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1- DTSA-II

DTSA-II is a multi-platform software package for quantitative x-ray microanalysis. DTSA-II was inspired by the popular Desktop Spectrum Analyzer (DTSA) package developed by Chuck Fiori, Carol Swyt-Thomas, and Bob Myklebust at NIST and NIH in the ’80’s and early ’90’s.

DTSA-II has being designed with the goal of making standards-based microanalysis more accessible for the novice microanalyst. We want to encourage standards-based analysis by making it as easy as possible to get reliable results. Many operations which had previously required user intervention under DTSA now are performed entirely by the software. Furthermore, the software attempts to guide the user step-by-step through common processes while performing quality control sanity checks. While this might not provide the flexibility that some sophisticated users may desire, we feel that this philosophy is more consistent with the way laboratories are moving towards technicians responsible for multiple techniques and away from experts in single techiques. We encourage users who desire the additional power and flexibility available in the EPQ library to learn to script using Jython or to create their own alternative user interface. EPQ is much more capable than the fraction exposed via DTSA-II.

DTSA-II is based on an entirely new code base written by Nicholas W. M. Ritchie. The codebase has been carefully divided into a shared algorithm library which forms the basis for a handful of software products and a user interface shell. DTSA-II is the user interface shell and the EPQ library is the algorithm library.

DTSA-II remains under active development. Many features – some fairly basic – remain unimplemented. Other features have not been tested as much as the developer might like. The program made available to the public via this web site represents the current best available version in the judgement of the developer. DTSA-II remains experimental software and no representations are made regarding the suitability of the product for any particular application.

Major features:

• Basic IO and Display
  • Read energy dispersive x-ray spectra in a variety of different commercial and non-commercial formats including the industry standard EMSA format
  • Display and overlay spectra with various scaling options on linear/log/sqrt axes
  • Copy/save/print the spectrum display as a bitmap/PNG file
  • Output the spectra as a GNUPlot file for publication quality output
  • Overlay labeled x-ray emission lines and x-ray absorption edges
  • Define and integrate regions-of-interest
  • View spectrum contextual information
  • Archive spectra to a searchable database
  • Sub-sampling of spectral data to simulate shorter acquisition times
  • Basic spectrum math functions
  • Background modeling or background stripping
  • Energy axis linearization
  • Spectrum smoothing
  • Peak removal (trimming)
  • Peak search / identification
• Spectrum Simulation
  • Analytical (φ(ρz)) simulations of energy dispersive x-ray spectra
    • Normal or oblique incidence angle
    • Variable beam energies, beam fluxes, materials
  • Monte carlo simulations of energy dispersive x-ray spectra
    • Spectra from bulk samples
    • Mounted or unmounted thin films
    • Cubical or spherical particles with or without a substrate
  • Simulated spectra may be manipulated as experimental spectra
  • Variety of detector options including Si(Li), SDD and microcalorimeter
• Standards-based Quantification
  • Standards-based quantification of EDS spectra
  • Filter-fit linear-least squares fitting of reference spectra
  • Quantification based on references or like-standards
  • φ(ρz) correction of the k-ratios
  • ζ-factor correction of thin-film samples
  • Results reported as HTML with estimates of uncertainty
• Reporting
  • Actions are recorded in a daily HTML activity report
  • Report may be opened in an alternative HTML viewer
• Platforms and Source Code
  • DTSA-II is based on the EPQ library – a full-featured library of electron probe quantification algorithms
  • DTSA-II only exposes a fraction of the power within the EPQ library. The remainder may be accessed via custom Java applications or via Jython scripting.
  • The EPQ library includes the full NISTMonte for Monte Carlo simulation of electron/x-ray transport
  • DTSA-II / EPQ library are available as source code
  • DTSA-II / EPQ library are written in Java SE 6 compatible source
  • DTSA-II / EPQ library can execute on any platform supporting Java SE 6 or later
  • DTSA-II / EPQ library is regularly tested on Windows XP, Ubuntu Linux & Apple OS X

Disclaimer

This software was developed at the National Institute of Standards and Technology by employees of the Federal Government in the course of their official duties. Pursuant to title 17 Section 105 of the United States Code this software is not subject to copyright protection and is in the public domain. DTSA and the EPQ library are experimental systems. NIST assumes no responsibility whatsoever for its use by other parties, and makes no guarantees, expressed or implied, about its quality, reliability, or any other characteristic. We would appreciate acknowledgement if the software is used. This software can be redistributed and/or modified freely. The author requests that any derivative works bear some notice that they are derived from it, and any modified versions bear some notice that they have been modified.

Any mention of commercial products is for information only; it does not imply recommendation or endorsement by NIST nor does it imply that the products mentioned are necessarily the best available for the purpose.

See: https://cstl.nist.gov/div837/837.02/epq/dtsa2/

2. HyperSpy

HyperSpy is an open source Python library which provides tools to facilitate the interactive data analysis of multi-dimensional datasets that can be described as multi-dimensional arrays of a given signal (e.g. a 2D array of spectra a.k.a spectrum image). HyperSpy aims at making it easy and natural to apply analytical procedures that operate on an individual signal to multi-dimensional arrays, as well as providing easy access to analytical tools that exploit the multi-dimensionality of the dataset. Its modular structure makes it easy to add features to analyze different kinds of signals.

Highlights

• Two families of named and scaled axes: signal and navigation.
• Visualization tools for multi-dimensional spectra and images.
• Easy access multi-dimensional curve fitting and blind source separation.
• Built on top of NumPy, SciPy, matplotlib and scikit-learn.
• Modular design for easy extensibility.

The development has been motivated by the data analysis needs of the electron microscopy community but it is proving useful in many other fields.

