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Anal. Chem. 1981, 53, 1457-1460
will lead to a slightly distorted second derivative curve; Le., the result is only approximately the second derivative. In contrast, the distortions in derivative spectra obtained by means of the Fourier transform method are smaller than the noise in such spectra. This results from the truncation just below the point in the interferogram when the noise dominates, as computed with eq 14. Consequently, the derivatives resulting from the Fourier transform method are very close to those given by eq 22. Secondly, while A,&) = 0 for 1x1 > L, As&) oscillates about zero. This results in an increase of noise in the derivative spectrum. Similar effects result from the use of the other Savitzky-Golay convoluting functions.
SUMMARY We have described the computation of derivative and self-deconvoluted spectra using Fourier transforms and carried out a comparison of first-order derivatives with Fourier self-deconvoluted spectra. There are two main advantages in the use of Fourier transforms to compute the first-order derivatives. Firstly, distortions in the derivatives are smaller than the noise. Secondly, the computation is very easy, as there is only one parameter, L, used in the smoothing function, and this parameter depends mainly on the signal-to-noise ratio in the original spectrum.
The signal-to-noise ratio also defines the highest utilizable derivative of the spectrum. In the case of the more useful even order derivatives, the use of the sixth order is restricted to spectra with (SIN), 5 10000, the fourth order to spectra with (SIN), 5 1000, and the second order to spectra with (SIN), 5 100. Generally, Fourier self-deconvolution yields by far the highest degree of information regarding the band structure, particularly when the bandwidths of the individual component bands axe similar. In the case where bandwidths in the region of interest differ substantially, the advantages of Fourier self-deconvolution will not be immediately apparent due to the restrictions imposed by the narrower lines. However, by employment of the band separation technique (1)to remove such lines the full advantages can readily be achieved.
LITERATURE CITED (1) Kauppinen, J. K.; Moffatt, D. J.; Mantsch, H. H.; Cameron, D. G.Appl. Spectrosc. 1981, 35, 271-276. (2) Kauppinen, J. K.; Moffatt, D. J.; Cameron, D. G.; Mantsch, H. H. Appl. opt. i g a i , 20, 1866-1879. (3) Savitzky, A,; Golay, M. J. E. Anal. Chem. 1964, 36, 1627-1639. (4) Stelnier, J.; Termonia, V.; Deltour, J. Anal. Chem. 1972, 44, 1906.
RECEIVED for review February 2, 1981. Accepted April 24, 1981. NRCC Publication No. 19286.
Modulated Differential Reflectance Spectroscopy of Lead Dioxide Films during Growth R. J. Gale,”‘ J. Sefaja,2 and M. Fleischmann Electrochemistry Group, Chemistry Department, The University, Southampton SO9 5NH, England
External reflectance spectroscopy has been used to study the dynamic growth of electrochemical lead dioxide fllms on a platlnum substrate. The reflectance-the and pulse modulated reflectance-time relations have been recorded slmultaneously durlng film formation and theoretical models are proposed to account for the experimental results. Optical and coulometrlc estimations of the film thicknesses were in satlsfactory agreement. A normallred dlfferentlal reflectlvlty simulation has been made for the ilnear accumulatlon of absorblng and nonabsorblng product material in a three-phase optical model. It Is demonstrated that ac optical techniques coupled wlth a knowledge of chemical product propertles enable selective monltorlng of surface faradaic processes.
Specular reflectance spectroscopy (SRS) is particularly suitable for in situ film formation studies, and in this paper we report a novel procedure and analysis for the differential reflectivity of a dynamically growing Pb02 film on a platinum substrate. Admittance spectroscopy techniques using sweep frequency correlation methods are becoming increasingly important for characterizing electrode (metal and semiconducPresent address: Chemistry Department, Colorado State University, Fort Collins, CO 80523. Present address: Faculty of Mining and Metallurgy, University of Pristina, Kosovska Mitrovica, Yugoslavia.
