ associated with the light by [110]:P(1)j=ε0χ(1)jkEk,Pj(1)=ε0χjk(1)Ek,(3)

where ε₀ is the permittivity of free space, χ_jk is the dielectric susceptibility of the material (a rank two tensor) and the convention of summation over repeated indices is implied [109]; the superscript (1) signifies that this is the first-order contribution to the polarisation [1]. The polarisability tensor is a function of the nuclear coordinates which, by extension, means that it will also depend on the (ro-)vibrational frequency. Assuming the modulation is small, the dependence can be expressed in a Taylor series with respect to the coordinates of vibration as follows:χ(1)jk(k⇀p,ωp)≈χ(1)jk(k⇀p,ωp)u⇀=0+ul⎛⎝⎜∂χ(1)jk(k⇀p,ωp)∂ul⎞⎠⎟u⇀=0+ulum⎛⎝⎜∂2χ(1)jk(k⇀p,ωp)∂ul∂um⎞⎠⎟u⇀=0+…,χjk(1)(k⇀p,ωp)≈χjk(1)(k⇀p,ωp)u⇀=0+ul(∂χjk(1)(k⇀p,ωp)∂ul)u⇀=0+ulum(∂2χjk(1)(k⇀p,ωp)∂ul∂um)u⇀=0+…,(4)

where u⇀u⇀ is the nuclear displacement vector, the indices j, k, l and m indicate different spatial coordinates with repeated indices in any of the terms implying the summation of the constituents of that index. If we write the electric field associated with the light as follows:E⇀(r⇀,t)=E⇀(k⇀p,ωp)cos(k⇀p∙r⇀−ωpt),E⇀(r⇀,t)=E⇀(k⇀p,ωp)cos⁡(k⇀p∙r⇀−ωpt),(5)

and the nuclear displacement as follows:u⇀(r⇀,t)=u⇀(q⇀,ωosc)cos(q⇀∙r⇀−ωosct),u⇀(r⇀,t)=u⇀(q⇀,ωosc)cos⁡(q⇀∙r⇀−ωosct),(6)

an explicit expression for time dependence of P(1)jPj(1) can be found by substitution of these two mathematical equations of the monochromatic light and displacement. The numerous resulting terms pertain to optical processes such as Rayleigh scattering, optical absorption and Raman scattering. The term which pertains to the first-order Raman scattering is derived from the second term on the right-hand side of Eq. 4 and yields:Pj(r⇀,t,u⇀)=12ε0⎛⎝⎜∂χ(1)jk(k⇀p,ωp)∂ul⎞⎠⎟u⇀=0ul(q⇀,ωosc)Ek(k⇀p,ωp)×{cos[(k⇀p+q⇀)∙r⇀−(ωp+ωosc)t]∙+cos[(k⇀p−q⇀)∙r⇀−(ωp−ωosc)t]}Pj(r⇀,t,u⇀)=12ε0(∂χjk(1)(k⇀p,ωp)∂ul)u⇀=0ul(q⇀,ωosc)Ek(k⇀p,ωp)×{cos⁡[(k⇀p+q⇀)∙r⇀−(ωp+ωosc)t]∙+cos⁡[(k⇀p−q⇀)∙r⇀−(ωp−ωosc)t]}(7)

This term contains sum (anti-Stokes) and difference (Stokes) frequencies and demonstrates conservation of momentum as per Eqs. 1 and 2. This formulation follows the classical description from refs. [1, 109].

The quantum mechanical description of the Raman process states that the (ro-)vibrational energy of the molecules/phonons are discrete quanta. Figure 1a shows an energy level diagram illustrating the Raman processes with Stokes emission at ω_S and anti-Stokes emission at ω_AS.

In Raman scattering, the intermediate states of the perturbation imposed by the incident pump photon (| r 〉 and | l 〉 in Fig. 1a, b) generally do not correspond to electronic states of the system and are said to be virtual energy states. These virtual intermediate states do not represent a well-defined energy state of the system. As the frequency of the pump photon approaches the energy of the electronic states, the strength of the Raman effect increases due to resonance effects and is termed pre-resonance Raman. If the intermediate state corresponds to a discrete electronic energy state, the interaction is described as resonance Raman scattering and the signal strength is expected to exceed that of virtual-intermediate-state Raman scattering by orders of magnitude. If the energy of the incident light is in the range of dissociative energy levels, the process is described as continuum resonance Raman scattering [1].

Raman scattering transitions between certain quantum states are forbidden. In materials with inversion symmetry (i.e. centrosymmetric crystal structure [113]), the initial and final states must have the same parity and are mutually exclusive with absorptive transitions (optically active transitions). In other words, transitions can be either Raman active or optically active. For linear molecules, the symmetric stretching modes of vibration or bending are Raman active and are optically inactive; those with anti-symmetric modes are Raman inactive and optically active (i.e. mutually exclusive) [1]. This rule is general and for nonlinear molecules, mutual exclusion is relaxed. In materials without inversion symmetry, (ro-)vibrational mode transition can be both Raman and optically active [1, 108].

The Stokes Raman signal for molecules is more intense than the anti-Stokes signal as the population of energy states is governed by thermal statistics [1, 108]. For bosonic systems, such as phonons in crystals, the probability of the scattering target occupying a given vibrational quantum energy state obeys Bose-Einstein statistics. Under nonresonant Raman scattering and thermal equilibrium, the ratio of the anti-Stokes and Stokes scattered intensity is given by [109]:IASIS=(ωp+ωoscωp−ωosc)4e(−ℏωosckT)IASIS=(ωp+ωoscωp−ωosc)4e(−ℏωosckT)(8)

where I_S and I_AS are the intensity of the Stokes and anti-Stokes light, respectively, ℏ is Planck’s constant divided by 2π, k is the Boltzmann constant and T is the temperature associated with the scattering species. This equation is sometimes used to measure the temperature via Raman spectroscopy [65]. This relation becomes inaccurate for resonance Raman scattering because the Stokes and anti-Stokes processes occur at different pump photon frequencies [109].

In the case of spontaneous Raman scattering, the Raman effect is very weak; typically, 1 in 10⁸of the incident radiation undergoes spontaneous Raman scattering [6]. The transition from the virtual excited state to the final state can occur at any point in time and to any possible final state based on probability. Hence, spontaneous Raman scattering is an incoherent process. The output signal power is proportional to the input power, scattered in random directions and is dependent on the orientation of the polarisation. For example, in a system of gaseous molecules, the molecular orientation relative to the incident light is random and hence their polarisation wave vector will also be random. Furthermore, as the excited state has a finite lifetime, there is an associated uncertainty in the transition energy which leads to natural line broadening of the wavelength as per the Heisenberg uncertainty principle (∆E∆t ≥ ℏ/2) [1]. The scattered light, in general, has polarisation properties that differ from that of the incident radiation. Furthermore, the intensity and polarisation are dependent on the direction from which the light is measured [1]. The scattered spectrum exhibits peaks at all Raman active modes; the relative strength of the spectral peaks are determined by the scattering cross-section of each Raman mode [108]. Photons can undergo successive Rayleigh scattering events before Raman scattering occurs as Raman scattering is far less probable than Rayleigh scattering.

Nonlinear Susceptibility

The polarisation described by Eq. 3 is in agreement with first-order (i.e. linear) optics and describes the single-photon scattering process (two-wave mixing process). In wave mixing processes with more than two waves, nonlinear optical polarisation must be considered due to the products of the mixed electric field components. Nonlinear optical polarisation can be described by [110] the following:Pj=ε0[χ(1)jkEk+χ(2)jklEkEl+χ(3)jklmEkElEm+…],Pj=ε0[χjk(1)Ek+χjkl(2)EkEl+χjklm(3)EkElEm+…],(9)

where χ⁽²⁾ is the second-order susceptibility (rank three tensor), χ⁽³⁾ is the third-order susceptibility (rank four tensor) and the sum over repeated subscript indices is again implied. Each of the terms in Eq. 9 can be written in shorthand by P⇀(1)P⇀(1), P⇀(2)P⇀(2), P⇀(3)P⇀(3), etc. The physical processes that occur because of the second-order polarisation, P⇀(2)P⇀(2), tend to be distinct from those arising from the third-order polarisation, P⇀(3)P⇀(3). This polarisation can have electric dipole, quadrupolar, octupolar, (etc.) contributions. Under the electric dipole approximation, the second-order polarisation can only occur in crystals that are noncentrosymmetric (lack inversion symmetry). Hence, χ⁽²⁾ vanishes for media such as fluids (e.g. liquid/gas) and amorphous solids (e.g. glass). Third-order nonlinear optical interactions (i.e. those described by a χ⁽³⁾ susceptibility) can occur for both centrosymmetric and noncentrosymmetric systems [109, 110]. Electric quadrupolar, octupolar, (etc.) χ⁽²⁾ contributions do not disappear under inversion symmetry.

Stimulated Raman Scattering

While spontaneous Raman scattering is an incoherent process, SRS is a coherent four-wave nonlinear optical mixing process. The modes of oscillation are in phase forming a coherent modulation of polarisation in the sample with susceptibility χ⁽³⁾(ω_S; ω_p + ω_S − ω_p) [110]. The scattered light is also coherent [45]. The SRS process is dependent on the spontaneous Raman cross-section, the spectral linewidth, the path length of the light-field-matter interaction, the input intensity and optical feedback (light generation) of Stokes frequency light [110].

When photons of frequency ω_p and ω_S simultaneously interact with a molecule or crystal lattice in the ground state, the system vibrates with an induced frequency: ω_osc = ω_p − ω_S. Unlike spontaneous Raman scattering, the de-excitation (relaxation) time to and energy of the final state are determined by the stimulation effect. The interaction results in the transfer of energy from the pump photon to the molecule/lattice, and the molecule/crystal scatters a new photon with frequency and phase matching that of the incident light of frequency ω_S. Figure 2a shows the process schematically.

