Harrick - Frequently Asked Questions

Electromagnetic radiation is a transverse wave with mutually perpendicular electric and magnetic fields that are also perpendicular to the direction of propagation of the wave. The plane defined by the electric field vector and the direction of propagation is referred to as the plane of polarization of the electromagnetic wave. The electric rather than magnetic field is chosen for the definition of the plane of polarization because it is the electric field that significantly interacts with matter. In a spectroscopic measurement, it is often important to control the polarization of the incident radiation. This is readily achieved with optical devices called polarizers. There are several types of polarizers.

The type of polarizer most often used in FTIR spectroscopy is wire grid polarizer. An array of extremely fine metal wires is deposited on a face of an optically transparent window (usually KRS-5 or ZnSe). Since the electric field oriented along the direction of wires can induce electrical currents along the wires, the wire grid acts as a metal surface reflecting virtually all the radiation polarized along the direction of the wires. The electric field perpendicular to the direction of wires is unable to induce electrical current in the wire grid . Thus, the light transmits through the polarizer with only the reflectance losses from the substrate window. The efficiency of wire grid polarizers is much higher for wavelengths that are much longer than the grid spacing. This makes wire-grid polarizers useful in the mid-IR and especially in the Far-IR.

Another type of polarizer, called Brewster's angle polarizer, is constructed by stacking transparent plates in the beam tilted so that the angle of incidence on the plates is Brewster's angle. Since at Brewster's angle, the reflectivity of p-polarized light is zero, p-polarized component passes through the plates without loss, while s-component intensity is reduced by reflectance losses at every surface. The intensity reduction of the s-component depends on the strength of the reflectance as well as on the number of plates utilized. In the mid-IR region, transparent materials of very high refractive index are available (i.e. Si and Ge). Thus, it is possible to construct a polarizer with a sufficient polarizing efficiency that utilizes only two plates.

For the near-IR and UV-Vis spectral regions, the polarizer of choice is Glan-Taylor polarizer. This type of polarizer is based on the birefingent property of some materials. These materials have different refractive indices for different polarizations. The light is brought onto an internally reflecting interface at an angle of incidence that is below the critical angle for total internal reflection for one polarization and above critical angle for the other polarization. Thus, the unwanted polarization is deflected out of the beam while the wanted polarization is passed through. This yields a polarizer with a very high polarizing efficiency that is essentially constant throughout the transparent spectral range of the crystal.

Any measurement involves some level of noise superimposed onto a "true" value of the quantity measured by the experiment. This noise comes from the factors that influence the value of the quantity measured, but are not fully controlled by the experimenter. The spectroscopic measurement has yet another level of subtlety stemming from the fact that the quantity directly measured by the experiment is not the light intensity itself. The spectroscopic observable is a loss of the intensity due to the interaction of light with sample. In particular, we will examine factors influencing the S/N of an FTIR spectroscopic measurement.

In an FTIR spectrometer the quantity measured is not the the light intensity as a function of wavenumber (frequency, wavelength) but the Fourier transform of that quantity. This is a consequence of using Michelson interferometer and recording the interferogram.

The detector converts light intensity into a voltage which is subsequently digitized. The electrical circuit employed by the detector should ideally read zero in absence of light, but, in reality, there will always be some level of random voltage presented to digitizing circuitry. One source of noise present in the circuit is the so called Johnson noise. This noise is of thermal origin and the RMS of the detector voltage due to this noise is proportional to the square root of the product of bandwidth, absolute temperature and resistance. This noise is thus independent of the signal on the detector.

Another source of noise is due to the digitization process. The digitization process has finite resolution and rounding off of the continuous value introduces error into the measurement process. The minimization of this type of noise is achieved by appropriate amplification of the detector signal so that the full dynamic range of the A/D converter can be utilized. Yet another source of noise is due to triggering error in the measurement of a point of interferogram. Interferogram points are supposed to be measured at equally spaced intervals along the scanning mirror movement. To assure this, scanning mirror movement is tracked by the interferogram of a laser of a known wavelength. The interferogram of the tracking laser is a sine wave and positive zero crossings of the laser interferogram usually serve as triggers for reading of the IR signal. As with every other electrical signal, the laser interferogram contains some small level of random noise, hence the triggering includes small time fluctuations around the true triggering time. This time, the noise level is not independent of the signal measured. The noise due to triggering error at a point of interferogram is proportional to the product of the timing error and the slope of the interferogram in this point.

