Infrared Intensities of Liquids X: Accuracy of Current Methods of Obtaining Optical Constants from Multiple Attenuated Total Reflection Measurements Using the CIRCLE Cell

Infrared Intensities of Liquids X: Accuracy of Current Methods of Obtaining Optical Constants from Multiple Attenuated Total Reflection Measurements Using the CIRCLE* Cell

JOHN E. B E R T I E , t S H U L I A N G L. ZHANG, and RIZWAN M A N J I Department o[ Chemistry, University o/Alberta, Edmonton, Alberta T6G 2G2, Canada

The literature description of the Bertie-Eysel method for obtaining the optical constants (i.e., the real and imaginary refractive indices) of liquids from multiple attenuated total reflection measurements using the CIR- CLE cell is brought up to date in this paper. The accuracy of the com- putation methods is explored by analyzing pATR spectra which are themselves calculated from known k(~) spectra that contain single Lo- rentzian bands, and the corresponding known n(D spectra, and also from simulated, known, n(~) and k(~) spectra of pure liquid methanol and glacial acetic acid. The optical constants are recovered from the pATR spectra and compared with the known originals. It is shown that k(~) spectra that contain k(~) values up to 0.8, 0.7, and 0.6 can be obtained accurately when the real refractive indices are near 1.3, 1.4, and 1.5, respectively. The method is, thus, reliable for spectra that can be accurately measured from the multiple reflections in the CIRCLE cell. It is likely to be troublesome for higher values of the real and the imaginary refractive indices. However, these are best measured by single-reflection methods, and more direct ways of computing the optical constants are available for such methods.

Index Headings: Infrared intensities; Optical constants; Dielectric constants; Attenuated total reflection; ATR.

INTRODUCTION

The CIRCLE cell method for obtaining the optical constants of liquids was first described in 1985,1 and refinement of the method was described with further details in 1988. 2 The light beam is internally reflected about 6 times in the original CIRCLE cell, which means that pATR bands that are stronger than the OH stretch- ing band of water 3 absorb 99 % of the incident radiation or more, and cannot be measured accurately. The method was, consequently, limited to bands in the imaginary refractive index spectrum, k(D, that had kma x less than about 0.3. Furthermore, the programs to compute the optical constants from the pATR spectra were written for a 1978-vintage computer, the Aspect 2000 computer that controls our Bruker IFS 113V FT-IR spectrometer. This computer is slow by today's standards, and the memory is very small, only 160 Kbytes, so the software had to be written to accommodate these limitations.

Since 1988 we have developed a short liquid holder for our CIRCLE cell, in which the radiation is internally reflected about 3 times. This design allows pATR bands to be measured accurately even if the imaginary refractive index at the peak of the k(P) band is about 0.6. Furthermore, we have transferred all of our data manip- ulation to PC-type computers which run under Microsoft

* CIRCLE is a registered trade mark of Spectra-Tech Inc., Stamford, CT.

~- Author to whom correspondence should be sent.

DOS 5.0 or, for very large data sets, run under IBM OS/ 2. The programs have been completely rewritten, from the Pascal of the Aspect 2000 computer, in Microsoft Fortran, and have been combined and modified exten- sively to give a semi-automatic refinement process.

These improvements to our methods and programs have not been described in the literature, as the paper by Huang and Urban 4 reminds us. The purpose of this paper is to provide an up-to-date account of our method and computer programs, and to give the results of tests on simulated pATR spectra to illustrate the accuracy of the algorithms and programs. The simulated spectra are our simulations of the spectra of pure liquid methanol and glacial acetic acid, and the single band spectra used by Huang and Urban.

THE PUBLISHED METHOD

Our published method for obtaining optical constants from pATR spectra has been described in Refs. 1 and 2, and has been correctly summarized by Huang and Ur- ban. 4 It is summarized briefly in this section for reference.

