2766
Anal. Chem. 1906, 58, 2766-2771
Square Wave Voltammetry for a Pseudo-First-Order Catalytic Process Jilin Zeng and Robert A. Osteryoung* Department of Chemistry, State University of New York, Buffalo, New York 14214
A theoretlcal expression for square wave voltammetry for a pseudo-flrst-order catalytk process is derlved. The vaHdity of the theory Is tested by determlnation of rate constants for TIS+/NH,OH, TiS+/ClO3-, and Fe2+/NH,0H redox catalytlc systems. The rate constants found are 41.16 f 1.02 L/(mol s), (5.16 f 0.33) X lo4 L/(mol s), and 150.8 f 6.3 L/(mol s), respectively; these values are In good agreement with the literature. The advantages of square wave voltammetry for the catalytk case over the dc method for analytkal purposes are presented.
Polarographic currents controlled by the rate of a catalytic process that regenerates the substance reacting at the electrode have been employed analytically. The simplest case, the pseudo-fist-order catalytic process, has received considerable attention and has been treated theoretically by Brdicka and Wiesner ( l ) ,Pospisil ( 2 ) ,Miller (3),and Delahay and Stiehl (4)for dc polarography, Bess, Cranston, and Ridgway (5) for double potential step chronoamperometry, Kim and Birke (6) for differential pulse polarography, and O'Dea et al. (7)who presented a numerical solution for square wave voltammetry. Ti3+/NH20H(6, l o ) ,and Fe2+/NH20H Ti3+/C103-(6,8,9), ( 1 1 ) redox catalytic systems were employed in various investigations to verify the theoretical considerations. In this present treatment the boundary value problem for square wave voltammetry is solved analytically and a theoretical expression is derived. The dependence of the catalytic currents on the experimental parameters is evaluated. The rate constants for Ti3+/C103-Ti3+/NH20H,and Fe2+/NH20H redox catalytic systems are determined by use of a simplex optimization procedure based on he Nelder-Mead algorithm (12). The analytical utility of catalytic reactions employing square wave voltammetry is discussed.
where Cjo = Cb/(l + O j ) , Oj = exp[(Ej - El/2)nF/(RT)], Ejis the electrode potential at the j t h pulse, EIlzis the reversible half-wave potential, and 7 is the duration of a pulse. The concentration of the reduced form, C,(x,t),is the solution of the boundary value problem dC,(x,t)/dt = DId2C,(X,t)/dX2- kC,(x,t) ( t > 0, x > 0) (4)
C,(x,O) = 0 ( x > 0) C,(O,t) = Co(t),lim C,(x,t) = 0 x-m
(5)
( t > 0)
where k is the pseudo-first-order rate constant. This boundary value problem is simplified by introducing the transformation
u ( x , t ) = C,(x,t) exp(kt) (7) In terms of the function u(x,t)the boundary value problem is
( t > 0, x
d u ( x , t ) / d t = D,d2u(x,t)/dx2
u(x,O) = 0
(x
> 0)
> 0)
u(0,t) = u o ( t ) ,lim u ( x , t ) = 0 X--
THEORY
Ox
+ ne
Red
+Z
Red
~t
kc
Ox
(1) (2)