The collected interferogram consists of a "true" signal and a noise:

(1)

where I_n is the n^th measured interferogram point, is the true value of the interferogram at the n^th point, and d_n is the noise at that point. If N interferograms are co-added, the relative strength of the random portion of the noise is reduced by a factor . In computing the Fourier transform one gets:

(2)

Note that for random noise d_nthe value of D(k_m) is actually not a function of the wavenumber k. It is however useful to retain the nominal functional dependence to reflect the fact that the noise value is computed at a given wavenumber and will change from point to point. For an interferogram consisting of M points, the value of the noise can be estimated based on the randomness of d_n. If the RMS of d_nis d then the RMS of D(k_m) is:

(3)

The important consequence of the above result is that, everything else being the same, the larger the size of interferogram, i.e. the larger M, the worse S/N of the resulting single beam spectrum.

The transmission spectrum is calculated by ratioing a sample spectrum to a background spectrum. Thus, the noise from the single beam spectra propagates to the noise in the measured transmittance as follows:

(4)

The important consequence of the above result is that for the case that noise in the measurement of the interferogram is independent of the signal measured, the resulting uncertainty in the measured transmittance is independent of the transmittance.

The transmittance however is not the quantity of immediate interest in spectroscopy. Beer's "Law" states that the logarithm of transmittance is approximately proportional to the sample concentration. The negative logarithm of transmittance is called absorbance. Thus of interest is to find out how the noise acquired in collecting the interferogram is propagated into uncertainties in measured absorbance of the sample, since this uncertainty is directly proportional to the uncertainty in the estimate of the sample concentration that follows from it. Consequently:

(5)

from (5) it follows that:

(6)

Since by definition (5) that T=10^-A, we finally obtain that:

(7)

and since dT is independent of T, it is also independent of A. Absorbance thus represents the "signal" that has direct relevance to the analytic measurement and dA represents noise (or uncertainty) in that measurement. Hence signal to noise is given by the ratio:

(8)

It is easy to see that the S/N ratio for a spectroscopic measurement as a function of absorbance reaches maximum for the value of absorbance of A=1/ln(10)=0.434...

Fig. 1. S/N as a function of absorbance.

Two things are obvious from the graph in Fig.1. First, at best only 16% of the spectrometers S/N at a particular wavelength (1/dT) is available for the S/N of the absorbance measurement. Second, to maximize S/N of the measurement one must be able to control the level of absorbance at a particular wavelength in order to tune in to the maximum. In a transmission experiment, the level of absorbance is easily adjusted by adjusting the pathlength. This is straightforward with liquids and gasses. With solids, the adjustment of pathlength can be more problematic. Similarly, in an ATR measurement, a number of reflections, angle of incidence and/or refractive index of IRE can all be utilized to tune the absorbance level to a desired value.

G. Herzberg: Molecular Spectra and Molecular Structure I, Van Nostrand, Princeton 1953.

G. Herzberg: Molecular Spectra and Molecular Structure II, Van Nostrand, Princeton 1960.

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J. R. Ferraro, K. Krishnan (eds.): Practical Fourier Transform Infrared Spectroscopy, Academic Press, San Diego 1990.

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H. -U. Gremlich: Infrared and Raman Spectroscopy, in Ullman's Encyclopedia of Industrial Chemistry, 6th ed., WILEY-VCH Verlag GmbH, Weinheim 2000.

N. B. Colthup, L. H. Daly, S. E. Wiberly: Introduction to Infrared and Raman Spectroscopy, 3rd ed., Academic Press, San Diego 1990.

B. Schrader (ed.): Infrared and Raman Spectroscopy, VCH Verlagsgesellschaft, Weinheim 1995.

D. Lin-Vien, N. B. Colthup, W. G. Fateley, J. G. Graselli: The Handbook of Infrared and Raman Characteristic Frequencies of Organic Molecules, Academic Press, Boston 1991.

P. Hendra, C. Jones, G. Warnes: Fourier Transform Raman Spectroscopy, Ellis Horwood, Chichester 1991.

J. G. Graselli, B. J. Bulkin (eds.): Analytical Raman Spectroscopy, J. Wiley & Sons, New York 1991.

M. J. Pelletier (ed.): Analytical Applications of Raman Spectroscopy, Blackwell Science, Oxford 1999.

F. R. Dollish, W. G. Fatelyey, F. F. Bentley: Characteristic Raman Frequencies of Organic Compounds, Wiley Interscience, New York 1974.

K. G. R. Pachler, F. Matlok, H.-U. Gremlich: Merck FT-IR Atlas, VCH Verlagsgesellschaft, Weinheim 1988.

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B. Schrader: Raman/Infrared Atlas of Organic Compounds, 2nd ed., VCH Verlagsgesellschaft, Weinheim 1989.