tor)/electrolyte interphases. Coupled with optical probes, such techniques should form a powerful means of resolving POtential-modulated surface properties. Relatively few optical studies have been made of lead dioxide films despite their importance for the lead acid battery and diverse electrode applications. Lappe (2) has determined the absorption spectrum of the rutile form of PbOz filmsby transmission and found the band edge to be approximately 2.0 eV. The optical absorption, resistivity, and Hall effect properties of electrodeposited a- and @-Pb02films have been investigated by Mindt (2). Optical band gaps were reported as 2.0 and 1.7 eV for the a- and @-forms,respectively. From an X-ray photoelectron spectral study of the lead oxides, Kim et al. (3) proposed that two kinds of adsorbed water are found on electrodeposited PbOz. Additionally, the energy band structure of PbOz was investigated experimentally by Thomas and Tricker ( 4 ) and evaluated theoretically in semiempirical calculations by Jacquemin and Bordure (5). Recently, Peter and Sefaja have investigated the photoelectrochemical properties of partially reduced a-Pb02 films by interferometry and photocurrent measurements (6). Our purpose in this paper is to demonstrate that ac polarographic theoretical advances may be coupled to absorption spectroscopy of interphases to provide a means of resolving faradaic processes a t electrodes. EXPERIMENTAL SECTION Lead dioxide films were produced by using potentiostaticpulse techniques, following the procedure outlined by Fleischmann and
0003-2700/61/0353-1457$01.25/00 1981 American Chemical Soclety
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 9, AUGUST 1981
PHASE 3
n3=(1.8,3,81
Pt
SJBSTRATE
Flgure 1. Optical model for computer simulations.
o i /
1
50
1
100 TlVE
I
I
150
200
L 250
(SEC I
Figure 3. Experimental reflectance, differential reflectance (unnormalized) and current-time curves for PbOP film growth. Electrochemical conditions are bias potential +0.83 V, pulse +1.05 V (SCE), modulation 10 mV/120 Hz square wave. Optical conditions are = 546 nm, p-polarization, 56' incidence. LEAD 3 1 0 X I D E
FILM
THICKNESS lnrnl
Flgure 2. Calculated reflectivity variation with film thickness. Optlcal parameters are h = 546 nm, 45' incidence, p-polarization, n2 = (2.3, 0.0 (upper): 0.1 (middle);0.5 (lower)). Liler (7). The electrolyte, prepared from triply distilled water and analytical reagent chemicals, contained 1 M lead acetate, 1 M sodium acetate, and 1M acetic acid. The platinum substrate electrode, a disk of area 0.126 cm2 sealed in Pyrex glass, was polished with alumina pastes of successively finer grades (5, 1, 0.3 pm) prior to use. After the solution in the SRS cell was deoxygenated with purified N2 gas for 30 min, the rest potential was selected by nulling the current follower reading, usually at -0.80 V SCE. Reflected light was detected by using a solid-state photodiode. Alternatively, normalized spectra could be recorded with continuous scanning of the wavelength using a photomultiplier and filtered feedback system. The modulation and recording equipment have been described elsewhere (8).
RESULTS 1. Reflectance Behavior during Film Growth. Specular reflectance variations with increasing thickness (h) for an isotropic, homogeneous layer may be simulated by using stratified layer theory (9). The reflectance, W, is given by
R=
rlZ2+ rz32+ 2rlzr23cov 2@ 1 + rlZ2r232+ 2rl2rZ3cos 2@
(1)
in which rI2and ~ 2 are 3 the Fresnel coefficients for the appropriate polarization states (complex for absorbing interphases) and the phase difference @ = 2nn2h cos Bz/h. The three-phase optical model chosen for computer calculations is shown in Figure 1 and computational methods are given in the Appendix. Optical constants are taken from the International Critical Tables. Any effects introduced by platinum oxide on the metallic substrate have been disregarded for the purpose of these calculations. Simulated reflectance variations as a function of the optical layer thickness are illustrated in Figure 2. The reflectance is a periodic function of the film thickness for a nonabsorbing layer ( k = 0.0) and increasing absorptivity causes the first minimum to shift to greater thicknesses. The position of the first maximum is not affected appreciably by k values in the range 0.0-0.5. Lead dioxide films were prepared by the potential-step method and the current-time (A),the reflectance-time (W-t), and the differential reflectance-time (dW/dt) relations were recorded simultaneously during their growth. A typical data