We consider conditions of semiinfinite linear diffusion, a reversible electrode reaction with only the oxidized form initially present and an irreversible regeneration reaction (eq 2) with the oxidizing agent, Z, present in large excess. We assume the diffusion coefficients,Do and D,, are equal. The wave form has been described previously (7).For a reversible electron transfer process represented by eq 1, the concentrations of the electroactive species a t the electrode surface are related by the Nernst equation and are constant during the period of a pulse. Let Cb be the initial concentration of the oxidized form. The concentration of the reduced form at the electrode surface, C"(t),a t any time is 0003-2700/88/0358-2766$01.50/0
(8) (9)
( t > 0)
(10)
Taking the Laplace transforms of eq 8,9, and 10, we obtain d2ii(x,s)/dx2
- (s/D,)ii(x,s) = 0 ii(x,O)
(x
> 0)
=0
(11)
(12)
~ ( 0 , s ) = ii"(s), lim u(x,s) = 0 x-m
The pseudo-first-order catalytic process that we treat is given by the general equation
(6)
(13)
The solution that satisfies the conditions of eq 11through 13 is ii(x,s) = ii"(s) exp(-x(s/D,)1/2)
(14)
Since C,(x,t) = u(x,t)exp(-kt) (referring to eq 7), according to the theorem on substitution (13)the Laplace transform of Cr(x,t),C,(x,s), is c,(x,s) = P ( s ) exp(-x((s
+ k)/D,)1/2)
(15)
where C O ( s )is the Laplace transform of C o ( t ) rn
co(s) = s - ~ C ( C O - ~Coj-,) exp(-stj),
tj =
0' - 117
(16)
]=1
We are interested in the flux of the reduced form at the electrode surface $(t) = Dr[dcr(x,t)/axlx=~ (17) Differentiating eq 15 with respect to x , introducing x-= 0, and substituting eq 16 into the resulting equation for Co(s), we obtain 0 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1986
2767
m
$(SI
= -(D,(s
+ k)'/'/s)C(Coj j=1
- Coj-J exp(-stj)
2
(18)
Taking the inverse transform of eq 18, we obtain the flux of the reduced form at the electrode surface
.,.
H
n
m
$ ( t ) = --D11'C(Coj -Coj-J[(r(t - t j ) ) - l / zexp(-k(t j=l
tj))
+ kc'/'
-
erf((k(t - t j ) ) l l 2 ) ] (19)
where the notation erf(X) represents the error function x erf(X) = ( Z / X ' / ~ ) J exp(-z2) dz (20) 8.1
The current is calculated by multiplying the flux of the oxidized form a t the electrode surface, Do[dCo(x,t)/dx],=o (=-o,[dC,(z,t)/dx],,,), by the area of the electrode, A , and by the charge involved in the reduction of one mole of the oxidized form
i(t) = nFA +(t)
-8.1
VS. REV. E((&?) C V )
Flgure 1. Calculated voltammograms in the purely kinetic region: n
= 1; E, = 5.0 mV; E,
(21)
Assuming the currents are measured a t the end of each pulse, the expression for the current measured a t the end of the mth pulse is
8.8 POTENKAL
= 50.0 mV; kr, (1) 2.0, (2) 4.0.
I
n n
m
i(m) = n F A ( o , / ~ r ) l / ~ C ~ C Q ~-[j( r+n1)-ll2exp(-k(m j=l
+ 1 ) ~+)( r ~ k )erf((k(m ~ / ~ - j + 1 ) ~ ) l /(22) ~)] where Qj = 1/(1+ 0,) - 1/(1+ 0,-,) -j
8
According to the reaction scheme represented by eq 1,the pseudo-first-order rate constant, k , is
k = k,C,
+
8.8
-8.1
POTENTIAL V S . REV. ECI/2> CV)
(23)
where Cz is the concentration of the oxidizing agent, Z. When k , approaches zero, or Z is not present, the exponential in eq 22, exp(-k(m - j l ) ~tends ) , to unity and the ~), zero. error function in eq 22, erf((k(m - j l ) ~ ) l / approaches Then eq 22 reduces to
+
8.I
Flgure 2. Calculated voltammograms in the mixed region: n
= 5.0 mV; E,
= 50.0 mV;
k T , (1) 0.02,
=
1; E,
(2)0.10, (3)0.25.