The effective number of reflections (NRF) in the CIR- CLE cell is calibrated 2 by measuring the pATR spectrum of benzene, for which the optical constants are known to a few percent, 2,~ s and calculating the pATR values at the peaks of about 13 bands 2 of benzene from Fresnel's equations, via equations 3.8 and 3.8a of Ref. 1 and the equation

pATR = -lOgl0{0.5[Rs NRr + R~NRF]}. (1)

Rs is the reflectance for light polarized perpendicular to the plane of incidence. This equation is appropriate for the conditions that exist I in the CIRCLE cell, namely 45 ° incidence, equal intensities of s- and p-polarized light, and retention of polarization throughout the multiple reflections. The root mean squared percent deviation (RMSPD) between the measured and calculated peak pATR values is calculated for various values of NRF. The NRF value that gives the smallest RMSPD is used in the refinement.

The experimental pATR spectrum is usually extended by adding zero values from about 6000 cm -1 to about 8500 cm -1, because the absorption is very weak in this region. The real refractive index at this high wavenumber limit of the extended pATR spectrum, n~, is calculated from the wavenumber-dependence of the real refractive index in the visible region of the spectrum. 2 With these two pieces of data the published method is the following:

1660 Volume 46, Number 11, 1992 0003-7028/92/4611-166052.00/0 APPLIED SPECTROSCOPY © 1992 Society for Applied Spectroscopy

Step 1. Calculate an approximate imaginary refractive index spectrum, ka(3), from the experimental pATR spectrum, by assuming the pATR spectrum is an absor- bance spectrum for a transmission cell with pathlength equal to twice the penetration depth of the evanescent wave times the number of reflections. Then calculate k,(D = ka(D{1 + V~a(D} and u s e k1(3 ) as the initial k(3) spectrum. Program CIRCLEP performs Step 1.

Step 2. Calculate n(D from n~ and Kramers-Kronig transform of k (3). The transform is done by an algorithm using two successive fast Fourier transforms (FFTs), in program AHILBERT.

Step 3. Calculate the pATR spectrum from k (3) and n(3) from equations 3.8 and 3.8a of Ref. 1 and Eq. 1.

Step 4. Adjust the k(D spectrum by calculating a new k(3) spectrum via the equation 2

kNEW(3) = kOLD(3){I + DMP(F(D - 1)} (2)

where

F(3) = pATRoBs(3)/pATRcALC(3) (3)

and DMP is a damping factor between 1 (no damping) and 0 (no change in k(D). This procedure assumes that k(D has to be increased if pATRcALc(D must be increased.

Steps 3 and 4 are done by program REFLECT. Step 4a. Repeat Steps 3 and 4 until k (3) converges (at

constant n(D). Step 5. Repeat Step 2, then repeat Steps 3, 4, 4a, and

2 until both n(D and k(D have converged and the pATR spectrum is well fitted. Convergence and fit were judged by

FSUM = ~[pATR(DoBs - pATR(~)CALC] 2, (4)

the sum of the squared deviations over the entire spectrum. FSUM was usually near 10 initially and near I × 10 .4 when successful calculations were stopped.

RECENT CHANGES AND THE PRESENT METHOD

General. The pATR spectra are now transferred from the Bruker instrument to a personal computer running under the DOS operating system. 7 They are imported into Spectra Calc$ or GRAMS/3865 and stored in Spec- tracalc's ".SPC" format. All of our programs now read and write spectral files in this ".SPC" format.

The programs used on the Aspect computer were written for the PC in Turbo Pascal, Version 5.0, and improved considerably in the process. They were then also coded in Microsoft Fortran, Version 5.0, and the Fortran programs were found to execute about twice as fast as the corresponding Pascal program. Henceforth all de- velopment was done in Fortran, and Version 5.1 of Mi- crosoft Fortran is currently used. The programs are now usually run on a 33-MHz 486 DX computer. They also run on a 16-MHz 386 SX computer with a 387 math co- processor, but about 6 times more slowly. Spectra Calc and GRAMS/386 are used for general spectral manipu- lation and plotting.

~: Spectra Calc and GRAMS/386 are registered trademarks of Galactic Industries Corporation of Salem, NH.

Changes to the Calibration Procedure. The effective number of reflections is now determined by calculating the areas under bands of benzene for several different values of NRF from the known optical constants of benzene 8 and comparing them with the areas under the same bands in the experimental spectrum. Again the value of NRF that gives the minimum root mean squared percent deviation of the calculated areas from the measured ones is used in the refinement procedure. This calibration with areas is less susceptible to baseline errors than is the previous calibration with peak heights, and the values of NRF determined from several different spectra agree to about 1%, which permits a 1% accuracy in the optical constants obtained by these methods.