set is shown in Figure 3. The initial rise portion of the i-t transient depended markedly on the state of preparation of the Pt electrode and the nucleation transients could become quite pronounced on fresh and highly polished substrates. These effects may be minimized, however, by reusing the electrode after solely an etch clean in dilute nitric acid or by the use of a short nucleation prepulse. After the passage of about 44 mC charge, the reflectance value decreased to about 3 4 % of the initial value by a sequence of damped oscillations. From a comparison of the experimental reflectances with the theoretical simulations, electrochemically formed PbOz appears to be absorbing a t h values in the range 400-600 nm, and the magnitude of k is between 0.1 and 0.5. Iterative computing procedures might be employed to determine more precise values for the extinction coefficient of films if reliable data exist for the substrate material. Attempts to determine the thickness of absorbing layers by optical procedures of this type are fraught with problems (IO). Firstly, the optical constants of a thin slice of material may differ from its bulk values. Secondly, absorption may diminish the intensity of the reflected radiation and thereby introduce considerable errors in measurements. Thirdly, the applicability of specular reflectance theory may be questionable due to surface disorder and the inhomogeneity of real films may give rise to practical problems for obtaining reliable (material) data. Nevertheless, as Schopper demonstrated for SbzSsfilms of 0-200 nm thickness ( I I ) , appropriately chosen values of n and k can be used to compute reasonably good fits to the reflectance and transmittance curves obtained experimentally. It is of interest to estimate the film thicknesses of P b 0 2 layers optically and to compare these with the coulometric estimations based on bulk properties. By integration of the i-t responses and with the assumption that the density of @-Pb02,p = 9.38, is a reasonable value (cf. ref 6), thicknesses derived from the inflection points of the experimental reflectivity curves may be compared to the coulometric thicknesses. We assume 100% faradaic efficiency for the deposition reaction
Pb
+ 2H20 - 4e- + PbOz + 4H+
-
(2)
The first minimum in Figure 1occurs at h 43 nm (k = 0.0) and shifts to about 35% greater thickness as k is increased to 0.5; the first maximum is affected less by the magnitude of k , at =I10 nm, and therefore is more useful for obtaining the approximate optical thickness. Table I contains a sum-
ANALYTICAL CHEMISTRY, VOL. 53, NO. 9, AUGUST 1981 9r
Table I. Comparison of Optical Thicknesses of First Maxima, h,, , and Coulometric Thicknesses, h, h Inm
435 577
h,,/nm 88 116
1459
h,lnm 75 101
-6t
-i-
-1 2
I
\
y
Flgure 5. Computer form of (d%/dt)%-' vs. film thickness for conditions of Figures 2 and 4.
-"\ I -4I \W / 3
Figure 4. Numerical simulation of derivative of reflectivlty function with increasing PbO, film thickness. Optical conddions are as given in Figure 2: c u r v e l , k = O . O ; c u r v e 2 , k = O . I ; c u r v e 3 , k = 0 . 5 .
mary of the experimental coulometric thicknesses and the theoretical optical values at wavelengths X = 435 nm and 577 nm. The ratio of the experimental values of the coulometric thicknesses (1.35) agrees reasonably well with the wavelength ratio (1.33). Thickness estimates from the first maxima and coulometric data differ by -16%. This discrepancy is reasonable considering the simplicity of the three-phase model and the approximate physical constants that were used in the calculations. Nevertheless, it is possible too that because of voids or irregularities in the film, the packing density is slightly less than that of bulk P-Pb02. Such a condition would modify the optical constants for the film with respect to those of bulk material, as well as density. 2. Differential Reflectance Spectroscopy. The differential reflectance function is readily calculable if the phase-detected signal arises primarily from fluctuations of f i i thickness (integral concentration) due to the small electrical modulation. In other words, % = f(h,t) and d R / d t = (d%/dh)(dh/dt) and it is assumed that (dhldt) is constant. Such modulation of the layer thickness implies that the faradaic reaction in question is sufficiently rapid with respect to the imposed signal frequency and that other modulation effects (e.g., space-charge! modulations) are constant with film thickness. In general, the faradaic reaction may or may not be reversible to the applied modulation, but a small superimposed ac pulse in this case is considered to modulate the growing layer thickness in a constant manner. Figure 4 is a computer simulation of the derivative of the reflectancethickness function obtained by differentiating the reflectance expression with respect tcl the layer thickness. The initial peak in this function may be useful for thickness estimations in the early stages of film growth because it occurs at a smaller layer thickness than the first inflection in the reflectance function. Figure 5 shows the simulated curves for (dR/dh)%-l vs. film thickness. This function is accessible experimentally using a feedback arrangement to normalize the reflected light intensity. Such damped functions, like the reflectivity-time curves, may be useful diagnostically or for extracting optical information. More importantly, it should be possible to extract optical informatioin from a product film grown by a faradaic reaction, for example, due to its unique molecular properties. This could aid in the delineation of superimposed, frequency-dependent processes. More precise experimental
measurements, especially in the early stages of film growth, will be required to ascertain the value of the derivative technique for obtaining solid film information.