It is common to employ an external radiation source tuned to the Stokes frequency in tandem with the pump laser beam to provoke this effect. This technique can lead to exponential gain in the Stokes signal, by transferring energy from the pump radiation, and rapid population of the final (ro-)vibrational state |f 〉 [115]. However, if the intensity of the incident light of frequency ω_p is sufficient, the generation of Stokes frequency photons within the material can self-promote SRS without the need for an external ω_S source. The intensity threshold of incident light in organic liquids, such as ethanol, for this kind of self-generated SRS typically requires an incident peak intensity of pump light > 10⁹ W/cm² for an optical path length of a few centimetres. However, the SRS threshold can be significantly reduced by extending the length of the pump and Stokes field interaction with an optical resonator, such as internal reflection in a droplet of liquid. The example shown in Fig. 2b is the SRS spectrum taken with droplets of ethanol directly compared to the spontaneous Raman spectrum of bulk ethanol. The droplets act to confine the light by internal reflection which feeds back the Stokes light as a self-SRS inducing optical resonator [114].

Coherent Anti-Stokes Raman Scattering

CARS is a third-order nonlinear four-wave optical mixing process. Figure 1b shows the energy level diagram for the process. A pump beam and probe beam of frequency ω_p and ω_pr are mixed with a third beam of frequency ω_S (Stokes frequency) and incident on the sample. The frequency difference (ω_p − ω_S) needs to match the frequency associated with the Raman active (ro-) vibrational mode ω_osc = ω_p − ω_S [4, 53, 56, 116]. The frequency of the Stokes beam is usually adjusted/tuned to satisfy this criterion [117]. Next, a probe photon of frequency ω_prprovides a perturbation for the anti-Stokes scattering process to occur at frequency ω_AS = ω_p − ω_S + ω_pr [5]. A macroscopic third-order polarisation, P⁽³⁾, is induced due to the coherent superposition of the microscopic dipole oscillations [53]. Hence, CARS is governed by the third-order susceptibility of the form: χ⁽³⁾(ω_AS; ω_p − ω_S + ω_pr).

There are numerous treatments and approaches to formulating expressions for χ⁽³⁾. If one assumes that the excitation field is much weaker than the intramolecular forces, then a perturbative approach can be adopted [5, 110]. If this is not the case, non-perturbative treatments can be considered [118]. By considering the density matrix equation of the system and expressing the external field interaction as a perturbation in the Hamiltonian, the semi-classical nonlinear optics theory generates an expression for χ⁽³⁾ with 48 terms, each of which contribute to the third-order susceptibility [5]. A generalised expression for dominant terms in resonant CARS is given by the following [51, 119]:χ(3)=ARωosc−(ωp−ωS)−iΓR+χ(3)NR,χ(3)=ARωosc−(ωp−ωS)−iΓR+χNR(3),(10)

where Γ_R is the half width at half maximum for the Raman line [51]; A_R is a constant representing the Raman scattering cross-section. The first term is the contribution due to CARS vibrational resonance as in Fig. 1b (ω_osc = ω_p − ω_S). The second term is the nonresonant background signal and is independent of the Raman shift (ω_osc ≠ ω_p − ω_S). The nonresonant background occurs because not all quantum pathways of the scattering process involve a resonance with a (ro-)vibrational state. This nonresonant contribution interferes with the resonant part of the signal. The nonresonant background causes distinctive distortions of CARS spectra in comparison with spontaneous Raman spectra and has prevented CARS from becoming a widespread technique [120].

The incident light beams of differing frequency move in and out of phase with each other in both time and space. Hence, the CARS signal reaches its first maximum when the field-sample interaction length scale is less than the coherence length scale to yield constructive interference [121, 122]. For plane-wave pump and Stokes beams, the intensity of the anti-Stokes signal is as follows [53, 123]:IAS∝∣∣χ(3)∣∣2IpIprIS⎛⎝⎜⎜sin(Δk⇀∙z⇀2)∣∣Δk⇀∣∣2⎞⎠⎟⎟2,IAS∝|χ(3)|2IpIprIS(sin⁡(Δk⇀∙z⇀2)|Δk⇀|2)2,(11)

where z⇀z⇀ is the sample thickness (vector normal to the lattice cell surface), k⇀k⇀ is the wavevector of light, Δk⇀=k⇀p−k⇀S+k⇀pr−k⇀ASΔk⇀=k⇀p−k⇀S+k⇀pr−k⇀AS is the wavevector mismatch (the velocity difference between the four waves) and I_i is the intensity of the wave denoted by the subscript. Phase matching is achieved when Δk⇀=0Δk⇀=0 and the intensity of the anti-Stokes signal is maximised because the energy and momentum transfer processes correspond to allowed transitions. As the magnitude of χ⁽³⁾ is linearly proportional to the number oscillators involved in the process, the intensity of the anti-Stokes signal is quadratically proportional to the number/concentration of oscillators [53].

Researchers typically employ the pump beam to provide the second virtual excitation (i.e. the probe light shown in Fig. 1b; i.e ω_pr = ω_p and ω_AS = 2ω_p − ω_S) [119]. The intensity of the CARS signal is therefore quadratically proportional to the intensity of the pump beam (see Eq. 11). The CARS signal is monodirectional due to the phase-matching condition [120]. However, high numerical aperture (NA) lenses or microscope objectives (confocal light) are commonly employed to satisfy the phase-matching condition without the need for complex mechanical systems to achieve phase-matched beam alignment [5, 117].

Raman resonances typically have coherence times of ~ 1 ps. Hence, the pump and Stokes beams are typically pulsed in picosecond timescales to obtain coherent excitation [124] and to inhibit multiphoton effects [53]. The CARS process takes place in the immediate vicinity of the beam’s focal spot. The signal produced is typically 10⁶ times that of spontaneous Raman scattering. CARS microscopy offers non-invasive characterisation and imaging of (ro-)vibrational spectra with high sensitivity and spectral resolution as well as three dimensional sectioning capabilities [116].

Surface Plasmons and Polaritons

Surface plasmons can occur at the interface between a dielectric and conducting material, such as a metal or degenerate semi-conductor [88, 125]. They are the light-induced coherent oscillations of surface conduction electrons about their equilibrium position. The nanoscale volume of opposing charge that remains acts as a restoring force on the electrons. The result can be described with a damped simple harmonic oscillator model, in which the oscillations of the free-charge carriers have an associated resonance. Surface plasmons can be excited by EM radiation and plasmonics is the study of these light-matter interactions [126].

Plasmonic nanoparticles that are much smaller than the wavelength of the incident light can support non-propagating surface plasmons that oscillate with a frequency known as the local surface plasmon resonance (LSPR) [127, 128]. The wavelength of surface plasmons is much shorter than that of the associated propagating light for a given frequency [129]. The LSPR wavelength is dependent on the nanoparticle’s size, shape, material, external dielectric properties and inter-nanoparticle separation [85, 127, 128, 130,131,132,133].

Surface plasmons that propagate are referred to as surface plasmon polaritons (SPPs) [134,135,136]. They are essentially light waves that are trapped at the interface due to their interaction with the free electrons of the conducting material [88]. For a planar dielectric-conducting interface, polaritons propagate in 2-dimensional space along the surface interface for length scales of tens to hundreds of micrometres [126, 134,135,136]. They decay evanescently in the direction perpendicular to the surface interface with 1/e decay lengths of up to 200 nm [126, 137]. The field intensity in this evanescent decay region is amplified by orders of 10 to 100 relative to the incident radiation [136]. Hence, light-matter interactions with adsorbed molecules on the surface are also enhanced.

In the case of LSPR, the surface roughness or surface nanoparticles cause local concentrations of charge carriers which further amplify the evanescent EM field due to the lightning rod effect [138]. Even larger field-enhancements (up to 10⁶) can be observed in gap plasmons (in the gap between two neighbouring plasmonic nanoparticles; see Fig. 1c) [85, 111]. This enhanced near-field effect gives rise to the technique known as SERS and is discussed in the next section.

Surface-Enhanced Raman Scattering

Raman is generally a very weak process; it is estimated that approximately one in every 10⁸photons undergo Raman scattering spontaneously [6]. This inherent weakness poses a limitation on the intensity of the obtainable Raman signal. Various methods can be used to increase the Raman throughput of an experiment, such as increasing the incident laser power and using microscope objectives to tightly focus the laser beam into small areas. However, this can have negative consequences such as sample photobleaching [139]. Placing the analyte on a rough metal surface can provide orders of magnitude enhancement of the measured Raman signal, i.e. SERS.

Two mechanisms have been proposed to explain the increase in Raman signal provided by SERS. The first is via EM enhancements where local surface plasmons concentrate the local electric field near the surface of the metal in ‘hot spots’ located on the sharp edges of nanostructures or in regions of concentrated free-charge carriers due to the lighting rod effect [140]. Figure 1c, illustrates the SERS process. This process can increase Raman generation by a factor of 10⁸ to 10¹¹ [86, 141,142,143,144]. The second method is chemical enhancement via charge transfer between the metal surface and the analyte, which enhances Raman scattering by a factor of approximately 10² to 10³ [86, 145,146,147]. However, the charge transfer mechanism only applies to specific molecules, whereas the EM mechanism is applicable for all analytes [4, 92, 102, 148].

The ubiquity of EM enhancements has led to the development of numerous SERS substrates, which can be divided into two groups: metallic nanostructures fabricated on a solid substrate [85] and colloidal suspensions of plasmonic nanoparticles [96, 141]. The most common materials used to fabricate SERS substrates are gold and silver because of their good plasmonic response [149]. Gold also benefits from chemical stability as it is a noble metal. Other metals are also being investigated, such as aluminium for UV Raman spectroscopy [150, 151].

Tip-Enhanced Raman Scattering

The diffraction limit of light restricts the focus spot size in standard optical techniques (such as Raman spectroscopy) to be at least half of the wavelength of the light according to Abbe’s criterion [152,153,154]. Light from the sample is composed of both propagating and non-propagating radiation. The non-propagating evanescent waves remain in the vicinity of their sources and do not participate in image formation in the far field. Instead, they extend laterally on the sample among the plasmon-active sites. Hence the spatial resolution is restricted by the size of the focal spot of the light. Even with a focal spot size of a half-wavelength (~ 250 nm for visible light), any objects that are much smaller than the half-wavelength would appear as a defuse shape.

