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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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The Scanning Electron Microscope (SEM) produces images by probing the specimen with a focused electron beam that is scanned across a rectangular area of the specimen (raster scanning).

There are two families of electron guns:

• Conventional thermionic emitters such as Tungsten (W) or Lanthanum hexaboride (LaB6) tipped filaments.
• Tungsten field emission gun (FEG) , warm or Cold FEG. A pointed emitter is held at several kilovolts (2000-7000 V) so that there is sufficient potential at the emitter surface to cause field electron emission.

Field emission gun (FEG) is used to produce an electron beam that is smaller in diameter, more coherent and up to three orders of magnitude greater current density or brightness.

scrollable

Energy of electrons is depending of Voltage: 1 Kev to 50KeV

Current (A): Number of electrons /unit of time

1 amp = 1 coulomb/sec 1 coulomb ~ 6 x10¹⁸ electrons

Example if the current measured at sample is around 10^-9A to 10^-12 A then the number of electrons is around 6X10⁶ to 6X10⁹ electrons/sec.

Environmental Scanning Electron Microscope (ESEM)

ESEM is a variety of SEM called environmental scanning electron microscope. It can produce images of sufficient quality and resolution with the samples being wet or contained in low vacuum or gas. This greatly facilitates imaging biological samples that are unstable in the high vacuum of conventional electron microscopes. The major disadvantage of transmission electron microscope is the need for extremely thin sections of the specimens, typically about 100 nanometers. Biological specimens are typically required to be chemically fixed, dehydrated and embedded in a polymer resin to stabilize them sufficiently to allow ultrathin sectioning. Sections of biological specimens, organic polymers and similar materials may require special treatment with heavy atom labels in order to achieve the required image contrast.

ESEM is especially useful for non-metallic, uncoated and biological materials. The presence of gas, mainly Argon, around a sample permits to work with pressure greater than 500 Pa compared to conventional SEM requirements samples under vacuum about 10-3 to 10-4 Pa. This vacuum level creates the possibility to operate on non-conductive samples without any preparation or hydrated specimens without charging.

Transmission Electron Microscope (TEM)

In a Transmission Electron Microscope (TEM), the electron beam is accelerated by an anode typically at +100 keV (40 to 400 keV) with respect to the cathode, focused by electrostatic and electromagnetic lenses, and transmitted through the specimen that is in part transparent to electrons and in part scatters them out of the beam. When it emerges from the specimen, the electron beam carries information about the structure of the specimen that is magnified by the objective lens system of the microscope.

The spatial variation in this information (the “image”) may be viewed by projecting the magnified electron image onto a fluorescent viewing screen coated with a phosphor or scintillator material such as zinc sulfide. Alternatively, the image can be photographically recorded by exposing a photographic film or plate directly to the electron beam, or a high-resolution phosphor may be coupled by means of a lens optical system or a fiber optic light-guide to the sensor of a digital camera. The image detected by the digital camera may be displayed on a monitor or computer.

A transmission electron microscope can achieve better than 50 pm resolution and magnifications of up to about 10,000,000x whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000x. Generally, the image resolution of an SEM is at least an order of magnitude poorer than that of a TEM. However, because the SEM image relies on surface processes rather than transmission, it is able to image bulk samples up to many centimeters in size and (depending on instrument design and settings) has a great depth of field, and so can produce images that are good representations of the three dimensional shape of the sample.

The Scanning Transmission Electron Microscope (STEM) rasters a focused incident probe across a specimen that (as with the TEM) has been thinned to facilitate detection of electrons scattered through the specimen. The high resolution of the TEM is thus possible in STEM. The focusing action (and aberrations) occurs before the electrons hit the specimen in the STEM, but afterward in the TEM.

Focused ion beam (FIB)

Focused ion beam, also known as FIB, is a technique used particularly in the semiconductor industry, materials science and increasingly in the biological field for site-specific analysis, deposition, and ablation of materials. A FIB setup is a scientific instrument that resembles a scanning electron microscope (SEM). However, while the SEM uses a focused beam of electrons to image the sample in the chamber, a FIB setup uses a focused beam of ions instead. Unlike an electron microscope, FIB is inherently destructive to the specimen.

When the high-energy gallium ions strike the sample, they will sputter atoms from the surface. Gallium atoms will also be implanted into the top few nanometers of the surface, and the surface will be made amorphous. A FIB-SEM consists in a system with both electron and ion beam columns, allowing the same feature to be investigated using either of the beams. A FIB-SEM system uses a beam of Ga+ ion to mill into the surface to locate a feature or defect of interest. The integrated SEM then uses a focused beam of electrons to image the sample in the chamber.

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Infrared (IR) spectroscopy is based on molecular vibrations caused by the oscillation of molecular dipoles. Bonds have characteristic vibrations depending on the atoms in the bond, the number of bonds and the orientation of those bonds with respect to the rest of the molecule. Thus, different molecules have specific spectra that can be collected for use in distinguishing products or identifying an unknown substance (to an extent.)

Collecting spectra through this method goes about one of three general ways. Nujol mulls and pressed pellets are typically used for collecting spectra of solids, while thin-film cells are used for solution-phase IR spectroscopy. Spectra of gases can also be obtained but will not be discussed in this guide.

Infrared Optical Materials and Handling

While it is all well and wonderful that substances can be characterized in this fashion one still has to be able to hold the substances inside of the instrument and properly prepare the samples. In an infrared spectrometer (Figure 4.2.14.2.1)

the sample to be analyzed is held in front of an infrared laser beam, in order to do this, the sample must be contained in something, consequently this means that the very container the sample is in will absorb some of the infrared beam.

This is made somewhat complicated by the fact that all materials have some sort of vibration associated with them. Thus, if the sample holder has an optical window made of something that absorbs near where your sample does, the sample might not be distinguishable from the optical window of the sample holder. The range that is not blocked by a strong absorbance is known as a window (not to be confused with the optical materials of the cell.)

Windows are an important factor to consider when choosing the method to perform an analysis, as seen in Table 4.2.14.2.1 there are a number of different materials each with their own characteristic absorption spectra and chemical properties. Keep these factors in mind when performing analyses and precious sample will be saved. For most organic compounds NaCl works well though it is susceptible to attack from moisture. For metal coordination complexes KBr, or CsI typically work well due to their large windows. If money is not a problem then diamond or sapphire can be used for plates.

Proper handling of these plates will ensure they have a long, useful life. Here follows a few simple pointers on how to handle plates:

• Avoid contact with solvents that the plates are soluble in.
• Keep the plates in a dessicator, the less water the better, even if the plates are insoluble to water.
• Handle with gloves, clean gloves.
• Avoid wiping the plates to prevent scratching.

That said, these simple guidelines will likely reduce most damage that can occur to a plate by simply holding it other faults such as dropping the plate from a sufficient height can result in more serious damage.

Preparation of Nujol Mulls

A common method of preparing solid samples for IR analysis is mulling. The principle here is by grinding the particles to below the wavelength of incident radiation that will be passing through there should be limited scattering. To suspend those tiny particles, an oil, often referred to as Nujol is used. IR-transparent salt plates are used to hold the sample in front of the beam in order to acquire data. To prepare a sample for IR analysis using a salt plate, first decide what segment of the frequency band should be studied, refer to Table 4.2.14.2.1 for the materials best suited for the sample. Figure 4.2.24.2.2 shows the materials needed for preparing a mull.

Preparing the mull is performed by taking a small portion of sample and adding approximately 10% of the sample volume worth of the oil and grinding this in an agate mortar and pestle as demonstrated in Figure 4.2.34.2.3 . The resulting mull should be transparent with no visible particles.

Another method involves dissolving the solid in a solvent and allowing it to dry in the agate pestle. If using this method ensure that all of the solvent has evaporated since the solvent bands will appear in the spectrum. Some gentle heating may assist this process. This method creates very fine particles that are of a relatively consistent size. After addition of the oil further mixing (or grinding) may be necessary.

Plates should be stored in a desiccator to prevent erosion by atmospheric moisture and should appear roughly transparent. Some materials such as silicon will not, however. Gently rinse the plates with hexanes to wash any residual material off of the plates. Removing the plates from the desiccator and cleaning them should follow the preparation of the mull in order to maintain the integrity of the salt plates. Of course, if the plate is not soluble in water then it is still a good idea just to prevent the threat of mechanical trauma or a stray jet of acetone from a wash bottle.

Once the mull has been prepared, add a drop to one IR plate (Figure 4.2.44.2.4 ), place the second plate on top of the drop and give it a quarter turn in order to evenly coat the plate surface as seen in Figure 4.2.54.2.5 . Place it into the spectrometer and acquire the desired data.

Always handle with gloves and preferably away from any sinks, faucets, or other sources of running or spraying water.

Spectra acquired by this method will have strong C-H absorption bands throughout several ranges 3,000 – 2,800 cm^-1 and 1,500 – 1,300 cm^-1 and may obscure signal.

Cleaning the plate is performed as previously mentioned with hexanes or chloroform can easily be performed by rinsing and leaving them to dry in the hood. Place the salt plates back into the desiccator as soon as reasonably possible to prevent damage. It is highly advisable to polish the plates after use, no scratches, fogging, or pits should be visible on the face of the plate. Chips, so long as they don’t cross the center of the plate are survivable but not desired. The samples of damaged salt plates in Figure 4.2.64.2.6 show common problems associated with use or potentially mishandling. Clouding, and to an extent, scratches can be polished out with an iron rouge. Areas where the crystal lattice is disturbed below the surface are impossible to fix and chips cannot be reattached.

FIgure 4.2.64.2.6 A series of plates indicating various forms of physical damage with a comparison to a good plate (Copyright: Colorado University-Boulder).

Preparation of Pellets

In an alternate method, this technique is along the same lines of the nujol mull except instead of the suspending medium being mineral oil, the suspending medium is a salt. The solid is ground into a fine powder with an agate mortar and pestle with an amount of the suspending salt. Preparing pellets with diamond for the suspending agent is somewhat illadvised considering the great hardness of the substance. Generally speaking, an amount of KBr or CsI is used for this method since they are both soft salts. Two approaches can be used to prepare pellets, one is somewhat more expensive but both usually yield decent results.

The first method is the use of a press. The salt is placed into a cylindrical holder and pressed together with a ram such as the one seen in (Figure 4.2.74.2.7 ). Afterwards, the pellet, in the holder, is placed into the instrument and spectra acquired.

