1144
V. S. SRINIVASAN AND T. KUWANA
Internal Reflection Spectroscopy at Optically Transparent Electrodes by V. S. Srinivasan and T. Kuwana Department of Chemistry, Case Western Reserse University, Cleveland, Ohio 44106
(Received J u l y 28, 1967)
The type of spectrum obtained by internal reflection spectroscopy’ (IRS) at optically transparent electrodes is theoretically and experimentally examined. It is found that the thin conducting film used as the electrode surface on the transparent substrate greatly affects the character of the spectrum. General formulas applicable to this problem are derived from concepts of physical optics.
Introduction Recently, IRS in the visible region of the spectrum was applied following the concentration of electrogenerated species essentially at the surface of an optically transparent electrode (OTE).z The electrode in this work was glass which was coated with a thin film of “doped” tin oxide. Such a film, as probably will be the case with most conductive films, has a high refractive index which influences the experimental IRS spectra. That is, the “background” IRS spectrum with the thin-film surface in contact with the background solution (e.q., aqueous solution containing a supporting electrolyte which is transparent in the visible region) has an absorbance which fluctuates as a function of wavelength. This fluctuation is reminiscent of an interference phenomenon. If an absorbing species is present in solution, as it would be when one generates it electrolytically at the surface, the absorbance due to the species is not superimposed on the background spectrum proportionally to its molar absorptivity, the molar absorptivity being evaluated from normal transmission spectroscopy. If IRS is to serve as a qualitative and quantitative tool for investigating surface reactions in electrochemistry, it is important to understand the factors which are responsible for determining the character of an IRS spectrum. Thus theoretical and experimental analyses were undertaken. These analyses are a further elaboration of a previous work12and particular emphasis will be on IRS using these tin oxide coated glasses. The general formulas applicable to this problem are derived from concepts of physical optics. Similar conclusions are obtained from Maxwell’s equations using suitable boundary condition^.^,^
Doubly distilled water and reagent grade chemicals were employed for solutions. Computations were performed on a Univac 1107 computer using ALGOL language.
Theory The light ray (as shown in Figure 1) enters the conducting film (hereafter referred to as a film) through the transparent glass substrate and undergoes multiple reflections in the film. These reflections give rise to an interference phenomenon which, of course, means that the light intensity emerging from the glass plate is wavelength dependent. A spectrum of a species at the surface of the film obtained by IRS would be, in some manner, superimposed on this interference pattern. For normal incidence of the light, an expression relating the reflection from thin films has been derived by Murmann and Forsterling.6 The derivation in this paper is a generalized formula valid for any angle of incidence. The problem is divided into two parts. First, the Fresnel reflective coefficients are calculated for reflections at the interface of two media, either one or both absorbing the radiation. These values are used next in the general formula first derived by Forsterling for normal incidence for reflection from thin films, but now modified to include any angle of incidence. Secondly, an approximate method to calculate the attenuation index of the material of the thin film from a single transmission experiment will be shown. The complex Fresnel reflective coefficient, 72, at the interface (see Figure 1) of the two absorbing media, film and solution, for light, polarized perpendicular to the plane of incidence is given by
Experimental Section Antimony-doped, tin oxide coated glasses were obtained from Corning Glass Co. (Corning, N. Y.) Details of surface properties, electrical contacts, and cell designs have been discussed.216 Thin films of gold were deposited on glass plates by vacuum evaporation method. Spectral measurements were performed using the Cary 15 spectrometer. An Eastman Kodak polascreen was used for polarizing the light beam. The Journal of Physical Chemistry
(1) Also referred to as attenuated total reflectance, ATR. (2) W. N. Hansen, T. Kuwana, and R. A. Osteryoung, Anal. Chem., 38, 1809 (1966). (3) W. N. Hansen, personal communication. (4) M. Born and E. Wolf, “Principles of Optics,” The Macmillan
Co., New York, N. Y.,1966. (6) J. W.Strojek and T. Kuwana, J . Electroanal. Chem., in press. (6) A. Vasicek, ”Optics of Thin Films,” North-Holland Publishing Co., Amsterdam, The Netherlands, 1960, pp 323-327.