TERS is a relatively new optical nanoimaging technique that combined Raman spectroscopy with scattering (or apertureless) scanning near-field optical microscopy. TERS offers spatial resolution far beyond the diffraction limit of the probing light. In the context of the a priori description, this is achieved by forcing the near-field evanescent light into the far-field image formation [86]. At the present date, the spatial resolution of TERS is typically reported to be 10–30 nm and is largely assumed to scale with the size of the tip’s apex [103, 155,156,157]. Incremental improvements to this resolution have been reported [104, 158]. Enhancement factors for TERS are significantly weaker than SERS due to the relative size of the probed signal volume. The enhancement factor (relative to spontaneous Raman scattering) is typically reported to be 10³ to 10⁶. As with SERS, two field enhancement mechanisms are thought to contribute to the Raman signal: EM and chemical enhancement [86].

TERS is implemented by positioning a plasmon-active (plasmonic) nanotip approximately 50 nm above the sample’s region of interest. The Raman probe light is focused onto the tip-surface cavity to induce LSPR within the tip’ apex and (in some circumstances) the sample surface. The surface plasmons may then enhance evanescent or near-field light with the incident probe light and/or the Raman scattered light. Hence, the LSPRs both confine and enhance the light field in the vicinity of the tip’s apex. The enhanced local EM field is most concentrated at the tip apex due to the lightning rod effect. This evanescent light at the tip apex can then excite or stimulate Raman, two-photon or second harmonic scattering from a nanoscale volume of the sample under the tip. A Raman image of the sample surface can be obtained by raster scanning the sample under the nanometric tip.

Experimental Considerations

Instrumentation

The nonresonant Raman effect is a very weak process. Hence, monochromatic, narrow-beam and high-intensity lasers are preferable to produce quality Raman spectra. The exploitation of microelectronics, such as stepper motor drives, photon counters, digital data acquisition and computational processing systems can further enhance the quality of spectra. As spontaneous Raman spectroscopy is naturally an incoherent process, continuous-wave laser sources are commonly used because pulsed lasers require higher peak powers for sufficient signal-to-noise ratio, which can photobleach/damage samples.

The choice of wavelength of the laser source depends on the required application. Lower visible wavelengths and UV cause strong photoluminescence in organic materials, which can mask the Raman peaks. Therefore, a longer visible or near-IR wavelength (500—830 nm) laser source is often suited for studying organic materials, because of the reduced photoluminescence. However, the Raman signal intensity is inversely proportional to the wavelength of the pump light. Hence, longer wavelengths of light require longer acquisition times [1, 6].

Raman spectroscopy is most often performed using laser sources at λ = 785 nm. This wavelength source is often selected as it balances the competing factors between Raman signal intensity, fluorescence, detector sensitivity and cost, and cost-effective/compact high-quality laser sources. However, visible lasers in the blue and green (e.g. λ = 532 nm) are becoming more common in Raman spectroscopy [159].

Raman scattering is measured in terms of the wavelength shift from the source wavelength. Ideally the illumination source for Raman measurements should be purely monochromatic, in other words, a single wavelength. However, all laser sources possess a spectrum of wavelengths known as a linewidth. The linewidth of a laser is usually measured in Hertz and is typically > 1 MHz for solid-state lasers used in Raman applications. A narrow linewidth is preferable for Raman spectroscopy because the measured shift in the Raman scattering process is limited by the laser’s linewidth.

Laser sources for Raman spectroscopy need to be stable in wavelength and power over extended periods of time and from use to use. Raman spectra are usually collected over long integration times and for many acquisitions. If the wavelength of the source drifts during a measurement, then the Raman peaks will drift as well, because Raman is measured as a shift relative to the pump light. Wavelength drift is also problematic from measurement to measurement as it causes peaks to shift, in turn making comparisons between measurements difficult. The output power stability of the source is important for similar reasons. If the laser power drifts from measurement to measurement, then quantitative comparisons cannot be made easily.

Spectral purity is another key criterion for Raman laser sources. The spectral purity of laser sources often requires side-mode suppression better than 60 dB. In many cases, side-mode suppression is sufficient if > 60 dB spectral purity is reached at ~ 1–2 nm from the laser wavelength peak. However longer wavelength (near-IR) Raman spectroscopy requires side-mode suppression ratios within a few hundreds of pm from the main peak. These criteria are discussed in the context of common Raman laser sources in the following paragraphs [159].

Most modern Raman systems use solid-state laser sources rather than gas lasers because of their spectral quality and stability. There are three main categories of continuous-wave solid-state laser sources used in Raman spectroscopy: Diode-pumped single-longitudinal mode (SLM) lasers; single-mode diode lasers (distributed feedback (DFB) or distributed Bragg reflection (DBR)); and volume Bragg-grating (VBG) frequency-stabilised diode lasers. These laser sources have varying optical characteristics.

Diode-pumped SLM lasers are readily available in compact form from the UV to the near-IR. Power levels of several Watts are achievable at 1064 nm in the near-IR. In the visible range, numerous lines in the blue-green-red region (457 to 660 nm) are available with output powers of ~ 100 mW. In the UV spectral range, power outputs of 10–50 mW at 355 nm are available. Hermite-Gaussian laser beam modes are described by their transverse electro-magnetic mode (TEM): TEM_m,n, where m and n represent the Hermite-Gaussian mode index [46]. Diode-pumped SLM lasers provide excellent TEM₀₀ mode beams, precise wavelengths with low drift, and a single-frequency linewidth > 1 MHz. The spectral purity of diode-pumped SLM lasers is typically > 60 dB in terms of their side-mode suppression ratio. Weak emissions that neighbour the laser’s main peak several nanometres in spectral shift can occur in diode-pumped SLM lasers. However, these neighbouring lines can be mitigated with dielectric band-pass filters. The wavelength of diode-pumped SLM lasers is typically stable to within 4 pm over a temperature change of 30 °C.

Single-mode diode lasers are compact and cost-effective pump illumination sources with single-frequency linewidth (> 1 MHz), single-TEM beam quality and output powers of up to ~ 100 mW. Wavelengths of λ = 785, 830, 980 and 1064 nm are most common in Raman spectroscopy. The side-mode suppression ratio is typically limited by sideband emission to ~ 50 dB at ~ 100 pm from the main peak.

VBG frequency-stabilised diode lasers use a narrow-linewidth VBG element with a diode-laser emitter to achieve narrow-line emission. These lasers are often used for applications requiring narrow-line emission at wavelengths that are not available for DFB or DBR laser sources. Frequency-locking multi-TEM diode lasers can be used to increase the output power of the narrow-linewidth emission. The stability of the output wavelength and linewidth requires careful thermomechanical control and high-precision alignment inside VBG frequency-stabilised diode lasers. Linewidths can range from single-frequency emission to ~ 10s of pm, depending on the wavelength and the output power. The side-mode suppression ratio is limited to ~ 50 dB, ~ 250 pm from the main peak emission. However, this can be improved using filters.

In confocal Raman imaging applications, it is necessary to use diffraction-limited TEM₀₀beams for optimum spatial resolution. However, this is relaxed for probe-based quantitative Raman analysis. In addition, confocal Raman setups require laser beam isolation as samples may generate optical feedback that is well aligned to the incident pump light. This counter-propagating feedback can induce power and noise instability and can even damage the laser source. Optical isolators are often integrated into the laser system itself because careful alignment must be achieved in the output after the isolator [4, 6, 159].

The spectrometer is a core component of any set-up used for measuring Raman spectra. The spectrometer should match the wavelength(s) of the laser source(s) used. The spectral range and resolution required will depend on the application. For example, the spectral range is determined by the position of the Raman peaks of interest (i.e. at large Δν∼Δν∼ ~ 3000 cm⁻¹or low Δν∼Δν∼ ~ 1 cm⁻¹). If the application requires closely spaced Raman peaks to be resolved, then spectral resolution is key. The spectral resolution of a spectrometer is largely determined by the slit width at the spectrometer entrance, the focal length of the spectrometer, the dispersion, the size of the grating (or prism) and the size and sensitivity/quality of the detector. There is a trade-off between the overall spectral range and resolution when considering the design of the experiment for a given application. In the case of weak Raman signals, optimising the signal-to-noise ratio is a priority.

Spectral filtering plays a vital role in the acquisition of Raman spectra. Firstly, the incident laser light must be spectrally pure, which is accomplished with a narrow-linewidth laser source as discussed previously. However, if the laser light is delivered to the sample by an optical fibre, then it is inevitable that Raman generation will occur in the fibre. Therefore, it is important to use a narrow band-pass filter to reject any Raman signal generated in delivering the laser to the sample. Narrow band-pass filters can provide transmission > 90 % at the laser wavelength while suppressing light to an optical density of OD > 5 at wavelengths differing by just 1% from the laser wavelength.

Importantly, light collected for detection requires filtering to block the laser wavelength. If the laser light is not filtered out, it can go on to generate Raman in the detection arm of the set-up and drown out the desired Raman signal when it reaches the spectrometer. The type of filter required depends on whether Stokes, anti-Stokes or both are to be measured. To only detect anti-Stokes Raman, a short-pass filter should be used as anti-Stokes Raman light has a higher energy and hence shorter wavelength than the laser source. To only detect Stokes Raman, a long-pass filter should be used as the Stokes Raman light has a lower energy and hence longer wavelength than the laser source. Long pass edge filters with edge-transition widths of < 3 nm and edge steepness < 40 cm⁻¹ are available. To detect both Stokes and anti-Stokes Raman light, a notch filter centred on the laser wavelength should be used as it allows both shorter and longer wavelengths to be detected. Notch filters with OD > 6 at the laser line wavelength are available. Multi-notch filters are also available and can block multiple laser lines simultaneously. Holographic notch filters significantly outperform dielectric notch filters, providing excellent attenuation of the Rayleigh line while passing light as near as 50 cm^–1from the Rayleigh line. Acousto-optic modulators can also be used in conjunction with an excitation laser to select emissions with a desired wavelength (as a filter) [160] or as a time-gated illumination system in tapping mode atomic force microscopy (AFM)-based TERS [161].