Changes to Step 2, the Kramers-Kronig Transform of k(3) to n(3). The Kramers-Kronig transform may be done by calculating the integral in equation 3.5 of Ref. 1. For digital data with constant spacing, Ohta and Ishida 9 have shown that the principal value of the sum can be calculated with greatest accuracy by using McLaurin's equation. We now use 1° McLaurin's equation and call this procedure the KK transform.

The Kramers-Kronig transform may also be done via two successive fast Fourier transforms with data manip- ulation before and between the transforms. This ap- proach performs a Hilbert transform, which is equivalent to the Kramers-Kronig transform for quantities with the properties of the optical constants. We call this procedure the Hilbert transform. TM

The algorithm used in the program AHILBERT, for the Hilbert transform from k (3) to n (3) via two successive fast Fourier transforms, has been shown to give errors of up to 4% in the calculated n(D spectrum2 ,1° A new procedure for the k (3) to n (3) Hilbert transform has been presented and shown '° to give results that are accurate to better than 0.1% in n(D, only marginally poorer than the 0.05% accuracy given by the KK transform program. '° For the transform from n(D to k(D, a different new procedure for the Hilbert transform yields k(D values accurate to <0.2 % of the largest k value in the spec- t r u m - b e t t e r accuracy than the <0.4% of the largest k value obtained from the KK transform program. ~°

It is well known that the Kramers-Kronig and Hilbert transforms from k(D to n(D must be inaccurate if the k (3) spectrum is incomplete. The most common form of incompleteness is that the low-wavenumber end of the spectrum occurs on the side of an absorption band, so that k (3) is not near the baseline at the end of the spectrum. It has been shown '° that both the Kramers-Kronig and Hilbert transforms can be improved by a factor of 10 if the k(D spectrum is extended linearly from the k value at the lowest wavenumber in the spectrum to zero at 0 cm-L

Consequently, we have improved our programs for pro- cessing CIRCLE cell spectra by replacing the inaccurate Hilbert transform program AHILBERT by either the new Hilbert transform program or the KK transform program.

Because the KK transform takes about two minutes for an 8192-point spectrum on a 33-MHz 486 DX computer and the Hilbert transform program takes only about two seconds if no zero-filling is used, ~° the Hilbert transform with no zero-filling is usually used until the refine-

APPLIED SPECTROSCOPY 1661

m e n t converges, and the more accurate K K t rans fo rm program is then used for the small n u m b e r of cycles needed to comple te the ref inement . In bo th cases the spectra l da ta can be ex tended 1° if desired to improve the accuracy of the optical constants calculated f rom an in- comple te p A T R spect rum.

The K K t r ans fo rm p rog ram also includes the opt ion of app rox ima te ly t r ipl ing its execut ion speed, a t the ex- pense of insignificant reduct ion in accuracy a t high wavenumbers , where the k(~) values are all essential ly zero, by per forming the t r ans fo rm only a t intervals of 100 or 200 cm -~ a t wavenumber s above a critical wavenumber , and then in terpola t ing the real refract ive index between the calculated points. T h e critical wavenumber is usual ly chosen near 5000 cm -1. T h e last few re f inement cycles are always done with the full K K t ransform.

C h a n g e s to the R e f i n e m e n t Cycle. T h e m u c h greater speed and m e m o r y size of 386- and 486-based personal computers , as comp a red with the Aspect 2000, enable spec t ra of 8192 (8K) da ta points, and even 16K or 32K da t a points under OS/2, to be processed. These advan- tages also mean tha t S tep 4a of the publ i shed me thod can be omit ted . This s tep was included to speed up the re f inement by refining k(P) several t imes before recal- culating n(P), because the Kramers -Kron ig t ransform was qui te slow on the Aspect , even though it used an assembly language F F T routine. On the PCs, a new n(P) spec t rum is calculated af ter every change in the k(P) spec t rum, S tep 4a is omit ted , and Step 5 of the re f inement procedure is now:

Step 5, R e p e a t S tep 2, then repea t S teps 3, 4 and 2 unt i l n(~) and k(P) have converged and the p A T R spec- t r u m is well fitted. T h e convergence and fit are judged by FSUM, as before, and also by R M S P D , the root mean squared percen t deviat ion of the calculated p A T R spec- t r u m f rom the observed one, where R M S P D equals:

L pATR(~)oBs J J

and the sum is over the whole spec t rum of N points. T h e cont r ibu t ion is set to zero for wavenumbers a t which the observed p A T R value is less t han 1.6 x 10 -5.