An alternate, and cheaper method requires the use of a large hex nut with a 0.5 inch inner diameter, two bolts, and two wrenches such as the kit seen in Figure 4.2.84.2.8 . Step-by-step instructions for loading and using the press follows:

1. Screw one of the bolts into the nut about half way.
2. Place the salt pellet mixture into the other opening of the nut and level by tapping the assembly on a countertop.
3. Screw in the second bolt and place the assembly on its side with the bolts parallel to the countertop. Place one of the wrenches on the bolt on the right side with the handle aiming towards yourself.
4. Take the second wrench and place it on the other bolt so that it attaches with an angle from the table of about 45 degrees.
5. The second bolt is tightened with a body weight and left to rest for several minutes. Afterwards, the bolts are removed, and the sample placed into the instrument.

Some pellet presses also have a vacuum barb such as the one seen in (Figure 4.2.84.2.8 . If your pellet press has one of these, consider using it as it will help remove air from the salt pellet as it is pressed. This ensures a more uniform pellet and removes absorbances in the collected spectrum due to air trapped in the pellet.

Preparation of Solution Cells

Solution cells (Figure 4.2.94.2.9 ) are a handy way of acquiring infrared spectra of compounds in solution and is particularly handy for monitoring reactions.

A thin-film cell consists of two salt plates with a very thin space in between them (Figure 4.2.104.2.10 ). Two channels allow liquid to be injected and then subsequently removed. The windows on these cells can be made from a variety of IR optical materials. One particularly useful one for water-based solutions is CaF₂ as it is not soluble in water.

Cleaning these cells can be performed by removing the solution, flushing with fresh solvent and gently removing the solvent by syringe. Do not blow air or nitrogen through the ports as this can cause mechanical deformation in the salt window if the pressure is high enough.

Deuterated Solvent Effects

One of the other aspects to solution-phase IR is that the solvent utilized in the cell has a characteristic absorption spectra. In some cases this can be alleviated by replacing the solvent with its deuterated sibling. The benefit here is that C-H bonds are now C-D bonds and have lower vibrational frequencies. Compiled in Figure 4.2.114.2.11 is a set of common solvents.

This effect has numerous benefits and is often applied to determining what vibrations correspond to what bond in a given molecular sample. This is often accomplished by using isotopically labeled “heavy” reagents such as ones that contain ²H, ¹⁵N, ¹⁸O, or ¹³C.

Basic Troubleshooting

There are numerous problems that can arise from improperly prepared samples, this section will go through some of the common problems and how to correct them. For this demonstration, spectra of ferrocene will be used. The molecular structure and a photograph of the brightly colored organometallic compound are shown in Figure 4.2.124.2.12 and Figure 4.2.134.2.13 .

Figure 4.2.144.2.14 illustrates what a good sample of ferrocene looks like prepared in a KBr pellet. The peaks are well defined and sharp. No peak is flattened at 0% transmittance and Christiansen scattering is not evident in the baseline.

Figure 4.2.154.2.15 illustrates a sample with some peaks with intensities that are saturated and lose resolution making peak-picking difficult. In order to correct for this problem, scrape some of the sample off of the salt plate with a rubber spatula and reseat the opposite plate. By applying a thinner layer of sample one can improve the resolution of strongly absorbing vibrations.

Figure 4.2.164.2.16 illustrates a sample in which too much mineral oil was added to the mull so that the C-H bonds are far more intense than the actual sample. This can be remedied by removing the sample from the plate, grinding more sample and adding a smaller amount of the mull to the plate. Another possible way of doing this is if the sample is insoluble in hexanes, add a little to the mull and wick away the hexane-oil mixture to leave a dry solid sample. Apply a small portion of oil and replate.

Figure 4.2.174.2.17 illustrates the result of particles being too large and scattering light. To remedy this, remove the mull and grind further or else use the solvent deposition technique described earlier.

Characteristic IR Vibrational Modes for Hydrocarbon Compounds

Table4.2.34.2.3 The stretching bands for alkenes.

Fourier Transform Infrared Spectroscopy of Metal Ligand Complexes

The infrared (IR) range of the electromagnetic spectrum is usually divided into three regions:

• The far-infrared is always used for rotational spectroscopy, with wavenumber range 400 – 10 cm⁻¹ and lower energy.
• The mid-infrared is suitable for a detection of the fundamental vibrations and associated rotational-vibrational structure with the frequency range approximately 4000 – 400 cm⁻¹.
• The near-Infrared with higher energy and wave number range 14000 – 4000 cm⁻¹, can excite overtone or higher harmonic vibrations.

For classical light material interaction theory, if a molecule can interact with an electromagnetic field and absorb a photon of certain frequency, the transient dipole of molecular functional group must oscillate at that frequency. Correspondingly, this transition dipole moment must be a non-zero value, however, some special vibration can be IR inactive for the stretching motion of a homonuclear diatomic molecule and vibrations do not affect the molecule’s dipole moment (e.g., N₂).

Mechanistic Description of the Vibrations of Polyatomic Molecules

A molecule can vibrate in many ways, and each way is called a “vibrational mode”. If a molecule has N atoms, linear molecules have 3N-5 degrees of vibrational modes whereas nonlinear molecules have 3N-6 degrees of vibrational modes. Take H₂O for example; a single molecule of H₂O has O-H bending mode (Figure 4.2.184.2.18 a), antisymmetric stretching mode (Figure 4.2.184.2.18 b), and symmetric stretching mode (Figure 4.2.184.2.18 c).

If a diatomic molecule has a harmonic vibration with the energy, 4.2.14.2.1 , where n+¹/₂ with n = 0, 1, 2 …). The motion of the atoms can be determined by the force equation, 4.2.24.2.2 , where k is the force constant). The vibration frequency can be described by 4.2.34.2.3 . In which m is actually the reduced mass (m_red or μ), which is determined from the mass m₁ and m₂ of the two atoms, 4.2.44.2.4 .En = −hv(4.2.1)(4.2.1)En = −hvF = −kx(4.2.2)(4.2.2)F = −kxω = (k/m)1/2(4.2.3)(4.2.3)ω = (k/m)1/2mred = μ = m1m2m1 + m2(4.2.4)(4.2.4)mred = μ = m1m2m1 + m2

Principle of Absorption Bands

In IR spectrum, absorption information is generally presented in the form of both wavenumber and absorption intensity or percent transmittance. The spectrum is generally showing wavenumber (cm^-1) as the x-axis and absorption intensity or percent transmittance as the y-axis.

Transmittance, “T”, is the ratio of radiant power transmitted by the sample (I) to the radiant power incident on the sample (I₀). Absorbance (A) is the logarithm to the base 10 of the reciprocal of the transmittance (T). The absorption intensity of molecule vibration can be determined by the Lambert-Beer Law, \label{5} . In this equation, the transmittance spectra ranges from 0 to 100%, and it can provide clear contrast between intensities of strong and weak bands. Absorbance ranges from infinity to zero. The absorption of molecules can be determined by several components. In the absorption equation, ε is called molar extinction coefficient, which is related to the molecule behavior itself, mainly the transition dipole moment, c is the concentration of the sample, and l is the sample length. Line width can be determined by the interaction with surroundings.A = log(1/T) = −log(I/I0) = εcl(4.2.5)(4.2.5)A = log(1/T) = −log(I/I0) = εcl

The Infrared Spectrometer

As shown in Figure 4.2.194.2.19 , there are mainly four parts for fourier transform infrared spectrometer (FTIR):

• Light source. Infrared energy is emitted from a glowing black-body source as continuous radiations.
• Interferometer. It contains the interferometer, the beam splitter, the fixed mirror and the moving mirror. The beam splittertakes the incoming infrared beam and divides it into two optical beams. One beam reflects off the fixed mirror. The other beam reflects off of the moving mirror which moves a very short distance. After the divided beams are reflected from the two mirrors, they meet each other again at the beam splitter. Therefore, an interference pattern is generated by the changes in the relative position of the moving mirror to the fixed mirror. The resulting beam then passes through the sample and is eventually focused on the detector.
• Sample compartment. It is the place where the beam is transmitted through the sample. In the sample compartment, specific frequencies of energy are absorbed.
• Detector. The beam finally passes to the detector for final measurement. The two most popular detectors for a FTIR spectrometer are deuterated triglycine sulfate (pyroelectric detector) and mercury cadmium telluride (photon or quantum detector). The measured signal is sent to the computer where the Fourier transformation takes place.

A Typical Application: the detection of metal ligand complexes

Some General Absorption peaks for common types of functional groups

It is well known that all molecules chemicals have distinct absorption regions in the IR spectrum. Table 4.2.74.2.7 shows the absorption frequencies of common types of functional groups. For systematic evaluation, the IR spectrum is commonly divided into some sub-regions.

• In the region of 4000 – 2000 cm^–1, the appearance of absorption bands usually comes from stretching vibrations between hydrogen and other atoms. The O-H and N-H stretching frequencies range from 3700 – 3000 cm^–1. If hydrogen bond forms between O-H and other group, it generally caused peak line shape broadening and shifting to lower frequencies. The C-H stretching bands occur in the region of 3300 – 2800 cm^–1. The acetylenic C-H exhibits strong absorption at around 3300 cm^–1. Alkene and aromatic C-H stretch vibrations absorb at 3200-3000 cm^–1. Generally, asymmetric vibrational stretch frequency of alkene C-H is around 3150 cm^-1, and symmetric vibrational stretch frequency is between 3100 cm^-1 and 3000 cm^-1. The saturated aliphatic C-H stretching bands range from 3000 – 2850 cm^–1, with absorption intensities that are proportional to the number of C-H bonds. Aldehydes often show two sharp C-H stretching absorption bands at 2900 – 2700 cm^–1. However, in water solution, C-H vibrational stretch is much lower than in non-polar solution. It means that the strong polarity solution can greatly reduce the transition dipole moment of C-H vibration.
• Furthermore, the stretching vibrations frequencies between hydrogen and other heteroatoms are between 2600 – 2000cm^-1, for example, S-H at 2600 – 2550 cm^–1, P-H at 2440 – 2275 cm^–1, Si-H at 2250 – 2100 cm^–1.
• The absorption bands at the 2300 – 1850 cm^–1 region usually present only from triple bonds, such as C≡C at 2260 – 2100 cm^–1, C≡N at 2260 – 2000 cm^–1, diazonium salts –N≡N at approximately 2260 cm^–1, allenes C=C=C at 2000 – 1900 cm^–1. The peaks of these groups are all have strong absorption intensities. The 1950 – 1450 cm^–1 region stands for double-bonded functional groups vibrational stretching.
• Most carbonyl C=O stretching bands range from 1870 – 1550 cm^–1, and the peak intensities are from mean to strong. Conjugation, ring size, hydrogen bonding, and steric and electronic effects can lead to significant shifts in absorption frequencies. Furthermore, if carbonyl links with electron-withdrawing group, such as acid chlorides and acid anhydrides, it would give rise to IR bands at 1850 – 1750 cm^–1. Ketones usually display stretching bands at 1715 cm^-1.
• None conjugated aliphatic C=C and C=N have absorption bands at 1690 – 1620 cm^–1. Besides, around 1430 and 1370cm^-1, there are two identical peaks presenting C-H bending.
• The region from 1300 – 910 cm^–1 always includes the contributions from skeleton C-O and C-C vibrational stretches, giving additional molecular structural information correlated with higher frequency areas. For example, ethyl acetate not only shows its carbonyl stretch at 1750 – 1735 cm^–1, but also exhibits its identical absorption peaks at 1300 – 1000 cm^–1 from the skeleton vibration of C-O and C-C stretches.