I
m
i(m) = ~ F A ( D , / ~ ~ ) ~ : z c- j~ + ~ iQ ) 1 /~ 2 / (24) (~ j=l
This is identical with that obtained in the theory of simple linear diffusion for square wave voltammetry (14). Properties of Catalytic Currents. First of all we consider a situation where kr is very large. In that case the exponential in eq (22) approaches zero and the error function tends to unity. Then eq 22 reduces to
+
i(m) = nFA(D,k,CZ)1~2Cb/(1 e,)
(25)
When the electrode potential is so negative relative to the reversible half-wave potential that 0, is essentially zero, the current reaches a limiting value, il
The current is then totally controlled by the kinetics of the redox catalytic system and is independent of the time scale of the experiments. In this purely kinetic region the voltammograms have a sigmoid shape and the plot of the staircase base potential against log [(il- i(rn))/i(m)] has a slope of 0.059 V/n a t 25.0 O C and the current is proportional to the square root of the concentration of the oxidizing agent. Voltammograms calculated for the kinetics in this region are presented in Figure 1. The function +(t)in Figure 1and elsewhere is defined by $(t ) = i(t) / [ ~ F A ( D , / T T ) ~ / ~ C ~ ] (27)
When k r is less than 2, both diffusion and the rate of the catalytic chemical reaction come into play. In this mixed
P O T r n L vs.
€(In> CY>
Flgure 3. Calculated voltammograms for net currents: n = 1; E, = 5.0 mV; E, = 50.0 mV; k T , (1) 0.02, (2) 0.10, (3) 0.50, (4) 1.00.
region the shape of the voltammogram is sensitive to the kinetic parameters. Voltammograms calculated for k r values in this region are shown in Figure 2. In the purely kinetic region the net current, Ai(m) = (i(m) - i(m + l)),is
~ i ( m= ) nFA(D,k,CZ)1/2Cb[i/(i + e,)
- i/(i
+ ern+&
(28) Note that i(m) and i(m + 1)correspond to the forward and reverse currents (7) and give rise to the off-set curves of Figure 1. In the mixed region the explicit expression for the net current is rather complex. The general features are best illustrated by the results of calculations. The voltammograms shown in Figure 3 were obtained by plotting the net currents vs. the staircase base potential (in both regions). It is seen that the voltammograms have a symmetric bell shape re-
2768
ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1986
Table I. Some Representative and Comparative Values of the Net Maximum Current Function and Peak PotentialsD kT
peak potential (mV) vs.
0.020 0.100 0.500 2.000 4.000 6.000 8.000
-0.24 -0.22 -0.14 -0.02 -0.00 -0.00 -0.00
Wmax W , , a x l ( k T P 2 0.931 0.947 1.190 1.915 2.667 3.263 3.768
6.583 2.995 1.683 1.354 1.333 1.332 1.332
"Conditions: n = 1; step height, 5.0 mV; amplitude, 50.0 mV; frequency, 100 Hz. gardless of the kinetic parameters. The peak potential coincides with the reversible half-wave potential. In the mixed region the net current is relatively insensitive to the kinetics of the system. In the purely kinetic region, it is proportional to the square root of k T (see Table I). Determination of Rate Constant from Experimental Currents. The rate constants can be evaluated in the mixed region by curve fitting employing a simplex optimization procedure. The experimental voltammogram is fitted to a normalized form of the theoretical expression for the currents rn
+(m)= CQ,[(m- j
+ 1)-1/2exp(-k(m
-j
,=1
(krT)lI2 erf((k(rn - j
+ 1 ) ~+)
+ l ) ~ l l l ~ (29) )]
In the purely kinetic region the rate constants can be calculated by employing eq 28. The values of A and the diffusion coefficient, D , needed in the calculation can be obtained by running the same experiment as in the measurement of the catalytic currents in the absence of the oxidizing agent. Under the conditions: nE, = 5.0 mV (E is the step height of the staircase base potential), nE, = 50.0 mV (Eswis the amplitude of the square wave measured from the staircase base potential), the value of nFAD1I2Cbis given by
nFAD1I2Cb= Aid,p(nr)1'2
(30)
where Aid,p is the net peak current measured in the pure diffusion experiment and T is the period of a pulse in the pure diffusion experiment. For the same value of nE, and nE,, the value of nFAD1I2Cb can be expressed as follows (referring to eq 27 and Table I):
nFAD112Cb= Aic,piri~z( 1.332k112)
(31)
where Aic,p is the net peak current measured in the purely kinetically controlled experiment. Substituting eq 30 for nFAD1I2Cbin eq 31, solving for the pseudo-first-order rate constant, k, one obtains
Analytical Utility. Catalytic currents employing dc polarography have been used for laboratory analysis for many years. When the catalytic currents are used for analysis, fast catalytic reactions are highly desired. The system is ideally in the purely kinetically controlled region. Therefore, we can take advantage of the fact that although the catalytic currents are independent of the square wave frequency, square wave voltammetry has a very low background level a t low frequencies. Under reasonably favorable conditions we can expect that when employing square wave voltammetry the detection limit of catalytic currents can be a t least an order of magnitude lower than when employing dc polarography. In addition, analysis times employing square wave voltammetry are significantly decreased.