See: https://hyperspy.org/

3. AZtec

• AZtecFeature is an innovative particle analysis system specifically optimised for usability and high-speed throughput. It combines the raw speed and sensitivity of the Ultim Max Silicon Drift Detector with the superior analytical performance and ease of use of the AZtec® EDS analysis suite to create the most advanced automated particle analysis platform on the market. Gunshot Residue Analysis in the SEM with AZtecGSR is fast and accurate: it gives reproducible Gunshot Residue Analysis results to ASTM E1588 – 10e1.
• AZtecGSR combines ease of use through its guided workflow, with the ultimate accuracy using the latest Ultim Max detectors and Tru-Q® algorithms. LayerProbe is an exciting software tool for thin film analysis in the SEM. An option for the AZtec EDS microanalysis system, LayerProbe is faster, more cost-effective and higher resolution than dedicated thin film measurement tools.The most powerful EBSD software available, AZtecHKL combines speed and accuracy of results for routine analysis, with the flexibility and power required for applications that push the frontiers of EBSD.
• AZtec3D combines simultaneous EDS and EBSD data acquisition & analysis with the automated milling capabilities of a FIB-SEM.AZtecLiveOne software platform is the ideal solution for carrying out a complex task like EDS as quickly and as easily as possible. No need for substantial training or advanced knowledge of the EDS technique. Users can be trained in a matter of minutes and will have complete confidence in their results. AZtecTEM is an innovative EDS software specifically optimised for advanced TEM applications. AZtecSynergy provides a powerful solution for the simultaneous collection of EDS and EBSD data. All of the tools to collect excellent integrated data are included in one place with no complicated switching from one navigator to another.
• AZtecSteel is an automated steel inclusion analysis package developed specifically for the analysis and classification of steel inclusions using Energy Dispersive X-ray microanalysis (EDS) in a scanning electron microscope (SEM). It detects, measures and analyses the inclusions, processes the resulting data set to published standard methods, and includes functionality to plot complex ternary diagrams. AZtecLive is a revolutionary new approach to EDS analysis that enables a radical change in the way users perform sample investigation in the SEM. It combines a live electron image with live X-ray chemical imaging to give an intuitive new way of interacting with your samples. Collecting good quality data is only the beginning of any complete EBSD analysis. AZtecCrystal provides all the necessary tools to process and interrogate your EBSD data and to solve your materials problems. Seamlessly integrated with AZtecHKL or operated as a standalone program, AZtecCrystal sets the standard in EBSD data processing for experts and novices alike.
• AZtecAM is a powerful, automated, solution for the analysis of metal powders used in additive manufacturing. Based on AZtecFeature, AZtecAM optimises the particle analysis workflow to enable the rapid and accurate characterisation of metal powders. AZtecMineral is a powerful, automated, Mineral Liberation Analysis solution. It enables ore characterisation, provides vital data on metal recovery and enables process yield characterisation using multipurpose SEMs. It is also a valuable tool for the characterisation of rocks in research environments, enabling the automation of otherwise laborious optical analyses.

See: https://engineering.virginia.edu/oxford-instruments-offering-free-aztec-suite-software-electron-microscopy-analysis

4. ESPRIT Family

ESPRIT 2 unites four analytical methods under a single user interface. These include EDS for SEM and (S)TEM, WDS, Micro-XRF for SEM and EBSD. This makes it easy for the user to switch between methods with a single mouse click. Additionally, it facilitates combining different method results from the same sample area and to so gain much more information. To name only the most important, coupling of following methods is supported:

• EDS and EBSD
• EDS and WDS
• EDS and Micro-XRF for SEM

The software is designed to suit the needs of all levels of users – from beginner to expert. Novices will benefit from the assistants that help performing routine tasks without having to learn details of the measurement method. More experienced users will value the option to drill down deeper, when they need it, meaning both detailed setup of measurements as well as in-depth analysis of results and automation of tasks.

See: https://www.bruker.com/en/products-and-solutions/elemental-analyzers/eds-wds-ebsd-SEM-Micro-XRF/software-esprit-family.html

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In this course the general introduction to Raman spectroscopy and microscopy will be provided and practical tips as well as examples will be given. The capability of Raman spectroscopy for the analysis of real-life samples (paint components, clays, coating materials, etc.) taken from historical and archaeological objects will be discussed.

1. Principles of Raman spectroscopy

Raman spectroscopy is widely used in the investigation of cultural heritage materials due to its high spatial resolution (typically in the range of 1 to 10 µm), large amount of obtainable information, non-destructivity and ability to perform in-situ analysis.^1,2 With Raman spectroscopy it’s possible to analyse various materials: minerals, inorganic and organic pigments, binding media, varnishes, ceramics, plastics, textile fibres etc.²

The following video explains the principles and instrumentation of Raman spectroscopy.https://www.uttv.ee/embed?id=29055

Similarly to infrared spectroscopy, Raman spectroscopy is classified as vibrational spectroscopy.³ Raman spectroscopy is based on Raman scattering (or Raman effect) that reveals the vibrational, rotational and other low frequency modes of molecules⁴. In this technique, the sample is exposed to an intense beam of monochromatic light (typically a laser beam) in the frequency range of visible, near-infrared or near-ultraviolet region.⁵ The electromagnetic radiation, interacting with a substance, can be transmitted, absorbed, or scattered⁶. When the monochromatic radiation is scattered by molecules, the majority of the radiation undergoes the common Rayleigh scattering (radiation’s  frequency/wavelength is unchanged). However, a small fraction of the scattered radiation is observed to have a slightly different frequency from that of the incident radiation. This is known as the Raman effect⁷. The Raman lines show up pairwise. The dominant Stokes lines have a lower frequency (longer wavelength) than the initial radiation, whereas the weaker (often nondetectable) anti-Stokes lines have a higher frequency (shorter wavelength).^4,5 The frequency shifts are virtually independent of the excitation wavelength and are characteristic of the particular substance/molecule. Usually one only records the relatively strong Stokes lines, which therefore are attributed a positive frequency shift. Such spectral coordinate is called the Raman shift and measured in wavenumbers (in cm^-1).⁴ See scheme in Figure 1.

Figure 1. Scheme of Raman scattering.

In Raman spectroscopy, as it is a scattering technique, samples are simply placed in the laser beam and the scattered radiation is collected and analysed⁸. Raman spectrometer measures the wavelength-dependent intensity of the inelastically scattered light.

The obtained Raman spectra are essentially vibrational spectra. Hence, if presented in the Raman shift scale, they are directly comparable to corresponding infrared absorption spectra (see Figure 2). However, Raman spectrum arises in a different manner and the rules, which vibrations are Raman-active (and thus produce signals in the spectrum), are different. It turns out that a vibration is Raman-active (i.e. revealed as a spectral line in the Raman spectrum), if the polarizability of the molecule changes during the vibration.⁷ It often happens that vibrations that are active (or give high-intensity signals) in Raman scattering are inactive (or give low-intensity signals) in the infrared, and vice versa.⁷Therefore, Raman spectra often provide complementary information to IR spectra.

Figure 2. Raman (laser 514.5 nm) and IR spectra of benzene.

1.1. Instrumentation

There are two types of Raman spectrometers: dispersive spectrometers (based on the use of diffraction grating) and interferometer containing Fourier-transform Raman spectrometers (FT-Raman)⁹.

In general the main components of Raman spectrometers are presented on the following scheme:

In Raman spectroscopy, the choice of excitation wavelength and intensity is very important. Different wavelengths are suitable for the analysis of different types of material. The wavelength will affect the Raman intensity, spatial resolution, background fluorescence, and potential damage to the sample. Almost exclusively lasers are used as excitation sources, because they are highly monochromatic, give high-intensity radiation and can be efficiently focused due to their high coherence. Only continuous wave (CW) lasers are used, as pulsed lasers easily damage the sample. Some popular CW lasers are presented in Table 1. Traditionally, laser wavelengths up to 830 nm have been used in dispersive instruments while the 1064 nm laser line has been employed in FT-Raman setups. With the availability of sensitive InGaAs array detectors, it has become meaningful to use also the 1064 nm lasers with dispersive Raman instruments.