The quantum efficiency of standard room-temperature silicon-based CCD devices for Raman signal detection degenerates above λ = 800 nm. For longer wavelengths, indium gallium arsenide array devices can be used, but these are less sensitive with higher noise levels and cost.

The visible to near-infrared wavelength range (λ = 500–830 m) is particularly suitable for inorganic materials (e.g. graphene, carbon nanotubes (CNTs) and fullerenes) and SERS. UV lasers are attractive for organic materials (e.g. pathogens, proteins, DNA, and RNA). For materials with strong fluorescence that require near-IR illumination, it is common to use a 1064-nm wavelength.

Spontaneous and Coherent Raman Scattering Setups

Spontaneous Raman spectroscopy is most commonly used for modes with forbidden single-photon absorption or emission experiments [108]. SRS is sometimes used for wavelength shifting of coherent light, light amplification, pulse compression, phase conjugation and beam combining [108]. Unlike spontaneous Raman scattering, SRS is highly directional and offers enhanced signal strength and the ability to time-resolve the evolution and dephasing of coherent (ro-)vibrational motion [45].

Figure 3a shows a typical Raman setup based on a confocal geometry used by Wiedemeier et al. [162]. Confocal setups of this type are commonly used and employ an infinity-corrected objective lens (large numerical aperture (NA) lens) to focus the pump light. Wiedemeier et al. [162] used a diode-pumped solid-state laser as a monochromatic light source centred at 532 nm. Confocal mode is achieved by the use of a pinhole module in front of the spectrometer to spatially filter the light. The pinhole only passes light that originates from the focal plane to the detector. For detection of the Raman signal, a holographic-imaging spectrometer with an attached CCD camera is used. A holographic transmission grating with high light throughput served as a dispersive element, which enables large spectral ranges in a comparatively short time period to be acquired. Raster scanning of the sample in a confocal setup needs to be precise. Hence, a piezo actuated nano-positioner is used for positioning of the specimen.

Spontaneous anti-Stokes scattering is weaker than Stokes Raman scattering due to the relatively low probability of thermal excitation. Hence, anti-Stokes Raman spectroscopy is typically used with stimulated or coherent spectroscopy. CARS spectroscopy offers a 10⁵increase in conversion efficiency, spectral and spatial discrimination against fluorescence and, most importantly, does not require a monochromator. Due to the required coherence of the process, high-peak power pulsed tuneable laser sources are employed. These peaks are readily available using picosecond or femtosecond light lasers, the choice of which is determined by the spectral resolution required and the timescale of interest [139].

Avoiding direct electronic excitations in the sample is an important consideration as photochemical damage (due to photobleaching) can occur in samples. Djaker et al. [139], for example, use near-infrared laser sources to mitigate photobleaching in their samples of polystyrene beads.

Figure 3b shows a typical CARS setup that measures both forward scattered light (F-CARS) and back- or epi-scattered light (E-CARS) [116, 139, 163]. The system has two synchronised picosecond pulse trains. The pump and Stokes beams are generated by two picosecond Ti:Sapphire lasers operating at 80 MHz and are tuneable from 700 to 1000 nm to cover the entire spectrum of molecular (ro-)vibrations in biological systems (up to Δν∼Δν∼ ~ 3000 cm⁻¹). The ps pulse duration is adjustable by a Gires-Tournois interferometer. The Ti:Sapphire lasers are pumped by a frequency-doubled CW Nd:Vanadate laser that provides monochromatic light at 532 nm. The two pulse trains were polarised with a pulse duration of 3 ps, corresponding to a spectral width of 1.76 cm⁻¹. The pump and Stokes beams are synchronously pulse picked through two Bragg cells to reduce the repetition rate of the pulse trains to several hundred kilohertz, thus avoiding photodamage of the sample while still maintaining high-peak power for CARS generation. The pump and Stokes beams are temporally synchronised by a SynchroLock system, which electronically adjusts the time delay between the two pulse trains. A small part of the output of the lasers are launched in optical fibres coupled to photodiodes and connected to a SynchroLock controller, which measures the lasers frequency or phase difference between the master and the slave; the timing jitter was reported to be ~ 250 fs. The spectral resolution was estimated to be 2.5 cm⁻¹, which is high enough to resolve Raman spectral features of biological samples. The use of a broadband Stokes wave enables the acquisition of a full CARS spectrum in only one measurement, with this configuration being known as multiplex or broadband CARS [164,165,166,167].

The two pulse trains are spatially filtered, collinearly combined and expanded through beam expanders. They are then sent into an inverted microscope and focused onto the sample by a water-immersion objective lens with a large NA. The E-CARS signal is collected by the same objective lens while the F-CARS signal is collected by a condenser lens with a lower NA. The E-CARS and F-CARS signals are filtered through a set of band-pass filters and detected by two avalanche photodiodes with a 200 μm × 200 μm active area. The CARS images are collected by raster scanning the sample, using an XYZ piezo flexure stage.

Several methods have been developed to suppress the nonresonant background associated with CARS. E-CARS is relatively insensitive to the nonresonant background of sample solvents [168]. Polarisation-sensitive CARS can differentiate the resonant and nonresonant signals by their polarisation [169]. However, these two techniques reduce the anti-Stokes signal strength [120]. Time-resolved CARS [170], temporal or spectral interferometry CARS [52, 171] and frequency-modulated CARS [172] can also suppress the nonresonant background. However, the setup in terms of both optics and electronics is challenging [120].

SERS Specific Considerations

A variety of nanostructures, such as bowtie antennas [173], nano-rings [174], nanovoids [175], nanoparticle aggregates [87, 176, 177], nanoflower [178], nanorod arrays [97] and nanowells [179] can be used for SERS. Each nanostructure can have a number of plasmonic resonances, and matching the excitation laser to these wavelengths can greatly enhance the SERS intensity [141, 180, 181]. Matching the plasmonic resonance to the pump laser can be done either by tuning the laser wavelength or by tuning the LSPR of the nanostructures [85, 182,183,184].

The difficulty faced in producing SERS substrates is consistency in fabrication and repeatability in measurements due to the inhomogeneity and randomness of SERS active hot spots [85, 185, 186]. For SERS substrates produced by top-down methods, such as electron beam lithography [187], the main challenge is scaling the fabrication. Conventional top-down methods limit the active area of the SERS substrate and are not conducive to large-area manufacturing. Bottom-up fabrication methods have their own set of problems. Even though bottom-up approaches allow wafer scale fabrication, consistency across the wafer is usually lacking [188]. This inconsistency hinders the repeatability of measurements, which is problematic for quantitative analysis. Colloidal SERS schemes suffer from complications introduced by stabilising agents at the surface of the nanoparticles, which help to keep nanoparticles in suspension. These stabilising agents can either impede or augment the measured Raman signal [189]. The chemical synthesis for nanoparticle colloids also requires precise optimisation. The poor reproducibility of nanoparticle colloidal synthesis hampers batch-to-batch consistency.

Often, only very few sites exhibit the highest SERS enhancement and the variability in size and shape can alter the plasmonic properties from the desired LSPR [85]. Figure 3c, shows a setup which combines SERS with dark-field spectroscopy. The dark-field spectrometer analyses the light scattered from the nanostructures (illuminated by the white-light source) to select nanostructures with the desired plasmonic properties.

TERS Specific Considerations

Scanning probe microscopy (SPM) techniques, such as atomic force microscopy (AFM), scanning tunnelling microscopy (STM) or shear force microscopy (SFM), are usually the tools of choice for TERS [86]. TERS has the ability to simultaneously measure topography by the conventional SPM mode of the system and obtain corresponding spectral information from a sample with nanometric spatial resolution and high sensitivity [86]. Certain SPM techniques ordain probe modifications for the plasmonically induced nanoscale evanescent light to activate/enhance the Raman signal. The tips can either be made of a metal or coated with a thin layer of metal to modify them for TERS. When the apex of a metallic or a metal-coated nanotip is illuminated with focused light at the LSPR wavelength, local surface plasmons around the tip apex are excited, and evanescent light is produced at the tip apex. This evanescent light can generate Raman scattering from a sample placed right under the tip apex. The process of Raman scattering takes place in the near-field and the spectral signal is scattered and converted back to the far-field by the tip apex, which is then collected by the usual optics and spectrometer in the far-field. Figure 3d shows such a TERS setup with a modified AFM. The setup consists of largely similar equipment shown in Fig. 3a (discussed in an earlier section). An inverted microscope illuminates the sample from underneath and the tip is placed at the top surface of the sample. The Raman back-scattered signal is then directed to the spectrometer. An evanescent mask blocks the central part of the laser beam inhibiting the low NA component of the incident light, so that only the high-NA component of the incident light reaches the sample so that total internal reflection occurs. This limits the transmitted light that falls onto the tip and, hence, only the evanescent light participates in the Raman scattering signal. Suppressing the participation of transmitted far-field light reduces the unfavourable background signal.

Polarisation-dependent TERS can be performed with light polarisation parallel to the tip apex in addition to the in-plane linear and radial polarisations. Polarisation dependent TERS is enabled by the large incidence angle from the high-NA objective lens and the use of devices that modify the polarisation state of the light such as a λ/2 waveplate [190]. The Raman scattered light is then collected in the low NA region through an apertured mask, which inhibits any residual laser light. As the tip apex approaches the sample within the focal spot, evanescent light is created at the tip’s apex [86]. Since the intensity distribution within laser focus is not uniform, it is very important to lock the relative position of laser focus to the tip [191, 192].