T h e U s e of O n e Program to Permi t R e f i n e m e n t under Computer Control . T h e cur ren t procedures require the exper imen ta l p A T R spec t rum to be cleaned of negat ive (noise) ord ina te values and, if the spec t rum is one for which no app rox ima te k(~) spec t rum is available, the p A T R spec t rum is first processed by C I R C L E P 1,2 to calculate the app rox ima te h (P) spec t rum. The p A T R spec- t r u m and the app rox ima te h(P) spec t rum are then processed by a single program, H R E F , which first calculates the n(P) spec t rum and then carries out the re f inement cycle (Steps 3, 4, and 2) au tomat ica l ly unt i l R M S P D reaches a reques ted l imit or unt i l F S U M reaches a reques ted l imit or unti l bo th reach reques ted limits. H R E F then writes the final h(P), n(D, and calculated p A T R spec t ra to disk, and also creates a file of R M S P D and F S U M values af ter each cycle, to record the progress of the ref inement . Faci l i ty also exists for in te rmedia te spec- t r a to be placed on disk during the ref inement , and for the initial calculat ion of n(P) to be omi t t ed if a sui table n(P) spec t rum exists. For the mos t accurate work, the

TABLE I. Accuracy measures of our current program KREF ~ for various spectra.

h ma. for a single Lorentzian band, FWHH = 6 cm -~ Quan- Acidic

tity 0.1 0.3 0.4 0.6 acid CH3OH

DMP b 1 1 1 0.1 1.0 0.4 RMSPD c 0.10 0.011 0.0083 0.0060 0.0047 0.0049 /i k × 100 d 0.084 0.25 0.30 0.45 0.025 0.035 5,, × 100 d 0.51 0.57 0.58 0.67 0.073 0.093

a The accuracy tests are described in the text. n~ = 1.5 for the results in columns 2 to 5, and 1.325 for acetic acid and methanol. In all cases the program stopped when FSUM (Eq. 4) reached 2 × 10 8.

b The damping factor used in Eq. 2. c The root mean squared percent deviation of the calculated pATR

spectrum from the observed one, defined by Eq. 5. d 5k is the root mean squared deviation of the recovered k' values from the original k values divided by the root mean squared k value. 5n is the root mean squared deviation of the recovered n' values from the original n values divided by the root mean squared value of n(~) - n~ (equations 6 and 7 of Ref. 4). For the single Lorentzian band spectra (columns 2 to 5), the averages for 5h and ~n were taken only from 1715 to 1685 cm ~. For the acetic acid and methanol spectra these ~ik and (~, averages were taken over the entire spectrum, as were the averages for RMSPD and FSUM for all spectra.

exper imenta l p A T R spec t rum and the k(P) and n(P) spec- t r a ou tpu t by H R E F are read into K R E F , which is iden- t ical to H R E F except t h a t it uses the K K t r ans fo rm and, consequent ly , is m u c h slower bu t more accurate .

When a strong, sharp band, such as the 1030-cm -1 band of l iquid methanol , was processed under the publ i shed re f inement scheme, the calculat ions f requent ly diverged ra the r t han converged. Such bands cause no difficulty in the new programs when a damp ing factor of abou t 0.4 is used in Eq. 2.

T H E A C C U R A C Y O F T H E C U R R E N T P R O G R A M S

H u a n g and U r b a n 4 tes ted the accuracy of the Bert ie and Eysel and the Dignam and Mamiche -Afa ra algo- r i thms, by synthesizing a k(D spec t rum which consists of a single Loren tz ian band and synthesizing the corresponding n(~) spec t rum, following equat ions 1 and 2 of Ref. 4. T h e y calculated 2048-point h(~) spec t ra be tween 2000 and 1400 cm 1, using Lorentz ians centered a t 1700 cm -1 with 6 cm -1 full width a t ha l f height ( F W H H ) and several dif ferent values of hm~. T h e y then calculated the p A T R spec t rum for a single reflection of unpolar ized l ight a t 45 ° incidence, with nROD = 2.38 for the A T R e lemen t and n~o = 1.5 for the sample. T h e y then used the two a lgor i thms to recover the h(D and n(D spec t ra f rom the p A T R spec t rum. We call the recovered spec t ra the k ' (D and n ' (D spectra .