General Introduction of Metal Ligand Complex

The metal electrons fill into the molecular orbital of ligands (CN, CO, etc.) to form complex compound. As shown in Figure 4.2.204.2.20 , a simple molecular orbital diagram for CO can be used to explain the binding mechanism.

The CO and metal can bind with three ways:

• Donation of a pair of electrons from the C-O σ* orbital into an empty metal orbital (Figure 4.2.214.2.21 a).
• Donation from a metal d orbital into the C-O π* orbital to form a M-to-CO π-back bond (Figure 4.2.214.2.21 b).
• Under some conditions a pair of carbon π electron can donate into an empty metal d-orbital.

Some Factors to Include the Band Shifts and Strength

Herein, we mainly consider two properties: ligand stretch frequency and their absorption intensity. Take the ligand CO for example again. The frequency shift of the carbonyl peaks in the IR mainly depends on the bonding mode of the CO (terminal or bridging) and electron density on the metal. The intensity and peak numbers of the carbonyl bands depends on some factors: CO ligands numbers, geometry of the metal ligand complex and fermi resonance.

Effect on Electron Density on Metal

As shown in Table 4.2.84.2.8 , a greater charge on the metal center result in the CO stretches vibration frequency decreasing. For example, [Ag(CO)]+show higher frequency of CO than free CO, which indicates a strengthening o

f the CO bond. σ donation removes electron density from the nonbonding HOMO of CO. From Figure, it is clear that the HOMO has a small amount of anti-bonding property, so removal of an electron actually increases (slightly) the CO bond strength. Therefore, the effect of charge and electronegativity depends on the amount of metal to CO π-back bonding and the CO IR stretching frequency.

If the electron density on a metal center is increasing, more π-back bonding to the CO ligand(s) will also increase, as shown in Table 4.2.94.2.9 . It means more electron density would enter into the empty carbonyl π* orbital and weaken the C-O bond. Therefore, it makes the M-CO bond strength increasing and more double-bond-like (M=C=O).

Ligation Donation Effect

Some cases, as shown in Table 4.2.94.2.9 , different ligands would bind with same metal at the same metal-ligand complex. For example, if different electron density groups bind with Mo(CO)₃ as the same form, as shown in Figure 4.2.224.2.22 , the CO vibrational frequencies would depend on the ligand donation effect. Compared with the PPh₃ group, CO stretching frequency which the complex binds the PF₃ group (2090, 2055 cm^-1) is higher. It indicates that the absolute amount of electron density on that metal may have certain effect on the ability of the ligands on a metal to donate electron density to the metal center. Hence, it may be explained by the Ligand donation effect. Ligands that are trans to a carbonyl can have a large effect on the ability of the CO ligand to effectively π-backbond to the metal. For example, two trans π-backbonding ligands will partially compete for the same d-orbital electron density, weakening each other’s net M-L π-backbonding. If the transligand is a π-donating ligand, the free metal to CO π-backbonding can increase the M-CO bond strength (more M=C=O character). It is well known that pyridine and amines are not those strong π-donors. However, they are even worse π-backbonding ligands. So the CO is actually easy for π-back donation without any competition. Therefore, it naturally reduces the CO IR stretching frequencies in metal carbonyl complexes for the ligand donation effect.

Geometry Effects

Some cases, metal-ligand complex can form not only terminal but also bridging geometry. As shown in Figure 4.2.234.2.23 , in the compound Fe₂(CO)₇(dipy), CO can act as a bridging ligand. Evidence for a bridging mode of coordination can be easily obtained through IR spectroscopy. All the metal atoms bridged by a carbonyl can donate electron density into the π* orbital of the CO and weaken the CO bond, lowering vibration frequency of CO. In this example, the CO frequency in terminal is around 2080 cm^-1, and in bridge, it shifts to around 1850 cm^-1.

Pump-probe Detection of Molecular Functional Group Vibrational Lifetime

The dynamics of molecular functional group plays an important role during a chemical process, chemical bond forming and breaking, energy transfer and other dynamics happens within picoseconds domain. It is very difficult to study such fast processes directly, for decades scientists can only learn from theoretical calculations, lacking experimental methods.

However, with the development of ultrashort pulsed laser enable experimental study of molecular functional group dynamics. With ultrafast laser technologies, people develop a series of measuring methods, among which, pump-probe technique is widely used to study the molecular functional group dynamics. Here we concentrate on how to use pump-probe experiment to measure functional group vibrational lifetime. The principle, experimental setup and data analysis will be introduced.

Principles of the Pump-probe Technique

For every function group within a molecule, such as the C≡N triple bond in phenyl selenocyanate (C₆H₅SeCN) or the C-D single bond in deuterated chloroform (DCCl₃), they have an individual infrared vibrational mode and associated energy levels. For a typical 3-level system (Figure 4.2.244.2.24 , both the 0 to 1 and the 1 to 2 transition are near the probe pulse frequency (they don’t necessarily need to have exactly the same frequency).

In a pump-probe experiment, we use the geometry as is shown in Figure 4.2.254.2.25 . Two synchronized laser beams, one of which is called pump beam (E_pu) while the other probe beam (E_pr). There is a delay in time between each pulse. The laser pulses hit the sample, the intensity of ultrafast laser (fs or ps) is strong enough to generated 3^rd order polarization and produce 3^rd order optical response signal which is use to give dynamics information of molecular function groups. For the total response signals we have \label{6} , where µ₁₀ µ₂₁ are transition dipole moment and E₀, E₁, and E₂ are the energies of the three levels, and t₃ is the time delay between pump and probe beam. The delay t₃ is varied and the response signal intensity is measured. The functional group vibration life time is determined from the data.

S = 4μ410e−i(E1−E0)t3/h−Γt3(4.2.6)(4.2.6)S = 4μ104e−i(E1−E0)t3/h−Γt3

Typical Experimental Set-up

The optical layout of a typical pump-probe setup is schematically displayed in Figure 4.2.264.2.26 . In the setup, the output of the oscillator (500 mW at 77 MHz repetition rate, 40 nm bandwidth centered at 800 nm) is split into two beams (1:4 power ratio). Of this, 20% of the power is to seed a femtosecond (fs) amplifier whose output is 40 fs pulses centered at 800 nm with power of ~3.4 W at 1 KHz repetition rate. The rest (80%) of the seed goes through a bandpass filter centered at 797.5nm with a width of 0.40 nm to seed a picosecond (ps) amplifier. The power of the stretched seed before entering the ps amplifier cavity is only ~3 mW. The output of the ps amplifier is 1ps pulses centered at 800 nm with a bandwidth ~0.6 nm. The power of the ps amplifier output is ~3 W. The fs amplifier is then to pump an optical parametric amplifier (OPA) which produces ~100 fs IR pulses with bandwidth of ~200 cm^-1 that is tunable from 900 to 4000 cm^-1. The power of the fs IR pulses is 7~40 mW, depending on the frequencies. The ps amplifier is to pump a ps OPA which produces ~900 fs IR pulses with bandwidth of ~21 cm^-1, tunable from 900 – 4000 cm^-1. The power of the fs IR pulses is 10 ~ 40 mW, depending on frequencies.

In a typical pump-probe setup, the ps IR beam is collimated and used as the pump beam. Approximately 1% of the fs IR OPA output is used as the probe beam whose intensity is further modified by a polarizer placed before the sample. Another polarizer is placed after the sample and before the spectrograph to select different polarizations of the signal. The signal is then sent into a spectrograph to resolve frequency, and detected with a mercury cadmium telluride (MCT) dual array detector. Use of a pump pulse (femtosecond, wide band) and a probe pulse (picoseconds, narrow band), scanning the delay time and reading the data from the spectrometer, will give the lifetime of the functional group. The wide band pump and spectrometer described here is for collecting multiple group of pump-probe combination.

Data Analysis

For a typical pump-probe curve shown in Figure 4.2.274.2.27 life time t is defined as the corresponding time value to the half intensity as time zero.

Table 4.2.104.2.10 shows the pump-probe data of the C≡N triple bond in a series of aromatic cyano compounds: n-propyl cyanide (C₃H₇CN), ethyl thiocyanate (C₂H₅SCN), and ethyl selenocyanate (C₂H₅SeCN) for which the ν_C≡N for each compound (measured in CCl₄ solution) is 2252 cm^-1), 2156 cm^-1, and ~2155 cm^-1, respectively.

A plot of intensity versus time for the data from TABLE is shown Figure 4.2.284.2.28 . From these curves the C≡N stretch lifetimes can be determined for C₃H₇CN, C₂H₅SCN, and C₂H₅SeCN as ~5.5 ps, ~84 ps, and ~282 ps, respectively.

From what is shown above, the pump-probe method is used in detecting C≡N vibrational lifetimes in different chemicals. One measurement only takes several second to get all the data and the lifetime, showing that pump-probe method is a powerful way to measure functional group vibrational lifetime.

Attenuated Total Reflectace- Fourier Transform Infrared Spectroscopy

Attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) is a physical method of compositional analysis that builds upon traditional transmission FTIR spectroscopy to minimize sample preparation and optimize reproducibility. Condensed phase samples of relatively low refractive index are placed in close contact with a crystal of high refractive index and the infrared (IR) absorption spectrum of the sample can be collected. Based on total internal reflection, the absorption spectra of ATR resemble those of transmission FTIR. To learn more about transmission IR spectroscopy (FTIR) please refer to the section further up this page titled Fourier Transform Infrared Spectroscopy of Metal Ligand Complexes.

