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Attenuated total refection spectroscopy under conditions weak absorption: New method for determination of integrated intensities
Abstract
The basic principles of attenuated total reflection (ATR) spectroscopy are briefly described and its main areas of application
are listed. It is shown using symbolic calculations that in the case of ATR spectra measured under conditions of weak absorbance,
the area under the curve of absorbance of an isolated Lorentz absorption band is directly proportional to the integral band
intensity. It is shown that the proportionality factor between these quantities contains a single a priori unknown parameter,
i.e., the real part of dielectric constant of the studied medium in the maximum of the studied band. This fact offers a new
scope for determining the integrated intensities of isotropic condensed media directly based on experimental ATR data.
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The history of internal reflection spectroscopy (IRS), also known as attenuated total reflection spectroscopy (ATR), began nearly two centuries ago with the observation by Newton [l] of an evanescent field in a lower index of refraction medium in contact with a higher index of refraction medium in which a propagating wave of radiation undergoes total internal reflection (TIR). However, the exploitation of this phenomenon for the production of absorption spectra did not begin until the pioneering development work of Harrick [2, 31 and Fahrenfort [4]. After the disclosure on the technique in the literature in 1960, a flurry of publications exploiting it for a wide variety of applications ensued. By 1967 a large body of literature existed which was sufficient to justify a monograph by Harrick [5] and a review by Wilks and Hirschfeld [6], These publications thoroughly reviewed the history and applications of IRS up until that time. Although the IRS technique appeared to promise a ready solution for a wide range of problems which were difficult or intractable by other techniques, such as transmission IR, its general use was hampered by doubts about its reproducibility and capability to be quantitative, Some of the problems which diminished the use of the IRS technique include sample contact to the internal reflection element (IRE) 7-91, spectrometer requirements [101, and data-handling requirements [111.
Internal-reflection spectroscopy has found considerable use in the infrared for studying vibration-band properties, optical constants, surface electromagnetic waves, and guided modes in thin-film channels. This paper discusses the principal ideas, including the forms of the evanescent waves and the effects of refractive indices and absorption coefficients of various magnitudes, for various prism-sample combinations - for example, prism pressed against bulk sample, prism separated slightly from the sample and prism with thin film. Examples are included dealing with applications of the techniques to the studies of (a) vibration bands in opaque materials and thin films, (b) molecules adsorbed to surfaces, (c) Raman scattering in thin films, (d) fluorescence in thin films and (e) surface plasmons on bulk metal surfaces and on thin films.
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Infrared-active lattice vibrations have been studied in the cubic semiconductor iron pyrite (FeS2) by measuring the room-temperature reflectivity at near-normal incidence. A group-theoretical analysis of lattice vibrations at the Gamma point in the pyrite structure predicts five infrared-active modes belonging to the irreducible representation Gamma4-. Four of these modes are observed experimentally. An analysis of the data using classical dispersion theory is made to determine the high-frequency dielectric constant and the frequencies, strengths, and linewidths of the observed modes. In addition, a Kramers-Kronig analysis of the data is made to obtain the dielectric response. The frequencies of four transverse and four longitudinal optical modes are also determined. The implications of the infrared data concerning the interatomic bonding in FeS2 are discussed.
A method for the determination of the systematic errors of Harrick's formulas is proposed. The method is based on the expansion of the expressions for the optical density into a Maclaurin series in terms of the extinction coefficient of the medium under study. Using numerical calculations, it is shown that, under conditions of weak absorption, it is sufficient to consider only the first two terms of this series, with the relative systematic errors of Harrick's formulas being determined in this case by dividing the first term of the series by the second. The behavior of the relative systematic errors for perpendicular and parallel polarizations is compared. These errors are shown to decrease monotonically with an increase in the angle of incidence and have finite limits both for angles of incidence tending to the critical value and at grazing incidence of probe radiation.
By expanding Fresnel's formulae in McLaurin's series of the extinction coefficient (k2), expressions for the absorbances in the ATR spectra are obtained. It is shown that in the case of weak absorption the absorbance values are directly proportional to the values of the imaginary part of the dielectric constant (ε''2). Thus, the ATR spectra obtained under conditions of weak absorption are, in effect, dependences of ε''2 on the frequency (nu). It is also shown that the use of the effective thickness concept, introduced by Harrick, leads to an incorrect physical interpretation of the ATR spectra. Namely, they are considered as frequency dependences of the Lambert absorption coefficient (alpha2) that are somewhat distorted due to anomalous dispersion. It is found that there are three reasons which cause differences between ATR and transmission spectra. The relative contribution of each of them is illustrated on the absorption band with a maximum at nu0 = 3400 cm-1, assigned to the stretching vibration of water molecules. The anomalous dispersion influence is also demonstrated on the benzene absorption band with a maximum at nu0 = 1035 cm-1.