To assess the accuracy of the algori thms, they com- pa red the k'(P) and n'(P) spec t ra with the original h(~) and n(D spectra . To obta in a numer ica l measure of accuracy, they calculated the quant i t ies ~h and 5n, where 5h is the root mean squared deviat ion of the recovered h ' values f rom the original h values divided by the root mean squared h value, and 5n is the root m e a n squared deviat ion of the recovered n ' values f rom the original n values divided by the root mean squared value of n(D - n~ (equat ions 6 and 7 of Ref. 4). T h e averages were t aken over the region within 15 cm -1 of the band center, i.e., be tween 1715 and 1685 cm -I.

1662 Volume 46, Number 11, 1992

rY

EL

.2

.1

0

.1

.05

0

1.55

n

1.5

1.45 .

17'20 17'00 1 6'80 Wovenumber / c m - 1

FIG. 1. Spectra for the single-Lorentzian band with FWHH = 6 cm -1 and km~ = 0.1. Upper box: The synthesized pATR spectrum and, beneath it, 100 times the difference between it and the pATR calculated from the recovered optical constants. Middle and lower boxes." The synthesized k (~) (middle) and n(D (lower) spectra and, beneath them, 100 times the difference between them and the recovered h'(D (middle) or n'(D (lower) spectrum. The 100(n(D - n'(D) spectrum is really 1.46 units lower than shown in the lower box.

We present in Table I the results obtained for these tests f rom our current programs. The calculation of optical constants was judged successful if the ref inement converged, which means, in these tests, if the quant i ty F S U M (Eq. 4) reduced to 2 × 10 -8. This did not occur, so the calculation was not successful, for km~ greater than 0.60 with n~o = 1.5. For n~o = 1.4 or 1.3, optical constants were recovered successfully for km~ values up to 0.70 or 0.80, respectively. These maximum km~ values for successful recovery of the optical constants are independent of the wavenumber at which the bands occur and are essentially independen t of the bandwidth, at least up to 20 cm -1 F W H H .

In Table I we show the values of Huang and Urban 's 5k and 5n quanti t ies for the tests with n~ = 1.5 and F W H H = 6 cm-L These values can be compared with those in Huang and Urban 's tables II t.o IV, t where the entries in the rows labeled "McLaur in " should be used. The present ~k and ~,, values are far superior to those repor ted 4 in the rows labeled "Ber t i e " in tables II and III for the

<~ EL

.5

.6

.4

.2

0

n 1.5 ~ ~ ~

17'20 17'00 16'80 Wavenumber / c m - 1

FIG. 2. Spectra for the single-Lorentzian band with FWHH = 6 cm -~ and kmax = 0.6. Upper box: The synthesized pATR spectrum and, beneath it, 100 times the difference between it and the pATR calculated from the recovered optical constants. Middle and lower boxes: The synthesized k (~) (middle) and n(D (lower) spectra and, beneath them, 100 times the difference between them and the recovered k'(D (middle) or n'(D (lower) spectrum. The 100(n(D - n'(D) spectrum is really 1.20 units lower than shown in the lower box.

previously published Bert ie and Eysel algorithm, and are essentially the same as those repor ted 4 in the rows labeled "Dignam" for the Dignam and Mamiche-Afara algorithm. 11 In table IV of Ref. 4, the 5k and 5, values obta ined from Huang and Urban 's proposed algori thm are all smaller than those in Table I, suggesting tha t their proposed algori thm is capable of recovering optical constants more accurately as well as, of course, being able to deal with the very intense absorptions, with the very large values of k, tha t can be measured accurately in single-reflection a t t enua ted total reflection spectroscopy.

In Table I, we include the values of RMSPD, the quan- t i ty tha t we use, as well as FSUM, as a measure of the degree to which the p A TR spect rum is fitted. As noted above, the ref inement of the optical constants was stopped when F S U M reached 2 × 10 6, and R M S P D is usually near 0.01% when this occurs. R M S P D is larger than this at convergence if the entire spect rum is ra ther weak, as is i l lustrated by the column for km~ = 0.1 in Table I.

