plained by crystal lattice effects. Fadley et al. (18) have pointed out the importance of the lattice, or Madeling corrections, in binding energy measurements on solids. If the crystal structures of two compounds vary, the Madeling contribution to the binding energies would also vary, and thus affect relative binding energy measurements. The Madeling contributions to binding energy would be constant if the crystal structures were equivalent and thus not affect relative binding energy measurements. In the phosphonium salts studied here, one can best rationalize a difference in crystal structure for the triphenylphosphonium salt (No. 3). Since the proton (H) is so much smaller than any of the other R-groups in the series, it is likely that its crystal structure is different from the others. (18) C. S. Fadley, S. B. M. Hagstrom, M. P. Klein, and D. A. Shirley, J . Chem. Phys., 48,3779 (1968).
If this were the case, the phosphorus 2p binding energy observed for compound No. 3 would be expected to diviate from the observed linearity, since the Madeling contribution to the binding energy would be different than that for the other molecules. ACKNOWLEDGMEhT
We thank R. H. Cox of the Department of Chemistry at NMR data. the University of Georgia for obtaining the
RECEIVED for review February 1, 1971. Accepted April 15, 1971. One of us (W. E. S.) thanks the National Institutes of Health for a pre-doctoral fellowship during the term of this research. This work was supported in part through funds provided by the U. S. Atomic Energy Commission under Contract AT-(38-1)-645.
Spectroele,ctrochemistry-Application of Optically Transparent Minigrid Electrodes under Semi-Infinite Diffusion Conditions Milica Petek, T.E. Neal, and Royce W. Murray1 Department of Chemistry, University of North Carolina, Chapel Hill, N.C.27514 The Au minigrid electrode is evaluated for both potential and current step spectroelectrochemical experiments under semi-infinite diffusion conditions. The test reactions of 0-tolidine oxidation and titanium(1V) reduction using 2000 Ipi minigrid yield results where the optical response corresponds to linear diffusion theory at times exceedin 10-20 milliseconds. This is the period necessary for diffusion profile-averaging and is predictable by semi-theoretical arguments.
THE SPECTROELECTROCHEMICAL EXPERIMENT in which the course of an electrochemical reaction is monitored by transmission spectrophotometry of the electrode reaction diffusion layer was conceived in 1964 by Kuwana, Darlington, and Leedy ( I ) . These authors employed tin-oxide coated glass as a transparent working electrode and followed the absorbance of the quinone-imine oxidation product of otolidine in acidic aqueous solution. Kuwana and coworkers have continued study of transmission spectroelectrochemical experiments and have described the electrochemical and optical transmission properties of the SnOz-coated electrode (2, 3), sensitive kinetic spectrometers for fixed ( 4 ) and rapid (5) wavelength scan measurements, theoretical relations for transient absorbance-time response under potential step control (2, 6 4 , and several applications (2-8) which dem(1) T. Kuwana, R. K. Darlington, and D. W. Leedy, ANAL. CHEM., 36, 2023 (1964). (2) J. W. Strojek and T. Kuwana, J . Electroanal. Chem., 16, 471 (1968). (3) T. Osa and T. Kuwana, ibid., 22, 389 (1969). (4) T. Kuwana and J. W. Strojek, Discuss. Faraday SOC.,45, 134 (1968). (5) J. W. Strojek, G. A. Gruver, and T. Kuwana, ANAL. CHEM., 41, 481 (1969). (6) J. W. Strojek, T. Kuwana, and S. W. Feldberg, J . Amer. Chem. Soc., 90, 1353 (1968). (7) N. Winograd, H. N. Blount, and T. Kuwana, J. Phys. Chem., 73, 3456 (1969). (8) G . C. Grant and T. Kuwana, J. Electroanal. Chem., 24, 11 ( 1 970).