EXPERIMENTAL SECTION Materials. All chemicals were reagent grade. Potassium chlorate and triethanolamine hydrochloride were purified by recyrstallization (twice); others were used without further purification. A stock solution of Ti(1V) was prepared by dissolving 0.2396 g of titanium powder with 25 mL of H2S04(l:l),oxidizing with 6 drops of perchloric acid, and then fuming three times to expel the excess perchloric acid. The concentration of the stock solution of titanium sulfate was 2.0 X M and 0.8 M in HzS04. Deionized water was distilled over potassium permanganate before use. Aqueous stock solutions were used except for hydroxylamine hydrochloride, which was weighed out just prior to use. Oxygen was removed by purging with nitrogen purified by passing through vanadous solutions twice and saturated with water vapor. Apparatus. Electrochemical experiments were carried out employing a PDP-12 digital computer interfaced with a homemade potentiostate (15) and a stationary mercury drop electrode (EG&G PARC Model 301). The electrode area was chosen to be "large" ( A = 0.0272 cm2). The temperature of the electrochemical cell was controlled at 25.0 f 0.1 "C. Potentials were measured with respect to a Ag/AgCl reference electrode prepared according to Meites (16) unless otherwise stated. Programs for wave form generation and data acquisition as well as data processing were written in FORTRAN iv and in assembly language. A simplex optimization program based on he Nelder-Mead algorithm (12) was employed to simultaneously evaluate the reversible half-wave potential and the pseudo-first-order rate constant by fitting the experimental currents to the dimensionless current function (eq 29). The program starts with the peak potential of the experimental voltammogram and an arbitrarily chosen rate constant, then adjusts these values to minimize the complement of the correlation coefficient of the linear regression of the experimental data vs. the calculated dimensionless current function. The procedure terminates when the best estimates and the next to the best estimates differ by less than 0.1%. RESULTS AND DISCUSSION Determination of Rate Constants. The Ti3+/C103-, Ti3+/NH20H,and Fe2+/NH20Hredox catalytic systems were studied. The results of previous studies found in the literature are summarized in Table 11. In the following experiments the step height of the base staircase was 10 mV and E,, was 50 mV. Currents were averaged over 10 measurements. Dependence of il on the Concentration of the Oxidizing Agent, Cz, and the Determination of Rate Constants in the Purely Kinetic Region. Sigmoid voltammograms were obtained with the Ti3+/C103- system a t a frequency of 20 Hz and a t concentrations of C10; as low as 0.01 M. The composition of the electrolyte was 0.2 M H2S04,0.1 M H2C20,, and varying amounts of KC103. The concentration of Ti(1V) M in catalytic experriments and 5.0 X M was 1.0 X for purely diffusion controlled measurements. Representative voltammograms are shown in Figure 4. The limiting current, i,, or the net peak current. Ai,, normalized with respect to the square root of the concentration of KC103, is constant (165.9 & 4.7 WAL1/2/mo11/2).Rate constants, calculated employing eq 32, are in good agreement