We illustrate in the figures the qual i ty of fit repre-


.4

r Y

.2 cb

0

k

.4

.2

0

1.4

1.2

1

4000

L

50'00 20'00 10'00 0 Wavenumber / cm-1

FIG. 3. Spectra for simulated acetic acid. Upper box: The synthesized pATR spectrum and, beneath it, 100 times the difference between it and the pATR calculated from the recovered optical constants. Middle and lower boxes: The synthesized k (D (middle) and n (D (lower) spectra and, beneath them, 100 times the difference between them and the recovered k'(D (middle) or n'(D (lower) spectrum. The 100(n(~) - n'(D) spectrum is really 1.00 units lower than shown in the lower box.

sented by these numerical criteria. Figures 1 and 2 show the synthesized spectrum, and, underneath it, the spectrum of the deviation, multiplied by 100, of the spectrum calculated by our program KREF from the synthesized spectrum, for each of the pATR(~), k(3), and n(D spectra, for the cases with km=x equal to 0.1 (Fig. 1) and 0.6 (Fig. 2). The percent deviation is less than 0.2 % in all cases, except that it ranges from 0.25 to 0.5% for k'(~) for the Lorentzian with kma x = 0.6 (Fig. 2). Note that in the bottom boxes of each figure the spectrum of 100 times the deviation of n has been offset to reduce the range of n in the figure.

We also tested our programs with the k(~) and n(D spectra of acetic acid and methanol that were synthesized from the classical damped harmonic oscillator model in connection with our study of the KK and Hilbert transforms. 1° It should be noted that this model gives Lorentz- ian bands in the imaginary dielectric constant spectrum and gives slightly unsymmetrical bands in the k (3) spectrum, whereas the model of Huang and Urban gives Lo- rentzian bands in the k(~) spectrum. The details of the

r Y

n

.5

0 JX_

.6

.4

.2

1.6

n l . 4

1.2

1

4000 50'00 20'00 10'00 0 Wovenumber / cm-1

FIG. 4. Spectra for simulated methanol. Up0er box: The synthesized pATR spectrum and, beneath it, 100 times the difference between it and the pATR calculated from the recovered optical constants. Middle and lower boxes: The synthesized k (D (middle) and n (D (lower) spectra and, beneath them, 100 times the difference between them and the recovered k'(D (middle) or n'(~) (lower) spectrum. The 100(n(D - n'(D) spectrum is really 0.95 units lower than shown in the lower box.

bands used to construct the acetic acid and methanol spectra are given in table 1 of Ref. 10. The spectra contain 8039 points between 7800 and 50 cm -1. The pATR spectra were calculated for a single reflection of unpolarized light at 45 ° incidence with an ATR element of n = 2.38; n(7800 cm -1) was taken to be 1.325 for both acetic acid and methanol, which is correct for methanol and about 0.05 low for acetic acid.

Figure 3 shows the synthesized pATR, k(3), and n(D spectra of acetic acid below 4000 cm -~ and shows, for each, the spectrum of percent deviation between the synthesized spectrum and that calculated by KREF. Figure 4 shows the same for methanol, and the 5k, 5n, and RMSPD values, each calculated over the entire spectrum, are included in Table I. It is clear that the pATR spectrum is fitted to better than 0.1%, and the recovered k(3) and n(3) spectra are accurate to better than 0.1%.

REASONS FOR NONCONVERGENCE

Figures 1 and 2 show that a peak occurs at lower wavenumber in the pATR spectrum than in the imaginary

1664 Volume 46, Number 11, 1992

refractive index spectrum, and that the shift is larger, the stronger the band. The peak in the initial estimate of the k(~) spectrum is at the same wavenumber as in the pATR spectrum, and the refinement must shift the peak to the correct wavenumber for the k(D spectrum. For strong bands, the refinement sometimes diverges while it is shifting the peak, because the n(D spectrum gets distorted during this process. The use of a damping factor less than 1, and as small as 0.02 in extreme cases, prevents this from happening.