The refractive index, and vibrational absorption band intensities, of some liquids have been determined by a new method involving attenuated total reflexion at a solid liquid interface. The principles of the method have been explained and the factors which determine a choice of optimal working conditions have been discussed. The method has been applied to absorption bands of benzene, carbon tetrachloride, chloroform, bromoform, sym-tetrabromoethane, and carbon disulphide. Data have been obtained on the variation of refractive index across the absorption bands, and the computed band intensities have been compared with those obtained previously by other methods.
Internal reflection spectroscopy has a number of advantages over other spectroscopic techniques. It can be used with liquid or solid samples, and little or no sample preparation is required. Since it is necessary only to bring the sample in contact with the sampling surface of an internal reflection element (IRE), sample handling is much simpler than it is for other techniques. This is especially important for very small samples (e.g., microgram and nanogram quantities), for which there is currently very wide interest. Furthermore, it has been shown that the interaction of the light (electromagnetic wave), under the right conditions, is stronger for internal reflection than it is for transmission or external specular reflection. Therefore, because of the above-mentioned advantages, internal reflection is the preferred method of micro- and nanosampling.
The CIRCLE ATR accessory has been used to measure the optical and dielectric constants of organic liquids and water. The method, based on Fresnel's equations, is described in detail, and the agreement between the results obtained and literature values is shown to be adequate for chemical use. The utility of optical and dielectric constants for the calculation of traditional infrared intensities in liquids and of dipole moment derivatives is outlined.
Formulas for reflectivities under conditions of attenuated total reflection (ATR.) are expanded to fourth power in attenuation index, κ. From these expansions, absorption rules are derived for single and multiple ATR spectrometer cells. Equations are given for all types of polarization. It is found that if ATR parameters are selected properly and κ is not too large, absorbance is linear with κ, and with concentration of absorbing species if Beer's law holds. Comparison of ATR and transmission spectra and calculation of optical constants using the expanded formulas are discussed.
The validity of the Polo—Wilson equation is examined for a pure liquid taking explicit account of the frequency dependence of the refractive index in the region of the absorption band. It is shown that the equation is valid with the usual assumptions regardless of the intensity of the band provided the appropriate refractive index is used.
Improved experimental procedures for the ATR technique including a multiple-reflection method and a double-beam accessory are described. For the determination of optical constants an explicit solution is given for the equations corresponding with the two-angle method. Programmed for an electronic computer this solution gives numerical results rapidly. It was used to assess the influence of experimental errors and to find the optimum conditions for the recording of spectra. Values of n and κ for the 1035 cm−1 band of liquid benzene yielded a band intensity in good agreement with accurate absorption measurements.
A general method for spectroscopic determination of the incidence angle and number of reflections in ATR devices is described. This technique extends the inherent advantages of ATR by simplifying general quantitative spectroscopic measurements. Effects of polarization, beam focusing, errors of alignment, indices of refraction, handling of the optical elements, and surface activity of internal standard are discussed. Measured ATR absorbances are fitted mathematically with the use of incidence angle as a parameter. A standardizing solution, molar absorptivities for that solution, and knowledge of the dimensions of the internal reflection optical element are required. Application of the method to a cylindrical internal reflection (CIR) device gives the averaged incidence angle in the CIR with greater accuracy than is otherwise obtainable. With the use of a side-focusing Fourier transform spectrophotometer, the average incidence angle in the Spectra-Tech, Inc. "Micro-cell" "CIRCLE" CIR was 49.68 degrees ± 0.78%, and the number of solution-sensing internal reflections was 7.52 ± 1.95%.
An ATR technique for calculating the optical constants has been developed that uses two reflectivities taken with different prisms at preset angles. These reflectivities can be solved exactly for the optical constants by a simple algebraic expression. The technique is the sole extant method that will give accurate optical constants for media of arbitrary anisotropy without any approximations. Thus nx, ny, nz and kx, ky, kz can all be determined separately for the same sample. The accuracy of the method is high and comparable to the two-angle technique under optimum conditions. The variation of accuracy with prism index, incidence angle, and the type of error in the measurement is studied for various ranges of samples n and k. Under optimal conditions the relative accuracy in k approaches the relative accuracy of the energy loss in reflection, which may be much better than 1%. Another unique feature of the method is that it works at constant penetration, thus allowing work with samples showing some extent of depth inhomogeneity. In some cases the variation of both constants with depth can be obtained with reduced precision.
