2356
Anal. Chem. 1982, 54,2356-2361
reagent will require more data before a clear explanation is possible.
CONCLUSION The present data are consistent with the three features of ion-interaction model for reversed-phase, paired-ion chromatography (1, 9, 21). In addition, a generalization can be made about the concentration perturbations in the eluent caused by ionic samples and pure solvent “samples”. The data suggest that the stationary phase is an adsorbed “liquid phase” consisting of components from the eluent. Any solute which is injected as a “sample” will cause perturbations of the adsorbed “liquid phase”. The results further indicate that ionic strength can influence the separating power of UV-visualization systems and alter the detector response. For the present system, Figures 2,3, and 5 imply that reproducible chromatographic data will be most readily obtained at the extremes of ionic strength. Work is currently progressing in our laboratory to test this prediction and to further investigate the elution order and detector response for high ionic strength eluents.
ACKNOWLEDGMENT The authors thank K. Bergeron, C. Tronerud, and P. Watson for help in the preparation of the manuscript and J. Ekmanis, R. King, and S. Deming for helpful discussions.
LITERATURE CITED ( I ) Bldllngmeyer, B. A.; Deming, S. N.; Price, W. P., Jr.; Sachok, B.; Pe-
trusek, M. J. Chromatogr. 1979, 786, 419. (2) Wittmer, D. P.; Nuessle, N. 0.; Haney, W. G., Jr. Anal. Chem. 1975, 47,1422. (3) Sood, S. P.; Sartori, L. E.; Wittmer, D. P.; Haney, W. G., Jr. Anal. Chem. 1978, 48, 796. Molnar, P. Anal. Chem. 1977, (4) Horvath, Cs.; Melander, W.; Moinar, I.; 49, 2295. (5) Kraak, J. C.; Jonker, K. M.; Huber, J. F. K. J. Chromatogr. 1977, 742, 671.
(6) Hoffman, N. E.; Liao, J. C. Anal. Chem. 1977, 49, 2231. (7) Kisslnger, P. T. Anal. Chem. 1977, 49,883. (8) Van de Venne, J. L. M.; Hendrlkx, J. L. H. M.; Deelder, R. S. J. Chromatogr. 1978, 767, 1. (9) Bldllngmeyer, B. A. J. Chromatogr. Sci. 1980, 78, 525. (IO) Cantweli, F. F.; Puon, S. Anal. Chem. 1979, 57, 623. (11) Iskandarani, 2.; Pletrzyk, D. J. Anal. Chem. 1982, 54,1065. (12) Deeider, R. S.;Van Den Berg, J. H. M. J. Chromatogr. 1981, 278, 327. (13) Moinar, I.; Knauer, H.; Wiik, D. J . Chromatogr. 1980, 201, 225. (14) Stranahan, J. J.; Demlng, S. N. Anal. Chem. 1982, 54, 1540. (15) BJerrum, N. K. Dan. Vidensk. Selsk. 1928, 7 , 9. (16) Knox, J. H.; Hartwlck, R. A. J. Chromatogr. 1981, 204, 3. (17) Deming, S.N.; Kong, R. C. J. Chromatogr. 1981, 217. 421. (18) Kong, R. C.; Sachok, B; Deming, S. N. J. Chromatogr. 1980, 799, 307. (19) Pletrizyk, D. J.; Iskandarani, Z. “Book of Abstracts”, 183rd National Meeting of the American Chemical Society, Las Vegas, NV; Abstract No. 20, March 28, 1982. (20) Melander, W. R.; Kaighatgl, K.; Horvath, C. J. Chromatogr. 1980, 207. 201. (21) Bldllngmeyer, B. A.; Deming, S. N.; Price, W. P.; Sachok, B.; Petrusek, M. J., paper presented at Advances in Chromatography, 14th Internatlonai Symposium, Lausanne, Switzerland, Sept 24-28, 1979, (22) Crommen, J.; Fransson, 8.; Schili, G. J. Chromatogr. 1977, 142, 283. (23) Paris, N. Anal. Blochem. 1979, 700,250. (24) Bidlingmeyer, B. A.; Deming, S. N.; Sachok, B. paper presented at 13th International Symposlum On Chromatography, Cannes, France, July 2, 1980. (25) Paris, N. J. Llq. Chromatogr. 1980, 3 , 1743. (26) Denkert, M.; Hackzell, L.;Schill, G.; Sjogren, E. J. Chromatogr. 1981, 218, 31. (27) Sachok, 8.;Deming, S. N.; Bidiingmeyer, B. A. J. Liq. Chromatogr. 1982, 5 , 389. (28) Reiiiey, C. N.; Hildebrand, G. P.; Ashley, J. W. Anal. Chem. 1982, 34, 1198. (29) Scott, R. P. W.; Scott, C. G.; Kucera, P. Anal. Chem. 1972, 44,100. (30) Slais, K.; Krejci, M. J. Chromatogr. 1974, 9 7 , 161. (31) Hendrix, D. L.; Lee, R. E., Jr.; Baust, J. G. J. Chromatogr. 1981, 270, 45. (32) Kraak, J. C.; Huber, J. F. K. J . Chromatogr. 1974, 702, 333.