1145
INTEIINAL REF:LECTION SPECTROSCOPY
Figwe 1. hfultiple reflections in the thin film.
where fi2 and fiaare the complex refractive indices which are equal to n2(l ik2) and n3(l i&), respectively. The refractive indices n2 and n3 and the attenuation indices k 2 and k3 are for the film and for the solution, respectively. The angle of incidence and the angle of refraction $3 are for the light ray entering at the interface. I n the above equation the angles are also complex, but they can be replaced in terms of the experimental quantities of angle of incidence $l of the light beam a t the substrate-film interface and of refractive index n1of the transparent substrate. These terms are interrelated through Snell's law as follows, assuming the media are isotopic
+
nl sin
+
=
$1
sin d2 =
fi2
f i 3 sin
43
(2)
Equation 1 can be simplified by the usual complex algebraic method, and one obtains i'2
(3)
= PZ exp(i@)
with the amplitude p 2 of
f 2 given
by
4% - 0
=
p2
where
4
=
x2
+ y2 + p2 + q2
7 =
z =(l/z/Z)[(Nz2
(4)
2(PZ
+ q!/)
(6)
- N22k22- sin2 $1)
V ( N z 2- N221c22- sin2 $J2
+
+ (2N22k2)2]-2 (7)
y = (l/d'2) [- (Nt2 - N ~ ~ k 2sin2$1)
Y ( N Z 2- N22k22- sin2 $J2
(5)
+
+ ( 2 N 2 2 k 2 ) 2 ] - 2(8)
Similar functions can be written for p and q with N3 replacing N z and ka replacing kt, where N Z = n2/nl and N 8 = n3/n1. The phase angle 0 associated with the above electric vector is then given by (9) For each reflection, the amplitude and the phase angle can be evaluated from the above equations with the corresponding numerical values. The complex refractive index could have been defined in the form a = n( 1- ik) and the same results could have been obtained. The electric vector evaluated using this complex refractive index would be the conjugate value. The
AIR SUBSTRATE FILM AIR Figure 2. Near-normal incidence of light on the thin-film and multiple reflections.
magnitude and the phase angle of the electric vector were calculated on the computer. It should be pointed out that since the phase angle is obtained only between the angles -x/2 and +n/2 from the arctan computations, the proper quadrant is chosen by examination of the sign of the real part of the solution. Murmann-Forsterling Formula. For completeness, a brief account of the derivation for the reflectivity from thin films on glass substrates will be given here. I n Figure 1, the light ray is refracted in the substrate a t an angle $1 and is partially reflected with a Fresnel coefficient f1 = p1 exp(i7). It is partly transmitted through the film of thickness d with a coefficient 21. This transmitted part is reflected at the film-solution interface a t C with a coefficient 72 = p2 exp($), the refracted angle being #2 in the film. The light ray CD is once again partly reflected at D with a coefficient 73, which is equal to -Tl, and transmitted at the filmsubstrate interface (point D) with a coefficient &. The progressively attenuated rays thus undergo multiple reflections in thin films with the attenuation indices of solution and thin film determining the character of the rays. The emergent ray DH is out of phase by S = 4nnzd cos $2/X due to the path difference of 2da2 cos $2 in the film. These partly emergent electric vectors may constructively or destructively interfere with the first reflected ray. The ratio of the resultant to the incident amplitude of the electric vectors is then given by the summation of all these
E
=
(&/E,) = Tl
+ &k(l +
?2T3
exp(i8)
?22f32
+
exp(2iS). . .
(10)
Making use of the relationship TI = -% and T12 = 1 - 1122, the geometric summation gives
E
= TI
+
exp(i8)/l
+
exp(i8)
(11) and the reflectivity is then given by EE*. On simplifying, one obtains for reflectivity T2
TIT2
Volume 78, Number 4
April 1968
V. S. SRINIVASAN AND T. KUWANA
1146
+ (aPd2+ 2PlPZa cos (7 - (P + 6)) + (aPlPz)2+ 2PlPZa [Y + (P + 611
P12
R=
1
COS
(12)
with a = exp(-8i,) and 6 = 6, (im = imaginary, re = real). The reflections from thin films can be simulated through calculations using this equation. Determination of Attenuation Index from Transmission Measurements. In Figure 2 the light ray is near normal incident to the air-glass interface with a transmission coefficient of tag(the subscripts a = air, g = glass, f = film). Part of this ray is further transmitted at the glass-film interface with a coefficient of lgf. This ray travels through the thin film of thickness d, and the refractive index a2of the film is
+ ikz)
az = nz(l
(13)
The film introduces a phase shift 8, and with incident angle e very small (cos 0 S l), the phase shift is given by 2a
1=
--nzG?
x
Part of the ray in path BC is then reflected at the filmair interface with a coefficient ffswhich is reflected again at the film-glass interface with a coefficient of f f g . All of these partly emerging electric vectors can constructively or destructively interfere. The resultant ratio of amplitude of these electric vectors is then
I:[
E =
-
=
Zaglgf[Zfa exp(iS)
+ exp(3iB)
=
LgtgAf,exp(i8)/[1
+.