Table 1. Laser sources for Raman spectroscopy.

Raman scattering efficiency decreases with increasing excitation wavelength as λ⁻⁴. However, short-wavelength lasers more easily induce fluorescence, absorb in the sample or cause other undesirable effects due to their high photon energy. Hence, most common laser wavelengths in Raman spectroscopy are in the visible and NIR region (such as 633 or 785 nm) which offer low fluorescence whilst retaining relatively high Raman intensity. For samples which exhibit fluorescence even under red excitation (for example dyes), the 1064 nm laser may be needed. While near-infrared lasers have a smaller photon energy, compared to visible lasers, they are usually more powerful, in order to compensate for the reduced Raman scattering efficiency. Therefore, they may still damage the sample. It is especially important for strongly absorbing (black) samples, in which case the UV/visible lasers (operating at lower intensities) may yield a stronger Raman signal.

Dispersive Raman spectrometers

A dispersive spectrometer utilizes a diffraction grating to angularly disperse the light. As a result, at the detector plane, different wavelengths become spatially separated. Nevertheless, prior to entering the spectrometer, the incoming light should go through a special edge or notch filter to suppress the primary (Raman-scattered) light and thereby reduce the scattering inside the spectrometer. A matrix detector is used to record the dispersed spectrum. Typically, a silicon-based cooled CCD is used, which is very sensitive in the visible and NIR region (up to 1100 nm).

FT-Raman spectrometers

Commercial FT-Raman spectrometers were introduced in the late 1980s¹⁰. Their operating principle is similar to that of FTIR spectrometers and is based on an interferometer. As the Raman-scattered light enters the instrument, the interferometer selectively modulates the individual spectral components by systematically changing an optical path length difference. The resulting beam of light is recorded by a point detector. FT-Raman is superior to a dispersive instrument in the near-IR region beyond 1000 nm. Commonly, the 1064 nm laser excitation along with germanium or indium gallium arsenide (InGaAs) detector is used. They also offer excellent wavelength accuracy and can potentially combine IR absorption and Raman measurement capacity in single instrument. However, FT-Raman frequently needs to use high laser intensities due to the reduced Raman scattering efficiency at longer wavelengths, which may damage the sample.

Different types of Raman Spectroscopy

A variety of Raman instruments and special techniques are used for the analysis of cultural heritage materials. The choice of instrument determines the sensitivity, spectral range and resolution, spatial resolution, availability of different excitation sources, and convenience of operation. 

• Micro-Raman spectrometer (or Raman microscope) is the most common bench-top Raman instrument. A high-resolution spectrometer (either dispersive or FT) and one or several laser sources are coupled through an optical microscope. The excitation beam is focused and the secondary emission is collected simultaneously by the microscope objective in backscattering geometry. A high-numerical aperture (NA) objective yields both a high spatial resolution and a high collection efficiency.
• Surface-enhanced Raman spectroscopy (SERS) involves inelastic light scattering by molecules placed close to nanometal surfaces, which amplify the scattering by plasmonic resonance. One approach is to study molecules adsorbed onto corrugated metal surfaces such as silver or gold nanoparticles¹¹. Another approach is to stimulate the molecules by a sharp metal tip. Such tip-enhanced Raman spectroscopy is typically implemented by combining a confocal microscope and a scanning probe microscope. 
• In Resonance Raman spectroscopy (RRS) the incident photon energy is close in energy to an electronic transition of a compound or material under examination. 
• In a portable Raman spectrometer, a miniature dispersive spectrometer and a small laser source are integrated into a portable, hand-held device. Hence, the instrument can be used to perform in situ analysis in museums, archives, also outdoors on archaeological sites for the analysis of mural or cave paintings. Such portable devices frequently employ a fiber-optic probes. 

1.2. Problems with Raman spectroscopy

Compared to IR absorption, the primary disadvantage of Raman spectroscopy is the fluorescent background (see Figure 3). As Raman scattering is inherently weak, one has to use an intense laser beam for excitation, and for many materials, this results in a strong fluorescence – either due to the material itself of impurities. Sometimes even trace impurities – if they are strongly fluorescent – can lead to disturbing fluorescence background. Fortunately, Raman lines are spectrally close to the laser beam whereas fluorescence has typically a large Stokes shift. 

Figure 3. Example of the fluorescence in the Raman spectrum of red lead containing paint.

Relative to the Raman signal, the fluorescent background can be highly intense and even the tail of the fluorescence band may obscure the Raman spectrum. Although the problem can be partially resolved by careful sample preparation, time resolved spectroscopy or coherent anti-Stokes Raman spectroscopy (CARS), there will always be experiments that remain difficult to perform.⁷

In addition to fluorescence, intense focused laser irradiation can cause heating and degradation of the sample. The problems are typical for organic, soft, photosensitive or dark/coloured materials whereas transparent inorganic materials have usually quite high damage threshold.

2. Analysis with Raman spectroscopy

In the following video Senior Research Fellow Dr. Valter Kiisk demonstrates and explains how to perform measurements with a typical micro-Raman spectrometer.https://www.uttv.ee/embed?id=29396

Identification of the composition of the studied material is often based on the comparison of its Raman spectrum with a spectral library of reference materials.¹² Different papers and books have been published from where Raman spectra or information about excitation wavelengths and list of wavenumbers in the Raman spectra are available ^5,13,14. Also a very valuable on-line database is made available by the Infrared & Raman Users Group (IRUG)– http://irug.org/ – from where different Raman (and also IR) spectra of cultural heritage materials can be obtained free of charge.

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Interaction of an electron beam with a sample target produces a variety of emissions, including x-rays. An energy-dispersive (EDS) detector is used to separate the characteristic x-rays of different elements into an energy spectrum, and EDS system software is used to analyze the energy spectrum in order to determine the abundance of specific elements. EDS can be used to find the chemical composition of materials down to a spot size of a few microns, and to create element composition maps over a much broader raster area. Together, these capabilities provide fundamental compositional information for a wide variety of materials.

How it Works – EDS

EDS systems are typically integrated into either an SEM or EPMA instrument. EDS systems include a sensitive x-ray detector, a liquid nitrogen dewar for cooling, and software to collect and analyze energy spectra. The detector is mounted in the sample chamber of the main instrument at the end of a long arm, which is itself cooled by liquid nitrogen. The most common detectors are made of Si(Li) crystals that operate at low voltages to improve sensitivity, but recent advances in detector technology make availabale so-called “silicon drift detectors” that operate at higher count rates without liquid nitrogen cooling.

An EDS detector contains a crystal that absorbs the energy of incoming x-rays by ionization, yielding free electrons in the crystal that become conductive and produce an electrical charge bias. The x-ray absorption thus converts the energy of individual x-rays into electrical voltages of proportional size; the electrical pulses correspond to the characteristic x-rays of the element.