RECEIVED for review May 14, 1982. Accepted August 18, 1982. This work was presented in part at the Seventeenth International Symposium on Advances in Chromatography, Las Vegas, NV, April 5-8, 1982.
Microsecond Spectroelectrochemistry by External Reflection from Cylindrical Microelectrodes Robert S. Robinson, C. Wllllam McCurdy, and Rlchard L. McCreery” Department of Chemistry, The Ohio State University, Columbus, Ohio 432 10
A laser beam reflected by 5-280 pm radius gold and platinum electrodes was used to carry out spectroelectrochemical experiments. The expected absorbance vs. tlme behavior for an electrogenerated absorber was calculated from existing equations on heat transfer, and the experlmental results agree well wlth theory for the first 300 ms after a potentlal step to the dlffuslon Ilmit. Due to the small currents Involved, a two-electrode conflguratlon wlth no potentlostat was employed, and the tlme constant of the cell was less than 1 ps due to low electrode area. The transient response of the system was therefore excellent, yleldlng theoretically predlcted results 4 ps after initlation of electrolysls. A slgnlflcant deviation from expected absorbance occurs after 300 ms, but the deviation may be mlnlmlzed by using low laser power. I n Its present form, the technique is useful for examining reactions occurrlng In the microsecond tlme scale, and wlth further development submlcrosecond tlme resolutlon should be accessible.
A variety of electrochemical methods have been developed
for examining the kinetics of fast charge transfer reactions as well as reactions preceding or following the charge transfer process. These techniques can be broadly classified into AC methods such as impedance measurements (I), faradaic rectification (2),and AC polarography (3)and relaxation methods initiated by potentiostatic ( 4 ) ,galvanostatic ( 5 ) ,or coulostatic pulses (6). Of relevance to the present discussion are applications of these techniques to the reactions of unstable materials generated a t an electrode surface. In such applications, heterogeneous charge transfer provides a well-controlled and convenient means to generate a reactive species, which can then be monitored by a suitable electrochemical or optical technique. This general approach has been used to study a variety of organic and inorganic reactions, with the common feature of all applications being the involvement of a heterogeneous charge transfer reaction. Time resolution is of obvious importance when examining fast reactions of electrogenerated species, and this parameter varies greatly for different techniques. AC methods can provide information in the microsecond or occasionally submicrosecond time scale, but interpretation of the results is
0003-2700/82/0354-2356$01.25/0 0 1982 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 2c " f
d
h
p
1982 2357 ,800
t Workirg electrode
I
Flgure 1. Apparatus for spectroelectrochemistry with microelectrodes using
a
two-electrode configuration.
often complex. The kinetic information must be deconvoluted from capacitive, diffusion,d, and resistive impedances and the resulting complexity has limited application to only a few kinetic systems. Galvanostatic and coulostatic methods can also provide microsecond time resolution but involve the measurement of electrode potential. The observed potential is highly dependent on charge transfer kinetics and therefore the relationship between the potential vs. time transient and the rate of reaction of an electrogenerated species is difficult to establish. For these and other reasons, potentiostatic methods have been most successful for monitoring reactions associated with charge transfer. When the applied potential is sufficient to drive the heterogeneous reaction to the diffusion limit, the kinetics of charge transfer do not perturb the kinetic process of interest. A constant potential also provides welldefined conditions for the charge transfer reaction, and negligible double layer charging current flows after several cell time constants have elapsed after a potential step. The best time resolution for measuring meaningful faradaic current following a potential step to the diffusion limit is about 10 ps (7-9), with the delay being caused by double layer charging. When an optical probe is used to monitor the electrogenerated species, a time resolution of 4 ps was achieved with internal reflection spectroelectrochemistry (IRS) (9). While IRS provides the significant advantage of spectral monitoring of any reactions occurring after charge transfer, fast experiments require a high power (500 W) potentiostat to charge the double layer. With the exception of coulostatics, the major impediment to fast experiments is the time (and power) required to charge the double layer so the heterogeneous electron transfer maction can occur. In addition, those techniques involving a constantly varying potential such as coulostatics or galvanostatics will always contain an error in the measurement due to capacitive current. The present paper describes a technique for examining fast reactions based on spectralelectrochemistry at small electrodes with areas of ca. lo4 cm2. Similarly small electrodes have been used for voltammetry and steady-state measurements by Wightman (10, I I ) , Jouvet (12), and Hills (13)with both cylinder and disk geometries being used. As the electrode area is reduced, both the double layer capacitance and the faradaic current are also reduced, so the cell time constant and iR error become small enough to carry out experiments without special concerns about potential control. An initial report (14) described spectroelectrochemistry using external reflection geometry carried out on 12 pm cylindrical carbon fibers, and several features of the approach were discussed. The present report extends that work to the microsecond time scale using platinum and gold fiber electrodes. The need for a potentiostat is eliminated, and reliable data were obtained on an electrogenerated absorber 4 ps after a potential step.