The strength and resolution of TERS depends on the ability of the tip to enhance and confine the light field at the tip’s apex, respectively. In STM systems, the tips are made of solid metal and the substrates need to be conductive in order to control the tunnelling current [193]. The STM tip resembles a long and smooth nanocone, with an apex diameter of ~ 20 nm. The length of the tip (~ tens of micrometres) makes them plasmonically unfavourable for visible light enhancement. However, the tunnelling gap between the tip and the sample can be tuned to the desired LSPR wavelength, creating a strong hotspot within the gap [143, 194, 195]. Some of the more advanced STM systems allow high-vacuum and low-temperature measurements [196]. As the substrate in STM needs to be conductive (often opaque in the visible wavelength range), the setup shown in Fig. 3d would not be suitable. Hence, a side illumination and side collection configuration is more common with STM-based TERS. To prevent the objective from mechanically interfering with the STM tip, a lens with a long working distance is required. It is therefore not trivial to tightly focus the incident light on the tip apex. A parabolic mirror can be used to mitigate mechanical interference and tightly focus the incident light to the tip apex as well as to collect the Raman signal [196, 197].

The spatial resolution in TERS is comparable to the size of the metallic nanostructure at the tip apex [86]. The gain in spatial resolution comes at a cost to overall signal enhancement (relative to SERS) due to the reduction of the Raman active volume.

In AFM systems, the tips are usually semiconductor cantilevers, with an apex diameter of ~ 5 nm. Figure 4 shows five examples of AFM-based TERS tips that have been demonstrated in the literature. The semiconductor tips are usually coated with metal either by thermal evaporation under high-vacuum [202] or electroless metal plating (mirror reaction) [203] techniques. Figure 4a shows an example of a smooth AFM TERS tip. As the substrate does not need to be conductive, AFM-based TERS can be performed in either bottom-up transmissive illumination (as in Fig. 3d) or in side/top reflective illumination configurations; the transmissive configuration in Fig. 3d is more common.

The surface of AFM tips becomes nanostructured during the coating process resembling aggregated nanoparticles on the semiconducting tip (Fig. 4b) [198]. These nanostructures are suitable for the resonant excitation of LSPR and SPPs. The smooth tip shown in Fig. 4a has been fabricated by subsequently depositing a thin granular layer of additional metal. Other researchers have tested AFM tips with a metallic nanoparticle attached to the tip apex (Fig. 4c) [198], or a segregation in the tips coating to form an antenna (Fig. 4d) by focused ion beam lithography [115]. Tips can also be created by electrochemical deposition [204].

For transparent dielectric substrates, a thin metal film (thin enough to be transparent) can be coated onto the substrate to further enhance the field in the tip-sample gap [205]. It is also possible to perform TERS in liquids with AFM-based systems, which is favourable for biological specimens which require liquid environments to function [206]. Performing TERS in liquid with STM systems is much more difficult [86, 106]. SFM-based TERS is also an attractive technique and maintains many of the properties of AFM-based TERS with the exception of the tip material which resembles similar TERS properties of STM-based TERS [86, 156, 207, 208].

Some TERS setups have demonstrated vastly improved signal-to-noise ratio in TERS by SPP nanofocusing [201, 209, 210]. This technique focuses the laser onto a plasmon-coupling nanostructure (in the form of a grating) on the upper area of the tip, usually at a distance of ~ 10 μm from the tip apex. Figure 4e shows a typical nanofocused SPP-based TERS setup (i), the process of SPP nanofocusing by coupling the incident light to a focused ion beam-fabricated grating (ii), and an example SEM image of a SPP-nanofocusing tip (iii). The excited plasmons then propagate toward the tip apex through the process of adiabatic compression and create a confined EM field at the tip apex [209].

Tuning the Plasmon Resonance

The size, shape, composition of the nanostructures and inter-nanostructure spacing all affect the wavelength of the surface plasmon resonance [85, 86]. Metals are most often used as the conducting medium for surface plasmons; however, semiconductors also possess plasmonic characteristics [125]. Gold shows strong enhancement factors in the red spectral region [111, 177, 211, 212], silver in the blue-green spectral region [132, 213] and aluminium in the UV and deep UV spectral regions [150, 151, 175]. The blue-green spectral region is the most commonly used Raman spectroscopy range. However, silver is prone to oxidation which degrades the plasmonic characteristics within a few hours of exposure to atmosphere. For this reason, silver is often mixed with other metals, such as titanium [214].

The range of plasmon resonance can be tuned by the thickness and choice of coating metal, e.g. tungsten, gold, silver or aluminium. In TERS, the grain size of the metal coating corrugations (Fig. 4b) is roughly comparable to the wavelength of the LSPR/SSP. Unlike STM tips, it is possible to control the LSPR/SPP wavelength by adjusting the size of the nanoparticles. The surface plasmon resonance wavelength is also dependent on the refractive index of the dielectric material. In AFM-based TERS, for example, the silicon cantilever tip can be heated to ~ 1000 °C in the presence of water vapour to oxidise the silicon into silicon dioxide [215]. As SiO₂ has a lower refractive index than Si, the surface plasmon resonance is blue shifted [86].

The size and shape of the metal-coated AFM tip apex can also be modified to tune the LSPR [199, 200]. Fabricating a single metallic nanoparticle attached to the tip’s apex (Fig. 4c) or segregated antenna-shaped tip (Fig. 4d) has been demonstrated as a means to finely tune the surface plasmon resonance in AFM-based TERS [199, 200, 208, 216]. However, the most commonly used tips for AFM-based TERS are the tips that have disconnected metal nanoparticles evaporated on a semiconductor cantilever in the standard coating process (Fig. 4b) described a priori [198].

Analysis Methods

A Note on Units

By convention, Raman spectra are considered in terms of the wavenumber ν∼ν∼ in units of cm⁻¹. The conversion from angular frequency is as follows:ν∼=ω2πc0,ν∼=ω2πc0,(12)

where c₀ is the speed of light in vacuum and ω is the angular frequency. Raman spectra are usually plotted in terms of the wavenumber shift from the incident excitation radiation. This shift is defined as follows:Δν∼=ν∼p−ν∼scat,Δν∼=ν∼p−ν∼scat,(13)

where ν∼pν∼p is the wavenumber of the pump beam with angular frequency ω_p and ν∼scatν∼scat is the wavenumber of the scattered light accordingly. For Stokes Raman scattering, ν∼scat=ν∼p−ν∼oscν∼scat=ν∼p−ν∼osc (where ν∼oscν∼osc is the molecule or lattice vibration wavenumber) and Δν∼Δν∼ is positive. By contrast, for anti-Stokes Raman scattering, ν∼scat=ν∼p+ν∼oscν∼scat=ν∼p+ν∼osc and Δν∼Δν∼ is negative [1].

Raman spectra are (by standard) presented with the wavenumber shift linearly increasing from right to left on the horizontal axis. The vertical axis ordinate is linear and proportional to intensity. However, researchers also present Raman spectra with wavenumber shift denoted simply as wavenumber and/or increasing from left to right instead of right to left [1].

Spontaneous Raman Spectra

Figure 5a shows the Rayleigh and the Raman spectrum of carbon tetrachloride (liquid) excited by an argon ion laser, ν∼1ν∼1 ~ 20,487 cm⁻¹ (487.99 nm). This spectrum is presented according to recommendations of the International Union of Pure and Applied Chemistry. It contains a strong band at ν∼1ν∼1 ~ 20,487 cm⁻¹ due to the Rayleigh scattering of the incident laser radiation and a number of weaker bands with wavenumbers, ν∼1±ν∼oscν∼1±ν∼osc: ν∼oscν∼osc = 218, 314, 459, 762 and 790 cm⁻¹. The Stokes Raman lines are shown on the left-hand side of the plot (Fig. 5a); the anti-Stokes Raman lines are shown on the right. The ν∼oscν∼osc values relate to the fundamental vibrations of the carbon tetrachloride molecule [1]. In the original work by Raman and Krishnan [220], the same spectrum was measured using mercury arc radiation (ν∼1ν∼1 = 22,938 cm⁻¹, 435.83 nm). In this seminal work, the anti-Stokes bands at ν∼1+762ν∼1+762 and ν∼1+790ν∼1+790 cm⁻¹ were not observed. Hence, after the invention of the laser, Rayleigh and Raman scattering experiments are preferably performed using monochromatically intense lasers.

Layered Two-Dimensional Systems

Raman spectroscopy can be used to determine the layer thickness in two-dimensional materials with atomic level precision, using either the inter-layer or intra-layer vibrational modes [19]. Lee et al. [12] demonstrated the technique with two intra-layer Raman modes of molybdenum disulphide (MoS₂). Figure 5b shows representative Raman spectra for single- and few-layer MoS₂ samples. Among the four Raman-active modes of bulk 2H phase MoS₂crystal (shown in Fig. 5b v), Lee et al. [12] only observed the E12gE2g1 and A_1g modes near Δν∼Δν∼ = 400 cm⁻¹. The authors surmised that the other modes were not observed either because of the selection rules for the scattering geometry (E_1g) [217] or because of the limited rejection of the Rayleigh scattering radiation (E22gE2g2) [13]. The authors [12] report that single-layer MoS₂exhibits a strong in-plane vibrational mode at Δν∼Δν∼ ~ 384 cm⁻¹, corresponding to the E12gE2g1mode of the bulk 2H-MoS₂ crystal. For all film thickness, the Raman spectra in Fig. 5b i show strong in-plane E12gE2g1 and out-of-plane A_1gvibration signals. As the sample thickness increases (Fig. 5b i and ii), the E12gE2g1 mode red shifts and the A_1g mode blue shifts. For films of four of more layers, the E12gE2g1 and A_1g modes converge on the bulk values. Spatial maps of a MoS₂ film sample for the E12gE2g1 mode is shown in Fig. 5b iii; that of the A_1g mode is shown in Fig. 5b iv. These maps demonstrate that the frequency of the two modes only slightly vary in regions of the sample with a given layer thickness. Hence, Raman spectra can provide a convenient and reliable means of determining the layer thickness in two-dimensional crystalline materials with atomic level precision.