Strengths

• When used in “spot” mode, a user can acquire a full elemental spectrum in only a few seconds. Supporting software makes it possible to readily identify peaks, which makes EDS a great survey tool to quickly identify unknown phases prior to quantitative analysis.
• EDS can be used in semi-quantitative mode to determine chemical composition by peak-height ratio relative to a standard.

Limitations

• There are energy peak overlaps among different elements, particularly those corresponding to x-rays generated by emission from different energy-level shells (K, L and M) in different elements. For example, there are close overlaps of Mn-K_α and Cr-K_β, or Ti-K_α and various L lines in Ba. Particularly at higher energies, individual peaks may correspond to several different elements; in this case, the user can apply deconvolution methods to try peak separation, or simply consider which elements make “most sense” given the known context of the sample.
• Because the wavelength-dispersive (WDS) method is more precise and capable of detecting lower elemental abundances, EDS is less commonly used for actual chemical analysis although improvements in detector resolution make EDS a reliable and precise alternative.
• EDS cannot detect the lightest elements, typically below the atomic number of Na for detectors equipped with a Be window. Polymer-based thin windows allow for detection of light elements, depending on the instrument and operating conditions.

Results

A typical EDS spectrum is portrayed as a plot of x-ray counts vs. energy (in keV). Energy peaks correspond to the various elements in the sample. Generally they are narrow and readily resolved, but many elements yield multiple peaks. For example, iron commonly shows strong K_α and K_βpeaks. Elements in low abundance will generate x-ray peaks that may not be resolvable from the background radiation.

EDS spectrum of multi-element glass (NIST K309) containing O, Al, Si, Ca, Ba and Fe (Goldstein et al., 2003). 

EDS spectrum of biotite, containing detectable Mg, Al, Si, K, Ti and Fe (from Goodge, 2003). 

References

• Severin, Kenneth P., 2004, Energy Dispersive Spectrometry of Common Rock Forming Minerals. Kluwer Academic Publishers, 225 p.–Highly recommended reference book of representative EDS spectra of the rock-forming minerals, as well as practical tips for spectral acquisition and interpretation.
• Goldstein, J. (2003) Scanning electron microscopy and x-ray microanalysis. Kluwer Adacemic/Plenum Pulbishers, 689 p.
• Reimer, L. (1998) Scanning electron microscopy : physics of image formation and microanalysis. Springer, 527 p.
• Egerton, R. F. (2005) Physical principles of electron microscopy : an introduction to TEM, SEM, and AEM. Springer, 202.
• Clarke, A. R. (2002) Microscopy techniques for materials science. CRC Press (electronic resource)

Related Links

• Petroglyph–An atlas of images using electron microscope, backscattered electron images, element maps, energy dispersive x-ray spectra, and petrographic microscope– Eric Chrisensen, Brigham Young University
• SEM/EDX webpage from Indiana University – Purdue University Fort Wayne

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X-ray is a kind of electromagnetic wave, the same as light. The wavelength of visible light is 400 to 800nm, while the wavelength of x-ray is much shorter (higher energy), at 0.001nm to 10nm, and is known to have strong penetrating power.

Fig. 1 shows the interactions between a material and X-ray, and various analysis methods that make use of these interactions. These interactions provide important clues for learning the state of a material. As a familiar example, an X-ray image for medical application is a well-known use of transmission X-ray. Here we will introduce an elemental analysis method called fluorescent X-ray spectrometry.

Fig.1 Analytical methods and its application interaction of X-ray and matter

Fluorescent X-ray Spectrometry

When irradiating X-rays onto a material, fluorescent X-ray (characteristic X-ray), which has energy (wavelength) unique to the element that composes the material will be generated. When we measure the fluorescent X-ray energy, the contained element is identified (qualitative analysis), and we can calculate the concentration (quantitative analysis) from the intensity of the fluorescent X-ray of each element. Thus, the qualitative or quantitative analyses of a material by irradiating X-rays onto an unknown material and analyzing the fluorescent X-ray that is generated, is called fluorescent X-ray spectrometry.

There are two types of fluorescent X-ray spectrometry; the wavelength dispersive type (WDXRF) using analyzing crystals, and the energy dispersive type (EDXRF) using semiconductor detectors (EDS).

Comparison between Energy Dispersive Type and Wavelength Dispersive Type Spectrometers

The characteristics of a wavelength dispersive type spectrometer (WDXRF) are high sensitivity, high accuracy, high resolution, and high reproducibility. We can expect sensitivity and accuracy at levels one order of magnitude higher than those of the energy dispersive type spectrometer (EDXRF). These characteristics are provided by a high-power X-ray tube (3 to 4 kW) and its cooling device, a goniometer which makes complicated movements and an exchange mechanism for the analyzing crystal and detector and so on. Naturally, the instruments are larger, with a complicated structure and high price. The specimen surface is required to be flat and the available analysis area is from several mm to 30mm or so. This type of device is suitable for process management where specimens with the same form are analyzed one after another.

The characteristics of the energy dispersive type spectrometer (EDXRF) are simple structure and low price, its adaptability to a variety of specimens, and its user-friendliness. The X-ray bulb is compact (several tens W) and air-cooled, and since the EDS (semiconductor detector) itself performs the analysis, a complicated spectroscopy section is not necessary.

The roughness or shape of specimen does not matter, so analysis of large specimens or micro areas is possible. Each characteristic is shown in Fig. 2. The images are the large instrument for WDXRF, and the compact simple instrument for EDXRF.

Wavelength Dispersive Type (WDXRF) Advantages: High Sensitivity, High Resolution High Accuracy, High Reproducibility Disadvantages: Complicated and large-sized, high price Specimen is limited to flat platesEnergy Dispersive Type (EDXRF) Advantages: Simple Operation, compact, low price Flexibility in specimen shape Disadvantages: Low resolution (overlapped peaks) Cooling mechanism requiring liquid nitrogen or the like

Fig.2 Comparison between Wavelength Dispersive Type (WDXRF) and Energy Dispersive Type (EDXRF)

Sampling of Solid/Powder/Liquid Samples

One of the characteristics of EDXRF is the ease of use. Sampling of solid, powder, and liquid samples is explained below.

Sampling of Solid Sample

Analysis of a solid sample is possible by simply placing the sample at the X-ray illumination position.

In case of small sample, use of a dedicated cell will make it easier to set the sample. Fig. 3 shows a simplified illustration of the solid sample sampling method.

Fig.3 Sampling of Solid Sample

Sampling of Powder Sample (rock, soil, incinerated ash, etc)

Powder samples are typically analyzed by producing a pellet using a compression device. As a simplified method, analysis is possible on the powder placed into a specially-designed cell. Fig. 4 shows a simplified illustration of the powder sample sampling method.

Fig.4 Sampling of Powder Sample

Sampling of Liquid Sample

For liquid samples, a dedicated cell is used. Fill a dedicated cell with the liquid and analyze. In addition, there is another method where you can drop liquid onto a filter, dry it, and then analyze it. Fig. 5 shows a simplified illustration of liquid sample sampling methods.