THEORY The experimental configuration employed for the majority
Rodius
Figure 2. Calculated R, and R,C,
x
104,cm
as a functlon of electrode radius cm, h = 0.12 cm, pe = 9.8
for a Pt microelectrode ( r o = 5 X X lo-' 0 cm), immersed In 1 M H2S04(p, = 2.8 R cm). Assumes from the end of the electrode. negligible contribution to Rce,,Cdl
of this work is shown in Figure 1. A three-electrode arrangement is of little value since a large fraction of the solution resistance occurs within a few radii of the working electrode, due to the cylindrical current field. Therefore a separate reference electrode is of little value unless its tip is within a few radii of the electrode, an arrangement which is both impractical and unnecessary, as shown below. Consider a two-electrode configuration with a cylindrical working electrode and a large concentric cylindrical counterelectrode with a radius of 1 cm. The resistance for such a configuration has contributions from two sources: internal working electrode resistance and solution resistance. The internal electrode resistance is easily calculated from the resistivity of the material and geometric constants for the design. The solution resistance can be calculated by integrating a similar resistivity expression from the working electrode radius (ro)to the counterelectrode radius (rl). The total cell resistance is given by eq 1, with the first term being the contribution from the working electrode itself and the second being solution resistance
where pe = electrode resistivity, R cm; L = total working electrode length, cm; h = length of working electrode exposed to solution, cm; and ps = resistivity of solution, R cm. The cell resistance is in series with the double layer capacitance, given by 2rrohCo where C" is the capacitance per unit area, assuming negligible contribution from the exposed end of the cylinder. Therefore the time constant for the cell is given by eq 2.
Rcelland RcellCdlcalculated from eq 1 and 2 are shown in Figure 2 for typical experimental parameters as would be appropriate to a 5-pm radius platinum electrode in 1M H2S04 R cm, h = 0.12 cm, L = 1 cm, ps = 2.8 Q cm, ( p , = 9.8 X C" = 40 pf/cm2). A minimum in the calculated values of RceuCdloccurs at ro = 2.4 pm, where Rce&l = 0.42 ps for this case, with Cd = 7.2 X lo4 F and Reel = 59 Q. At smaller radii, the internal electrode resistance increases rapidly, so there is no decrease in time constant for radii less than 2.4 pm. Furthermore the ohmic potential error increases at smaller radii, so the optimum value of radius will be somewhat larger than 2.4 ym. In this work, the smallest radius was 5 pm due to mechanical strength limitations of platinum. At this radius, the calculated Rcell is 35 R and cd1 is 0.015 p F (based on C" = 40 pF cm-2) yielding a ce!l time constant of 0.53 ps. Note
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
that this entire discussion is based on the assumption that the contribution of R or C from the end of the fiber is negligible, a reasonable assumption since the area of the fiber end is 0.2% that of the cylinder. The theoretical absorbance vs. time behavior was obtained by constructing the solution, C,(r,t), of the diffusion equation by using a numerical Laplace transform approach. For the case of a stable absorbing product (P) generated from a colorless reactant (R) the absorbance, A(t), as a function of time is given by
A(t) =
EpCp(r,t)dr
Jm
(3)
r0
where tp and C, are the molar absorptivity and concentration of the electrogenerated product, respectively, and the integration begins at r equal to the radius of the cylinder Po. Equation 3 has the same form as in the case of a planar electrode but C,(r,t) is dictated by cylindrical diffusion. Carslaw and Jaeger (15) have solved the diffusion equation in the cylindrical case using the Laplace transform approach and have cast the solution, which is given by an inverse Laplace transform, in the form
Table I. Absorbance for Cylindrical Electrode, Calculated from Equation 4a ( D t ) ’”lr, AIAphar (Dt)‘ ”lro AIApknar 0.0222 0.993 3.02 0.677 0.0237 0.975 5.78 0.607 0.0692 0.959 10.4 0.547 0.102 0.949 19.4 0.488 0.165 0.931 30.2 0.450 0.203 0.922 44.6 0.420 0.329 0.893 60.0 0.398 0.365 0.885 74.0 0.384 0.531 0.856 88.9 0.372 0.993 0.798 194 0.327 1.036 0.794 381 0.296 1.939 0.727 600 0.279 2.54 0.697 873 0.266 a D = diffusion coefficient, ro = electrode radius, Auknar is given by eq 7.