with those obtained by Birke et al. (6) using differential pulse polarography. The results are listed in Table 111. Determination of Rate Constants in the Mixed Region. In this region rate constants were evaluated by the curvefitting procedure described above. ( 1 ) Ti3+/NH20HSystem. Voltammograms were recorded for 1.0 X M Ti(1V) and 0.1 M ",OH in 0.2 M H2C204 a t frequencies ranging from 10 through 200 Hz. The results, which are representative for the data analysis in the mixed region, are listed in Table IV. Representative voltammograms (symbols) and their theoretical fits (solid curves) are shown in Figure 5. Figure 6 shows a representative linear regression plot (experimental currents vs. the calculated dimensionless current function of the theoretical fit). The rate constant found was 41.3 f 1.1L/mol s), which is in good agreement
ANALYTICAL CHEMISTRY, VOL. 58,
NO. 13, NOVEMBER 1986 2769
Table 11. Summary of Evaluated Constants for Tia+/C1Oc,Ti3'/NH20H, and FeZt/NH20H Catalytic Redox Systems catalytic redox system
rate constant, L/(mol s)
background electrolytes
Ti3+/NHz0H
0.2 M HzCzO4 0.1 M HzCzO4,0.1 M HzS04(pH ca. 0.9)
Ti3+/C103-
0.2 M HzCzO4, 0.4 M H2S04,0.25 M NaZSO4,0.1' gelatin 0.2 M HZC2O4, corrected for comparison by a stoichiometric factor of 6 0.1 M HzCzO4, 0.2 M HzS04(pH ca. 0.9)
42.0 f 0.2 22 46 41.16 f 1.02
10 6
8 9 6
0.1 M HzCzO4, 0.2 M HzS04
104 2.6 x 104 5.6 x 104 6.1 x 104 (5.61 f 0.33)
0.1 N NaOH, 0.01 M TEA, 0.002% gelatin 0.1 N NAOH, 0.01 M TEA
186 f 10 150.8 j~6.3
0.2 M H2CzO4
Fezt/NHz0H
ref
a
lo4
X
a
11 a
This study. Table 111. Dependence of the Catalytic Currents on k T and the Evaluation of Rate Constants in the Purely Kinetic Regiona Cz, M
il/CzlIz, FA L1/z/moll/z
0.01 0.02 0.04 0.08 0.10
164.5 167.9 169.2 169.5 158.2
K, L/(mol s) 5.26 5.72 5.93 5.91 5.15
x 104 x 104 x 104
x 104 x 104
(5.61 i 0.33)
x 104 a 1.0 X lo4 M Ti(S04)2, 0.2 M H2S04,0.1 M H2C204,KC103, freq = 20 Hz, AE = 5 MV, E,, = 50 mV.
1
I
Table IV. Evaluation of the Rate Constants and the Reversible Half-Wave Potentials of Ti3+/NH20HSystem in the Mixed Regiona freq, Hz
rev Ellz,V
rate constants, L/(mol s)
10 25
-0.279 -0.278
40.06 40.76
50 50 50 50 50 50
-0.278 -0.278 -0.277 -0.278 -0.277 -0.277
40.54 40.63 40.71 40.64 40.72 40.65
75 100 150 200
-0.277 -0.278 -0.277 -0.277
41.36 41.55 43.57 42.73 41.16 f 1.02
h
5
a 1.0 X M Ti(S04)*,0.1 M NHzOH,0.2 M HZCZO4, AE = 10 mV, E., = 50 mV.
5
a
POTENTIAL
vs.
JCE
(V)
Flgure 4. Voltammograms in the purely kinetic region: 1.0 X
M Ti(S04),, 0.2 M H2S04,0.1 M H2CzO4, KClOB(1) 0.02 and (2)0.10 M. frequency = 20 Hz, E, = 10 mV, E,, = 50 mV.
with the result reported by Blazek and Koryta (IO). (2) Ti3+/C10
Figure 7. Voltammograms at different frequencies; comparison to theoretical fit: 5.0 X M Ti(SO,),; 5.0 X M KClO3; 0.2 M H,SO,; 0.1 M HzC,O,; E, = 10 mV; E, = 50 mV: frequency (1) 450, (2) 550: (3)700 Hz; symbols, experimental data: solid curves, theoretical fit.
n
-8.81 -8.1
-8.2.
-8.4
-8.3
POTENTIAL VS. S C E
Figure 10. Voltammograms of 5.0 X
-8.5
lV1
lo-'
M Ti(SO,),: background electrolytes, 0.5 M (NH,),SO,, 0.2 M H,S04, 0.1 M H,C,04, 0.1 M KCIO,, E, = 10 mV, E, = 50 mV: frequency = 10 Hz; (1) background, (2)without subtraction of background, (3)background subtracted.