F. M. Mirabella (ed.): Modern Techiques in Applied Molecular Spectroscopy, J. Wiley & Sons, New York 1998.

N. J. Harrick: Internal Reflection Spectroscopy, Harrick Scientific Products, Inc., New York 1987.

F. M. Mirabella, N. J. Harrick: Internal Reflection Spectroscopy: Review and Supplement, Harrick Scientific Products, Inc., New York 1985.

F. M. Mirabella (ed.): Internal Reflection Spectroscopy: Theory and Application, Marcel Dekker, New York 1992.

R. G. Messerschmidt, M. A. Harthcock (eds.): Infrared Microspectroscopy: Theory and Applications, Marcel Dekker, New York 1988.

H. -U. Gremlich, B. Yan (eds.): Infrared and Raman Spectroscopy of Biological Materials, Marcel Dekker, New York 2001.

J. L. Koenig: Spectroscopy of Polymers, American Chemical Society, Washington, D.C. 1992.

G. Zerbi et al.: Modern Polymer Spectroscopy, WILEY-VCH Verlag GmbH, Weinheim 1998.

D. O. Hummel: Atlas of Polymer and Plastics Analysis, 3rd ed., VCH Verlagsgesellschaft, Weinheim 1991.

M. E. Swartz: Analytical Techniques in Combinatorial Chemistry, Marcel Dekker, New York 2000.

K. Nakamoto: Infrared and Raman Spectroscopy of Inorganic and Coordination Compounds, Part A: Theory and Applications in Inorganic Chemistry, 5th ed., J. Wiley & Sons, New York 1997.

K. Nakamoto: Infrared and Raman Spectroscopy of Inorganic and Coordination Compounds, Part B: Applications in Coordination, Organometallic, and Bioinorganic Chemistry, 5h ed., J. Wiley & Sons, New York 1997.

W. O. George, H. A. Willis (eds.): Computer Methods in UV, Visible and IR Spectroscopy, The Royal Society of Chemistry, Cambridge 1990.

D. L. Massart et al.: Handbook of Chemometrics and Qualimetrics, Part A, Elsevier, Amsterdam 1997.

D. L. Massart et al.: Handbook of Chemometrics and Qualimetrics, Part B, Elsevier, Amsterdam 1998.

I. Murray, I. A. Cowe (eds.): Making Light Work: Advances in Near Infrared Spectroscopy, VCH Verlagsgesellschaft, Weinheim 1992.

G. Ewing: Analytical Instrumentation Handbook, 2nd ed., Marcel Dekker, New York 1997.

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M. D. Fayer (ed.): Ultrafast Infrared and Raman Spectroscopy, Marcel Dekker, New York 2001.

R. A. Nyquist: Interpreting Infrared, Raman, and Nuclear Magnetic Resonance Spectra, Vol 1 & 2, Academic Press, Boston 2001.

J. Workman (ed.): Handbook of Organic Compounds, Academic Press, Boston 2000

Wesley Wm. Wendtlandt, Harry G. Hecht: Reflectance Spectroscopy, John Wiley and Sons, New York, 1966.

To clean optical elements, most people use cotton-tipped applicators with a suitable solvent. The applicators must be the kind that are free of any extra chemicals, oils, etc. Suitable solvents for various optical materials are given individually for the materials in the special section on optical materials. In general, avoid the use of water or solvents with water when cleaning salts (e.g., KBr, NaCl). Many non-salt materials can be cleaned with water. Many materials in general can be cleaned with organic solvents such as alcohol, acetone, and methyl ethyl ketone (MEK). The end of the applicator is dipped in the solvent. Then the applicator is gently rubbed against the optical element. This process is repeated with a new applicator until the optical material is clean. (A used applicator is never redipped in the solvent.) MEK is a particularly good solvent for cleaning optical materials, because of its high volatility. If evaporation of a thin film of MEK from the optical material surface occurs in patches, the surface is probably not clean. If the same film seems to disappear all at once, the surface is probably clean.

Another method of cleaning windows and ATR elements is to use an ultrasonic cleaning bath. With this equipment, cleaning is accomplished without abrasion. (Such cleaning baths are available through the major laboratory equipment suppliers.) The optical elements are placed in a tray or shallow bottle, on top of a soft material (e.g., Teflon), so that no two elements are touching. The elements are then covered with a suitable solvent and the cleaner turned on for approximately one hour. Non-contact cleaning of optical elements may also be accomplished using the Harrick Plasma Cleaner. See the Basic Model (PDC-32G, PDC-32G-2) and the Expanded Model (PDC-001, PDC-002).