4 for which most of the contribution to the integral is from small values of x. The results for A(t) from this integration scheme are shown as a function of the dimensionless parameter (DRt)”’/ro in Table I. Aplanaris the absorbance for a planar electrode (19),given by Aplanar(t) = (4/71’2)€pCRb(DRt)1’2
where DR is the diffusion coefficient of the colorless reactant,
Jo and Yoare Bessel functions of the first and second kind of order zero (16), and CRb is the bulk concentration of reactant. The approach to computing A(t) is to perform both the integration over x in eq 4 and the integration over r in eq 3 numerically using Simpson’s rule (17) for each value o f t to generate an entire A vs. t transient. However the integrand in eq 4 is singular a t x = 0, and even though this is an integrable singularity, it makes direct numerical evaluation of the integral difficult. This problem can be avoided by the simple device of subtracting off the singular portion of the integrand and evaluating its integral analytically. Denoting the entire integrand in eq 4 by g ( x ) ,its limiting form for small x is given by
Ax)
f(x)
(54
2~ In ( r / r o )
f(x) = -
x(r2
+ 4(ln(x/2) + T ) ~ )
(5b)
where y is Euler’s constant (18). The integral of the limiting form, f ( x ) , on any interval can be performed analytically, so by adding and subtracting f ( x ) to g(x) the following expression, suitable for numerical evaluation, can be obtained
Lzmg(x)dx = Jxm(g(x) 0 - f ( x ) ) dx 27r In ( r / r o ) [
$ tan-l (:(In
2+
7 ))
+ j] (6)
where x, is a number large enough that g(x,) is effectively zero. The integral on the right-hand side of eq 6 has no singularity in its integrand and can be evaluated easily with Simpson’s rule or other integration method whereas the integral of g(x) on the left-hand side is extremely difficult to evaluate numerically, particularly at large values of t in eq
(7)
As shown in Table I, the absorbance for a cylindrical case equals that for the plane at short times, as expected when the diffusion layer thickness is thin relative to the electrode radius. As time progresses, the two absorbances deviate fairly quickly, with the cylindrical case being 1% lower than the planar case at (DRt)li2/ro = 0.224 and 5% low a t (DRt)li2ro= 0.099. For D = 4 X lo* cm2/s and ro = 5 pm, there will be a 1% deviation from the planar case at 31 MS and 5% deviation a t 0.61 ms. At (DRt)1’2/l^0= 19.4 the absorbance is 49% of the planar case, a situation occurring at 23.5 s for ro = 5 pm and D = 4 X lo4 cm2/s.