ACKNOWLEDGMENT We are grateful to A. Bewick for the use of experimental facilities and to L. Peter for helpful discussion. R.J.G. acknowledges the support of a Research Fellowship at Southampton and recent support from the Solar Energy Research Institute, Golden, CO, and the Chemistry Department, Colorado State University. Paul Beaulieu, Chemistry Department, Colorado State University, aided with computer operation and figure preparation. APPENDIX Reflectance-thickness relationships may be calculated from the modulus of the square of the Fresnel coefficient for the three-layer model
R = lrlZ3l2= U / V
(3)
+
r12 r23e2i@ r123
=
(4)
1 + r12r23e2i@
in which p = 2an2h cos O/A. Both ns and the angle 0 will be complex for absorbing layer 2. F o r a numericafsimulation of the derivative, these expressions were expanded to obtain the squared modulus and then differentiated with respect to the layer thickness h. Let 20 = (x + iy)h, r12= (xl + iyJ, and r23 = ( x 2 + iyz), then
U = x12+ y12+ e - 2 y h ( ~ 2+2y Z 2 )+ 2e-Yh(xlx2 + y1y2)cos xh + 2e-Yh(y1x2- x l y 2 )sin xh V = 1 + e-2Yh(xl2x? + y t y ?
+
+ yl2x? + x12y22) 2e-Yh(x1x2- y l y 2 ) cos xh - 2e-Yh(xzy1+ xlyJ sin xh
dU = 2e-Yh[-ye-Yh(xZ2+ y22)- (x1x2+ yly2)(ycos xh + x sin xh) - (ylx2- x,y2)(ysin xh - x cos xh)] dV =
+ yl2yZ2+ yl2xZ2+x12y22,- ye-yh cos xh + x sin xh) - (xzyl +
( ~ 1 x 2- yly2N.y
x1y2)(x cos xh - y sin xh)]
The derivative is computed from (VdU - UdV)VL.
LITERATURE CITED Lappe, F. J . fhys. Chem. Solids 1962, 23, 1563. Mlndt, W. J. Nectrochem. SOC.1969, 116, 1078. Kim, K. S.; OLeary, T. J.; Winograd, N. Anal. Chem. 1973. 45, 2214. Thomas, J. M.; Tricker, M. J. J. Chem. SOC.,Faraday Trans. 2 1975, 71, 329. ( 5 ) Jacquemin, J. L.; Bordure, G. Solid State Commun. 1972, 11, 1563; J . fhys. Chem. Solids 1975, 36, 1081. (1) (2) (3) (4)
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Anal. Chem. 1981, 53, 1460-1462
(6) Peter, L. M.; SefaJa,J. Surf. Sci., in press. (7) Fleischmann, M.; Lller, M. Trans. Faraday Soc. 1958, 54, 1370. (8) Bewick, A.; Robinson, J. Surf. Sci. 1976, 55, 349, Bewick, A,; Gale, R. J., paper in preparation. (9) Born, M.; Wolf, E. ”Principles of Optics”, 5th ed.; Pergamon Press: New York, 1975; Chapter 13.
(10) Heavens, 0.S. “Optical Properties of Thin Solid Films”; Academlc Press: New York, 1955; Chapter 5. (11) Schopper, H. Z . Phys. 1952, 131, 215.
RECEIVED for review January 27,1981. Accepted May 5,1981.
Structure Elucidation from the Hydroxyl Stretching Region of Vapor-Phase Infrared Spectra Mlchael F. Delaney” and F. Vincent Warren, Jr. Department of Chem;stty, Boston University, Boston, Massachusetts 022 15
The hydroxyl stretching region of over 400 vapor-phase infrared spectra Is examined. Correlations between peak wavelength and functionality are observed for primary, secondary, and tertiary alcohols, phenols, carboxylic acids, and oximes. Peak shifts due to steric crowding and Intramolecular hydrogen bonding are seen. The use of the tabulated results for ldentlflcatlon of compounds separated by gas chromatography Is discussed.