onstrate the considerable utility of transmission experiments for mechanistic understanding and kinetic characterization of electrode processes involving coupled chemical reactions. Previous semi-infinite diffusion transmission spectroelectrochemical data have been acquired mainly with the Sn02coated electrode. The deposited thin metal film (Au or Pt) electrodes, developed for internal reflection (9-11) and thin layer (12, 13) spectroelectrochemistry, are also logically adaptable to the transmission experiment (3). The mirrorlike deposited metal films could alternatively be employed in a reflecting mode under semi-infinite diffusion conditions to acquire the same absorbance-time information. Another transparent working electrode, the Au minigrid electrode, has been introduced, to transmission spectroelectrochemistry for thin solution layer experiments (14-16). Certain advantages could accrue with this particular electrode in semi-infinite diffusion transmission experiments. Because the optical transparency of the minigrid is derived from its perforated character, the minigrid electrode transmission response should be less susceptible to artifacts caused by film deposition during electrolysis. The minigrid surface properties seem to be essentially those of bulk gold, which lacks many of the eccentricities exhibited by the SnOz electrode material. Lastly, the minigrid electrode, unlike the SnOzcoated and metal film electrodes, has a low internal ohmic (9) B. S. Pons, J. S. Mattson, L. 0. Winstrom, and H. B. Mark, Jr., ANAL. CHEM., 39, 685 (1967). (10) A. Prostak, H. B. Mark, Jr., and W. N. Hansen, J. Phys. Chem., 72, 2576 (1968). (11) W. von Benken andT. Kuwana, ANAL. C H E M . 1114(1971). ,~~, (12) A. Yildiz, P. T. Kissinger, and C. N. Reilley, ibid., 40, 1018 (1968). (13) C. N. Reilley, Reu. Pure Appl. Chem., 18, 137 (1968). (14) R. W. Murray, W. R. Heineman, and G. W. O'Dom, ANAL. CHEM., 39, 1666 (1967). (15) W. R . Heineman, J. N. Burnett, and R. W. Murray, ibid., 40, 1970 (1968). (16) Ibid., p 1974. ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
1069
Table I. Au Minigrid Electrode Dimensions
Mesh, lpi 2000 1000T” loo0 500 100
Wire width,”
Wire thickness, I(
Hole sue,” I(
6.35 7.6 7.6 13.97 26.8
6.35 17.6 17.6 36.8 227
Larger wire thickness purchased on special order. Manufacturer’s stated dimensions. e Measured by weighing. d Calculated for linear diffusion potential step for C(=,t)/C’ = 0.50 hole size.
Z T 22 42 45 60 82
AmiciAmac
2.87c 7.6 f0 . 9 ~ 3.3 f 1 . 8 ~ 3.320 3 . 3 f 1.8“
Diffusion profile averaging time, secd
0.99 0.98 0.72 0.60
0.26
0.011 0.088 0.088 0.385 14.6
0
=
e r f ( ~ / 2 D ~ ’ ~assuming t~/~), D
resistance. While effects of electrode resistance are usually avoidable in potential step experiments, resistance effects can become apparent in potential sweep experiments (I 7) and are severe in controlled current experiments. The advantages of the minigrid electrode become real only under circumstances where the perforated electrode diffusionally behaves as a planar surface, permitting application of linear diffusion spectroelectrochemical theory. Certain diffusion theory arguments, presented in this report, indicated that the requisite pseudo-planar surface conditions could be attained under practical electrochemical conditions. A series of experiments has accordingly been carried out, using the oxidation of o-tolidine and the reduction of Ti(1V) in aqueous media as diffusion-only model reactions, to test the pseudo-planar diffusion predictions under both potential and current step conditions.
