Attenuated total reflection (ATR) spectroscopy is now the most popular sampling technique for the measurement of infrared spectra of condensed phase samples. Most practitioners of ATR spectroscopy use the equation for depth of penetration, d(p), to estimate the path length of the evanescent wave through the sample. However, the effective path length, d(e), of the evanescent wave in an ATR measurement, i.e., the equivalent path length in a transmission measurement that would lead to an absorption band of the same intensity, is a more accurate metric than d(p). In measurements designed to obtain the absorptivity of bands in the spectrum of a strongly absorbing viscous liquid, we have shown that the refractive index used in the expressions for d(e) must be modified to take into account the effect of anomalous dispersion before accurate effective path lengths and band absorptivities can be measured.

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KBr disks of caffeine were prepared quantitatively so that the absorptivity of caffeine in this environment could be measured. The disks were then ground up finely and their diffuse reflection spectrum was measured. The average path length traveled by remitted photons was then calculated by the simple application of the Beer-Lambert law. The path length that an average photon travels within a finely powdered matrix of KBr is approximately 4 mm when the concentration of a uniformly dispersed, strongly absorbing analyte such as caffeine is 0.01% or less. This path length then decreases as the concentration of the analyte increases as more photons are absorbed by the analyte. When carbon black is added to the mixture of caffeine and KBr and the measurements are repeated, the effective path length drops even further. The average photon that is remitted from a fine infrared-transparent powder containing a very low concentration of an analyte has been shown to encounter at least 400 particles, indicating a highly random path. The more strongly the matrix absorbs, the shorter the path length. When 0.1% of carbon black is added to the disk, the path length drops to about 100 microm.

Diffuse reflection (DR) spectrometry using mid-infrared Fourier transform spectrometers has become a popular technique for measuring the spectra of powdered materials. [1][2][3] In most midinfrared DR measurements, samples consist of a mixture of the analyte and a nonabsorbing matrix. Dilution of the sample is necessary because the effect of front-surface reflection distorts the DR spectrum excessively for neat samples. The reflectance of a sample, R ∞ , is obtained by calculating the ratio of the singlebeam spectrum of an "infinitely thick" sample to that of the matrix, which is commonly powdered KCl or KBr. (The term "infinite thickness" implies that the spectrum does not change when the thickness of the sample is increased.) Spectra are then typically converted to the Kubelka-Munk function, f (R ∞ ), by the operation Kubelka-Munk theory 4,5 shows that f (R ∞ ) is proportional to the ratio of the absorption coefficient, k, to the scattering coefficient, s, of the sample. Thus, for binary mixtures of an absorbing analyte mixed with a nonabsorbing matrix, a plot of f (R ∞ ) versus the concentration of the analyte, C, should be linear.In practice, several factors can lead to nonlinearity of these plots. These include absorption by the matrix, the effect of specular (Fresnel) reflection from the front surface of the sample, 6 baseline offsets, 7 and variations in the packing of the sample. 8 It should also be noted that the preparation of homogeneous mixtures of powdered components can be very difficult, 9 so the standard deviation of plots of f (R ∞ ) versus C (known as Kubelka-