One common method to verify that the window or ATR element is clean is to run a single beam spectrum and look for unusual peaks that were not present in previous background spectra using the same equipment.

Obviously, no amount of cleaning will restore an optical element which has been scratched, chipped, or broken. Minor defects can be corrected using the Harrick Optical Polishing Kit (OPK-1XX). Note that Harrick's optical facilities also offer reconditioning for damaged windows and ATR elements. This can be less costly than replacement for the more expensive materials (e.g., KRS-5, ZnSe).

Reflection occurs at an interface between two media of differing refractive indices. Each reflection splits the incoming beam into a transmitted and reflected component. Typically, it is the transmitted component that is of further interest. In these cases, the reflected component is the unwanted byproduct and the light lost to the reflection only subtracts from the overall light available to the measuring process.

An example is a gas transmission cell. The gas is contained inside the cell during the measurement. The light is brought into the cell through an optically transparent window. A window has two interfaces, both reducing the intensity of the transmitted light. The light is generally incident perpendicular to the window, and for the perpendicular incidence, the intensity loss per surface is:

(1)

where n is the refractive index of the window material and the refractive index of air as well as the sample is assumed to be one. The expression for the transmittance of a window is:

(2)

The reason the transmittance is not simply 1-2R is that the light reflected back from the second interface is re-reflected forward by the first interface. For a typical case of a cell with two KBr windows (n=1.5), the loss of light is approximately 20%.

In a liquid cell, the situation is somewhat different. First, the sample refractive index is no longer essentially one. Thus the cell contains two window-air interfaces and two window-sample interfaces. The reflectance at window air interfaces is still controlled by (1). The window-sample reflectance is:

(3)

where n_s is the refractive index of the sample.

With liquid samples in IR, the cell pathlength is very short. Multiple reflections through the cell interfere and yield so called interference fringes in the transmitted light spectrum. These fringes have period:

(4)

where d is the cell pathlength and ns is the refractive index of sample. Since these fringes originate from the multiple reflections on window-sample interfaces, one method of reducing their effect is to match refractive index of windows to that of the sample. In that case, according to (3), the reflectivity of the interface vanishes and so do fringes.

The other issue is one of reducing the reflection losses due to the windows. Coating the interface with a transparent film can modify the reflectance of an interface. The exact results depend on the refractive index and thickness of the coating. A single layer coating with a material with refractive index roughly square root of the refractive index of the window inhibits reflection at a particular set of wavelengths. The wavelengths of vanishing reflectance can be fine tuned by the choice of the thickness of the coating. By combining a number of films of different refractive indices and thicknesses, the reflectance could be minimized in a broader spectral range. Broadband anti-reflection (BBAR) coatings effective over almost the entire IR range have been developed.

Only cells with metal bodies should be pressurized. Those with plastic bodies should not be used for high pressure applications. Be sure to review the specification for the particular device. If the pressure rating given in the specification is lower than that calculated below, then use the lower figure as the maximum pressure.

All cells are capable of operation from vacuum to ambient pressure. The question is, how high above ambient pressure can any particular cell configuration tolerate. The maximum operating pressure, ppsi (in pounds per square inch, psi) for a gas, liquid or solid cell is given by

(1)

where t is the thickness of the window in mm, m is the modulus of rupture in pounds per square inch (psi), and d is the unsupported diameter of the window, also in mm. From this formula, it can be seen that increasing t or decreasing d will have a great effect on increasing p and that the pressure is directly proportional to m.

The quantity t is dictated by the windows and d is governed by the accessory design. The modulus of rupture is based on the material used for the window and can be found in Table 1 and in the Optical Materials Table. For Harrick accessories, the window thickness, diameter and unsupported diameter are shown in Table 2. Note that the window diameter is not the same as the unsupported diameter, d, and only the latter should be used in the calculation.