THEORY In a spectroelectrochemical experiment in which the optical absorbance of the diffusion profile of a stable, soluble product R of an electrode reaction 0 ne + R is monitored by normal incidence of the optical beam on a transparent working electrode, the absorbance ( A b s ) ~of the product is related to the total Faradaic charge passed, Q,by the equalion
+
(A~s)R/Q = 1 0 3 € ~ / n ~ ~
(1)
where t R is the molar absorbance coefficient of R and n, F, and A have their usual electrochemical meaning. For any form of potential or current control, the time-dependency of is derived by combining Equation 1 with the chargetime expression appropriate to the electrochemical control. Such relations have been given previously by Kuwana and coworkers ( I , 2, 7) for current and potential steps under semi-infinite linear diffusion conditions. For transparent electrodes with two electrochemicallyactive faces, such as the Au minigrid electrode, the optical beam traverses two R diffusion profiles, and Equation 1 is modified accordingly: ( A ~ s ) R / Q= 2
x
1O3fR/nFA
(2)
where A is the total electrode area. Potential and currentstep relations for two-face electrodes are, for convenience, briefly reviewed here. Potential Step. For a potential step giving Co(o,r) = 0, the chronocoulometric charge-time result (18) is, after double layer charge correction, (17) T. Osa,A. Yildiz, and T. Kuwana, J. Amer. Chem. Soc., 91, 3994 (1969). 1070
ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
Q
1.0 X
=
cma/secand x
2nFACo”(Df/r)1/2
=
=
one-half
(3)
For a double potential step experiment (19), the charge after the reversal time r is Q(T) - Q = ~ ~ F A C : B ( D / T ) I / ~
(4)
where g, =
Ti/2
-
ti/z
+ (t -
r)i/z
(5)
Application of Equation 2 gives for the absorbance-time response of a single potential step (Abs)R = 4
x
103€RCob(Df/*)1’2
(6)
and for a double potential step (Abs)R,r - (Abs)R = 4
x
103 € Rc:e(D/r)’/2
(7)
Analysis of Q and ( A b s ) ~data involves inspection for linearity and proper slope dependencies of plots against t’’* and 0 or, alternatively, assessment of time and C,”-independency of the (Abs)R/Q-ratio of Equation 2. Decomposition of R is detected by non-adherence of data to Equations 2 , 4 , 6 , or 7. Current Step. Description of the response to a current step, i , follows identification of the product of current and time as Q of Equation 2 : (AbS)R/i = 2 X 1O3c~t/nFA
(8)
For stable R, the absorbance ( A b s ) ~rises linearly with time and will fall linearly with time upon current reversal. The electrochemical response to the current step is a potentialtime curve terminating in a transition time, r , given by the Sand equation 7112
= nF~~,b(~7r)l/*,Ui
(9)
The limit of time-linear ( A b s ) ~response is r , at which point the absorbance is
( Abs)R,maX
=
103nFAe R D r (C,b)’/2i
(10)
Equation 10 finds use in design of the current step experiment, Le., selection of (C,b)2/i to permit readily measurable ( A b s ) ~ values within the bounds of r . Diffusion Properties of Minigrid Electrodes. The Au minigrid electrode is not strictly a planar surface, consisting instead of a fine Au foil in which a highly regular pattern of square holes has been etched. Physical dimensions of some (18) J. H. Christie, G. Lauer, R. A. Osteryoung, and F. C. Anson, ANAL.CHEM., 35, 1979 (1963). (19) F. C. Anson, ibid., 38, 54 (1966).
j i&yj : ‘........... *..> .-............ ............
1
-.: .*.
‘ i /
j
1 : j ............,
,
I
:
I
I
,
I ,
j
I
4
4 II
y:
A D Figure 2. Mounting of gold minigrid for semi-infinite diffusion experiments. Dimensions: a = 0.8cm; 6 = 0.3 cm; c = 2.5cm Gold minigrid Front glass slide with center drilled C. Rear glass slide with center drilled D. Teflon FEP or epoxy seal E. Aluminum foil contact to gold grid (fold-pressed and epoxycemented)