For bands that are slightly too strong for successful recovery, such as a single-band spectrum with no~ = 1.5 and kmax = 0.65, the damping factor effectively stops the divergence which results from shifting the peak, but the refinement oscillates slowly instead of converging. Study of the observed and calculated pATR spectra and of the correct and calculated k spectra shows that this is due to the fact identified by Huang and Urban and shown graphically in figure 2 of Ref. 4--namely, that the refinement depends on the pATR value decreasing when the k value decreases. This factor also presumably causes the larger percent deviations of k (P) noted above for the kin,, = 0.6 case of Fig. 2, in spite of the pATR being fitted to better than 0.1% throughout. A more sophisticated refinement algorithm, such as that suggested by Huang and Urban, may allow such spectra to be treated successfully.

It should be remembered that bands that are too strong to be treated successfully by this method are also usually too strong to be measured in the CIRCLE cell, provided that the real refractive index of the sample is about 1.5 or less. They are better measured by single-reflection ATR, for which an algorithm like that of Dignam and Mamiche-Afara or that proposed by Huang and Urban is more direct and, therefore, preferable.

SUMMARY

Recent changes to our methods and programs, HREF and KREF, for the recovery of optical constants from pATR spectra obtained from the CIRCLE cell have been presented. The program has been tested on pATR spectra that were calculated from known, synthesized, optical constant spectra, both for single-band spectra and for simulations of the spectra of pure acetic acid and meth-

anol liquids. Figures 1 to 4 show some of the spectra used. Figures 1 to 4 also show the deviations, multiplied by 100, of the recovered spectra from the known spectra, and Table I contains average numerical quantities, both of which indicate the goodness of fit and the accuracy of the recovered optical constants.

The evidence presented shows that our current program KREF, for the recovery of optical constants from pATR spectra, gives optical constants of accuracy 0.2 % or better for all except the strongest bands in the multiple attenuated total reflection spectra that are obtained with the CIRCLE cell for liquids with refractive indices of 1.5 or less. The strongest bands that can be refined successfully may give errors up to 0.5% in the recovered k (D spectrum, even though the pATR spectrum is fitted to 0.1% or better. The method is likely to be less successful for liquids with real refractive indices that average above 1.5 in the infrared.

When cases are encountered for which the program fails, the failure is evident from the FSUM and RMSPD values that are recorded after each cycle of refinement. Bands that are too strong to be measured in the CIRCLE cell are best measured by single-reflection attenuated total reflection, for which an algorithm like that of Dig- nam and Mamiche-Afara 11 or that proposed by Huang and Urban 4 is preferable for calculating the optical constants.

1. J. E. Bertie and H. H. Eysel, Appl. Spectrosc. 39, 392 (1985). 2. J. E. Bertie, H. Harke, M. K. Ahmed, and H. H. Eysel, Croat.

Chem. Acta 61, 391 (1988). 3. J. E. Bertie, M. K. Ahmed, and H. H. Eysel, J. Phys. Chem. 93,

2210 (1989). 4. J. B. Huang and M. W. Urban, Appl. Spectrosc. 46, 1666 (1992). 5. T. G. Goplen, D. G. Cameron, and R. N. Jones, Appl. Spectrosc.

34, 657 (1980). 6. J. E. Bertie, R. N. Jones, and V. Behnam, Appl. Spectrosc. 40, 427

(1986). 7. J. E. Bertie, C. D. Keefe, and R. N. Jones, Can. J. Chem. 69, 1609

(1991). 8. J. E. Bertie, R. N. Jones, and C. D. Keefe, "Infrared Intensities of

Liquids XII: Optical Constants and Molar Absorption Coefficients of Benzene between 6200 and 500 cm -~ from Spectra Recorded in Several Laboratories," paper to be submitted to Appl. Spectrosc.

9. K. Ohta and H. Ishida, Appl. Spectrosc. 42, 952 (1988). 10. J. E. Bertie and S. L. Zhang, Can. J. Chem. 70, 520 (1992). 11. M.J. Dignam and S. Mamiche-Afara, Spectrochim. Acta 44A, 1435

(1988).


Documents

Infrared Intensities of Liquids X: Accuracy of Current Methods of Obtaining Optical Constants from Multiple Attenuated Total Reflection Measurements Using the CIRCLE Cell