- I .8
-I . I POTENTIAL v s . AgiAgCl
1 -1.2
-1.3
[VI
Figure 8. Voltammograms at different frequencies: 5.0 X M Fe(II1); 5.0 X lo-* M TEA: 5.0 X lo-' M ",OH; 0.1 M NaOH; E, =
10 mV; E , = 50 mV; frequency, (1)25, (2) 100,(3) 500 Hz; symbols, experimental data; solid curves, theoretical fit. f 10 L/(mol s) (11). They are in good agreement considering the interference of oxygen. Analytical Utility. We do not present the following experimental conditions as optimized for the determination of microamounta of titanium; rather they should be taken in the context of dealing with the practical problem associated with catalytic currents applied to the determination of microamounts of material employing square wave voltammetry. Choice of Electrolyte. In the following experiments ammonium sulfate was used. It was shown by evaluating the rate
constants at varying concentrations of KC103that the addition of ammonium sulfate had no effect on the kinetics of the redox catalytic system. However, in the presence of ammonium sulfate the background was improved. Figure 9 shows the background in the presence and in the absence of ammonium sulfate. Low Frequency. In the kinetically controlled region the catalytic currents are independent of frequency; however, the charging current decreases as the frequency decreases. Therefore, a low frequency is desired for the measurement of the catalytic currents and 10 Hz was employed. Current Measurement. In analytical use we measure and integrate the catalytic currents over a fraction (the last 1/3) of a period. This is actually an analog filtration that significantly reduces the background level. Constant Temperature. Catalytic currents are significantly influenced by the temperature of the solution. In all experiments the temperature of the electrochemical cell was controlled a t 25.0 f 0.1 "C. A calibration curve was constructed for solutions 0.5 M in (NH4)$04, 0.2 M in H2S04,0.1 M in H2C204,and 0.1 M in KClO,. The concentrations of Ti(SO,), ranged from 5 X lo-@
Anal. Chem. 1886, 58, 2771-2777
M through 1X lo4 M. The slope of the calibration curve was 0.506 f 0.035 pA/pM. The minimum detectable difference between the background and sample solution estimated by paired measurements (5) was 0.025 pM,which is over an order of magnitude lower than in the dc polarographic method (17). A voltammogram of a 5.0 X lo4 M Ti(IV) solution is presented in Figure 10. ACKNOWLEDGMENT The authors thank Janet Osteryoung for helpful discussion. Registry No. Ti, 7440-32-6;Fe, 7439-89-6;“,OH, 7803-49-8; ClOs-, 14866-68-3. LITERATURE CITED (1) Brdicka, R.; Wlesner, K. Collect. Czech. Chem. Commun. 1847, 72, 39. (2) Pospisil. I . Collect. Czech. Chem. Commun. 1953, 18, 337. (3) Miller, S. L. J . Am. Chem. SOC.1852, 7 4 , 4130. (4) Delehay, P.; Stlehl, G. L. J . Am. Chem. SOC. 1852, 7 4 , 3500. (5) Bess, R. C.; Cranston, S. E.; Rldgway, T. H. Anal. Chem. 1976, 4 8 , 1619.
2771
(6) Kim, M.-H.; Birke, R. L. Anal. Chem. 1983, 55, 522. (7) O’Dea, J. J.; Osteryoung, Janet; Osteryoung, R. A. Anal. Chem. 1981, 53, 659. (8) Koryta, J.; Tenygi, J. Collect. Czech. Chem. Commun. 1854, 79, 839. (9) Smith, D. E. Anal. Chem. 1863, 35, 610. (10) Blazek, A.; Koryta, J. Collect Czech. Chem. Commun. 1853, 18, 326. (1 1) Koryta, J. Collect Czech. Chem. Commun . 1854, 79, 666. (12) Olson, D. M. J . Qualify Techno/. 1874, 6 , 53. (13) Doetch, G. GUMS to the Applications of the Laplace and 2. Transforms, 2nd English ed.;ReinhoM: London, New York, 1971; p 23. (14) Krause, M. S., Jr.; Ramaiey, L. Anal. Cttem. 1868, 47, 1362. (15) O’Dea, John J. Ph.D. Dissertation, Colorado State University, Fort Collins, CO, 1979. (16) Meites, L. In PolarmraDhic Technloues, 2nd ed.: Wllev: New York. - . 1956; p 68. (17) Mashinskaya, S. Ya.; Chlkrgzova, E. G.; Vatama, I. I.; Baskin, V. N. Zavod. Lab. 1884. 50(7), 11.