EXPERIMENTAL SECTION The cell and optical arrangement were described in ref 14, with the only difference in the present work being a metal rather than carbon working electrode. The Pt auxiliary electrode was placed about 1 cm from the working electrode, but its placement was not critical to performance. A fiber optic collector received reflected light from the microelectrode, and the cell shape reduced scattered light from other sources. The working electrodes were made from various sizes of platinum and gold wires, mounted in the tip of a disposable pipet with jewelers wax. Wires with radii of 50 pm or less were purchased from Goodfellow Metals (Pt) or Consolidated Refining Co. (Au). After being mounted, the wires were cut off with a scalpel to leave ca. 1 mm exposed to the solution. Contact with a platinum lead was made through mercury, with a small amount of graphite powder between the wire ends and mercury to slow amalgamation. The total length of metal fiber was kept short (ca. 1 cm) to minimize internal resistance. The counter/reference electrode for the two-electrode experiments was a standard SCE coupled to a 1 mm diameter Pt wire through a 20-fiF capacitor. The AC coupled platinum electrode lowered the impedance of the counter/reference electrode by providing a current shunt at high speeds. The majority of the current required to conduct the experiment passes initially through the platinum counterelectrode, causing a slight change in its potential as its double layer is charged. However, since its area is so much larger (a factor of 103-104)than the working electrode, its potential changes by only a few millivolts. Toward the end of the applied potential pulse, and during the relaxation period between pulses, the SCE conducts and the reference potential is reestablished. The overall effect is a low impedance counter/reference electrode with a slight (ca. 1 mV) change in potential occurring during the first few microseconds of an applied pulse. This arrangement is very similar to that described by Pilla (20)for a dual reference electrode, except is its designed to conduct higher currents. For both two- and three-electrode experiments,
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
no special attention was paid to electrode placement, since it would have little affect on reducing the cell resistance. For three-electrode experiments the same potentiostat described previously (14) was employed, with a simple SCE reference electrode and Pt wire auxiliary electrode. For two electrode runs, the working electrode was connected to the output of a Date1 VR12B3C DAC interfaced to an HP lo00 computer system, while the counter/reference elecitrode was grounded. The DAC settled to 1% in less than 2 ps with a 90% risetime of 250 ns. A 1P28 photomultiplier housed in a dry ice cooled housing monitored the reflected laser light as described earlier (14). The optical a r rangement was the same at3 the previous experiment with various neutral density filters used to attenuate the input beam. After conversion to voltage by an Analog Devices 455 amplifier configured as a current follower, the PMT output was monitored by an Analog Devices 1103 ADC interfaced to the HP computer. A sample and hold amplifier tmk a reading at 4 I.LSafter the potential step and at 5-ps intervals thereafter. Absorbance transients were calculated by using the PMT reading preceding the pulse as a reference, and the transients were time averaged as indicated in figure legends. The test system was o-dianisidine hydrochloride (Sigma anhydrous grade no. 510-50) oxidation in 1 M H2S04. The o-dianisidine (OD) employed was of high purity and needed no further purification, although lesri pure samples caused irreproducible results. Colorless OD is oxidized by a two-electron process to it5 quinoid form ( E = 22700 at 515 nm) (21), and the diffusion coefficient of the reduced fiorm in this medium is 4.4 X lo4 cmz/s (22). Chloride ion was harmful to both platinum and gold electrodes during electrochemical oxidation due to attack of the electrode by C1- (for Au) or Clz (for Pt). This caused a gradual decrease in absorbance values when the C1- concentration was above a few millimolar. For a high speed runs (lasting 200 ps or less), the reflectance change caused Iby the potential step was large enough to be significant, so blank runs were carried out in 1 M HzS04 containing the same concentration of C1- as present in OD solutions. The double layer capacitance was measured by an established method (23),in which a small triangularly varying potential was imposed and the resulting square wave current measured with an oscilloscope. The cell impedance was measured by monitoring the current resulting from ai 140-mV (root mean square) sine wave using a digital oscilloscope. The current was measured as a voltage drop across a resistor in series with the cell.
RESULTS As measured by the reeponse to a triangular wave potential centered a t 0.4 V vs. SCE, the capacitance of a 5 pm radius platinum electrode varied from 6 X lo4 to 1.9 X lo-’ F (20-60 pF/cm2) for the frequency range from 10 to lo6 Hz. The cell impedance varied as shown in Figure 3, a8 measured by the ratio of the potential to root-mean-squared current for a sine wave. The minimum in impedance at 2 MHz is 38 Q, implying that the solution resistance is no more than 38 Q for the two-electrode arrangement. For Cdl = 40 pF/cm2 (0.015 pF for a 5 pm electrode) and R,“ = 40 Q, RceuCd= 0.6 ps. A plot of In i vs. t for a potential step into a solution containing only electrolyte was nonlinear, but the slope indicated a time constant in the range of 0.4 to 1.4 ps. If a simple SCE lacking the AC coupled platinum wire was used in the two-electrode configuration, the minimum impedance was 400 Q at 600 kHz. Finally, the current for a. 5-pm electrode (h = 1.2 mm) in a 2.4 mM OD solution measured 4 ps after a potential step from 0.3 to 1.1 V vs. SCE was 300 pA. Experimental absorbance vs. time transients for a 100-ms potential step using both1 two- and three-electrode configurations are compared with theory in Figure 4. The variation in response with electrode radius is shown in Figure 5, with all but the largest electrode exhibiting a negative deviation from theory a t long times. The first 200-ps portion of the transient for a 1-ms experiment is shown in Figure 6, with the background corrected abworbance vs. t * i 2plot for the entire
2359
105r
10
2
3
I
I
I
I
I
J
4
5
6
7
8
9
log ( frequency, H z )
Figure 3. Cell impedance vs. frequency for a 5 pm radius Pt electrode in 1 M H,SO,, 4 mM CI-, the electrode configurations as shown in Figure 1. Impedance minimum shifted to 400 at 600 kHz, if AC
coupled F’t electrode was dlsconnected. I
0
2
06
18
24
30
J;- ( S b ) Flgure 4. Absorbance vs. t transients for a 12.5 pm radius platinum M OD: open circles, electrode in 1 M H,SO4 containing 3.5 X theoretically predicted response; solid line, experimental response for a conventional three-electrode arrangement, average of 100 runs; solid circles, response for the two-electrode configuration shown in Figure 1, average of 60 runs. Eappwas stepped from 0.3 to 1.1 V vs. SCE. Laser power = 20 mW/cm2.