The composition and structure at the surface of polymeric materials can vary with depth as a result of surface treatments, surface-specific processing variables, or thermodynamic forces active at the surface. For example, low molecular weight oils are applied to the surface of polymers for lubrication purposes. The distribution or depth gradient of the oil in the polymer depends on a variety of interacting factors, such as diffusion, solubility, temperature, chemical or physical interaction, porosity, etc. In the coatings and lamination industries, gradients can occur as a result of the direct deposition of Material A on the surface of Material B. When A does not mix with B, as is often desirable, the integrity of the surface is of importance. The thickness of the layer(s) and the sharpness of the interface(s) can be critical to the intended application of the material. Polymer surfaces are often treated to obtain specific surface properties. An example of this is in the corona poling of such surfaces to improve the printability in commercial applications. Material properties are based on the depth to which the surface treatment propagates, the chemistry of the reactions, and the resulting products.
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The relative error of the optical constants determined by attenuated total reflectance at two polarizations and the same incidence angle is calculated as a function of the reflectance errors by a perturbation method. The variations in the error as a function of the incidence angle are then plotted for various values of the optical constants. The experimental accuracy is optimized by either shallow incidence angles and low index optics or by high index optics in the close vicinity of the critical angle. In either case, the number of reflections should be chosen to give strong attenuation. Under optimum conditions, the method gives reasonably good accuracies.
DOI:https://doi.org/10.1103/RevModPhys.17.227
The single‐resonance damped oscillator model for molecular polarizability is combined with the Lorentz model for the local field in order to obtain expressions describing the dielectric constant and absorption coefficient of pure condensed phases. These expressions are functions of three parameters: the transition dipole matrix element, the molecular resonance frequency, and the lifetime. It is found that condensed phases exhibit a macroscopic resonance frequency different from the molecular resonance frequency, and equations are supplied whereby one may calculate this shift. The shape of the condensed phase absorption coefficient is found to be unsymmetrical about the resonance frequency for intense bands; a method is described in which one exploits this lack of symmetry in order to find the transition dipole matrix element. Attenuated total reflection data for four liquid phase infrared bands are analyzed in terms of the absorption model.
This paper reports absolute infrared absorption intensities of liquids methan‐d3‐ol (CD3OH) and methanol‐d4 (CD3OD) at 25 °C between 8000 and 350 cm−1. Measurements were made by multiple attenuated total reflection spectroscopy with the CIRCLE cell, and by transmission spectroscopy with transmission cells fitted with calcium fluoride windows. In both cases, the spectra were converted to infrared real and imaginary refractive index spectra. The refractive indices obtained by these two methods agreed excellently and were combined to yield an imaginary refractive index spectrum k(ν) between 7244 and 350 cm−1 for CD3OH and between 5585 and 350 cm−1 for CD3OD. The imaginary refractive index spectrum was arbitrarily set to zero from 8000 to 7244 cm−1 (CD3OH) or 5585 cm−1 (CD3OD), where k is always less than 4×10−6, in order that the real refractive index can be calculated below 8000 cm−1 by Kramers–Krönig transformation. The results are reported as graphs and tables of the refractive indices between 8000 and 350 cm−1, from which all other infrared properties of the two liquids can be calculated. The estimated accuracy, not precision, of the imaginary refractive index is ±3%, except for ±10%, where k is less than 4×10−5. The estimated accuracy of the real refractive index is better than ±0.5%.
A set of procedures is described which have been developed to obtain optical constants (refractive index extinction coefficient) for isotropic samples from attenuated total reflection measurements in the region of infrared absorption bands. Data are presented for the 675- and 1035-cm-1 bands of benzene, the 760-cm-1 band of CHCl3, and the 770-cm-1 doublet of CCl4.
We have recorded multiple attenuated total reflection spectra of liquid H2O and D2O, using the Spectra-Tech CIRCLE cell, and calculated from them the infrared optical and dielectric constants and molar conductivities from 9000 to 1250 cm-1 for H2O and from 8500 to 700 cm-1 for D2O. Our results agree well with the literature for H2O, while our results for D2O are the most extensive reported to date. We have calculated the dipole moment derivatives with respect to stretching and bending internal coordinates from the areas under the bands in our molar conductivity spectra. For lack of information, we have used the assumptions of the simple bond-moment model, a diagonal force field, and neglect of stretch-bend interaction. We found ∂μ/∂r for the stretching vibrations to be 3.02 D/Å ±1% and 3.04 D/Å ±0.5% for H2O and D2O, respectively, and ∂μ/∂θ for the bending vibration to be 0.73 D ±3% for H2O and 0.63 D ±5% for D2O. The two values for the stretching vibrations are indistinguishable, but this is not true for the bend. The disagreement for the bending vibration is probably due, at least in part, to our simulation of the absorption by three distinct bands of mixed Gauss-Lorentzian character, in order to try to separate the bending mode from the background absorption. It is probable that no such separation exists precisely. The bond moments for H2O and D2O agree with those calculated by the same approximations from literature data for HDO to about the extent allowed by the approximations. The intensities for liquid H2O are compared with those for water in the gas phase, in Ba(ClO3)2·H2O, in ice I, and in lithium β-aluminate. The intensity of the bending mode, v2(H2O), is essentially independent of the strength of the hydrogen bonds. That of the OH stretching modes increases with hydrogen bond strength in Ba(ClO3)2·H2O, liquid water, ice I, and lithium β-aluminate being 20, 17.5, 25, and 40, respectively, times more intense than in the gas. Explanations for this are briefly summarized.