Enhanced Raman Scattering Through SERS

Ault et al. [221] were the first to use SERS to enhance the Raman scattering signal of previously undetectable secondary organic aerosol particles on Ag nanoparticle-coated quartz substrates. Fu et al. [96] demonstrated enhancement factors of 6 for the Raman spectra of ammonium sulphate (AS) at the Raman active mode ν∼sν∼s(SO₄²⁻) at 970 cm⁻¹ with Klarite. Figure 5c shows a microscope image of a large AS particle on the surface of Klarite (Fig. 5c i), the corresponding Raman mapping image is in Fig. 5c ii. Figure 5c iii shows another sample of AS particle but on a silicon wafer. The corresponding Raman mapping image is shown in Fig. 5c iv. Aside from the three larger AS particles, small (sub-micron) AS particles are apparent in Fig. 5c iii. However, in the absence of SERS, these smaller particles are undetectable. On the other hand, the SERS Raman mapping image (Fig. 5c ii) shows a vastly enhanced signal intensity, as is evident from the scale bars, to the point where a number of small spots yield a signal at the ν∼sν∼s(SO₄²⁻) Raman mode. Such spots most likely correspond to small AS particles that are observable in Fig. 5c ii but are not apparent in Fig. 5c i.

Insights into Cellular Structure with CARS

CARS microscopy is relevant to the chemical [64, 222,223,224,225], materials [78, 226, 227], biological and medical fields [29, 36, 61, 63, 167, 228] and can provide unparalleled insights into cellular structures [53]. Spontaneous Raman and infrared micro/spectroscopy can provide adequate chemical specificity and sensitivity to delineate a variety of neoplasms [229,230,231,232,233,234,235,236,237] but require long integration times and have a coarse spatial resolution, which may limit accurate tumour-boundary identification and early-stage tumour detection. However, coherent Raman imaging techniques have demonstrated high-speed, high-spatial-resolution imaging, but with contrast limited to single or few Raman peaks [36, 53, 167, 232]. Figure 5d presents images of orthotopic xenograft brain tumours from within a murine brain [167]. Figure 5d i shows a broadband CARS image with nuclei in blue (Δν∼Δν∼ = 730 cm⁻¹), lipid content in red (Δν∼Δν∼ = 2850 cm⁻¹) and red blood cells in green (Δν∼Δν∼ = 1548 cm⁻¹ + 1565 cm⁻¹: C-C stretch from haemoglobin [238]). The large tumour mass and a projection of neoplastic cells within healthy tissue are clearly shown (Fig. 5d i). Figure 5ii shows several small regions of main tumour mass migrating into the healthy brain matter. Figure 5 iii shows the boundary between normal brain tissue, white matter and tumour masses, which contrasts lipids in red (Δν∼Δν∼ = 2850 cm⁻¹); CH₃ stretch-CH₂ stretch (Δν∼Δν∼ = 2944 − 2850 cm⁻¹), a general contrast; and nuclei in blue (Δν∼Δν∼ = 785 cm⁻¹). The image shows the fibrous texture of the white matter and strands of myelination around cancer cell clusters. Figure 5d iv presents a set of single-pixel spectra from an intra-tumoural nucleus, the white matter and normal brain, respectively. The spectra indicate that lipids are most concentrated in the white matter and least in the tumour regions.

Raman Thermography

Advances in electronic and opto-electronic semiconductor devices, such as high electron mobility transistors (HEMTs), have led to thermal management challenges [65]. Conventional thermal characterisation approaches such as infrared thermography are often no longer applicable for the accurate characterisation of high-power density devices due to limited spatial resolution which can result in the underestimation of the device peak temperature [239]. Batten et al. [218] have demonstrated temperature profiling in AlGaN/GaN HEMTs using Raman thermography by exploiting the E₂ and A₁ (LO) phonon modes. Both the E₂ and A₁ (LO) modes shift to lower frequency when operating the device. Figure 5e shows a comparison of the temperature rise in a AlGaN/GaN HEMT on a SiC substrate from Raman thermography and thermal simulations. The device was operated at a source-drain voltage of 40 V and a power density of 25 W/mm and had a thermal resistance of 8 °C/(W/mm).

Measuring Strain on the Nanoscale Using TERS

TERS microscopy is an effective means of imaging nanostructures beyond the spatial resolution of the so-called light diffraction limit [152,153,154, 219]. Nanostructures such as DNA molecules [240], carbon nanotubes (CNTs) [241, 242], silicon devices [101, 243], dye molecules [244] and single molecules [83] can be imaged using TERS. The technique can even be used to measure the local molecular strain in nanostructured materials. For example, AFM can be used to manipulate CNTs with nanoscale precision to develop a local strain [245,246,247,248]. Figure 5f (left) illustrates the process of CNT manipulation using contact-mode AFM. Although local strain in CNTs has previously been studied using AFM and transmission electron microscopy [245], TERS microscopy is the only optical technique that can provide images of such local structural distribution of nanomaterials. When a straight CNT is deformed by manipulation, a local breakdown in symmetry is induced. This causes the selections rules of Raman scattering to become relaxed, allowing forbidden Raman modes to become visible in the vicinity of the local curvature [219]. The position of the characteristic G-mode Raman scattering line in graphene can be used to deduce local strain using TERS [249]. Figure 5f (right) shows a TERS image of a deformed CNT which has been constructed from the peak positions of the G⁺-mode [219]. The image has a spatial resolution better than 20 nm which is about 25 times finer than the diffraction limit of the excitation wavelength of light (488 nm). The colour variation (as indicated by the scale bar) corresponds to the local peak position of the G⁺-mode and represents the variation of strain along the CNT.

Recent Results

Stimulated Raman Scattering Microscopy

Unlike CARS, SRS microscopy does not contain a nonresonant background signal that degrades image contrast. However, SRS can be affected by cross-phase modulation (where light at one wavelength modulates the refractive index in the medium affecting another wavelength of light), transient-absorption (which is characteristic of femtosecond light pulses) and photo-thermal effects which can modify the vibrational energy levels and reduce hyperspectral image contrast [250,251,252]. SRS is quantified by the amount of energy transfer from the pump light to the Stokes light when the difference frequency between the pump and Stokes light matches a specific vibrational frequency, ω_osc. In addition, the resulting signal from SRS is strongly sensitive to the incident polarisations when the orientation of the probed vibrating species is ordered. This polarisation dependence can be exploited to probe the orientational order of vibrational modes in samples. However, currently developed techniques are not able to perform large-field fast time scale dynamics instantaneously due to the requirement of point-wise scanning over the sample space. Conventional polarisation-resolved techniques take minutes because each point of the scanning area must be polarisation tuned sequentially [74, 80, 253, 254].

Multi-lamellar myelin plays a crucial role for efficient transmission of nerve impulses as an electrical insulator [255]. The lipids and proteins in myelin self-assemble into a highly ordered and stable structure to form a tightly packed membrane [256]. In neurological disorders, this compact structure is highly perturbed leading to dysfunctions of the central nervous system [257, 258]. As these biological processes are highly dynamic, researchers seek to observe the dynamics of molecular order with sufficient resolution and frame rate. Hofer et al. [259] have recently demonstrated fast-polar-SRS by exploiting high-speed amplitude- and polarisation modulation with an acousto-optic modulator (AOM) and electro-optical polarisation modulation, respectively, to read out the molecular order and orientation at a fast rate. They therefore obtain both amplitude and phase information. The authors report the ability to retrieve density maps of molecular bonds with the absolute value of molecular order. The linear polarisation direction of the pump beam is rapidly rotated while the Stokes polarisation is circularly polarised to avoid polarisation dependence from the Stokes beam. The polarisation is further modified by a quarter-wave plate. The polarisation modulation leads to an α-dependant response of the signal intensity given by the following:I(α)∝a0+S2cos2(α−φ2)I(α)∝a0+S2cos⁡2(α−φ2)(14)

where α is the rotating pump polarisation direction in the sample plane, a₀ is the total measured intensity, and S₂and φ₂ are the amplitude and phase of the second-order induced modulation [259].

Figure 6a.i shows a comparison of conventional polarisation SRS with that from Hofer’s fast-polarisation SRS on a multi-lamellar lipid vesicle (MLV). The fast-polarisation SRS image in the bottom of Fig. 6a i was obtained in 1 s which is two orders of magnitude faster than the conventional-SRS image (top) using the same incident powers, number of pixels and dwell time per pixel. Figure 6a ii shows sub-second frame-rate imaging of a MLV using double EOM-AOM modulation SRS at two instances in time. The measurement technique was remarked to have little effect on the lipid order properties during the measurement. Hofer et al.[259] were able to observe second-timescale dynamics in thin lipid membranes down to the cell plasma membrane using fast-polarisation-resolved SRS as shown in Fig. 6a iii.

Flow cytometry (FC) is one of the most important technologies for high-throughput single-cell analysis. FC is a technique used to measure physical/chemical characteristics of a population of cells or particles suspended in a fluid [59, 261]. The fluid suspension flows through the instrument detectors for fluorescent labelling which is the primary approach for cellular analysis in FC. Figure 6b i shows an optical FC setup [260]. However, for small molecules, the fluorescent tags can perturb the biological function of the species. In addition, non-specific binding of fluorescent labels as well as cellular autofluorescence can also reduce the clarity of the result. SRS flow cytometry (SRS-FC) non-invasively detects chemical cell content but conventional techniques suffer slow acquisition rates.