First publicly proposed in 1959 by Jacques Fahrenfort from the Royal Dutch Shell laboratories in Amsterdam, ATR IR spectroscopy was described as a technique to effectively measure weakly absorbing condensed phase materials. In Fahrenfort’s first article describing the technique, published in 1961, he used a hemicylindrical ATR crystal (see Experimental Conditions) to produce single-reflection ATR (Figure 4.2.294.2.29 ). ATR IR spectroscopy was slow to become accepted as a method of characterization due to concerns about its quantitative effectiveness and reproducibility. The main concern being the sample and ATR crystal contact necessary to achieve decent spectral contrast. In the late 1980’s FTIR spectrometers began improving due to an increased dynamic range, signal to noise ratio, and faster computers. As a result ATR-FTIR also started gaining traction as an efficient spectroscopic technique. These days ATR accessories are often manufactured to work in conjunction with most FTIR spectrometers, as can be seen in Figure 4.2.304.2.30 .

Total Internal Reflection

For additional information on light waves and their properties please refer to the module on Vertical Scanning Interferometry (VSI) in chapter 10.1.

When considering light propagating across an interface between two materials with different indices of refraction, the angle of refraction can be given by Snell’s law, 4.2.74.2.7 , where none of the incident light will be transmitted.φc = φmax(4.2.7)(4.2.7)φc = φmax

The reflectance of the interface is total and whenever light is incident from a higher refractive index medium onto a lower refractive index medium, the reflection is deemed internal (as opposed to external in the opposite scenario). Total internal reflectance experiences no losses, or no transmitted light (Figure 4.2.314.2.31

Supercritical internal reflection refers to angles of incidence above the critical angle of incidence allowing total internal reflectance. It is in this angular regime where only incident and reflected waves will be present. The transmitted wave is confined to the interface where its amplitude is at a maximum and will damp exponentially into the lower refractive index medium as a function of distance. This wave is referred to as the evanescent wave and it extends only a very short distance beyond the interface.

To apply total internal reflection to the experimental setup in ATR, consider n₂ to be the internal reflectance element or ATR crystal (the blue trapezoid in Figure 4.2.324.2.32 )

where n₂ is the material with the higher index of refraction. This should be a material that is fully transparent to the incident infrared radiation to give a real value for the refractive index. The ATR crystal must also have a high index of refraction to allow total internal reflection with many samples that have an index of refraction n₁, where n₁<n₂.

We can consider the sample to be absorbing in the infrared. Electromagnetic energy will pass through the crystal/sample interface and propagate into the sample via the evanescent wave. This energy loss must be compensated with the incident IR light. Thus, total reflectance is no longer occurring and the reflection inside the crystal is attenuated. If a sample does not absorb, the reflectance at the interface shows no attenuation. Therefore if the IR light at a particular frequency does not reach the detector, the sample must have absorbed it.

The penetration depth of the evanescent wave within the sample is on the order of 1µm. The expression of the penetration depth is given in 4.2.84.2.8 and is dependent upon the wavelength and angle of incident light as well as the refractive indices of the ATR crystal and sample. The effective path length is the product of the depth of penetration of the evanescent wave and the number of points that the IR light reflects at the interface between the crystal and sample. This path length is equivalent to the path length of a sample in a traditional transmission FTIR setup.dp=λ2πn1(sinω−(n1n2)2)1/2(4.2.8)(4.2.8)dp=λ2πn1(sinω−(n1n2)2)1/2

Experimental Conditions

Refractive Indices of ATR Crystal and Sample

Typically an ATR attachment can be used with a traditional FTIR where the beam of incident IR light enters a horizontally positioned crystal with a high refractive index in the range of 1.5 to 4, as can be seen in Table 4.2.114.2.11 will consist of organic compounds, inorganic compounds, and polymers which have refractive indices below 2 and can readily be found on a database.

Single and Multiple Reflection Crystals

Multiple reflection ATR was initially more popular than single reflection ATR because of the weak absorbances associated with single reflection ATR. More reflections increased the evanescent wave interaction with the sample, which was believed to increase the signal to noise ratio of the spectrum. When IR spectrometers developed better spectral contrast, single reflection ATR became more popular. The number of reflections and spectral contrast increases with the length of the crystal and decreases with the angle of incidence as well as thickness. Within multiple reflection crystals some of the light is transmitted and some is reflected as the light exits the crystal, resulting in some of the light going back through the crystal for a round trip. Therefore, light exiting the ATR crystal contains components that experienced different number of reflections at the crystal-sample interface.

Angle of Incidence

It was more common in earlier instruments to allow selection of the incident angle, sometimes offering selection between 30°, 45°, and 60°. In all cases for total internal reflection to hold, the angle of incidence must exceed the critical angle and ideally complement the angle of the crystal edge so that the light enters at a normal angle of incidence. These days 45° is the standard angle on most ATR-FTIR setups.

ATR Crystal Shape

For the most part ATR crystals will have a trapezoidal shape as shown in Figure 4.2.314.2.31. This shape facilitates sample preparation and handling on the crystal surface by enabling the optical setup to be placed below the crystal. However, different crystal shapes (Figure 4.2.334.2.33 ) may be used for particular purposes, whether it is to achieve multiple reflections or reduce the spot size. For example, a hemispherical crystal may be used in a microsampling experiment in which the beam diameter can be reduced at no expense to the light intensity. This allows appropriate measurement of a small sample without compromising the quality of the resulting spectral features.

Crystal-sample contact

Because the path length of the evanescent wave is confined to the interface between the ATR crystal and sample, the sample should make firm contact with the ATR crystal (Figure 4.2.344.2.34 ). The sample sits atop the crystal and intimate contact can be ensured by applying pressure above the sample. However, one must be mindful of the ATR crystal hardness. Too much pressure may distort the crystal and affect the reproducibility of the resulting spectrum.

The wavelength effect expressed in \label{7} shows an increase in penetration depth at increased wavelength. In terms of wavenumbers the relationship becomes inverse. At 4000 cm^-1 penetration of the sample is 10x less than penetration at 400 cm^-1 meaning the intensity of the peaks may appear higher at lower wavenumbers in the absorbance spectrum compared to the spectral features in a transmission FTIR spectrum (if an automated correction to the ATR setup is not already in place).

Selecting an ATR Crystal

ATR functions effectively on the condition that the refractive index of the crystal is of a higher refractive index than the sample. Several crystals are available for use and it is important to select an appropriate option for any given experiment (Table 4.2.114.2.11 ).

When selecting a material, it is important to consider reactivity, temperature, toxicity, solubility, and hardness.

The first ATR crystals in use were KRS-5, a mixture of thallium bromide and iodide, and silver halides. These materials are not listed in the table because they are not in use any longer. While cost-effective, they are not practical due to their light sensitivity, softness, and relatively low refractive indices. In addition KRS-5 is terribly toxic and dissolves on contact with many solvents, including water.

At present diamond is a favorable option for its hardness, inertness and wide spectral range, but may not be a financially viable option for some experiments. ZnSe and germanium are the most common crystal materials. ZnSe is reasonably priced, has significant mechanical strength and a long endurance. However, the surface will become etched with exposure to chemicals on either extreme of the pH scale. With a strong acid ZnSe will react to form toxic hydrogen selenide gas. ZnSe is also prone to oxidation and care must be taken to avoid the formation of an IR absorbing layer of SeO₂. Germanium has a higher refractive index, which reduces the depth of penetration to 1 µm and may be preferable to ZnSe in applications involving intense sample absorptions or for use with samples that produce strong background absorptions. Sapphire is physically robust with a wide spectral range, but has a relatively low refractive index in terms of ATR crystals, meaning it may not be able to test as many samples as another crystal might.

Sample Versatility

Solids

The versatility of ATR is reflected in the various forms and phases that a sample can assume. Solid samples need not be compressed into a pellet, dispersed into a mull or dissolve in a solution. A ground solid sample is simply pressed to the surface of the ATR crystal. For hard samples that may present a challenge to grind into a fine solid, the total area in contact with the crystal may be compromised unless small ATR crystals with exceptional durability are used (e.g., 2 mm diamond). Loss of contact with the crystal would result in decreased signal intensity because the evanescent wave may not penetrate the sample effectively. The inherently short path length of ATR due to the short penetration depth (0.5-5 µm) enables surface-modified solid samples to be readily characterized with ATR.

Powdered samples are often tedious to prepare for analysis with transmission spectroscopy because they typically require being made into a KBr pellet to and ensuring the powdered sample is ground up sufficiently to reduce scattering. However, powdered samples require no sample preparation when taking the ATR spectra. This is advantageous in terms of time and effort, but also means the sample can easily be recovered after analysis.

Liquids

The advantage of using ATR to analyze liquid samples becomes apparent when short effective path lengths are required. The spectral reproducibility of liquid samples is certain as long as the entire length of the crystal is in contact with the liquid sample, ensuring the evanescent wave is interacting with the sample at the points of reflection, and the thickness of the liquid sample exceeds the penetration depth. A small path length may be necessary for aqueous solutions in order to reduce the absorbance of water.

Sample Preparation

ATR-FTIR has been used in fields spanning forensic analysis to pharmaceutical applications and even art preservation. Due to its ease of use and accessibility ATR can be used to determine the purity of a compound. With only a minimal amount of sample this researcher is able to collect a quick analysis of her sample and determine whether it has been adequately purified or requires further processing. As can be seen in Figure 4.2.354.2.35 , the sample size is minute and requires no preparation. The sample is placed in close contact with the ATR crystal by turning a knob that will apply pressure to the sample (Figure 4.2.364.2.36 ).

ATR has an added advantage in that it inherently encloses the optical path of the IR beam. In a transmission FTIR, atmospheric compounds are constantly exposed to the IR beam and can present significant interference with the sample measurement. Of course the transmission FTIR can be purged in a dry environment, but sample measurement may become cumbersome. In an ATR measurement, however, light from the spectrometer is constantly in contact with the sample and exposure to the environment is reduced to a minimum.

Application to Inorganic Chemistry

One exciting application of ATR is in the study of classical works of art. In the study of fragments of a piece of artwork, where samples are scarce and one-of-a-kind, ATR is a suitable method of characterization because it requires only a small sample size. Determining the compounds present in art enables proper preservation and historical insight into the pieces.

In a study examining several paint samples from a various origins, a micro-ATR was employed for analysis. This study used a silicon crystal with a refractive index of 2.4 and a reduced beam size. Going beyond a simple surface analysis, this study explored the localization of various organic and inorganic compounds in the samples by performing a stratigraphic analysis. The researchers did so by embedding the samples in both KBr and a polyester resins. Two embedding techniques were compared to observe cross-sections of the samples. The mapping of the samples took approximately 1-3 hours which may seem quite laborious to some, but considering the precious nature of the sample, the wait time was acceptable to the researchers.