Example:

A Temperature Controlled Demountable Liquid Cell, TFC-S13-3, uses two 13mm Zinc Sulfide windows. From Table 1, the value for m is 10,000 psi. From Table 2, t is equal to 2mm and d is 8mm. Substituting in Equation 1 gives:

The pressure in atmospheres can be readily calculated by:

(2)

So, for the example above,

In a similar fashion, the pressure in torr (equivalent to mm of Hg) can be calculated by:

(3)

For the example above,

Table 1. Modulus of Rupture for Some Common Window Materials

Material	Modulus of Rupture, m (psi)
Barium Fluoride (BaF2)	3900
Calcium Fluoride (CaF2)	5300
Potassium Bromide (KBr)	160
Sapphire (Al2O3)	65,000
Silicon (Si)	9000
Sodium Chloride (NaCl)	350
UV Quartz (SiO2)	7100
Zinc Selenide (ZnSe)	8000
Zinc Sulfide (ZnS)	10,000

Table 2. Window Thicknesses and Unsupported Window Diameters for Various Harrick Cells

Cell	Diameter (mm)	Window Thickness, t (mm)	Unsupported Diameter, d (mm)
High Temperature Cell	32	3	26.8
Dewar	25	2	20
	25	4	20
	32	3	26.8
Demountable Liquid Cells: DLC-S13, TFC-S13	13	2	8
Demountable Liquid Cells: DLC-S25, TFC-S25	25	2	20
High Pressure Liquid Cells: HPC-C, HPL-TC	13	6	8
Temperature Controlled Gas Cell	25	2	20
Temperature Controlled Gas Cell	25	4	20
HVC Reaction Chamber (vacuum/low pressure)	15	2	13.2
HVC Reaction Chamber (high pressure)	15	4	13.2
Low Temperature Reaction Chamber (CHC-CHA)	15	2	13.2

One common technique for preparing a sample for FTIR analysis is to mix the finely ground sample with powdered spectroscopic grade KBr and press a pellet from the mixture. The pellet may then be analyzed using transmission spectroscopy. Although this process may seem straightforward, certain complications do exist.

Obviously, this technique is not suitable for liquids. For non-powder solid samples, the sample must first be ground into a powder, prior to mixing it with KBr. For reproducible results, the powder size of the sample and of the KBr should be kept uniform. Also for reproducible results, efficient mixing with KBr must be accomplished, something which requires considerable technique considering that the ratio of KBr to sample is typically 100:1. During grinding and mixing procedures, the sample and KBr should be kept dry, to avoid water band interference in the spectra. On humid days, it may be necessary to dry the mixture in an oven prior to making a pellet.

Prior to placing the sample in the press, the analyst must be sure that the press itself is dry. Heating of the press, or sections thereof, may be required to remove water. The sample is then placed in the press. Some mechanical assembly is typically required. With some presses, the quality of the pellet produced depends on a careful amount of mixed sample being placed in the press. Pressure is then placed on the sample to produce the pellet. During this procedure, vacuum is often applied to the press. One must also know the correct amount of pressure to apply to produce a good pellet. The sample is then allowed to stand for a few minutes and the press is disassembled.

Some presses allow the pellet to be analyzed directly without removing it completely from the press body. With others, removal is required. Here, breakage of the pellet is a possibility. In both cases, special transmission sample holders are required. Here again, the independent pellet is subject to breakage when handled. Note that a second KBr pellet, one without sample, must be run as the reference. This same pellet, if kept dry, can be used as the reference for a number of different sample pellets.

The above process involves a considerable amount of experience and technique to repeatedly produce usable pellets. The time involved in gaining this expertise, as well as the actual sample preparation time, are serious drawbacks to the KBr pellet technique.

One alternative to KBr pellets is the use of ATR. Here, sample preparation is minimized. Solid and powder samples may be analyzed directly. No mixing of samples is required, as the built-in small pathlength of the ATR technique provides sufficient attenuation for virtually all samples. Air is run as the reference sample. The Harrick Scientific MVP™, using a ZnSe ATR element, the SplitPea™, using a silicon ATR element, and the Meridian™, using a diamond ATR element, are three examples of single reflection ATR accessories which can be used to replace the KBR pellet technique and associated equipment.

A second alternative to KBr pellets is the use of diffuse reflection. As with ATR, both solids and powders may be analyzed. With solids, however, the surface must be rough or be roughened. Although many samples may be analyzed neat, it is often necessary to dilute the sample by mixing with KBr to reduce distortions due to reststrahlen bands. The Harrick Scientific Praying Mantis™; and the Cricket™ are two examples of diffuse reflection accessories that can also be used to replace KBR pellets. As with ATR, these two diffuse reflection accessories can also be used to analyze liquids using the Harrick Scientific TransFlex™ substrates.

Transmission spectroscopy was once a standard against which all other spectroscopic techniques were compared. In the area of infrared (IR) spectroscopy, however, ATR has become more widely for all but gaseous samples.