A. B.
Figure 1. Schematic potential step diffusion layer profile depths around cross-section of minigrid wires for distance where C,,,,,/Cb = 0.50. To scale for 2000 lpi minigrid, numbers are time in milliseconds minigrid meshes are given in Table I ; both hole and wire dimensions are quite small. We now inquire into the applicability of the above linear diffusion theory to this type of working electrode. The dotted lines of Figure 1 represent potential step diffusion layer “depths” for a series of electrolysis times at a 2000 lpi minigrid electrode. If we measure charge us. time during this experiment, it is clear that at times sufficiently short that the diffusion layer depth is small compared to the wire dimension, linear diffusion conditions will prevail, and linear Q-t1l2 plots (Equation 3) are obtained with slope proportional to the total surface area (“microscopic area,” A,,,) of the rectangular wires. Likewise, at sufficiently long electrolysis times, the diffusion layer depth becomes large compared to both hole and wire dimensions, and the merging of profiles emanating from individual wires again yields an effectively linear diffusion pattern. The minigrid under this averaged profile condition is a pseudo-planar surface, and linear Q-r1/2 plots with slope proportional to the total cross sectional (“macroscopic”) minigrid area, A,,, are expected. For any given minigrid, then, chronocoulometric Q-t1’2 plots, inspected over a sufficient range of time, should exhibit short- and long-time linear segments. For the special condition Amio = A,,, these linear segments have the same slope, and the Q - t 1 / 2 response should then be linear at all times. Table I shows that the Amin= A,, area equality occurs in the 2000 and l00OT lpi minigrids, and these electrodes are accordingly quite suitable for the chronocoulometric experiment. The above remarks on the charge-time response of the minigrid electrode also apply to their absorbance-time response (Equations 6 and 7) under potential step control. There is one significant difference. The charge-time data reflect electrolysis on both the inner walls of the minigrid “holes” and on the outer wire surfaces. The optical response measured, on the other hand, is only that of the solution present in or above a hole; a species R above an outer wire surface is “shadowed” and not observed. It is necessary, therefore, for linear ( A b s ) d ’ 2 behavior, for the true averaged-profile condition to be attained, and the special equality Amic = A,,, does not benefit the optical response as it does the charge-time result. The duration of electrolysis
needed to attain the pseudo-planar condition depends primarily on the minigrid hole dimension and can be roughly estimated by calculating the time required to produce a profile depth equal to one-half the hole size (see Table I). It is evident that the 2000 lpi minigrid gives the most favorable situation for short-time, theoretically interpretable opticaldata. Formulation of Equation 8 for the absorbance-time response to a current step experiment does not involve presumption of linear diffusion conditions. The “shadowing” effect, noted above for the potential step experiment, also applies, however, to current step experiments. A nonlinear absorbance-time response can accordingly be anticipated for times short of those producing diffusion profile-averaging. Comments on Spectroelectrochemical Current Step Experiments. While the chronopotentiometric Equation 9 is mathematically rigorous, the practical difficulties of chronopotentiometric transition time measurements are well known. Some comment on the specific differences of the optically conducted current step experiment from the conventional chronopotentiometric one is accordingly in order. Two important facts should be recognized. First, the pertinent linear ( A b s ) ~ - toptical response is attained prior to the chronopotentiometric transition time. ( A b s ) ~ data at or beyond T are in fact not used. The most serious difficulty of conventional chronopotentiometry is, thus, avoided. Second, difficulties with the double layer charging interval immediately following current step application can in the optical experiment be circumvented through application of a small bias current preliminary to the main current step. This serves to force the working electrode potential closer to the potential of the 0 + R reaction and can eliminate most of the double layer charging attrition of the primary current step. The same zero time background absorbance this generates is of no consequence in the optical response (unless R decays very rapidly). The practical difficulties of quantitative chronopotentiometric measurements are, thus, not necessarily transposed to the optically conducted current step experiment. EXPERIMENTAL
Cell and Electrodes. The Au minigrid electrodes were obtained from Buckbee-Mears Co. (Minneapolis). Figure 2 illustrates their mounting for semi-infinite diffusion exANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
*
1071
’
Figure 3. Spectroelectrochemical cell. Dimensions: a = 0.8 cm; b = 4.0 cm
Figure 4. Kinetic spectrometer Power supply for light source: two Hewlett-Packard Model 6281A dc power supplies in parallel B. Light source (visible region): Cenera1 Electric ribbon Rlament lamp Model 9A/T8-1/2/1(9Aat 6 V) C. Monochromator: Bausch and Lamb Model 33-8602 D. Sample compartment E. Sample PMT: Whittaker EM1 Model 6256s F. Current follower for sample PMT: Philbrick/h'exus Model p25 G. Reference PMT: same as E H. Current follower for reference PMT: same as F I. PMT power supply: Fluke Model 412B J. Electrochemical instrument K. OTE cell L. Beam splitter E(b). Bucking voltage taken from current follower operational ampliRer power supply: Philbrick/NexusModel 2301 A.