The optical microscope picture ( Figure 4.2.374.2.37 ) shows a sample of a blue painted area from the robe of a 14^th century Italian polychrome statue of a Madonna. The spectra shown in Figure 4.2.384.2.38 were acquired from the different layers pictured in the box marked in Figure 4.2.374.2.37 . All spectra were collected from the cross-sectioned sample and the false-color map on each spectrum indicates the location of each of these compounds within the embedded sample. The spectra correspond to the inorganic compounds listed in Table 4.2.124.2.12 , which also highlights characteristic vibrational bands.

The deep blue layer 3 corresponds to azurite and the light blue paint layer 2 to a mixture of silicate based blue pigments and white lead. Although beyond the ATR crystal’s spatial resolution limit of 20 µm, the absorption of bole was detected by the characteristic triple absorption bands of 3697, 3651, and 3619 cm^-1 as seen in spectrum d of Figure 4.2.374.2.37 . The white layer 0 was identified as gypsum.

To identify the binding material, the KBr embedded sample proved to be more effective than the polyester resin. This was due in part to the overwhelming IR absorbance of gypsum in the same spectral range (1700-1600 cm^-1) as a characteristic stretch of the binding as well as some contaminant absorption due to the polyester embedding resin.

To spatially locate specific pigments and binding media, ATR mapping was performed on the area highlighted with a box in Figure 4.2.374.2.37 . The false color images alongside each spectrum in Figure 4.2.384.2.38 indicate the relative presence of the compound corresponding to each spectrum in the boxed area. ATR mapping was achieved by taking 108 spectra across the 220×160 µm area and selecting for each identified compound by its characteristic vibrational band.

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Atomic force microscopy (AFM) is a technique with multiple applications in biology. This method is a member of the broad family of scanning probe microscopy and was initially developed in 1986 by Binnig et al to overcome the disadvantages of the scanning tunneling microscopy (STM) [1]. In the case of STM, only conductive materials can be studied as the resolution is obtained by using a tunneling current between a sharp probe and the sample surface[1]. In contrast, AFM uses small forces on the surface by a probe, thus do not damage samples and can provide information of surface topography of biological materials. AFM soon attracted the attention of the biophysical scientists in biomembrane as well as synthetic membrane research due to its capability of observing biological molecular system with resolution on nanometer scale and its possibility of three dimensional imaging [2].

Fundamental Elements of AFM

An atomic force microscope consists of a flexible cantilever containing a sharp probe, laser, photodiode detector, piezoelectric scanner and feedback electronics [3]. The microscope obtains the surface topography by scanning the tip in gentle touch with the sample. The tip motion is monitored by the piezoelectric scanner. As the tip scans the sample, the forces between the tip and the sample surface cause the cantilever to bend. A photodiode detector detects the deflection of a laser beam reflected off the back of the cantilever onto a two- segment photodiode. In most operating modes, a feedback circuit connected to the cantilever deflection sensor keeps the interaction between the tip and the sample at a fixed value and controls the tip-sample distance. The feedback signal is recorded by a computer to reconstruct a 3D image of the surface topography.

The force between the probe and the sample surface depends on the spring constant (stiffness of the cantilever) and the tip-sample distance). The amount of force is calculated based on Hooke’s law:F=−kx(6.1.1)(6.1.1)F=−kx

• FF: Force
• kk: spring constant
• xx: cantilever deflection.

Imaging modes

There are three primary imaging modes in AFM: contact, non-contact and intermittent (tapping) mode [4]. During contact mode, the probe is in contact with the sample and repulsive Van der Waals forces prevail, whilst attractive Van der Waals forces are dominant when the tip moves further away from the sample surface [5].

Contact Mode

In contact mode, the tip is constantly in touch with the sample surface. The applied force is kept constant while the tip scans the surface, creating the surface image [4]. This imaging mode is good for samples with rough and rigid surfaces as it provides fast scanning with high resolution. One disadvantage of this imaging mode is that soft samples like tissues can be deformed or damaged due to the applied force. This drawback can be solved by measuring the sample in aqueous environments to reduce the interaction force between the tip and the sample.

Tapping Mode

In tapping mode, the tip is not in constant contact with the sample surface. Instead, the cantilever is oscillated at its resonant frequency, which makes the tip lightly tap on the surface during scanning. A constant tip-sample interaction is maintained by monitoring the oscillation amplitude and an image is obtained [4]. Several parameters that affect the image contrast are the height, phase signals and amplitude [6]. Phase signals are influenced by material properties of the sample, for example viscoelasticity [6]. The force during scanning is greatly reduced, therefore this mode is useful for biological samples, where the samples are easily damageable or loosely bound to their surface. However, this imaging mode requires a slower scanning speed and is more challenging to measure in liquids.

Non-contact mode

There is no contact between the sample surface and the probe in non-contact mode. The probe oscillates above the sample surface, forming a weak attractive force between the tip apex atom and the sample surface atom. Feedback signals are obtained by measuring a frequency shift in the mechanical oscillation of the cantilever [6].

The force exerted on the surface sample is very low in this case. Moreover, as there is no contact between the probe and the surface, the probe lifetime can be extended. Another advantage of this operating mode is the possibility to observe an atomic defect if the very weak attractive force can be detected. The drawback of this mode is the reduction of resolution, and the oscillation of the cantilever is affected in case there are contaminants on the sample surface. Usually this operation mode requires a careful control of the environment (in UHV) to carry out [7].

Cantilever and Tips

The scanning probe is an important component of the AFM. The dimensions of the cantilever are in micrometer range, while its tip has a radius of a few nanometers [4]. Different cantilever lengths, shapes and materials lead to various spring constants and resonant frequencies. The most common materials of the probes are silicon nitride (Si₃N₄) or silicon (Si) [5]. Figure 6.1.46.1.4 shows a scanning electron microscope (SEM) image of a silicon nitride (4a, 4b) and silicon (4c, 4d) cantilever chip, where a tiny tip having a pyramid shape is integrated at the end. The silicon nitride probe is often used in static contact mode, where the stiffness of the cantilever should be as low as possible [4]. The silicon probe is usually used in dynamic operation mode, which requires higher values for the spring constant to reduce noise and instabilities [4].

Typically, spring constants of AFM cantilevers vary between 0.01 Nm^-1 and 100 Nm^-1, enabling a force sensitivity of 10-11N [4]. The force sensitivity is influenced by thermal, electrical and optical noise. [5] For biological samples, cantilevers in contact mode often have resonance frequencies between 5 and 50 kHz in vacuum [8]. Figure 6.1.56.1.5 reports an AFM tip made of carbon nanotubes (CNTs), which was a breakthrough in terms of resolution. CNTs tips have a high aspect ratio, small diameter, and a well-defined surface chemistry, therefore appearing to be the ideal probe for biological applications [4].

AFM on membranes

Native membranes studied by AFM

Biomembrane sample preparation

In order to study membranes using AFM, the membranes need to be fixed on a flat solid support [8]. Several solid supports such as mica, highly ordered pyrolitic graphite (HOPG), template stripped gold and molybdenum disulfide have proved to give high resolution images [6, 8]. While mica is an insulator and exposes a hydrophilic surface, HOPG is a good conductor and hydrophobic [8]. The similarity between these two substrates is an atomically flat surface [8]. Based on chemical adsorption mechanism, membranes are attached onto the solid support by adjusting pH and ionic strength. As the gap between membrane and the support is very small (0.5-2nm), this may cause impaired mobility for membrane proteins that are directly attached to the support [6]. Furthermore, the adsorption force may affect the conformation of the membrane proteins. To sum up, current sample preparation methods still need further consideration in order to study dynamics and structure of native membrane proteins.

AFM images of native membrane

AFM can obtain the images of native membranes at submolecular resolution, which is a great advantage comparing to other methods [6]. It is effective in providing information of the native organization of membrane proteins and their complexes. Figure 6.1.66.1.6 shows an example of the study of native membrane using AFM. Disk membranes were prepared from mouse retina and then attached on mica support [6]. The AFM image revealed tight rows of dimers packed in the structure arrangement of rhodopsin [6]. This provides a platform for interaction with arrestin and transducin.

Model lipid membranes studied by AFM

Preparation of supported lipid bilayers.

Supported lipid bilayers (SLBs) have been used as a biomimetic model for biomembranes in numerous studies [3, 9]. This system consists of two lipid leaflets spread on a solid support [3]. Although this model lacks some features of the real membranes, it still provides an insight of the structural organization and characteristics of cell membranes. The first method to prepare SLBs is the fusion of lipid vesicles on solid supports [9]. The vesicles are prepared via sonication or extrusion, then adsorbed on the surface of the solid support. The adsorbed vesicles either form larger vesicles by fusing together, or directly rupture and form SLBs.

Another method is to use a hydrophilic substrate on which two consecutive lipid monolayers are deposited by Langmuir-Blodgett transfer [3]. A Teflon-coated trough contains the aqueous solution, with two movable Teflon barriers used to control the area for lipid spread and form a monolayer at the air-water interface. There is also a balance to measure the surface pressure, controlling lipid packing. The solid support is then pulled vertically through the lipid monolayer, depositing the first lipid layer on the substrate. The transference of the second lipid layer can be completed by dipping the lipid support either horizontally or vertically. This technique can be applied to fabricate SLBs having two different lipid composition.

AFM studies of SLBs formation.

SLBs formation process by fusing lipid vesicles on solid supports can be studied in situ by AFM technique, as illustrated in Figure 6.1.76.1.7. The vesicles spread from the edge towards the center, then stacked on top of each other. The edges of the top and bottom bilayers are joined together to form bigger patches.

Different protocols to prepare multi-component and phase-separated SLBs can affect the asymmetry of the resulting SLBs. In Figure 6.1.86.1.8, the extruded small unilamellar vesicles (SUVs) composed of DLPC/DSPC are heated at 65⁰C, then fused on mica at 20⁰C. The resulting SLB are fully symmetric fluid/gel membranes. On the other hand, using sonicated SUVs heated at 20⁰C prior to fusion results in a completely asymmetric SLBs.

Summary

AFM is a powerful technique for scientists to have an insight in membrane biophysics. Advantages of this method including:

• The ability to image cell surfaces, molecular assemblies in their native aqueous environment at a very high resolution.
• No requirement of a conductive sample.
• Provide 3-D surface profiles.
• The ability to operate in liquid environment and ambient air.

Disadvantages of AFM are limited scanning area and the scanning speed.

Recently there have been some progress in improving AFM scanning speed and resolution, for example high speed AFM (HS-AFM) or high resolution AFM (HR-AFM) [10, 11]. HF-AFM consists of modified components in order to maximize scanning seed, for example soft small cantilevers having high resonance frequencies, high resonance frequency scanners and fast data acquisition devices [10]. AFM is also combined with several techniques such as fluorescence microscopy to acquire more efficient data [9]. The potential improvement of AFM will enhance the possibility to apply this technique in a wider range of biological fields.