,
...]
+ ff,ftg exp(i28)1
(15) (16)
The ratio of the intensities is obtained by multiplying eq 13 by its conjugate. The corresponding magnitudes of the complex quantities are tag, tgf, tfa, rf,, and rfg. It is easy to see that the function has a cosine term in the denominator and is capable of having a maximum and minimum value for the extreme values of 1 or -1 for the cosine function. In terms of the magnitudes, the extreme values are then evaluated by using
I- -
tgf2tag2tfa2a/
[I
A
a2rfa~rg]
IO
and
The experimentally obtained quantity is the absorbance which is equal to -log (I/Io). Using different values of the attenuation index kz for the film, tin oxide in the present case, the absorbance at various wavelengths is evaluated. The kz which produces a calculated interference-type spectrum with the magnitude of minimum and maximum of absorbance at various wavelengths corresponding to the experimentally observed spectrum is taken as the best value of ICz. The assumption is made that kz is independent of wavelength. The value of IC2 = 0.0035 is found and is in reasonable agreement with the value of 0.004 reported by Hansen.s
ResuIts and Discussion The experimental reflection spectra of glass coated with a tin oxide film in contact with air and with water for light polarized-normal to the plane of incidence is shown in Figure 3, where the absorbance A is defined as -log (reflectivity). The index of refraction of the borosilicate glass was 1.49 and the angle of incidence, 4, was 72". The optical constants of the tin oxide film nz, kZ,and the thickness, d, were determined from the transmission experiments to be 1.88,0.0035 and 960 mp, respectively. The value of d is near the 1 p thickness suggested by the supplier of these coated glasses. Using the above values, theoretical spectra were reconstructed from computer calculations which were in fair agreement with the experimental ones, although agreement at all wavelengths is not expected since the
(17)
where a = e x p (-T4 n s Z/wi)
Both tgf and tfa can be obtained from the transmittance equations, where 1
I
420
460
I
500
I
540
1 580
I
620
Wavelength, mB.
with nl equal to the refractive index of glass. The magnitudes of the other transmission and reflection coefficients can be evaluated by eq 19 and The Journal of Physical Chemistry
Figure 3. Reflection spectra of SnOg glass: - - - -, air; , solution. Discontinuities of curves due to changing absorbance scale of spectrometer.
-
660
1147
INTERNAL REFLECTION SPECTROSCOPY
380
420
460
500
540
580
620
Wavelength, mp.
Figure 4. IRS of eosin-Y dye under various conditions. Effect of ks on absorbance.
510
520
530
540
550
560
Wavelength, mp.
assumed independence of refractive indices on wavelength is not completely valid. The results, as confirmed by both the experimental and simulated spectra, clearly show that changes in the position and the magnitude of the interference maxima are caused entirely by a change in the index d refraction of the third phase from 1.00 (air) to 1.33 (water). If the absorbance of a species is independent of wavelength and the film is absent, the IRS spectrum would be a straight line parallel to the wavelength axis. The presence of the tin oxide film causes the usual interference pattern, but the absorbing species superimposed on this spectra would not be a straight line. A maximum absorbance due to the species would be observed and would coincide with the maximum of the interference peaks, assuming a constant value of k3. The experimental absorption spectra is determined as the difference between a solution with k3 equal to zero, i.e., water, and the test solution where lc3 is greater than zero. In Figure 4 the relative change in absorbance is plotted as a function of wavelength with k3 = 0.005. Notice that as long as the index of refraction of the reference base line is the same as the index of refraction of the test solution, concentration of the absorbing species will be proportional to k3 at a constant wavelength. The shape of the spectrum for a species at the solution-film interface is greatly dependent on the index of refraction n2 of the tin oxide film and on the thickness of the film, but as can be seen from eq 7 and 8,kz, since it is much less than 1, does not affect the spectrum to the first order. To study the IRS of an absorbing species with and without the tin oxide film, aqueous solutions of eosin-Y and sodium indigo sulfonate were examined. Figure 5A shows a spectrum of eosin-Y using a plastic plate for the cell. This plate was used rather than a glass plate because there was evidence of less surface adsorption by eosin-Y. By use of ey 1 and 3, the ka value for the dye was calculated. With this value, a simuIcLted spectrum for a glass plate coated with the tin oxide film was found from eq 12. This spectrum,
Figure 5. IRS of sodium indigo sulfonate under various conditions: A, ATR; B, simulated; C,experimental.