Zhang et al. [260] have recently demonstrated label-free high-throughput single-particle SRS-FC with a 32-channel multiplexing technique. Their technique measured single-particle chemistry at a rate of 5 μs per SRS spectrum, approaching that of standard fluorescence-based FC. The SRS-FC technique was based on broadband laser excitation and a multiplex spectral detection system. The systems allowed the acquisition of 200,000 spectra per second, more than 11,000 particles per second. The subpopulations of species, such as mixed polymer beads and 3T3-L1 cells, could be separated and distinguished through compositional principle component analysis (CPCA) of the SRS signals. The principle components were designated according to their Raman spectra. An agglomerative clustering procedure was performed on the resulting CPCA spectral matrix. This procedure assumed the number of cluster groups (κ) was known to separate the clusters of principle components in the CPCA analysis. Figure 6b ii shows the CPCA of the SRS spectra for a mixture of three types of beads: poly-methyl-methacrylate (PMMA), polystyrene (PS) and polycaprolactone (PCL), all with a 10-μm mean diameter, mixed at a 2:1:1 ratio of PMMA:PS:PCL and a final concentration of 2% solids in the fluid. The flow speed was ≈ 0.16 ms⁻¹, the SRS-FC data was acquired in 6 s. The CPCA plot (Fig. 6b ii) shows three distinct clusters of principle components. The agglomerative clustering procedure (κ = 3) allowed the quantification of ~ 7100 PMMA bead (red), ~ 3400 PS beads (blue) and ~ 3600 PCL beads (green) as shown in Fig. 6b ii. Their measurement demonstrated the ratio of ≈ 2:1:1 (PMMA:PS:PCL) at a throughput rate of ~ 2350 particles per second and that their multiplex SRS-FC system, paired with the CPCA analysis, could distinguish different chemical components with small spectral differences. Zhang et al. [260] were able to detect beads as small as 1 μm and were even able to detect single Staphylococcus aureus bacteria flowing through the laser focus highlighting the potential to characterise subcellular organelles with SRS-FC.

Zhang et al. [260] also demonstrated the discrimination of 3T3-L1 cells at different stages of cell differentiation according to their difference in lipid amount using SRS-FC. After insulin-induced differentiation, 3T3-L1 cells acquire an adipocyte-like phenotype with a significantly increased amount of triglycerides which aggregate to form large lipid droplets. This aggregation of triglycerides causes the intensity of the methylene symmetric vibration at Δν∼Δν∼= 2850 cm⁻¹ from fatty-acid acyl chains to become stronger compared to that of non-differentiated cells which provides the means for CPCA analysis. Figure 6b iii shows the CPCA scatter plot of the cell mixture measured by Zhang et al. [260] which were separated using the agglomerative clustering approach. The insert SRS images (Fig. 6b iii, right) show a non-differentiated 3T3-L1 cell and a differentiated cell with the formation of large lipid droplets.

Twisted Laguerre-Gaussian lasers, with orbital angular momentum (OAM) and characterised by doughnut-shaped intensity profiles, are of great interest to a number of growing research fields such as ultra-cold atoms [262,263,264], microscopy and imaging [265, 266], atomic and nanoparticle manipulation [267, 268], ultra-fast optical communication [269, 270], quantum computing [271], astrophysics [272] and plasma accelerators [47]. Spiral phase plates or computer-generated holograms are usually used to generate visible light with OAM [273,274,275,276]. Spiral phase plates can produce light with predefined OAM modes. By using plasma as an optical medium to generate and amplify laser pulses with OAM and relativistic intensities, well above the damage threshold of optical devices, could provide for high-energy-density science and applications. Plasmas also allow for greater flexibility in the level of OAM in the output laser beam than conventional optics. Vieira et al. [46] have shown that SRS in nonlinear optical media with Kerr nonlinearity (e.g. plasmas, optical fibres and nonlinear optical crystals) can be used to generate and amplify OAM light. The authors show that it is possible to generate and amplify light with OAM when no net OAM is initially present. Figure 6a i illustrates the process in which the pump EM fields can have different OAM components in both transverse directions x and y (blue and orange in Fig. 6a i). l_0x is the pump electric field component of OAM in the x direction. Likewise, l_0y is the pump electric field component of OAM in the y direction. The initial seed electric field component has an OAM component l_1x. After interacting with the plasma, the pump is depleted, and a new electric field component appears in the seed with OAM l_1y = l_1x + l_0x − l_0y.

The authors [46] use an analytical theory for arbitrary transverse laser field envelope profiles and particle-in-cell simulations for plasma. Stimulated Raman backscattering in plasma is a three-wave mode coupling process in which a pump pulse decays into an electrostatic (Langmuir) plasma wave as well as a counter-propagating seed laser. The plasma can be viewed as a high-intensity mode converter. The presence of OAM in the pump and/or seed results in additional matching conditions that ensure the conservation of angular momentum of the pump when the pump decays into a scattered electro-magnetic wave and a Langmuir wave [40].

Particular superpositions of Hermite-Gaussian modes TEM modes are mathematically equivalent to Laguerre-Gaussian modes [277]. Vieira et al. [46] therefore explore the use of Stimulated Raman backscattering to generate and amplify light with OAM using TEM laser beams with no initial net OAM. Each Hermite-Gaussian beam in the simulation is described by TEM_m,n, where m and n represent the Hermite-Gaussian mode index. Figure 6c ii and iii show the 3D simulation results from the setup shown in Fig. 6c i. The simulations show that SRS results in a new OAM mode with l₁ = 1 linearly polarised at 45°. The field topology of the seed normalised vector potential changes from plane isosurfaces in Fig. 6c ii, to helical isosurfaces in (Fig. 6c iii). Hence, light with OAM has been generated from light with no net OAM. The authors [46] note that their results could be extended to other nonlinear optical media with Kerr nonlinearity. In the case of plasma, the interaction between the seed light and the pump light occurs via an electron Langmuir wave. This interaction ensures that the frequency, wavenumber and OAM matching conditions are conserved.

Coherent Anti-Stokes Raman Scattering Microscopy

CARS results from an induced anti-Stokes scattering of radiation, ω_AS, which is enhanced when ω_p − ω_S = ω_OSC. One of the main challenges with CARS microscopy is the nonresonant background. The existence of the nonresonant background can either distort or even saturate the resonant signal of Raman peaks, which reduces the image contrast. Qin et al. [278] have recently demonstrated multi-colour background-free coherent anti-Stokes Raman scattering microscopy using an all-fibre, low-cost, multi-wavelength time lens source. A time lens, in analogy to a spatial lens, is simply a quadratic optical phase modulator in time, which can be approximated by a portion of a sinusoidal phase modulator [279,280,281]. Three different wavelength picosecond pulse trains were provided by the time lens source, at 1064.3 nm (stable), 1052–1055 nm (tuneable) and 1040–1050 nm (tuneable). The time lens was used to apply temporal quadratic phase modulation to a continuous-wave laser to broaden its spectral bandwidth [279, 282,283,284,285,286,287,288]. In this instance, the time lens was applied with fibre-integrated electro-optic radio-frequency phase modulators. The phase modulation and pulse synchronisation were derived from a mode-locked Ti:Sapphire laser that provided synchronised multi-colour picosecond pulses with dispersion compensation. Electronic tuning of the pulse delay was used to achieve temporal overlap between the pump and Stokes laser pulse trains, which is a convenient substitution for mechanical optical delay paths. Two of the three wavelengths of light from the time lens source were used for two-colour on-resonance imaging and the third wavelength for off-resonance (nonresonant background subtraction) imaging. Pixel-to-pixel wavelength switching was achieved, which provided simultaneous two-colour CARS imaging with real-time nonresonant background subtraction. Qin et al. [278] demonstrated the technique with an excised fresh tissue sample from a mouse ear and imaged molecular stretching vibrations at 2845 cm⁻¹ (CH₂) and 2940 cm⁻¹ (CH₃) and non-resonance background at Δν∼Δν∼ = 2770 cm⁻¹. Figure 7a i–iii shows the process applied to the Raman peak of CH₃ stretching vibration from the mouse ear tissue sample.

The nonresonant background signal in CARS can also be suppressed by applying an external static electric field to the sample known as electro-CARS. Capitaine et al. [120] demonstrate this electro-optical technique on n-alkanes in solution with broadband multiplex coherent anti-Stokes Raman scattering spectroscopy. The nonresonant background is suppressed due to the orientation response of the molecules to the electric field. The molecular orientation is related to the induced electric dipole moment. The enhancement of the CARS signal-to-noise ratio was achieved in the case of the CH₂ and CH₃ symmetric/asymmetric stretching vibrational modes.

Conventional CARS provides information about the chemical nature but not about the molecular organisation or symmetry in the system. The Cartesian components of the nonlinear susceptibility tensor χ⁽³⁾ represent the vibrational symmetry properties of the material [290, 291]. These tensor elements can be extracted with polarisation-resolved coherent Raman scattering schemes [72, 74, 169, 259, 292,293,294,295]. However, these schemes often involve the acquisition of multiple images from different polarisation angles requiring long acquisition times due to limits imposed by polarisation tuning [259] and time-consuming post-processing [67].

Cleff et al. [289] have recently demonstrated a label-free microscopy technique that uses circularly polarised light to probe the symmetry as well as the chemical fingerprint of the probed sample in a single acquisition. This symmetry-resolved CARS (SR-CARS) depends on both the presence of (ro-)vibrational modes as well as their local organisation. By switching between combinations of left- and right-handed circular polarisation states for the involved fields, the individual symmetry contributions of the sample can be imaged. This technique offers a straightforward means to access the local organisation of (ro-)vibrational bonds with improved image contrasts (with 1 to 2 orders of magnitude) for anisotropic samples, as well as improved chemical selectivity without post-processing and independently of sample orientation in the transverse plane. In addition, SR-CARS provides higher chemical selectivity with the contrast in symmetry characteristics, which are not accessible with conventional spontaneous Raman or SRS microscopy.

Multi-lamellar lipid vesicles (MLVs) are made of a tight packing of lipid layers forming a ring of highly ordered matter with twofold symmetry and a lipid orientation distribution close to a Gaussian angular shape [74].

Figure 7b i shows a conventional CARS image of an aqueous MLV at Δν∼Δν∼ = 1133 cm⁻¹ (C-C stretching vibration) which illustrates the expected poor contrast due to the nonresonant background [289]. Figure 7b ii and iii show the zeroth and second-order mF¯¯¯¯mF¯-value image of the same MLV as in Fig. 7b ii. The mF¯¯¯¯mF¯-value is the summation of the light circular polarisation handedness quantum numbers of the incident light beams:mF¯¯¯¯=mp−ms+mpr−masmF¯=mp−ms+mpr−mas(15)

When light with field tensor F¯¯¯¯F¯ probes matter with nonlinear susceptibility tensor χ⁽³⁾, in a CARS process, the light probes only the parts of the matter with identical rotational invariant symmetries (i.e. identical mF¯¯¯¯mF¯). Hence, by engineering the field tensor of the light, specific sample symmetries can be directly read out, creating a symmetry-based image contrast mechanism [289]. The aqueous solution surrounding the MLV is only visible in the mF¯¯¯¯=0mF¯=0image (Fig. 7b ii) due to its purely isotropic nature. Background-free imaging of the MLV with superior contrast with respect to conventional CARS is shown in Fig. 7b iii at mF¯¯¯¯=2mF¯=2, which results from the symmetric microscopic organisation of the lipids in the MLV. Imaging at mF¯¯¯¯=4mF¯=4 (not shown) lacked sufficient signal strength to provide an image of the MLV due to the lack of anti-symmetry in the lipid organisation.