References

1. Binnig, G., C. F. Quate, and C. Gerber, Atomic force microscope. Phys. Rev. Lett, 1986(56): p. 930–933.
2. D.J.Muller, Y.F.D., Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology. Nat.Nanotechnol, 2008. 3: p. 261-269.
3. Morandat, S., et al., Atomic force microscopy of model lipid membranes. Anal Bioanal Chem, 2013. 405(5): p. 1445-61.
4. Alessandrini, A. and P. Facci, AFM: a versatile tool in biophysics. Measurement Science and Technology, 2005. 16(6): p. R65- R92.
5. Bullen, R.A.W.a.H.A., Lecture notes: Introduction to Scanning Probe Microscopy
6. Frederix, P.L., P.D. Bosshart, and A. Engel, Atomic force microscopy of biological membranes. Biophys J, 2009. 96(2): p. ​329- ​38.
7. S. Morita, R.W., E. Meyer, Noncontact Atomic Force Microscopy. Springer, 2002. 1.
8. Muller, D.J. and A. Engel, Atomic force microscopy and spectroscopy of native membrane proteins. Nat Protoc, 2007. 2(9): p. ​2191-7.
9. Goksu, E.I., et al., AFM for structure and dynamics of biomembranes. Biochim Biophys Acta, 2009. 1788(1): p. 254-66.
10. Ando, T., T. Uchihashi, and N. Kodera, High-speed AFM and applications to biomolecular systems. Annu Rev Biophys, 2013. ​42: p. 393-414.
11. Bippes, C.A. and D.J. Muller, High-resolution atomic force microscopy and spectroscopy of native membrane proteins. Reports on Progress in Physics, 2011. 74(8): p. 086601.

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Introduction

The physical properties of colloids (nanoparticles) and suspensions are strongly dependent on the nature and extent of the particle-liquid interface. The behavior of aqueous dispersions between particles and liquid is especially sensitive to the ionic and electrical structure of the interface.

Zeta potential is a parameter that measures the electrochemical equilibrium at the particle-liquid interface. It measures the magnitude of electrostatic repulsion/attraction between particles and thus, it has become one of the fundamental parameters known to affect stability of colloidal particles. It should be noted that that term stability, when applied to colloidal dispersions, generally means the resistance to change of the dispersion with time. Figure 2.5.12.5.1 illustrates the basic concept of zeta potential.

From the fundamental theory’s perspective, zeta potential is the electrical potential in the interfacial double layer (DL) at the location of the slipping plane (shown in Figure 2.5.12.5.1 ). We can regard zeta potential as the potential difference between the dispersion medium and the stationary layer of the fluid attached to the particle layer. Therefore, in experimental concerns, zeta potential is key factor in processes such as the preparation of colloidal dispersions, utilization of colloidal phenomena and the destruction of unwanted colloidal dispersions. Moreover, zeta potential analysis and measurements nowadays have a lot of real-world applications. In the field of biomedical research, zeta potential measurement, in contrast to chemical methods of analysis which can disrupt the organism, has the particular merit of providing information referring to the outermost regions of an organism. It is also largely utilized in water purification and treatment. Zeta potential analysis has established optimum coagulation conditions for removal of particulate matter and organic dyestuffs from aqueous waste products.

Brief History and Development of Zeta Potential

Zeta potential is a scientific term for electrokinetic potential in colloidal dispersions. In prior literature, it is usually denoted using the Greek letter zeta, Ζ, hence it has obtained the name zeta potential as Ζ-potential. The earliest theory for calculating Zeta potential from experimental data was developed by Marian Smoluchowski in 1903 (Figure 2.5.22.5.2 ). Even till today, this theory is still the most well-known and widely used method for calculating zeta potential.

Interestingly, this theory was originally developed for electrophoresis. Later on, people started to apply his theory in calculation of zeta potential. The main reason that this theory is powerful is because of its universality and validity for dispersed particles of any shape and any concentration. However, there still some limitations to this early theory as it was mainly determined experimentally. The main limitations are that Smoluchowski’s theory neglects the contribution of surface conductivity and only works for particles which have sizes much larger than the interface layer, denoted as κ_a (1/κ is called Debye length and a is the particle radius).

Overbeek and Booth as early pioneers in this direction started to develop more theoretical and rigorous electrokinetic theories that were able to incorporate surface conductivity for electrokinetic applications. Modern rigorous electrokinetic theories that are valid almost any κa mostly are generated from Ukrainian (Dukhin) and Australian (O’Brien) scientists.

Principle of Zeta Potential Analysis

Electrokinetic Phenomena

Because an electric double-layer (EDL) exists between a surface and solution, then any relative motion between the rigid and mobile parts of the EDL will result in the generation of an electrokinetic potential. As described above, zeta potential is essentially a electrokinetic potential which rises from electrokinetic phenomena. So it is important to understand different situations where electrokinetic potential can be produced. There are generally four fundamental ways which zeta potential can be produced, via electrophoresis, electro-osmosis, streaming potential, and sedimentation potential as shown from Figure 2.5.32.5.3 .

Calculations of Zeta Potential

There are many different ways of calculating zeta potential . In this section, the methods of calculating zeta potential in electrophoresis and electroosmosis will be introduced.

Zeta Potential in Electrophoresis

Electrophoresis is the movement of charged colloidal particles or polyelectrolytes, immersed in a liquid, under the influence of an external electric field. In such case, the electrophoretic velocity, v_e (ms^-1) is the velocity during electrophoresis and the electrophoretic mobility, u­­_e (m ² V ^-1 s ^-1 ) is the magnitude of the velocity divided by the magnitude of the electric field strength. The mobility is counted positive if the particles move toward lower potential and negative in the opposite case. And therefore, we have the relationship v_e­= u_eE, where E is the externally applied field.

Thus, the formula accounted for zeta potential in electrophoresis case is given in EQ, where ε_rs is the relative permittivity of the electrolyte solution, ε₀ is the electric permittivity of vacuum and η is the viscosity.ue =εrsε0ζη(2.5.1)(2.5.1)ue =εrsε0ζηve =εrsε0ζηE(2.5.2)(2.5.2)ve =εrsε0ζηE

There are two cases regarding the size of κa:

1. κa < 1: the formula is similar, 2.5.32.5.3 .
2. κa > 1: the formula is rather complicated and we need to solve equation for zeta potential, 2.5.42.5.4 , where yeζ= eζ/kTyeζ= eζ/kT , m is about 0.15 for aqueous solution.

ue=23εrsε0ζη(2.5.3)(2.5.3)ue=23εrsε0ζη32ηeεrsε0kTue=32yek−6[yek2−ln 2ζ{1−e−ζyek}]2+ka1+3m/ζ2e−ζyek2(2.5.4)(2.5.4)32ηeεrsε0kTue=32yek−6[yek2−ln 2ζ{1−e−ζyek}]2+ka1+3m/ζ2e−ζyek2

Zeta Potential in Electroosmosis

Electroosmosis is the motion of a liquid through an immobilized set of particles, a porous plug, a capillary, or a membrane, in response to an applied electric field. Similar to electrophoresis, it has the electroosmotic velocity, v_eo (ms ^-1 ) as the uniform velocity of the liquid far from the charged interface. Usually, the measured quantity is the volume flow rate of liquid divided by electric field strength, Q_eo,E (m ⁴ V ^-1 s ^-1 ) or diveided by the electric current, Q_eo,I (m ³ C ^-1 ). Therefore, the relationship is given by 2.5.52.5.5 .Qeo= ∫∫veodS(2.5.5)(2.5.5)Qeo= ∫∫veodS

Thus the formula accounted for Zeta potential in electroosmosis is given in EQ.

As with electrophoresis there are two cases regarding the size of κa:

• κa >>1 and there is no surface conduction, where Ac is the cross-section area and KL is the bulk conductivity of particle.
• κa < 1, 2.5.82.5.8 , where Δu =KσKLΔu =KσKL is the Dukhin number account for surface conductivity, KσKσ is the surface conductivity of the particle.

Qeo,E=−εrsε0ζηAc(2.5.6)(2.5.6)Qeo,E=−εrsε0ζηAcQeo,I=−εrsε0ζη1KL(2.5.7)(2.5.7)Qeo,I=−εrsε0ζη1KLQeo,I=−εrsε0ζη1KL(1+2Δu)(2.5.8)(2.5.8)Qeo,I=−εrsε0ζη1KL(1+2Δu)

Relationship Between Zeta Potential and Particle Stability in Electrophoresis

Using the above theoretical methods, we can calculate zeta potential for particles in electrophoresis. The following table summarizes the stability behavior of the colloid particles with respect to zeta potential. Thus, we can use zeta potential to predict the stability of colloidal particles in the electrokinetic phenomena of electrophoresis.

Instrumentation

In this section, a market-available zeta potential analyzer will be used as an example of how experimentally zeta potential is analyzed. Figure 2.5.42.5.4 shows an example of a typical zeta potential analyzer for electrophoresis.

The inside measuring principle is described in the following diagram, which shows the detailed mechanism of zeta potential analyzer (Figure 2.5.52.5.5 ).

When a voltage is applied to the solution in which particles are dispersed, particles are attracted to the electrode of the opposite polarity, accompanied by the fixed layer and part of the diffuse double layer, or internal side of the “sliding surface”. Using the following formula below of this specific Analyzer and the computer program, we can obtain the zeta potential for electrophoresis using this typical zeta potential analyzer (Figure 2.5.62.5.6 .

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Dynamic light scattering (DLS), which is also known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QLS), is a spectroscopy method used in the fields of chemistry, biochemistry, and physics to determine the size distribution of particles (polymers, proteins, colloids, etc.) in solution or suspension. In the DLS experiment, normally a laser provides the monochromatic incident light, which impinges onto a solution with small particles in Brownian motion.

And then through the Rayleigh scattering process, particles whose sizes are sufficiently small compared to the wavelength of the incident light will diffract the incident light in all direction with different wavelengths and intensities as a function of time. Since the scattering pattern of the light is highly correlated to the size distribution of the analyzed particles, the size-related information of the sample could be then acquired by mathematically processing the spectral characteristics of the scattered light.

Herein a brief introduction of basic theories of DLS will be demonstrated, followed by descriptions and guidance on the instrument itself and the sample preparation and measurement process. Finally, data analysis of the DLS measurement, and the applications of DLS as well as the comparison against other size-determine techniques will be shown and summarized.