500
540
580
620
660
700
Wavelength, rnp.
Figure 6. Effect of kz on absorbance: B, simulated; C,experimental.
A, ATR;
Figure 5B, is compared to the experimentally determined one, Figure 5C, for eosin-Y in the cell with a tin oxide coated glass plate. Sodium indigo sulfonate was studied in the same manner, and these results are shown in Figure 6. Of particular interest is the relationship between the position of the absorption maximum with and without the tin oxide film. For eosin-Y without the film, the absorption maximum occurs near 520 mp, and for sodium indigo sulfonate, it occurs near 610 mp. When the tin oxide film is introduced, however, the eosin-Y peak shifts to 550 mp, while the sodium indigo sulfonate peak shifts in the opposite direction to 570 mp. Thus compounds with well separated absorption maxima absorb at nearly the same wavelength when studied a t a tin oxide film. It is evident from these results that without a thorough knowledge of the absorption properties of a species produced by an electrochemical reaction, an investigator may conclude erroneously about its spectral characteristics. Volume 79,Number 4
April 1968
A. ET. VIJH
1148
-36 t
I
SEC1
I
I
Time.
Figure 7. Change in absorbance for supporting electrolytos at applied potentials.
An additional interesting phenomenon is observed when these thin films are used as electrodes in contact with electrolytic solutions. That is, the IRS absorbance changes with applied potential in the absence of any electrolysis of electroactive species. For example, a change, similar to that noted previously for tin oxide filmsj2is shown in Figure 7 for a tin oxide film in contact with an acetate buffer solution when a square-wave potential pulse of $0.6 V vs. reference saturated calomel electrode is applied. The rate of change of absorbance lags considerably behind the rise and fall of the poten-
tial. The maximum absorbance change again occurs at the maximum of the “interference” peaks. Similar changes also occur with glass coated with vapor-deposited gold films, with the only difference being that the absorbance changes are much faster than with tin oxide. It is important that these changes affect the magnitude of the absorbance only and not the wavelength of the “interference” maximum. This suggests that the refractive index is not being changed in the immediate vicinity of the film surface. Perhaps optical rotation of the penetrating electric vector at the film solution interface due to the applied potential can explain these observations. Further work is necessary to understand these results.
Acknowledgment.
The fruitful discussions with
W. N. Hansen of the North American Aviation Science Center are greatly appreciated. The assistance of
R. Chang during the early part of this work is acknowledged. The authors gratefully acknowledge the support of this work by Grant No. G X 14036 from the Research Grant Branch of National Institutes of General Medical Sciences, National Institutes of Health, and by Navy Ordnance Laboratory Contract N123(62738)56006A.
Electrolytic Hydrogen Evolution Reaction on Aluminum in Acidic Solutions by A. K. Vijh R h D Laboratories, Sprague Electric Company, North Adams, Massachusetts
01247 (Received J u l y 31, 1967)
The mechanism of the electrolytic hydrogen evolution reaction (h.e.r.) has been studied on aluminum in several acidic solutions. Experimental measurements consist of galvanostatic current-potential relationships, open-circuit decay from initial cathodic potentials, cathodic-charging curves, and determination of apparent heat of activation. Mechanistic conclusions are based on Tafel slopes, exchange current densities, reaction orders, apparent heat of activation, absence of arrests in the charging curves and potential-decay profiles, nature of capacity-potential curves calculated from open-circuit decay profiles, and some general considerations, e.g., melting point and heat of atomization of aluminum. Significance of other approaches for determination of mechanism of h.e.r. in relation to aluminum is briefly discussed. Initial discharge step is suggested as the likely rate-determining stage (rds) in the over-all reaction; this inference, however, is not entirely conclusive, owing to the difficulties involved in distinguishing initial discharge step from the electrochemical desorption step as the probable rds.
I. Introduction In the present investigations, an attempt has been made to examine the mechanism of the hydrogel1 evolution reaction (h,e.r.) on aluminum in acidic solutions. The solutions in which the h.e.r. has been studied are Oa2 H2S04,Oa5 H2S047o‘s6 HzS04, la7 H2S04J 1 N CH3COOH, and (2 N CH3COOH -I- 1 N NH4COThe Journal of Physical Chemistry
OCH3). The only previous results available in the literature are the galvanostatic evaluation of the Tnfel slopes for the h.e.r. on aluminum in 1 h’ HC1’ and in 2 N H2S04.2 These studies, however, were carried out (1) A. Hickling and F. W. Salt, Trans. Faraday Sac., 36, 1126 (1940).