Fig.5 Sampling of Liquid Sample

FP Quantitative Method / Film Thickness Analysis of Thin Film Sample

FP (fundamental parameter) quantitative method

The EDXRF instrument employs a theoretical calculation method called the FP quantitative method, allowing quantitative analysis of an unknown sample without the need for a standard sample.
The FP quantitative method assumes that the sample is uniform, sufficiently large and thick, and that all elements (100% in total) are quantified. Naturally, a sample must satisfy these assumptions, so attention is needed.The flow chart of FP quantitative method is shown in Fig. 6.

Fig.6 The flow chart of FP quantitative method

Flow Chart Explanation

1. First, measure the unknown sample and obtain the measurement intensity.
2. Assume the initial concentration of the sample and obtain a calculated intensity using the FP method.
3. Compare the measurement intensity and the calculated intensity.
4. Change the assumed concentration so that the measurement intensity and the calculated intensity match.
5. Obtain a new calculated intensity with the new assumed concentration using the FP method.
6. Repeat steps 3 to 5.
7. The assumed concentration that gives a calculated concentration that matches the measurement concentration is the analysis result.

Film Thickness Analysis of Thin Film Sample

In the case of a thin film sample, there is a correlation between the x-ray intensity of the elements composing the film and the film thickness. Therefore, by irradiating X-rays onto the surface of a thin film and measuring the X-ray intensity of the elements composing the film, the film thickness can be analyzed without destroying it.

A Single layer film can be analyzed using a calibration curve, but with the calibration curve method, a standard sample must be prepared for each kind of film. When the thin film FP quantitative method is used, it is not only possible to analyze single layer films, but also to analyze the thickness and composition of each layer in a multi-layer thin film, up to 5 layers , without a standard sample, which is very convenient. Fig. 7 shows a diagram of the thin film FP method, Fig. 8 shows a measurement example of Au/Ni/Cu film.

Thin Film FP (fundamental parameter) method

• Simultaneous non-destructive analysis of thickness and composition of thin film
• Up to 5 layers, and up to 20 elements for each layer
• Film thickness of about 10nm to 10μm (differs depending on element)
• Standard sample is not necessary (theoretical calculation)
• Information of layering order, elements, and density of the film is needed.

Fig.7 Schematic diagram of a thin film FP method

Fig.8 Measurement of the film Au / Ni / Cu thin film FP method

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What is EDS?

Energy-dispersive X-ray spectroscopy (also known as EDS, EDX, or EDXA) is a powerful technique that enables the user to analyze the elemental composition of a desired sample. The major operating principle that allows EDS to function is the capacity of high energy electromagnetic radiation (X-rays) to eject ‘core’ electrons (electrons that are not in the outermost shell) from an atom. This principle is known as Moseley’s Law, which determined that there was a direct correlation between the frequency of light released and the atomic number of the atom.

Removing these electrons from the system will leave behind a hole that a higher energy electron can fill in, and it will release energy as it relaxes. The energy released during this relaxation process is unique to each element on the periodic table, and as such bombarding a sample with X-rays can be used to identify what elements are present, as well as what proportion they are present in.

Shown below is an example of how EDS works. The letters K, L, and M refer to the n value that electrons in that shell have (K electrons, closest to the nucleus, are n=1 electrons), while α and β indicate the size of the transition. The relaxation from M to L or L to K are therefore described as Lα or Kα, while going from M to K would be a Kβ transition. The means that are used for describing these processes as a whole are known as Siegbahn notation.

How is data collected?

EDS functions with a series of three major parts: an emitter, a collector, and an analyzer. These parts are additionally typically equipped on an electron microscope such as SEM or TEM. The combination of these three pieces enables analysis of both how many X-rays are released, as well as what their energy is (in comparison to the energy of the initial X-rays that were emitted).

The EDS data is presented as a graph with KeV on the x-axis and peak intensity on the y-axis. The peak location on the x-axis are converted into the atoms that the energy changes represent by a computer program.

Figure. EDS chart from a research group that was analyzing the composition of shrimp and the associated bacteria that associate with these minerals. The EDS helped support the researcher’s case that the endosymbiotic bacteria living on these shrimp actually do influence the iron oxide composition in these minerals. This is evident by the peaks at 0.5 and 6.5 KeV.² 

What are some drawbacks of EDS?

Although EDS is an extremely useful technique, there are a number of difficulties involved with the process which hinder its utility. First, EDS is generally not a particularly sensitive technique. If the concentration of an element in the sample is too low, the amount of energy given off by X-rays after hitting the sample will be insufficient to adequately measure its proportion. Second, EDS generally does not work for elements with a low atomic number. Hydrogen and helium both only have an n=1 shell, meaning there aren’t core electrons to be removed that can allow for X-ray emission. Lithium and beryllium, meanwhile, have sufficiently low atomic numbers that the energy of X-rays given off by Li or Be samples is insufficient for measurement, and often times they cannot be tested as a result.

One additional difficulty associated with the technique is the thickness of the sample. Sample thickness can bring energy levels closer together, thus making electrons easier to move to outer energy levels, which can in turn cause deviation in the results. Another error source is overlapping emitted x-rays, which can alter the KeV readings. Additionally, X-rays are not particularly effective at penetrating beyond several nanometers in samples, which means that only surface layers can be efficiently measured by the technique. As such, if there is a discrepancy between the outer and inner material layers, it will not necessarily appear in EDS.

Work Cited

1. https://en.wikipedia.org/wiki/Energy-dispersive_X-ray_spectroscopy
2. https://cfamm.ucr.edu/documents/eds-intro.pdf
3. L. Corbari, M.-A. Cambon-Bonavita, G. J. Long, F. Grandjean, M. Zbinden, F. Gaill, and P. Compere “Iron oxide deposits associated with the ectosymbiotic bacteria in the hydrothermal vent shrimp Rimicaris exoculata” Biogeosciences 2008, 5, 1295–1310.

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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.

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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.

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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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David Harvey (DePauw University)

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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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It is the shift in wavelength of the inelastically scattered radiation that provides the chemical and structural information. Raman shifted photons can be of either higher or lower energy, depending upon the vibrational state of the molecule under study. A simplified energy diagram that illustrates these concepts is shown below.

Stokes radiation occurs at lower energy (longer wavelength) than the Rayleigh radiation, and anti-Stokes radiation has greater energy. The energy increase or decrease is related to the vibrational energy levels in the ground electronic state of the molecule, and as such, the observed Raman shift of the Stokes and anti-Stokes features are a direct measure of the vibrational energies of the molecule. A schematic Raman spectrum may appear as shown below.

The energy of the scattered radiation is less than the incident radiation for the Stokes line and the energy of the scattered radiation is more than the incident radiation for the anti-Stokes line. The energy increase or decrease from the excitation is related to the vibrational energy spacing in the ground electronic state of the molecule and therefore the wavenumber of the Stokes and anti-Stokes lines are a direct measure of the vibrational energies of the molecule.