DLS Theory

The theory of DLS can be introduced utilizing a model system of spherical particles in solution. According to the Rayleigh scattering (Figure 2.4.12.4.1), when a sample of particles with diameter smaller than the wavelength of the incident light, each particle will diffract the incident light in all directions, while the intensity II is determined by 2.4.12.4.1 , where I0I0 and λλ is the intensity and wavelength of the unpolarized incident light, RR is the distance to the particle, θθ is the scattering angel, nnis the refractive index of the particle, and rr is the radius of the particle.

I = I01 +cos2θ2R2(2πλ)4(n2 − 1n2 + 2)2r6(2.4.1)(2.4.1)I = I01 +cos2⁡θ2R2(2πλ)4(n2 − 1n2 + 2)2r6

If that diffracted light is projected as an image onto a screen, it will generate a “speckle” pattern (Figure 2.4.22.4.2 ); the dark areas represent regions where the diffracted light from the particles arrives out of phase interfering destructively and the bright area represent regions where the diffracted light arrives in phase interfering constructively.

In practice, particle samples are normally not stationary but moving randomly due to collisions with solvent molecules as described by the Brownian motion, 2.4.22.4.2, where (Δx)2¯¯¯¯¯¯¯¯¯¯¯¯¯(Δx)2¯ is the mean squared displacement in time t, and D is the diffusion constant, which is related to the hydrodynamic radius a of the particle according to the Stokes-Einstein equation, 2.4.32.4.3 , where kB is Boltzmann constant, T is the temperature, and μ is viscosity of the solution. Importantly, for a system undergoing Brownian motion, small particles should diffuse faster than large ones.(Δx)2¯¯¯¯¯¯¯¯¯¯¯¯¯ = 2Δt(2.4.2)(2.4.2)(Δx)2¯ = 2ΔtD =kBT6πμa(2.4.3)(2.4.3)D =kBT6πμa

As a result of the Brownian motion, the distance between particles is constantly changing and this results in a Doppler shift between the frequency of the incident light and the frequency of the scattered light. Since the distance between particles also affects the phase overlap/interfering of the diffracted light, the brightness and darkness of the spots in the “speckle” pattern will in turn fluctuate in intensity as a function of time when the particles change position with respect to each other. Then, as the rate of these intensity fluctuations depends on how fast the particles are moving (smaller particles diffuse faster), information about the size distribution of particles in the solution could be acquired by processing the fluctuations of the intensity of scattered light. Figure 2.4.32.4.3 shows the hypothetical fluctuation of scattering intensity of larger particles and smaller particles.

In order to mathematically process the fluctuation of intensity, there are several principles/terms to be understood. First, the intensity correlation function is used to describe the rate of change in scattering intensity by comparing the intensity I(t) at time t to the intensity I(t + τ) at a later time (t + τ), and is quantified and normalized by 2.4.42.4.4 and 2.4.52.4.5 , where braces indicate averaging over t.G2(τ)= ⟨I(t)I(t + τ)⟩(2.4.4)(2.4.4)G2(τ)= ⟨I(t)I(t + τ)⟩g2(τ)=⟨I(t)I(t + τ)⟩⟨I(t)⟩2(2.4.5)(2.4.5)g2(τ)=⟨I(t)I(t + τ)⟩⟨I(t)⟩2

Second, since it is not possible to know how each particle moves from the fluctuation, the electric field correlation function is instead used to correlate the motion of the particles relative to each other, and is defined by 2.4.62.4.6 and 2.4.72.4.7 , where E(t) and E(t + τ) are the scattered electric fields at times t and t+ τ.G1(τ)= ⟨E(t)E(t + τ)⟩(2.4.6)(2.4.6)G1(τ)= ⟨E(t)E(t + τ)⟩g1(τ)=⟨E(t)E(t + τ)⟩⟨E(t)E(t)⟩(2.4.7)(2.4.7)g1(τ)=⟨E(t)E(t + τ)⟩⟨E(t)E(t)⟩

For a monodisperse system undergoing Brownian motion, g₁(τ) will decay exponentially with a decay rate Γ which is related by Brownian motion to the diffusivity by 2.4.82.4.8 , 2.4.92.4.9 , and 2.4.102.4.10 , where q is the magnitude of the scattering wave vector and q² reflects the distance the particle travels, n is the refraction index of the solution and θ is angle at which the detector is located.g1(τ)= e−Γτ(2.4.8)(2.4.8)g1(τ)= e−ΓτΓ = −Dq2(2.4.9)(2.4.9)Γ = −Dq2q=4πnλsinΘ2(2.4.10)(2.4.10)q=4πnλsinΘ2

For a polydisperse system however, g₁(τ) can no longer be represented as a single exponential decay and must be represented as a intensity-weighed integral over a distribution of decay rates G(Γ) by 2.4.112.4.11 where G(Γ) is normalized, 2.4.122.4.12 .g1(τ)=∫∞0G(Γ)e−ΓτdΓ(2.4.11)(2.4.11)g1(τ)=∫0∞G(Γ)e−ΓτdΓ∫∞0G(Γ)dΓ = 1(2.4.12)(2.4.12)∫0∞G(Γ)dΓ = 1

Third, the two correlation functions above can be equated using the Seigert relationship based on the principles of Gaussian random processes (which the scattering light usually is), and can be expressed as 2.4.132.4.13 , where β is a factor that depends on the experimental geometry, and B is the long-time value of g₂(τ), which is referred to as the baseline and is normally equal to 1. Figure 2.4.42.4.4 shows the decay of g₂(τ) for small size sample and large size sample.g2(τ)= B + β[g1(τ)]2(2.4.13)(2.4.13)g2(τ)= B + β[g1(τ)]2

When determining the size of particles in solution using DLS, g₂(τ) is calculated based on the time-dependent scattering intensity, and is converted through the Seigert relationship to g₁(τ) which usually is an exponential decay or a sum of exponential decays. The decay rate Γ is then mathematically determined (will be discussed in section ) from the g₁(τ) curve, and the value of diffusion constant D and hydrodynamic radius a can be easily calculated afterwards.

Experimental

Instrument of DLS

In a typical DLS experiment, light from a laser passes through a polarizer to define the polarization of the incident beam and then shines on the scattering medium. When the sizes of the analyzed particles are sufficiently small compared to the wavelength of the incident light, the incident light will scatters in all directions known as the Rayleigh scattering. The scattered light then passes through an analyzer, which selects a given polarization and finally enters a detector, where the position of the detector defines the scattering angle θ. In addition, the intersection of the incident beam and the beam intercepted by the detector defines a scattering region of volume V. As for the detector used in these experiments, a phototube is normally used whose dc output is proportional to the intensity of the scattered light beam. Figure 2.4.52.4.5 shows a schematic representation of the light-scattering experiment.

In modern DLS experiments, the scattered light spectral distribution is also measured. In these cases, a photomultiplier is the main detector, but the pre- and postphotomultiplier systems differ depending on the frequency change of the scattered light. The three different methods used are filter (f > 1 MHz), homodyne (f > 10 GHz), and heterodyne methods (f < 1 MHz), as schematically illustrated in Figure 2.4.62.4.6 . Note that that homodyne and heterodyne methods use no monochromator of “filter” between the scattering cell and the photomultiplier, and optical mixing techniques are used for heterodyne method. shows the schematic illustration of the various techniques used in light-scattering experiments.

As for an actual DLS instrument, take the Zetasizer Nano (Malvern Instruments Ltd.) as an example (Figure 2.4.72.4.7), it actually looks like nothing other than a big box, with components of power supply, optical unit (light source and detector), computer connection, sample holder, and accessories. The detailed procedure of how to use the DLS instrument will be introduced afterwards.

Sample Preparation

Although different DLS instruments may have different analysis ranges, we are usually looking at particles with a size range of nm to μm in solution. For several kinds of samples, DLS can give results with rather high confidence, such as monodisperse suspensions of unaggregated nanoparticles that have radius > 20 nm, or polydisperse nanoparticle solutions or stable solutions of aggregated nanoparticles that have radius in the 100 – 300 nm range with a polydispersity index of 0.3 or below. For other more challenging samples such as solutions containing large aggregates, bimodal solutions, very dilute samples, very small nanoparticles, heterogeneous samples, or unknown samples, the results given by DLS could not be really reliable, and one must be aware of the strengths and weaknesses of this analytical technique.

Then, for the sample preparation procedure, one important question is how much materials should be submit, or what is the optimal concentration of the solution. Generally, when doing the DLS measurement, it is important to submit enough amount of material in order to obtain sufficient signal, but if the sample is overly concentrated, then light scattered by one particle might be again scattered by another (known as multiple scattering), and make the data processing less accurate. An ideal sample submission for DLS analysis has a volume of 1 – 2 mL and is sufficiently concentrated as to have strong color hues, or opaqueness/turbidity in the case of a white or black sample. Alternatively, 100 – 200 μL of highly concentrated sample can be diluted to 1 mL or analyzed in a low-volume microcuvette.

In order to get high quality DLS data, there are also other issues to be concerned with. First is to minimize particulate contaminants, as it is common for a single particle contaminant to scatter a million times more than a suspended nanoparticle, by using ultra high purity water or solvents, extensively rinsing pipettes and containers, and sealing sample tightly. Second is to filter the sample through a 0.2 or 0.45 μm filter to get away of the visible particulates within the sample solution. Third is to avoid probe sonication to prevent the particulates ejected from the sonication tip, and use the bath sonication in stead.

Measurement

Now that the sample is readily prepared and put into the sample holder of the instrument, the next step is to actually do the DLS measurement. Generally the DLS instrument will be provided with software that can help you to do the measurement rather easily, but it is still worthwhile to understand the important parameters used during the measurement.

Firstly, the laser light source with an appropriate wavelength should be selected. As for the Zetasizer Nano series (Malvern Instruments Ltd.), either a 633 nm “red” laser or a 532 nm “green” laser is available. One should keep in mind that the 633 nm laser is least suitable for blue samples, while the 532 nm laser is least suitable for red samples, since otherwise the sample will just absorb a large portion of the incident light.

Then, for the measurement itself, one has to select the appropriate stabilization time and the duration time. Normally, longer striation/duration time can results in more stable signal with less noises, but the time cost should also be considered. Another important parameter is the temperature of the sample, as many DLS instruments are equipped with the temperature-controllable sample holders, one can actually measure the size distribution of the data at different temperature, and get extra information about the thermal stability of the sample analyzed.

Next, as is used in the calculation of particle size from the light scattering data, the viscosity and refraction index of the solution are also needed. Normally, for solutions with low concentration, the viscosity and refraction index of the solvent/water could be used as an approximation.