1. Gold minigrid OTE 2. Teflon compartment 3. Quartz window
4. Aluminum pressure plate Aluminum frame 6. Brass screw for pressure sealing O-rings 7. Protective rubber washer 8. O-ring (number 014)
5.
periments. The perimeter of the mounting hole is sealed with epoxy resin glue or, more durable for nonaqueous experiments, a 50-micron meltable Teflon (Du Pont) washer (Livingstone Coating Co., Charlotte, N. C.). For the latter, the glass slides, minigrid, and Teflon washer are aligned, secured with clamps, heated a t 320-350 "C. for about 30 minutes and allowed t o cool slowly. A practiced delicacy is necessary during the mounting operation t o avoid undue wrinkling of the fragile minigrid. The mounted electrode is incorporated into an electrochemical cell (Figure 3), which is positioned in the sample compartment of the kinetic spectrometer (Figure 4). The cell is readily disassembled for exchange of electrodes and uses quartz windows, Teflon body, and, for aqueous solutions, Viton O-rings. (For nonaqueous solutions, more suitable O-ring materials are Precise Rubber Products (Lebanon, Tenn.) Compound 3128, for C H F N and DMF, and Compound 17107A, for propylene carbonate, and Tri-Point Industries (Commack, N. Y .) Teflon TFE, general purpose.) The bridge connection t o the SCE reference electrode consists of the tube connection to the sample compartment (both filled with test solution), a glass frit, and an aqueous NaCl compartment. The refxence and auxiliary connection holes also serve as entrance and exit for filling and change of test solution. The optical beam is masked to a size slightly smaller than the working electrode dimension. For several experiments involving a Cary Model 14 spectrophotometer, a cell similar to that of Figure 3, but with two additional solution entrance and exit holes, was employed with the horizontal optical path of that instrument. Both cells were suitable for simultaneous acquisition of electrochemical and spectral data. Instrumentation. The instrument for electrochemical potential and current control (20) was based on Philbrick-Nexus solid state operational amplifiers, a Hewlett-Packard Model 467A Booster amplifier and utilized positive feedback (21) (20) T. E. Neal, Ph.D. Thesis, University of North Carolina, Chapel Hill, iv. C., 1970. (21) G.A. Lauer and R. A. Osteryoung, ANAL. CHEM.,38, 1106 ( 1966). 1072
ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
and FET switching. Electrolysis spectra, and some slow > 5 seconds) absorbance-time experiments were recorded on a Cary Model 14 spectrophotometer. Most spectroelectrochemical absorbance-time transients were measured with a kinetic spectrometer of design similar to that of Kuwana and coworkers (3), Figure 4. It was insulated from floor vibrations by anti-vibration foam (-3M Company) and inflated inner tubes (Sears Minibike). Spectroelectrochemicl experiments can require accurate detection of exceedingly small optical absorbance changes, and optimization of the optical signal-to-noise (S/N) ratio can be a critical facet of the experimental procedure. In general, the optical SIN is improved by operation of the photomultiplier tube (PMT) at low gain. The procedure used in this work involved setting the PMT cathode voltage at -500 (gives low gain) and adjusting the variables R I , monochromator slit width, and light source intensity (through source current) so that the initial output voltage E&) = 10 volts. R1 is typically 5 megohms and the exit slit width (depending on required resolution) ranges from 0.5 to 2 mm. At wavelengths of low source intensity, or with electrodes of low ZT,it may be necessary to increase the PMT voltage somewhat at this point. A bucking voltage E* = E&) is now applied for total base-line suppression so that small optical intensity changes during the electrolysis can be accurately recorded. Capacitative noise damping is provided by CI;RICl is generally selected for an instrumental (t