Propagation of light through a homogeneous medium is easily understood within the framework of Maxwell's theory. The solution to Maxwell's equations is a plane wave. When the direction of propagation is along x-axis, the expression simplifies to:

where:

is the complex refractive index of the sample and:

is the wavenumber of the propagating radiation. Since the radiation intensity I(x) is proportional to the square of absolute value of the amplitude:

The expression (4) is the law of transmission of radiation through an absorbing sample. If light transmits through a sample of thickness d, the transmitted intensity is:

ignoring the reflections at the two faces of the sample. Transmittance is then defined as the fraction of incident light that transmits through the sample:

If the absorption bands are not too strong, the effects of reflections at the two faces of the sample could be eliminated by ratioing a measured spectrum of a sample to the transmission spectrum of a nonabsorbing sample of a similar refractive index (hence similar reflection losses). The result is:

where the approximate part of the above relation holds only in the low absorption limit.

The equivalent expression in the low absorption limit for internal reflection (ATR) is:

where index i stands for the different polarizations and the coefficients bi are functions of the refractive indices and the angle of incidence. The fundamental similarity of these two expressions inspired the original introduction of ATR spectroscopy. In both cases, a negative logarithm (absorbance transform) of the measured spectroscopic observable is proportional to the absorption index. However, while for the transmission measurement this linear dependence holds even at high absorbance values, the linearity breaks down with increasing strength of absorbance in ATR. Furthermore, in the transmittance equations, the wavenumber is an explicit factor, distorting the result of the absorbance transform by artificially enhancing it at shorter wavelengths (i.e. higher wavenumbers). Thus, either multiplying the absorbance transform of the ATR spectrum by wavenumber, or dividing the absorbance transform of the transmission spectrum by wavenumber can achieve a superficial resemblance between the transmission and ATR spectra.

We know that the absorbance value or value of the peaks of interest should be in the vicinity of 0.43A, especially when quantitative results are desired.

If only very small amounts of material are available, then sample size alone will probably limit the analysis to a micro-sampling single reflection device (e.g., the MVP accessory or SplitPea accessory). The exception to this rule of thumb is if the solid sample is actually a paste, foam, or other fairly flexible solid material. In this case, the ConcentratIR multiple-reflection ATR accessory would be a possibility.

If there is sufficient solid sample, then either single or multiple reflection ATR are options. The exception to this rule of thumb is if the solid is very hard. In this case, a single reflection ATR accessory is generally required, where the force pushing the sample against the ATR element can be concentrated in the smallest possible area. The ATR element should be harder than the sample. The Meridian, with its single reflection diamond ATR element, would be one accessory which would fulfill these requirements.

If there is sufficient solid sample and the sample is not very hard, then an attempt should first be made to analyze this sample by single reflection ATR. This is probably the simplest method to analyze samples and will probably provide adequate spectral contrast (and S/N) for qualitative studies. If absorbance values of 0.3-0.5A are obtained for peaks to be used for quantitative analysis, then the single reflection technique is, again, chosen.

If absorbance values are too high with single reflection ATR, then, obviously, going to multiple reflection ATR would only exacerbate the problem. In this case, one can choose an ATR material of higher refractive index (e.g., change from ZnSe to Ge with the FastIR accessory), or increase the angle of incidence (e.g., change from 45^o to 60^o with the variable angle Seagull accessory).

If absorbance values are too low with single reflection ATR, then the spectral contrast can be enhanced by choosing an ATR material of lower refractive index (change from ZnSe to ZnS with the FastIR accessory), or decrease the angle of incidence (e.g., change from 45^o to 40^o with the variable angle Seagull accessory). These two techniques must be used with care, however, as approaching or exceeding the critical angle, will yield distorted spectra. (The critical angle is that angle, for a given ATR material refractive index and a given sample refractive index, at which total internal reflection no longer occurs. This can be calculated using the CristalCalc software.)

If absobance values are still too low, there is sufficient sample, and the sample is not too hard, then, and only then should the analyst try multiple reflection ATR. Based on the preliminary results obtained with single reflection ATR, one should be able to quickly determine the additional number of reflections required to reach the 0.3-0.5A range. The caution here, is that for such a calculation to work, one assumes that the contact with the multiple reflection ATR element is as good as the contact with the single reflection element.