As with SRS, the CARS signal is sensitive to the polarisation of the incident light when the orientation of the scattering species is ordered. Polarisation-resolved CARS (PR-CARS) requires monitoring of the CARS signal response depending on the relative rotation of the incident light polarisations (pump and Stokes) to the sample, in species with ordered orientations. Provided that the molecular bonds are oriented, the detected intensity of the anti-Stokes signal is maximised when the incident polarisations lie along the averaged direction of the bonds. The ability to monitor lipid order without the need for fluorescent labels can provide information on lipid packing properties. As mentioned, PR-CARS schemes often involve long acquisition times due to limits imposed by polarisation tuning and time-consuming post-processing.

In addition to fast-polar-SRS, Hofer et al. [259] have recently demonstrated fast-polar-CARS imaging with combined electro-optic polarisation and acousto-optic amplitude modulations. Figure 7c shows fast-polarisation CARS with similar sensitivity to that of SRS (shown in Fig. 6a). Despite the requirement of lock-in amplification for the detection of low modulation over a large nonresonant background, the fast-polarisation technique demonstrated by Hofer et al. [259] can considerably improve the signal-to-noise ratio in CARS imaging. Despite the robustness of MLVs, occasional alteration of molecular order in MLVs could be observed at the time scale accessible in Hofer’s experiment (0.25–1 s per image). MLVs could detach from the sample surface, inducing motion (Fig. 7c) or shape change. The modifications observed in Fig. 7c were attributed to a local membrane disruption, followed by its spontaneous reformation. Hofer et al. [259] demonstrated the possibility of visualising local modification during MLV displacement that was not accessible using the minute-time-scale conventional polarisation Raman experiments.

There have also been a number of developments in CARS flow cytometry (CARS-FC) [58, 296, 297]. However, these techniques were shown to be much slower than fluorescence-based FC. Out-of-focus microparticles can randomly impede CARS-FC and the fluid often generates a strong nonresonant background limiting CARS-FC from achieving high-throughput single-cell analysis. Recently, however, O’Dwyer et al. have demonstrated that it is possible to significantly enhance the fraction of unambiguously and instantly recognised in-focus microparticles, in unconstrained flows by co-monitoring CARS-FC with linear scattering of light.

CARS is invariably performed with two synchronised picosecond laser sources owing to the coherence life time of Raman resonance. Ti:Sapphire oscillators [168] or optical parametric oscillators pumped by a picosecond frequency-doubled Nd:Vanadate laser [53] are the instruments of choice, which are generally very expensive and the synchronisation mechanisms can be challenging. In addition, the spectral drift in the pump wavelength can introduce errors in the calculation of ω_osc. Langbein et al. [124] have demonstrated CARS micro-spectroscopy using a single Ti:Sapphire laser oscillator and simple passive optical elements. Vibrational excitation, tuneable over a large spectral range with adjustable spectral resolution, was achieved by spectral selection with dichroic mirrors and linear chirping by glass elements.

Tip-Enhanced Dual Wavelength Coherent Anti-Stokes Raman Scattering Microscopy

TERS offers spatial resolution far beyond the diffraction limit of the probing light. The more conventional technique is to directly illuminate the tip-sample cavity [86]. This technique achieves the desired resolution (beyond the diffraction limit) by forcing the evanescent light into the far field image formation. However, the far field light presence in the tip-sample cavity generates an unfavourable background light source. It is possible to perform TERS by coupling the far-field excitation light to the tip a few tens of micrometres from the tip apex [298]. Femtosecond laser pulses can be coupled to the tip surface by shining the light on a grating fabricated on the tip surface. The SPPs then propagate to the tip apex and generate background-free localised optical excitation [210].

Toma et al. [298] previously demonstrated selective excitation of a single Raman mode and its CARS imaging of CNT using ultra-fast SPP pulse nanofocusing using an Au tapered tip. In a more recent publication, seminal work by Tomita et al. [155] demonstrated simultaneous nanofocusing of ultra-fast SPP pulses at 440 and 800 nm, which were coupled with a common diffraction grating structure. Figure 8a i, illustrates the scheme. The Al-tapered tip had an apex radius of ≈ 35 nm. Selective CARS microscopy that combined an 800 nm (ω) SPP pump pulse and a 440-nm (2ω) SPP probe pulse was achieved. Figure 8a ii illustrates the energy level process of ω– and 2ω-CARS. The pump pulse achieves selective vibrational excitation by spectral focusing [299,300,301,302]. Raman shift intensities with this 2ω-CARS scheme were reported to increase by as much as 4 compared with that of ω-CARS for monolayer graphene. The selectivity of vibration band excitation and background noise suppression were confirmed on the CARS intensity probed by a 2ω-SPP plasmon pulse for a monolayer graphene sample. Venezuela et al. [8] reported the Raman lines in graphene associated with both phonon-defect processes (such as the D line at Δν∼Δν∼ ~ 1350 cm⁻¹) and two-photon processes (such as the 2D line). The 2D-band intensity in graphene was reduced monotonously when the defect concentration was increased, contrary to the D-band. Tomita et al. [155] applied their multi-vibrational-mode 2ω-CARS imaging method to a multi-walled CNT (MWCNT) at the D, G and 2D bands. This dual-wavelength nanofocusing technique could open new nanoscale micro-spectroscopy and optical excitation schemes in SPM, such as sum frequency mixing, two-photon excitation (ω+2ω) and pump-probe schemes.

Figure 8b i shows a topography image of a MWCNT with a diameter of ~ 175 nm measured by the Al-tapered tip. Figure 8b ii shows a composite image of three 2ω-CARS images of the MWCNT using the 2ω-CARS spectrum from D- (red), G- (blue), and 2D- (green) bands. In ref. [155], the D- and 2D-band showed a negative correlation (in agreement with ref. [8]) except for the central part of the MWCNT. The 2D- and G-bands were intense near the central part of the MWCNT. Tomita et al. [155] indirectly estimated the spatial resolution of their technique to be less than 90 nm by taking the profile of the 2D-band signal across the axis of the MWCNT.

Conclusions

This review detailed the numerous applications of Raman spectroscopy and its advanced derivatives: stimulated Raman scattering, coherent anti-Stokes Raman scattering and surface- and tip-enhanced Raman spectroscopy. A description of the fundamental physics that underpins these techniques has been provided. Experimental considerations have been discussed with examples of typical instrumentation used. Examples of the analysis techniques employed to interpret the Raman spectroscopic data were presented and discussed.

The Raman effect now underpins prominent spectroscopic techniques in biology, medicine, crystallography and flow cytometry and has gained interest in plasma physics. It is employed as a non-invasive label-free chemically selective hyperspectral imaging technique with recent advances enabling the probing of molecular orientation and chemical composition. SRS and CARS are used to enrich signal detection at specified wavelengths associated with vibrational modes that are prescribed for spectral-selective imaging. Unlike SRS, CARS carries with it a nonresonant background contribution to the spectrum. This review detailed some of the efforts to suppress this unfavourable contribution.

Surface-enhanced Raman scattering is an ultrasensitive Raman technique that has enabled the detection of trace amounts of molecular species in samples that would otherwise be undetectable in spontaneous- or coherent Raman scattering techniques. The enhancement effect is largely associated with the plasmonic activity of the sample surface, which augments the light-matter interaction. This enhancement effect is optimised by tuning the plasmons associated wavelength with plasmonically active surface nanostructures.

Tip-enhanced Raman scattering spectroscopy is a relatively new technique that can capture hyperspectral images with spatial resolution beyond the diffraction limit of light. As light is fundamental to the Raman effect, the spatial resolution offered by TERS is so far unparalleled by other Raman scattering techniques. The surface plasmon wavelength can also be tuned for TERS techniques and recent advances have exploited surface plasmon polaritons to focus evanescent light at the tip apex with light coupled remotely from the tip apex. This technique has yielded enhanced the signal-to-noise ratio by removing the far-field light from the apex region. Recent advances have demonstrated this technique with dual-wavelength CARS.

Abbreviations

AFM:

Atomic force microscopyAOM:

Acousto-optic modulatorAS:

Ammonium sulphateCARS:

Coherent anti-Stokes Raman scatteringCARS-FC:

CARS flow cytometryCNT:

Carbon nanotubeCPCA:

Compositional principle component analysisCRS:

Coherent Raman scatteringDBR:

Distributed Bragg reflectionDFB:

Distributed feedbackE-CARS:

Epi-scattered CARSEM:

Electro-magneticFC:

Flow cytometryF-CARS:

Forward scattered CARSHEMTs:

High electron mobility transistorsLSPR:

Local surface plasmon resonanceMLV:

Multi-lamellar lipid vesicleMoS₂ :

Molybdenum disulphideMWCNT:

Multi-walled carbon nanotubeNA:

Numerical apertureOAM:

Orbital angular momentumPCL:

PolycaprolactonePMMA:

Poly-methyl-methacrylatePR-CARS:

Polarisation-resolved CARSPS:

PolystyreneSERS:

Surface-enhanced Raman scatteringSFM:

Shear force microscopySLM:

Single-longitudinal modeSPM:

Scanning probe microscopySPP:

Surface plasmon polaritonSR-CARS:

Symmetry-resolved CARSSRS:

Stimulated Raman scatteringSTM:

Scanning tunneling microscopyTEM:

Transverse electro-magnetic modeTERS:

Tip-enhanced Raman scatteringVBG:

Volume Bragg-grating