RECEIVED for review February 3,1986. Accepted June 9,1986. This work was supported in part by the National Science Foundation under Grant CHE-8305748.
High-Resolution Spatially Resolved Visible Absorption Spectrometry of the Electrochemical Diffusion Layer Chwu-Ching Jan and Richard L. McCreery*
Department of Chemistry, The Ohio State University, Columbus, Ohio 43210
Concentration vs. distance profiles are fundamental to a variety of electrochemical processes but have not been observed previously at resolutions better than 25 pm. I n the present work, a collimated He-Ne laser beam was passed parallel to a planar electrode surface and then magntfied and imaged onto an array detector. Each pixel of the detector monitored the beam intensity passing the electrode at a particular distance from the surface, with a solution of better than 5 pm. Concentration vs. distance proflies were obtained for an eiectrogenerated absorber during single and double potential step and linear sweep voitammetry experiments. The advantages of the method over previous interferometric approaches include selectivity, sensitlvity, and higher spatial resolution. The limit on resolution Is determined by diffraction near the electrode and in the imaging optics. Results and future applications of the technique are discussed.
The magnitude of the current for an electrochemical process involving an electrode in solution is determined in part by mass transport by diffusion (I, 2),convection (3,4),and migration (5). For finite current processes involving either diffusional or convective mass transport, there are concentration gradients a t the electrode/solution interface that provide the driving force for mass flow. The involvement of mass transport in electrochemistry is widespread in the areas of electroanalysis, electrosynthesis, biological electrochemistry, and electrochemical engineering, and significant theoretical and experimental effort has been expended to describe the concentration gradients and resulting mass fluxes involved. In several important but simple cases, such as planar and spherical diffusion (1,2)and the rotating disk electrode (3, 6, 3, the equations for mass transport have been solved analytically, but in the cases of complex electrode shapes (8, 0003-2700/66/0356-2771$01.50/0
9), nonideal convective systems (4),or complex reaction mechanisms, exact theories are not available. For example, flow cells used in electrosynthesis and chromatography detectors (IO,11) and density-driven “roll cells” observed in electrochemical cells containing static or flowing electrolyte (12,13) have not been rigorously described theoretically, and the behavior of concentration gradients is known approximately or not a t all. The recent interest in studying mass transport to microelectrodes (14-19)has created a need to experimentally monitor diffusion profiles to individual microelectrodes as well as microelectrode arrays. The objective of the present work is to observe complete concentration vs. distance profiles near an electrode surface at high resolution for the first time. Because of the significance of concentration profiles to electrochemical processes, numerous techniques have been developed for observing their shapes and behavior. The problem is challenging because the electrochemical boundary layer is thin, usually less than 200 pm for electroanalytical and hydrodynamic systems. Spectroelectrochemical techniques have been used very successfully for identifying and monitoring electrogenerated species (20-23),and in some cases have been used to determine concentration vs. distance profiles. Existing spectroelectrochemicaltechniques for spatially resolving an electrochemical diffusion layer involve a light beam passing parallel to the active surface of the electrode. These methods may be divided into two groups on the basis of the measured variable-refractive index or absorption. The most common technique that depends on the refractive index change during an electrochemical reaction is interferometry (24-31). The electrogenerated concentration gradient produces a corresponding refractive index gradient near the electrode which alters an interference pattern formed after the beam passes by the electrode. Although interferometric methods have been useful in several cases, they are constrained 0 1986 American Chemical Soclety