t
I
4
-3
i
-3 Time Function (sec]1/2
0 , 5 / / ,
Figure 5. Potential step response for lOOOT (U), 2000 (-n--), and 100 (-A-) Ipi minigrid electrodes. 0.8mM o-tolidine. Heavy line is theoretical response for A,,, and D = 6.2 X cm-2/sec
time constant 1 second). Charge-time data for single potential steps with 2000, 1000T,and 100 lpi electrodes are plotted in Figure 5 according to Equation 3. The data for the 2000 and lOOOT lpi minigrids exhibit excellent linearity in the Q-tl’* analysis and also a reasonable correspondence to the theoretical response curve. Adherence to theory is anticipated for these minigrids, inasmuch as they should exhibit averaged-profile diffusion in this time range (see Table I) and also Amic= A,,,.
Figure 6. Double potential step response for 2000 Ipi minigrid. Forward step charge (-0-) and absorbance (-.-) plotted against t1I2; reverse step Q(T)-Q (-A-) and A(+ A (-A--) plotted against 8. 0.8 mMo-tolidine
The Q-t*’2 plot in Figure 5 for the 100 lpi electrode shows gross deviation from the theoretical response. This is likewise anticipated. Table I shows that the electrolysis times used are not sufficiently long to yield complete profileaveraging. The short-time slope of the Q - t 1 ’ 2 plot is about 20% of that of the theoretical one; this is consistent with the A,ic/Amm = 0.26 ratio for the 100 Ipi minigrid. Subsequent experiments emphasized the finer mesh minigrids. The charge and absorbance-time results of a double potential step experiment with a 2000 lpi electrode, analyzed according to Equations 3, 4, 6 , and 7 , are shown in Figure 6. The absorbance of the oxidized o-tolidine was monitored at 438 nm where e = 6.18 X l o 4 (22). The data are again in accord with the theoretical relations. Results are completely similar for a n experiment with the lOOOT lpi minigrid. From the geometrically measured electrode area, and application of Equation 2 to the time-independent Abs/Q ratios, E values of 6.18 =k 0.1 X lo4 (2000 Ipi electrode) and 6.16 f 0.08 X lo4 (1000T lpi electrode) were obtained for the oxidized o-tolidine. It can be shown from Equations 3 and 4 (23) that the ratio of the charge at the potential reversal time, T , to that recovered by time 27, Q,/Qb, is 0.586. The same value is expected for the corresponding absorbance ratio. From experiments such as that of Figure 6 , Q,/Qb = 0.595 and (Abs)f/(Abs)b= 0.587 for the 2000 lpi minigrid and Q l / Q b = 0.590 and (Abs)f/(Abs)b= 0.578 for the lOOOT 1pi minigrid. Experiments such as those above, when conducted with the Cary Model 14 spectrophotometer (minigrid in vertical position) revealed a time-dependent Abs/Q ratio after about 20 seconds. This was determined, by optical masking of horizontal sections of the electrode, to arise from an upward streaming of the solution around the electrode. Short-time charge and absorbance results of single potential step experiments with 2000 and 1000 lpi minigrids are shown in Figure 7. The Q-t1’2 response of the 2000 Ipi electrode is again linear; that of the 1000 lpi electrode shows only a slight curvature at the shortest times. These linearities are derived from the condition A,;, = A,,, rather than a complete diffusion profile averaging. It was noted above that complete diffusion profile averaging should be necessary to achieve correspondence of absorbance-time data to the linear (22) J. N. Burnett, University of North Carolina, Chapel Hill, N. C., unpublished results, 1968. (23) J. H. Christie, J. Electround. Chem., 13, 79 (1967). ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
1073
TIME (MSEC.)