In the example spectrum, notice that the Stokes and anti-Stokes lines are equally displaced from the Rayleigh line. This occurs because in either case one vibrational quantum of energy is gained or lost. Also, note that the anti-Stokes line is much less intense than the Stokes line. This occurs because only molecules that are vibrationally excited prior to irradiation can give rise to the anti-Stokes line. Hence, in Raman spectroscopy, only the more intense Stokes line is normally measured – Raman scattering is a relatively weak process. The number of photons Raman scattered is quite small. However, there are several processes which can be used to enhance the sensitivity of a Raman measurement.

Simplified energy diagram

If the wavelength of the exciting laser coincides with an electronic absorption of a molecule, the intensity of Raman-active vibrations associated with the absorbing chromophore are enhanced by a factor of 102 to 104. This resonance enhancement or resonance Raman effect can be extremely useful, not just in significantly lowering the detection limits, but also in introducing electronic selectivety. Thus the resonance Raman technique is used for providing both structural and electronic insight into species of interest.

Metalloporphyrins, carotenoids and several other classes of biologically important molecules have strongly allowed electronic transitions in the visible, making them ideal candidates for resonance Raman spectroscopy. Resonance selectivity has a further practical use, in that spectrum of the chromophoric moiety is resonance enhanced and that of the surrounding environment is not. For biological chromophores, this means that absorbing active centres can be specifically probed by visible excitation wavelengths, and not the surrounding protein matrix (which would require UV lasers to bring into resonance).

Resonance Raman spectroscopy is also an important probe of the chemistry of metal centred complexes, fullerenes, polydiacetylenes and other “exotic” molecules which strongly absorb in the visible. Although many more molecules absorb in the ultraviolet, the high cost of lasers and optics for this spectral region have limited ultraviolet (UV) resonance Raman spectroscopy to a small number of specialist groups.

Schematic Raman spectrum

Vibrations which are resonantly enhanced fall into two or three general mechanistic classes. The most common case is Franck-Condon enhancement, in which a component of the normal coordinate of the vibration occurs in a direction in which the molecule expands during an electronic excitation. The more the molecule expands along this axis when it absorbs light, the larger the enhancement factor. The easily visualized ring breathing (in-plane expansion) modes of porphyrins fall into this class. Vibrations which couple two electronic excited states are also resonantly enhanced, through a mechanism called vibronic enhancement. In both cases, enhancement factors roughly follow the intensities of the absorption spectrum. The fuller theory of resonance enhancement is beyond the scope of this section.

Resonance enhancement does not begin at a sharply defined wavelength. In fact, enhancement of 5x to 10x is observed if the exciting laser is within even a few 100 wavenumbers below the electronic transition of a molecule. This “pre-resonance” enhancement can be experimentally useful.

The Raman scattering from a compound (or ion) adsorbed on or even within a few Angstroms of a structured metal surface can be 103 to 106x greater than in solution. This surface-enhanced Raman scattering is strongest on silver, but is observable on gold and copper as well. At practical excitation wavelengths, enhancement on other metals is unimportant.

SERS arises from two mechanisms:

1. The first is an enhanced electromagnetic field produced at the surface of the metal. When the wavelength of the incident light is close to the plasma wavelength of the metal, conduction electrons in the metal surface are excited into an extended surface electronic excited state called a surface plasmon resonance. Molecules adsorbed or in close proximity to the surface experience an exceptionally large electromagnetic field. Vibrational modes normal to the surface are most strongly enhanced.
2. The second mode of enhancement is by the formation of a charge-transfer complex between the surface and analyte molecule. The electronic transitions of many charge transfer complexes are in the visible, so that resonance enhancement occurs. Molecules with lone pair electrons or pi clouds show the strongest SERS. The effect was first discovered with pyridine.

Other aromatic nitrogen or oxygen containing compounds, such as aromatic amines or phenols, are strongly SERS active. The effect can also be seen with other electron-rich functionalities such as carboxylic acids. The intensity of the surface plasmon resonance is dependent on many factors including the wavelength of the incident light and the morphology of the metal surface. The wavelength should match the plasma wavelength of the metal. This is about 382 nm for a 5μm silver particle, but can be as high as 600nm for larger ellipsoidal silver particles. The plasma wavelength is to the red of 650nm for copper and gold, the other two metals which show SERS at wavelengths in the 350-1000 nm region. The best morphology for surface plasmon resonance excitation is a small (<100nm) particle or an atomically rough surface. SERS is commonly employed to study monolayers of materials adsorbed on metals, including electrodes.

Other popular surfaces include colloids, metal films on dielectric substrates and, recently, arrays of metal particles bound to metal or dielectric colloids through short linkages. Although SERS allows easy observation of Raman spectra from solution concentrations in the micromolar (10x-6) range,non-reproducability of quantitative measurements has in the past marred its utility for analytical purposes. However, standardization in production of SERS active media is steadily improving its potential in this area also.

UVRRS is a powerful tool in the molecular analysis of complex biological systems. Most biological systems absorb UV radiation and hence have the ability to offer resonance with UV Raman excitation. This results in the highly selective resonance Raman effect enabling enhancement of important biological targets such as protein or DNA. For example, excitation around 200nm enhances the Raman peaks from vibrations of amide groups; excitation around 220nm enhances peaks from certain aromatic residues. The Raman scatter from water is weak, allowing for analysis of very weak aqueous systems.

Fiber optic UVRRS configuration

Due to the selective nature of UVRRS, a tunable laser is typically required as the excitation source. Since truly tunable continuous-wave lasers are not yet available, a Nd:YAG-pumped dye laser with frequency-doubled output is one suitable UVRRS system. Depending on the dyes used, this laser setup can give almost any required UV wavelength. Intensified CCDs (ICCDs) with UV photocathodes, back-illuminated CCDs or CCDs with UV enhancing (BASF lumogen)coatings can be used as detectors for UVRRS. These detectors are used on account of their high detection efficiency and multichannel capabilities. The primary obstacle to the merging of the worlds of UVRRS and fiber-optic spectroscopy is solarization, the process by which UV radiation causes opacity of fiber-optics (even quite pure silica fibers). This opacity impairs transmission, rendering standard fiber-optics useless for UVRRS.

Species of Interest

Pulsed lasers are typically utilized in the study of short-lived species. A laser pulse can be supplied to a molecular system with enough energy to redistribute the electrons in a molecule causing the formation of an excited state as illustrated on the right. The Raman spectrum of this excited state molecule can be studied either using the same laser pulse or a different pulse from a second laser (single color and two-color pulsed Raman). Excited states of interest can have lifetimes, from picoseconds to milliseconds, but the majority can be studied using gating in the order of 5ns. As the majority of excited states are generated using UV and visible lasers, photocathodes with high UV and visible Quantum Efficiencies (QEs) are typically suitable.