The defining feature of ATR spectroscopy is the presence of an evanescent wave. The evanescent wave is a special type of electromagnetic radiation:

It is present only in the regime of supercritical internal reflection
It propagates parallel to the interface
It is confined to a narrow region outside the sampling surface of the internal reflection element (IRE)
Its intensity decreases exponentially with the distance from the sampling surface of IRE
Its penetration depth outside IRE is on the order of wavelength
The penetration depth dp as a function of experimental parameters is:

The penetration depth is controllable through experimental parameters by either changing the refractive index of IRE (no) or changing the angle of incidence (Q). The ability to change the penetration depth enables depth profiling, i.e. the ability to distinguish the composition of surface from that of the bulk. Typical samples for which depth profiling is useful include:

Polymers with chemically modified surfaces
Samples with very thin coatings (thicknesses on the order of the infrared wavelength)
Contaminated surfaces

The information that can be extracted from depth profiling includes:

The chemical composition of surface layer
The chemical composition of substrate
The average thickness of surface layer

To demonstrate the effects of the changing the incident angle and the refractive index of the IRE on the spectra, infrared spectra were simulated using Harrick's SOS™ software. The sample chosen was a 2µm thick polyethylene coating on a glass substrate.

Spectra were simulated examining this sample with a ZnSe ATR element over a range of incident angles from 42° to 60° in 2° increments. The results are presented above.

Spectra were also generated using a higher refractive index ATR crystal, Ge, over a range of incident angles from 24° to 40°, in 2° increments. This is shown in the figure above. Now, let's examine the change in absorption with penetration depth for a distinctive band in each material.

The absorption of the polyethylene band at 2900 cm^-1 as a function of the penetration depth is shown in the figure above, while the absorption of the glass band at 900 cm^-1 as a function of the penetration depth is shown below. In both figures, the upper curve illustrated the absorption measurements using a ZnSe IRE and the lower curve shows the results using a Ge IRE.

For the polyethylene bands, the approximately linear relationship between absorbance and penetration depth continues to hold as the penetration depth tends to zero. This implies the presence of polyethylene at the very interface with IRE. For the glass bands, however, the absorbance drops to zero below a penetration depth of one micron, implying that glass is not present at the very surface of IRE. In ATR, the layers of sample closer to the IRE surface contribute much more strongly to the measured absorbance than do the layers further away from the surface.

The ability to vary the penetration depth (i.e. the mean penetration), by changing either the angle of incidence or the refractive index of the IRE, enables obtaining spectra with a contribution from a particular layer varying in proportion to the overall absorbance. Thus a number of spectra can be recorded at varying penetrations with an intention to extract the information on composition depth profile. However, ATR enables only a coarse depth profile.

In ATR spectroscopy, light internally reflects from the sampling surface of the ATR element. The portion of the sampling surface illuminated by the incoming light can be referred to as the hot-spot. The layer above the hot-spot within which the evanescent wave has a significant intensity can be considered the sampling volume. Only the parts of sample physically positioned within this sampling volume participate in the light absorption process, the rest of the sample is a nonparticipating bystander. If the sample completely fills the sampling volume, then there is no stray light in the measurement process. If, however, areas of the sampling volume contain no sample, there is stray light in the process where stray light is the portion of light involved in the measurement process that does not completely interact with sample. The phrase complete interaction does not imply that the light has to be completely absorbed, but that it only needs to be provided with a completely filled sampling volume.

So what is the damage to the measuring process if there is some stray light in a measurement? Let's look first into a transmission measurement with some stray light present. Imagine that the sample is a film of thickness d placed into the beam and that there is a hole within the portion of the sample illuminated by the beam. If the cross section of the beam is S and cross section of the hole is Sh than the transmittance measured is:

(1)

Absorbance is defined as a negative logarithm of transmittance. The relationship, in the case of no stray light yields a quantity proportional to absorption coefficient.

The graph above shows the relationship between the true absorbance and measured absorbance as a function of the amount of stray light present in the experiment. As expected, stray light introduces non-linearity.

In the case of ATR measurement, stray light is identified as the light that was detected by the spectrometer detector but did not interact with the sample. This occurs when the sample in contact with the ATR crystal is not fully covering the spot illuminated by the sampling radiation seen by detector. The obvious case of this happening is when the sample itself is smaller than the hot spot. The less obvious case if that of a sufficiently large sample pressed against the ATR crystal but with non-uniform contact over the area of hot spot. A familiar illustration of this second case is one of the powdered samples pressed against the crystal. Only the portions of the grains within the active sampling volume are participating in the measurement. The voids between the grains do not contribute to the measurement and hence the light that incompletely interacted with the sample is identified as stray light. Once stray light is present in the measurement, the same non-linearity shown above for the case of transmission follows.

If a sample is imbedded in an absorbing matrix, the problems caused by stray light are no longer of the quantitative type only. The absorbance bands due to the matrix interfere with the spectra of pure sample and must be subtracted. The subtraction may suffer from non-linearities described above, thus impeding the ability to cleanly subtract the matrix contribution, leaving spurious matrix bands in the spectrum of the sample.