Figure 8. Optical response of 2000 Ipi minigrid electrode to 0.4 mA/cm2 current step reduction of 10.0mM Ti(1V) in 0.75M oxalic acid. Instrumental time constant 0.01 second. Insets show potential variation at minigrid and cyclic voltammogram of 15mMTi(IV) solution a t minigrid Figure 7. Charge (.- X -- ) and absorbance (--0-) pctential siep respouse for 0.8 mMo-tolidine
Table TI. Current Step Spectroelectrochernical Results 2 m M o-tolidine, 0.5M acetic acid, 1.OM HCIO4, 0.504 cm22000 Ipi minigrid
;Curlent densit\. mA/cm2 0 983 0 492 0 247 0 123
[A(nbs)/Atl
(40,
cm2/mA-sec 0 654
0 643 0 619 0 644
6.9mM Ti(IV), 0.2M oxalic acid, 0.5M (NH4)gS04,0.442 cm* 2000 Ipi minigrid
Current density, niA/cm2 1 0 0 0 a
130 565 285 142
[A(Abs)/Ar]( A / l ) ,
cm2/rnA-sec 0 0 0 0
0064 0063 00731 00732
E f i n a ~US.
e,
Ti(II1) 309 305 353 354
SCE, Ve -0 50 -0 50 -0 44 -0 45
Potential sweep EPl2In this medium 1s -0 42 V
diffusion Equation 6. The short-time nonlinearity of the absorbance responses in Figure 7 is a reflection of this condition. The data approach linear diffusion behavior at about 10-20 msec, for the 2000 Ipi minigrid, and about 100 msec, for the 1000 Ipi electrode. These times are an experimental measure of the electrolysis period required for profile averaging; comparison with Table I shows that the condition C ( z , t ) / C b= 0.5, for x equals one-half hole size, does provide r fair theoretical estimate of the profile averaging time. Current Step Experiments. A series of current step experiments was carried out using the o-tolidine oxidation reaction and the 2000 lpi minigrid. The increase in absorbance at 438 nm was linear with time from about 10 msec, the period required for diffusion profile averaging, up to the chronopotentiometric transition time. The slope A(abs)/ At of this response, rvsults for which are given in Table 11, i s proportional to the applied current density as required by Equation 8. Recognizing that the e value for oxidized o-tolidine is accurately known ( 2 2 ) and that Equation 8 does 1074
ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
nct involve the diffusion coefficient parameter, the absorbance-time response for current step oxidation of otolidine provides an accurate determination of the macroscopic area of a mounted minigrid electrode. The current step experiment was also applied to the oneelectron reduction of titanium(1V) in oxalic acid medium. The evaluation of this reaction proved interesting since the titanium(II1) reduction product is a much less intense absorber than oxidized o-tolidine; its E value, determined by spectrophotometry in an air-free system, is 354 at 410 nm. Also, potential step study of this reaction would be complicated by the proximity of its wave to the background electrolysis on the Au minigrid (see cyclic voltammetry wave inset of Figure 8). In the current step experiment, use of a low current density can keep electrolysis confined to potentials near the foot of the wave. The titanium(II1) optical response is illustrated in Figure 8. Slopes of the linear absorbance-time response, and E values calculated using Equation 8, are given in Table 11. At high currents, background electrolysis leads to