Schematic of pump-probe (two color) Raman

The simplest pulsed laser experiments are so-called single-color experiments where high irradiance laser pulses are used both to initiate the photoreaction, and then to Raman probe the transient species created within the pulse width. By opening the intensifier tube as shown on the right, only the Raman spectrum of the excited state will be recorded. This pulse/ICCD gate combination will be repeated and accumulated hundreds to thousands of times in order to achieve a good overall signal-to-noise ratio with high dynamic range.

In Time Resolved Resonance Raman (TR3) spectroscopy, pairs of laser pulses of different wavelength are used to photolyse (optically “pump”) and then to Raman probe the transient species of interest. The spectral window of the spectrograph/detector is chosen so that it corresponds to the frequency range of the Raman scattering from the probe laser.

Pulsed two color Raman layout with delays under the control of a delay generator

In Time Resolved Resonance Raman (TR3) spectroscopy, pairs of laser pulses of different wavelength are used to photolyse (optically “pump”) and then to Raman probe the transient species of interest. The spectral window of the spectrograph/detector is chosen so that it corresponds to the frequency range of the Raman scattering from the probe laser.

The time evolution of the transient signal is monitored by recording a series of spectra at different delays after the photolysis event, i.e. at a series of time delays between the excitation and probe pulses. The ICCD camera or either of the lasers can supply the trigger. A delay generator is used to control the delays.

In Raman microscopy, a research grade optical microscope is coupled to the excitation laser and the spectrometer, thus producing a platform capable of obtaining both conventional images and in addition generating Raman Spectra from sample areas approaching the diffraction limit (~1 micron). Imaging and spectroscopy can be combined to generate “Raman cubes”, 3- dimensional data sets, yielding spectral information at every pixel of the 2D image.

A motorized xyz microscope stage can be used to automatically record spectral files, which will constitute the basis of Raman images, Raman maps or a set of Raman spectra recorded from preselected points. Specific software routines will allow the quick and easy reconstruction of these maps. The possibility of generating two-dimensional and three-dimensional images of a sample, using various special features, is an evident advantage over either traditional spectroscopy or microscopy.

Time delay sequences

The first ever Raman “instrument” was constructed in 1928. This instrument used monochromatized sunlight as a light source and a human eye as a detector. Raman instrumentation was developed (based around arc lamps and photographic plates) and soon became very popular up until the 1950s. Since these early days, Raman instrumentation has evolved markedly. Modern instrumentation typically consists of a laser, Rayleigh filter, a few lenses, a spectrograph and a detector (typically a CCD or ICCD).

Typical Continuous Wave (CW) Raman layout

One of the major advantages of dispersive Raman is that it offers the possibility to select the optimal laser excitation wavelength to permit the recording of the best Raman information. For example, wavelengths can be selected to offer the best resonance with the sample under investigation.

One might also need to tune wavelength to avoid fluorescence and thermal emission backgrounds. Nowadays, it is possible to use laser lines from UV, (down to 200nm) up to the infrared, (1.06μm Nd:YAG laser line), from microWatts up to several Watts.

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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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An obvious difference between certain compounds is their color. Thus, quinone is yellow; chlorophyll is green; the 2,4-dinitrophenylhydrazone derivatives of aldehydes and ketones range in color from bright yellow to deep red, depending on double bond conjugation; and aspirin is colorless. In this respect the human eye is functioning as a spectrometer analyzing the light reflected from the surface of a solid or passing through a liquid.

Although we see sunlight (or white light) as uniform or homogeneous in color, it is actually composed of a broad range of radiation wavelengths in the ultraviolet (UV), visible and infrared (IR) portions of the spectrum. As shown on the right, the component colors of the visible portion can be separated by passing sunlight through a prism, which acts to bend the light in differing degrees according to wavelength. Electromagnetic radiation such as visible light is commonly treated as a wave phenomenon, characterized by a wavelength or frequency. Wavelength is defined on the left below, as the distance between adjacent peaks (or troughs), and may be designated in meters, centimeters or nanometers (10^-9 meters). Frequency is the number of wave cycles that travel past a fixed point per unit of time, and is usually given in cycles per second, or hertz (Hz). Visible wavelengths cover a range from approximately 400 to 800 nm. The longest visible wavelength is red and the shortest is violet. Other common colors of the spectrum, in order of decreasing wavelength, may be remembered by the mnemonic: ROY G BIV. The wavelengths of what we perceive as particular colors in the visible portion of the spectrum are displayed and listed below. In horizontal diagrams, such as the one on the bottom left, wavelength will increase on moving from left to right. 

When white light passes through or is reflected by a colored substance, a characteristic portion of the mixed wavelengths is absorbed. The remaining light will then assume the complementary color to the wavelength(s) absorbed. This relationship is demonstrated by the color wheel shown on the right. Here, complementary colors are diametrically opposite each other. Thus, absorption of 420-430 nm light renders a substance yellow, and absorption of 500-520 nm light makes it red. Green is unique in that it can be created by absoption close to 400 nm as well as absorption near 800 nm.
Early humans valued colored pigments, and used them for decorative purposes. Many of these were inorganic minerals, but several important organic dyes were also known. These included the crimson pigment, kermesic acid, the blue dye, indigo, and the yellow saffron pigment, crocetin. A rare dibromo-indigo derivative, punicin, was used to color the robes of the royal and wealthy. The deep orange hydrocarbon carotene is widely distributed in plants, but is not sufficiently stable to be used as permanent pigment, other than for food coloring. A common feature of all these colored compounds, displayed below, is a system of extensively conjugated pi-electrons.

2. The Electromagnetic Spectrum

The visible spectrum constitutes but a small part of the total radiation spectrum. Most of the radiation that surrounds us cannot be seen, but can be detected by dedicated sensing instruments. This electromagnetic spectrum ranges from very short wavelengths (including gamma and x-rays) to very long wavelengths (including microwaves and broadcast radio waves). The following chart displays many of the important regions of this spectrum, and demonstrates the inverse relationship between wavelength and frequency (shown in the top equation below the chart).

The energy associated with a given segment of the spectrum is proportional to its frequency. The bottom equation describes this relationship, which provides the energy carried by a photon of a given wavelength of radiation.

To obtain specific frequency, wavelength and energy values use this calculator.

3. UV-Visible Absorption Spectra

To understand why some compounds are colored and others are not, and to determine the relationship of conjugation to color, we must make accurate measurements of light absorption at different wavelengths in and near the visible part of the spectrum. Commercial optical spectrometers enable such experiments to be conducted with ease, and usually survey both the near ultraviolet and visible portions of the spectrum.

The visible region of the spectrum comprises photon energies of 36 to 72 kcal/mole, and the near ultraviolet region, out to 200 nm, extends this energy range to 143 kcal/mole. Ultraviolet radiation having wavelengths less than 200 nm is difficult to handle, and is seldom used as a routine tool for structural analysis. Ultraviolet The visible region of the spectrum comprises photon energies of 36 to 72 kcal/mole, and the near ultraviolet region, out to 200 nm, extends this energy range to 143 kcal/mole. Ultraviolet radiation having wavelengths less than 200 nm is difficult to handle, and is seldom used as a routine tool for structural analysis.