Finally, to get data with better reliability, the DLS measurement on the same sample will normally be conducted multiple times, which can help eliminate unexpected results and also provide additional error bar of the size distribution data.

Data Analysis

Although size distribution data could be readily acquired from the software of the DLS instrument, it is still worthwhile to know about the details about the data analysis process.

Cumulant method

As is mentioned in the Theory portion above, the decay rate Γ is mathematically determined from the g₁(τ) curve; if the sample solution is monodispersed, g₁(τ) could be regard as a single exponential decay function e^-Γτ, and the decay rate Γ can be in turn easily calculated. However, in most of the practical cases, the sample solution is always polydispersed, g₁(τ) will be the sum of many single exponential decay functions with different decay rates, and then it becomes significantly difficult to conduct the fitting process.

There are however, a few methods developed to meet this mathematical challenge: linear fit and cumulant expansion for mono-modal distribution, exponential sampling and CONTIN regularization for non-monomodal distribution. Among all these approaches, cumulant expansion is most common method and will be illustrated in detail in this section.

Generally, the cumulant expansion method is based on two relations: one between g₁(τ) and the moment-generating function of the distribution, and one between the logarithm of g₁(τ) and the cumulant-generating function of the distribution.

To start with, the form of g₁(τ) is equivalent to the definition of the moment-generating function M(-τ, Γ) of the distribution G(Γ), 2.4.142.4.14 .g1(τ)= ∫∞0G(Γ)e−ΓτdΓ = M(−τ,Γ)(2.4.14)(2.4.14)g1(τ)= ∫0∞G(Γ)e−ΓτdΓ = M(−τ,Γ)

The mth moment of the distribution mm(Γ)mm(Γ) is given by the mth derivative of M(-τ, Γ) with respect to τ, 2.4.152.4.15 .mm(Γ)= ∫∞0G(Γ)Γme−ΓτdΓ∣−τ=0(2.4.15)(2.4.15)mm(Γ)= ∫0∞G(Γ)Γme−ΓτdΓ∣−τ=0

Similarly, the logarithm of g₁(τ) is equivalent to the definition of the cumulant-generating function K(-τ, Γ), EQ, and the mth cumulant of the distribution km(Γ) is given by the mth derivative of K(-τ, Γ) with respect to τ, 2.4.162.4.16 and 2.4.172.4.17 .ln g1(τ)=ln M(−τ,Γ) = K(−τ,Γ)(2.4.16)(2.4.16)ln g1(τ)=ln M(−τ,Γ) = K(−τ,Γ)km(Γ)=dmK(−τ,Γ)d(−τ)m∣−τ=0(2.4.17)(2.4.17)km(Γ)=dmK(−τ,Γ)d(−τ)m∣−τ=0

By making use of that the cumulants, except for the first, are invariant under a change of origin, the km(Γ) could be rewritten in terms of the moments about the mean as 2.4.182.4.18 , 2.4.192.4.19 , 2.4.202.4.20 , and 2.4.212.4.21 where here μm are the moments about the mean, defined as given in 2.4.222.4.22 .k1(τ)k2(τ)k3(τ)k4(τ)= ∫∞0G(Γ)ΓdΓ=Γ¯= μ2= μ3= μ4−3μ22⋯(2.4.18)(2.4.19)(2.4.20)(2.4.21)(2.4.18)k1(τ)= ∫0∞G(Γ)ΓdΓ=Γ¯(2.4.19)k2(τ)= μ2(2.4.20)k3(τ)= μ3(2.4.21)k4(τ)= μ4−3μ22⋯μm = ∫∞0G(Γ)(Γ − Γ¯)mdΓ(2.4.22)(2.4.22)μm = ∫0∞G(Γ)(Γ − Γ¯)mdΓ

Based on the Taylor expansion of K(-τ, Γ) about τ = 0, the logarithm of g₁(τ) is given as 2.4.232.4.23 .ln g1(τ)= K(−τ,Γ)= −Γ¯τ +k22!τ2 −k33!τ3 +k44!τ4⋯(2.4.23)(2.4.23)ln g1(τ)= K(−τ,Γ)= −Γ¯τ +k22!τ2 −k33!τ3 +k44!τ4⋯

Importantly, if look back at the Seigert relationship in the logarithmic form, 2.4.242.4.24 .ln(g2(τ)−B)=lnβ + 2ln g1(τ)(2.4.24)(2.4.24)ln(g2(τ)−B)=lnβ + 2ln g1(τ)

The measured data of g₂(τ) could be fitted with the parameters of km using the relationship of 2.4.252.4.25 , where Γ¯Γ¯ (k₁), k₂, and k₃ describes the average, variance, and skewness (or asymmetry) of the decay rates of the distribution, and polydispersity index γ = k2Γ¯2γ = k2Γ¯2 is used to indicate the width of the distribution. And parameters beyond k₃ are seldom used to prevent overfitting the data. Finally, the size distribution can be easily calculated from the decay rate distribution as described in theory section previously. Figure 2.4.62.4.6 shows an example of data fitting using the cumulant method.ln(g2(τ)−B)=]lnβ + 2(−Γ¯τ +k22!τ2 −k33!τ3⋯)(2.4.25)(2.4.25)ln(g2(τ)−B)=]lnβ + 2(−Γ¯τ +k22!τ2 −k33!τ3⋯)

When using the cumulant expansion method however, one should keep in mind that it is only suitable for monomodal distributions (Gaussian-like distribution centered about the mean), and for non-monomodal distributions, other methods like exponential sampling and CONTIN regularization should be applied instead.

Three Index of Size Distribution

Now that the size distribution is able to be acquired from the fluctuation data of the scattered light using cumulant expansion or other methods, it is worthwhile to understand the three kinds of distribution index usually used in size analysis: number weighted distribution, volume weighted distribution, and intensity weighted distribution.

First of all, based on all the theories discussed above, it should be clear that the size distribution given by DLS experiments is the intensity weighted distribution, as it is always the intensity of the scattering that is being analyzed. So for intensity weighted distribution, the contribution of each particle is related to the intensity of light scattered by that particle. For example, using Rayleigh approximation, the relative contribution for very small particles will be proportional to a⁶.

For number weighted distribution, given by image analysis as an example, each particle is given equal weighting irrespective of its size, which means proportional to a⁰. This index is most useful where the absolute number of particles is important, or where high resolution (particle by particle) is required.

For volume weighted distribution, given by laser diffraction as an example, the contribution of each particle is related to the volume of that particle, which is proportional to a³. This is often extremely useful from a commercial perspective as the distribution represents the composition of the sample in terms of its volume/mass, and therefore its potential money value.

When comparing particle size data for the same sample represented using different distribution index, it is important to know that the results could be very different from number weighted distribution to intensity weighted distribution. This is clearly illustrated in the example below (Figure 2.4.92.4.9 ), for a sample consisting of equal numbers of particles with diameters of 5 nm and 50 nm. The number weighted distribution gives equal weighting to both types of particles, emphasizing the presence of the finer 5 nm particles, whereas the intensity weighted distribution has a signal one million times higher for the coarser 50 nm particles. The volume weighted distribution is intermediate between the two.

Furthermore, based on the different orders of correlation between the particle contribution and the particle size a, it is possible to convert particle size data from one type of distribution to another type of distribution, and that is also why the DLS software can also give size distributions in three different forms (number, volume, and intensity), where the first two kinds are actually deducted from the raw data of intensity weighted distribution.

An Example of an Application

As the DLS method could be used in many areas towards size distribution such as polymers, proteins, metal nanoparticles, or carbon nanomaterials, here gives an example about the application of DLS in size-controlled synthesis of monodisperse gold nanoparticles.

The size and size distribution of gold particles are controlled by subtle variation of the structure of the polymer, which is used to stabilize the gold nanoparticles during the reaction. These variations include monomer type, polymer molecular weight, end-group hydrophobicity, end-group denticity, and polymer concentration; a total number of 88 different trials have been conducted based on these variations. By using the DLS method, the authors are able to determine the gold particle size distribution for all these trials rather easily, and the correlation between polymer structure and particle size can also be plotted without further processing the data. Although other sizing techniques such as UV-V spectroscopy and TEM are also used in this paper, it is the DLS measurement that provides a much easier and reliable approach towards the size distribution analysis.

Comparison with TEM and AFM

Since DLS is not the only method available to determine the size distribution of particles, it is also necessary to compare DLS with the other common-used general sizing techniques, especially TEM and AFM.

First of all, it has to be made clear that both TEM and AFM measure particles that are deposited on a substrate (Cu grid for TEM, mica for AFM), while DLS measures particles that are dispersed in a solution. In this way, DLS will be measuring the bulk phase properties and give a more comprehensive information about the size distribution of the sample. And for AFM or TEM, it is very common that a relatively small sampling area is analyzed, and the size distribution on the sampling area may not be the same as the size distribution of the original sample depending on how the particles are deposited.

On the other hand however, for DLS, the calculating process is highly dependent on the mathematical and physical assumptions and models, which is, monomodal distribution (cumulant method) and spherical shape for the particles, the results could be inaccurate when analyzing non-monomodal distributions or non-spherical particles. Yet, since the size determining process for AFM or TEM is nothing more than measuring the size from the image and then using the statistic, these two methods can provide much more reliable data when dealing with “irregular” samples.

Another important issue to consider is the time cost and complication of size measurement. Generally speaking, the DLS measurement should be a much easier technique, which requires less operation time and also cheaper equipment. And it could be really troublesome to analysis the size distribution data coming out from TEM or AFM images without specially programmed software.

In addition, there are some special issues to consider when choosing size analysis techniques. For example, if the originally sample is already on a substrate (synthesized by the CVD method), or the particles could not be stably dispersed within solution, apparently the DLS method is not suitable. Also, when the particles tend to have a similar imaging contrast against the substrate (carbon nanomaterials on TEM grid), or tend to self-assemble and aggregate on the surface of the substrate, the DLS approach might be a better choice.

In general research work however, the best way to do size distribution analysis is to combine these analyzing methods, and get complimentary information from different aspects. One thing to keep in mind, since the DLS actually measures the hydrodynamic radius of the particles, the size from DLS measurement is always larger than the size from AFM or TEM measurement. As a conclusion, the comparison between DLS and AFM/TEM is shown in Table 2.4.12.4.1 .

Conclusion

In general, relying on the fluctuating Rayleigh scattering of small particles that randomly moves in solution, DLS is a very useful and rapid technique used in the size distribution of particles in the fields of physics, chemistry, and bio-chemistry, especially for monomodally dispersed spherical particles, and by combining with other techniques such as AFM and TEM, a comprehensive understanding of the size distribution of the analyte can be readily acquired.

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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.