A method is presented for determining optimal peak integration intervals on the basis of known peak shapes and noise characteristics. General theoretical considerations lead to conditions yielding optimal integration intervals. Examples of frequently occurring peak shapes and noise types are given, such as gaussian or skewed peak shapes, with band-limited first-order noise or flicker noise superimposed. The optimal integration intervals are approximately independent of the signal-to-noise ratio, and they are considerably smaller than the integration intervals normally used. The resulting expected peak area estimation errors are compared with the estimation error resulting from peak maximum amplitude measurement. On the basis of this comparison, rules of thumb are proposed to determine whether piak maximum measurement or peak integration yields the best results. Simulation of different peak shapes with noise superimposed confirms the results obtained. A flexible method is presented for the optimal measurement of the area of peaks with an unknown shape. This on-line method is simple, and could be used as a simple peak-finding procedure. The method requires almost no computer memory, and can be implemented on a microcomputer. A simulated example of this procedure is given.
This paper is a continuation of the study of the integrated absorption intensities of benzene and its simple derivatives. In this paper, the imaginary molar polarizability spectrum reported earlier for fluorobenzene was fit with 169 classical damped harmonic oscillator bands. The standard deviation and RMSE of the fit are both 0.006 cm3 mol−1and the area under the fitted spectrum is 0.5% larger than the area under the experimental spectrum. Most of the required peaks are assigned to fundamentals, first overtones or binary combinations. From the parameters of the fitted peaks, the integrated intensities, transition moments and dipole moment derivatives with respect to normal coordinates of the infrared active fundamentals are determined. The F-Sum rule is used to compare the integrated intensities to those of benzene and bromobenzene in the literature. Remarkably, the F-Sums of the out-of-plane vibrations are the same in all the molecules while the in-plane F-Sums vary markedly between the different molecules.
The experimental and theoretical factors influencing the measurement of the profiles and intensities of infrared absorption bands for materials in condensed states are reviewed. The effects of the spectral slit function and of the time constants of the spectrophotometer recording system on the band shape are discussed, and the methods available for the experimental evaluation of these quantities are described.The theoretical and experimental problems associated with the determination of the true band-intensity parameters from the corresponding apparent band-intensity parameters are examined critically and the interrelationships among the various spectrophotometric variables, including spectral slit width, amplifier time constant, scanning rate and amplifier gain are considered both in terms of the theory of errors and with respect to general laboratory practice.
The absorption and scattering of light by small particles is discussed
in terms of basic theory, optical properties of bulk matter, and optical
properties of particles. The subjects addressed include: electromagnetic
theory, absorption and scattering by an arbitrary particle and by a
sphere, particles small compared with the wavelength, the Rayleigh-Gans
theory, geometrical optics, and miscellaneous particles. Also considered
are: classical theories of optical constants, measured optical
properties, extinction, surface modes in small particles, the angular
dependence of scattering, and applications.
The infrared (IR) spectra of ionic liquids involving 1-butyl-3-methylimidazolium (BMI) and the (CF(3)SO(2))(2)N(-), BF(4)(-), or PF(6)(-) anions, recorded in the transmission and attenuated total reflection (ATR) modes, exhibit strong differences in the most intense anion absorption profiles. These distortions come from optical effects and make difficult any quantitative analysis of, for example, the antisymmetric stretching vibrations of the BF(4)(-) and PF(6)(-) anions. A method is proposed to determine the optical constants, from which any type of experimental spectrum can be simulated. It is then possible to use the anion vibrational bands as spectroscopic probes of the local interactions occurring in the neat ionic liquids and in solutions. This is illustrated by a direct identification of ion pairs and separated ions in the IR spectra of BMI-PF(6) solutions.
Opticheskie postoyannye prirodnykh i tekhnicheskikh sred (Optical Constants of Natural and Technical Media)
- V M Zolotarev
- V N Morozov
- E V Smirnova