The energies noted above are sufficient to promote or excite a molecular electron to a higher energy orbital. Consequently, absorption spectroscopy carried out in this region is sometimes called “electronic spectroscopy”. A diagram showing the various kinds of electronic excitation that may occur in organic molecules is shown on the left. Of the six transitions outlined, only the two lowest energy ones (left-most, colored blue) are achieved by the energies available in the 200 to 800 nm spectrum. As a rule, energetically favored electron promotion will be from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO), and the resulting species is called an excited state. For a review of molecular orbitals click here.
When sample molecules are exposed to light having an energy that matches a possible electronic transition within the molecule, some of the light energy will be absorbed as the electron is promoted to a higher energy orbital. An optical spectrometer records the wavelengths at which absorption occurs, together with the degree of absorption at each wavelength. The resulting spectrum is presented as a graph of absorbance (A) versus wavelength, as in the isoprene spectrum shown below. Since isoprene is colorless, it does not absorb in the visible part of the spectrum and this region is not displayed on the graph. Absorbance usually ranges from 0 (no absorption) to 2 (99% absorption), and is precisely defined in context with spectrometer operation.

Because the absorbance of a sample will be proportional to the number of absorbing molecules in the spectrometer light beam (e.g. their molar concentration in the sample tube), it is necessary to correct the absorbance value for this and other operational factors if the spectra of different compounds are to be compared in a meaningful way. The corrected absorption value is called “molar absorptivity”, and is particularly useful when comparing the spectra of different compounds and determining the relative strength of light absorbing functions (chromophores). Molar absorptivity (ε) is defined as:

If the isoprene spectrum on the right was obtained from a dilute hexane solution (c = 4 * 10^-5 moles per liter) in a 1 cm sample cuvette, a simple calculation using the above formula indicates a molar absorptivity of 20,000 at the maximum absorption wavelength. Indeed the entire vertical absorbance scale may be changed to a molar absorptivity scale once this information about the sample is in hand. Clicking on the spectrum will display this change in units.

From the chart above it should be clear that the only molecular moieties likely to absorb light in the 200 to 800 nm region are pi-electron functions and hetero atoms having non-bonding valence-shell electron pairs. Such light absorbing groups are referred to as chromophores. A list of some simple chromophores and their light absorption characteristics is provided on the left above. The oxygen non-bonding electrons in alcohols and ethers do not give rise to absorption above 160 nm. Consequently, pure alcohol and ether solvents may be used for spectroscopic studies.
The presence of chromophores in a molecule is best documented by UV-Visible spectroscopy, but the failure of most instruments to provide absorption data for wavelengths below 200 nm makes the detection of isolated chromophores problematic. Fortunately, conjugation generally moves the absorption maxima to longer wavelengths, as in the case of isoprene, so conjugation becomes the major structural feature identified by this technique.
Molar absorptivities may be very large for strongly absorbing chromophores (>10,000) and very small if absorption is weak (10 to 100). The magnitude ofε reflects both the size of the chromophore and the probability that light of a given wavelength will be absorbed when it strikes the chromophore.

4. The Importance of Conjugation

A comparison of the absorption spectrum of 1-pentene, λ_max = 178 nm, with that of isoprene (above) clearly demonstrates the importance of chromophore conjugation. Further evidence of this effect is shown below. The spectrum on the left illustrates that conjugation of double and triple bonds also shifts the absorption maximum to longer wavelengths. From the polyene spectra displayed in the center diagram, it is clear that each additional double bond in the conjugated pi-electron system shifts the absorption maximum about 30 nm in the same direction. Also, the molar absorptivity (ε) roughly doubles with each new conjugated double bond. Spectroscopists use the terms defined in the table on the right when describing shifts in absorption. Thus, extending conjugation generally results in bathochromic and hyperchromic shifts in absorption.
The appearance of several absorption peaks or shoulders for a given chromophore is common for highly conjugated systems, and is often solvent dependent. This fine structure reflects not only the different conformations such systems may assume, but also electronic transitions between the different vibrational energy levels possible for each electronic state. Vibrational fine structure of this kind is most pronounced in vapor phase spectra, and is increasingly broadened and obscured in solution as the solvent is changed from hexane to methanol.

To understand why conjugation should cause bathochromic shifts in the absorption maxima of chromophores, we need to look at the relative energy levels of the pi-orbitals. When two double bonds are conjugated, the four p-atomic orbitals combine to generate four pi-molecular orbitals (two are bonding and two are antibonding). This was described earlier in the section concerning diene chemistry. In a similar manner, the three double bonds of a conjugated triene create six pi-molecular orbitals, half bonding and half antibonding. The energetically most favorable π  ^__> π* excitation occurs from the highest energy bonding pi-orbital (HOMO) to the lowest energy antibonding pi-orbital (LUMO). 
The following diagram illustrates this excitation for an isolated double bond (only two pi-orbitals) and, on clicking the diagram, for a conjugated diene and triene. In each case the HOMO is colored blue and the LUMO is colored magenta. Increased conjugation brings the HOMO and LUMO orbitals closer together. The energy (ΔE) required to effect the electron promotion is therefore less, and the wavelength that provides this energy is increased correspondingly (remember   λ = h • c/ΔE ).

Many other kinds of conjugated pi-electron systems act as chromophores and absorb light in the 200 to 800 nm region. These include unsaturated aldehydes and ketones and aromatic ring compounds. A few examples are displayed below. The spectrum of the unsaturated ketone (on the left) illustrates the advantage of a logarithmic display of molar absorptivity. The π ^__> π* absorption located at 242 nm is very strong, with an ε = 18,000. The weak n ^__> π* absorption near 300 nm has an ε = 100.

Benzene exhibits very strong light absorption near 180 nm (ε > 65,000) , weaker absorption at 200 nm (ε = 8,000) and a group of much weaker bands at 254 nm (ε = 240). Only the last group of absorptions are completely displayed because of the 200 nm cut-off characteristic of most spectrophotometers. The added conjugation in naphthalene, anthracene and tetracene causes bathochromic shifts of these absorption bands, as displayed in the chart on the left below. All the absorptions do not shift by the same amount, so for anthracene (green shaded box) and tetracene (blue shaded box) the weak absorption is obscured by stronger bands that have experienced a greater red shift. As might be expected from their spectra, naphthalene and anthracene are colorless, but tetracene is orange.

The spectrum of the bicyclic diene (above right) shows some vibrational fine structure, but in general is similar in appearance to that of isoprene, shown above. Closer inspection discloses that the absorption maximum of the more highly substituted diene has moved to a longer wavelength by about 15 nm. This “substituent effect” is general for dienes and trienes, and is even more pronounced for enone chromophores.