The use of vapor-phase infrared spectrometry (VPIR) directly interfaced to gas chromatography (GC) continues to develop as a viable alternative or complement to mass spectrometry (MS) for identifying the separated components. VPIR can facilitate isomeric assignments which are difficult or impossible by MS, and the instrumentation based on Fourier transform spectrometry (FTIR) has pushed detection limits down to nanogram levels ( I ) . Applications of GC-FTIR have recently been reviewed (2). The interpretation of IR spectra can be approached in several ways, depending upon the needs and time constraints of the laboratory being served, the available instrumentation, the skill and experience of the chemist, and the availability of a large body of reliable and computer-accessible spectra. The capabilities of computerized spectral interpretation methods are rapidly progressing. Automated approaches range from systems employing artificial intelligence techniques, designed to mimic a chemist’s strategy (3), to the more abstract and mathematically based pattern recognition (4) and library searching (5) methods. Manual and artificial intelligence based spectra interpretation both employ some form of a “correlation table” which relates the wavelength of spectral peaks to specific structural fragments in the simple molecule. The interpretation consists of identifying the stuctural fragments present and combining these together to yield the correct structure. Recently a theory has been proposed (6-8) which seeks to firmly define the function and structure of a correlation table using information theoretic concepts to optimize the division of the wavelength axis into functional group categories. This theory is expected to formalize and improve the interpretation systems, both under development (3) and commercially available (9),which identify possible structure units using a correlation table. While structure elucidation by IR is routine in many laboratories and extensive correlations between structure and IR adsorption wavelength have been published (IO), there are significant differences in the vapor phase, primarily due to 0003-2700/81/0353-1460$01.25/0
the absence of intermolecular interactions. As an example, Figure 1 compares a portion of the VPIR spectra of 2-isopropylphenol with the same region of the liquid-phase IR spectrum. The hydroxyl stretching band is seen to be quite broad in the condensed phase due to extensive intermolecular hydrogen bonding, while the gas-phase 0-H band is considerably sharper. Published correlations for vapor-phase spectra (11) are based on only few examples due to the previous lack of suitable instrumentation. The focus of our research (12-15) has been to facilitate the use of VPIR to identify components separated by GC by providing a reliable computerized interpretation system. Reported herein are our observations of structural correlations for various hydroxyl group containing compounds drawn from a large commercial library of VPIR spectra measured on a FTIR instrument. Using a commercially available, high-quality spectral library with extensive “biographical” information provided for each spectrum and with computerized data handling, we were able to rapidly compile functional group categories and to study these spectral correlations extensively for a large number of spectra.
EXPERIMENTAL SECTION The spectral library available was the Sadtler Research Laboratories VPIR collection (Sadtler Research Laboratories, Inc., Philadelphia, PA). Five thousand spectra were obtained on magnetic tape. Each spectrum was measured from 4000 to 450 cm-I at a sampling rate of 2 cm-’ and a resolution of 4 cm-I using a Digilab FTS-14 spectrometer and a CIRA GC (Sadtler Research Laboratories, Inc., Philadelphia, PA). The resulting spectrum contains 1842 data points which are background corrected with intensities digitized in milliabsorbance units. For compounds numbered 2001-4000, the information record, which contains the compound number, molecular formula, Chemical Abstracts Service (CAS) name and registry number, etc., were text searched by computer to find hydroxyl group containing compounds. For each compound the Wiswesser line notation (WLN) (16)was examined by computer to place spectra into the categories: primary, secondary, and tertiary alcohol, phenolic, oxime, and carboxylic acid. The members of each category were examined by using the CAS name to verify correct category assignments. In this manner 416 hydroxyl-containing compounds were found. For each compound, the spectral zone from 3400 to 3800 cm-l, encompassingthe hydroxyl group stretching region, was examined. Each spectrum was studied by using several programs to prepare tabulations of spectral information. The location of peak maximum positions using maximum absorbance and a peak picking algorithm (15) was examined, as were average spectra and a histogram of peak positions vs. number of spectra, for each functional group class. A visual assessment of a large fraction 0 1981 American Chemlcal Society