Diffuse reflectance was developed to facilitate analysis of materials such as papers and powders in their neat state. The common characteristic of these materials is their internal inhomogeneities. The propagation of light through such inhomogeneous media differs significantly from the propagation of light in a homogeneous material, since the light scatters off points in its path.

Thus the key to the theoretical description of diffuse reflection lies in the description of the propagation of light through inhomogeneous materials. However, only approximate descriptions exist. The most widely used model for diffuse reflection is the one put forward by Kubelka and Munk.

The Kubelka-Munk (K-M) model has a particularly simple solution in the case of semi-infinite samples. All the geometric peculiarities of the inhomogeneous sample are condensed into a single parameter, the scattering coefficient s. The diffuse reflectance

is given as:

This relatively simple form is easily solved for k/s yielding the familiar K-M transform:

The K-M transform of the measured spectroscopic observable

is approximately proportional to the absorption coefficient and hence is approximately proportional to the concentration.

A few words must be said about the scattering coefficient. This coefficient was introduced into the theoretical description of diffuse reflection as a semi-empirical parameter to account for the internal scattering processes. The scattering coefficient s is, in fact, dominated by particle size and refractive index of the sample. It is not a strong function of the wavelength or the absorption coefficient, so the K-M model considers it a constant. In reality, the scattering coefficient does vary slowly with wavelength. More importantly, it changes significantly with packing density, so care should be taken to pack powdered samples as reproducibly as possible if quantitative results are required.

Expression (2) is the analog of the absorbance transformation in transmission spectroscopy. Due to it simplicity, it has been widely incorporated as the diffuse reflectance transform in the standard infrared spectroscopy software of commercial FT-IR spectrometers.

The specular component of light reflected from a sample is that portion which is reflected, mirror-like, at the angle of incidence. When this happens in diffuse reflection experiments, the specularly reflected light does not, typically, contain information about the chemical composition of the sample, but rather information related to the surface texture. Under almost all conditions, the analyst is not interested in such surface texture information (i.e., how shiny the material is) contained in the specular reflection. He is, however, very much interested in the identification of the material, the chemical bonds in the material, and/or how much of a given component is in a matrix of material. Because specular reflection (whether is occurs from a glossy sample surface or from a crystal surface) produces inverted "reststrahlen bands," it distorts the chemical bond information that the analyst is really looking for. Such bands are particularly strong for highly absorbing samples. The distortion of peaks caused by reststrahlen bands can cause misidentification in qualitative analysis and mistakes in quantitative analysis.

One technique for minimizing or eliminating reststrahlen bands is to grind and dilute the sample in a non-absorbing powder such as KBr, KCl, Ge, or Si. Grinding reduces the contribution of reflection from large particle faces. Diluting ensures deeper penetration of the incident beam, thus increasing the contribution to the spectrum of the transmission and internal reflection components. It is not always possible or practical to perform such sample preparations. Under such conditions, it is necessary to employ optical designs, such as those used with the Praying Mantis and Cricket, to eliminate the specular component.

u General
	What are the major spectroscopic techniques and when do you use them?
	What does this term mean?
	What different types of infrared polarizers are available?
	What is the difference between s- and p- polarization?
	How do you convert from microns to wavenumbers and vice versa?
	What is the S/N for an FT-IR measurement?
	What books should our laboratory have in its library?
	Who manufactures FT-IR spectrometers?
	How can I adapt my Harrick liquid cell, with Luer fittings, for flow-through applications?
u Optics
	How can the mirrors on my accessory be cleaned?
	How can windows or ATR crystals be cleaned?
	What are reflection losses and how can they be minimized?
	What are the properties of the different optical materials?
	How can I calculate the maximum pressure for my gas, liquid or solid cell with FT-IR or UV-VIS windows?
u Transmission
	Why should I stop making KBr pellets?
	How can a liquid transmission cell be calibrated?
u ATR (Internal Reflectance)
	Why does an ATR spectrum look different from a transmission spectrum?
	Is single or multiple reflection ATR better for analyzing solids?
	What is a good rule of thumb for pathlength in ATR?
	How is ATR used for depth profiling?
	What is the effect of stray light on ATR spectra?
	Is the polarizer set for s- or p-polarization?
u Diffuse Reflectance
	What is Kubelka-Munk?
	What is the specular component from a diffusely reflecting sample and why is it important?
u Fiber Optics
	I am interested in interfacing my own fiber optics to the FiberMate™. What are the optical properties of the Harrick accessory?

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