’”
run appearing as Figure 7 . Comparable results were obtained with a 12.5-pm radius platinum electrode, a t a laser power of 4 mW/cm2. Gold electrodes had higher background “absorbance” (ca. a factor of 3 higher than platinum) and were not pursued for fast runs. Finally, the effect of laser power on response is shown in Figure 8, with the power being varied by insertion of neutral density filters preceding the cell. As power increased, large negative deviations from theory occurred, with the effect being more pronounced for longer times and larger electrodes.
DISCUSSION The agreement between the calculated R,u (35 0 for a 5-pm radius electrode) and observed minimum in cell impedance (38 0) indicates that there is no unexpected source of resistance. Given the differences in actual cell geometry from that assumed in the theory, this agreement may be partly fortuitous, but clearly the assumption of cylindrical geometry
2360
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
c
0-
/// ...'
1
2
3
4
5
6
7
8
9
t
1
0
, 31623
I
126
I
2 53
Flgure 5. Absorbance vs. t''' transients for different electrode radii.
JT
Meoretical curves calculated as described in the text, wtth A pnar given by eq 7. Experimental conditions as in Figure 4 with a conventional three-electrode configuration. Solid line is the linear planar response, others as indicated: - - - , theory, r o = 280 pm; --,theory, r o = 25 pm; - -, theory, r o = 6.4 pm; open circles, experimental, 280 p m radius platinum electrode, Cb = 2.6 mM, single run, 5 mW/cm'; solid circles, experimental, 25 p m radius platinum electrode, Cb = 2.8 mM, 10 runs averaged, 35 mW/cm2; squares, experimental, 6.4 p m radius gold electrode, Cb = 2.2 mM, 100 runs, 700 mW/cm'.
Flgure 8. Absorbance vs. t''' as a function of laser power for 2.6 mM OD on a 280 p m radius Pt wire: line is theory; circles are for laser
-
5'01
4.0
. .. ..
3.0
lot.. .. 0
0
I
. ..
. .
. 2 2 mM OD
.
blank
.. . . . . ..... .. .. .*. . . . .. . .. .. . ,
., I
I
I
I
I
20
40
60
80
100
I
120
I
I
140
I60
I
180
200
Time,psec
Flgure 6. Absorbance vs. time transients for first 200 ps of the 1 ms run shown in Figure 7: 5 p m radius Pt electrode, two-electrode configuration, laser power = 280 mW/cm2; upper curve, average of 2700 runs with Eeppstepped from 0.3 to 1.1 V vs. SCE in 2.2 mM OD in 1 M H2S04;lower curve, same conditions in 1 M H2S04and 4.4 mM HCI, 5700 runs. I ms
t 10
0
P 4
0
I
0006
I
1
I
I
00I 8
0012
I
0 024
I
0 030
,92(sli)
Flgure 7. Absorbance vs. t"' for entire 1 ms run of which Figure 6 is first 2 0 % . Absorbance is background corrected by simple sub-
traction of the blank absorbance. Line is theoretical and exhibits a 5 % deviation from linearity at 1 ms.
yields useful predictions of cell response. Above 2 MHz, the rapid rise in impedance is due to cell inductance and will depend on the cell geometry and external components. The range of capacitance observed is reasonable for platinum,
power
= 5
mW/cm*; triangles, 20 W/cm';
squares, 360 W/cm2.
indicating no pronounced surface roughness or other sources of capacitance. The observed time constant for the cell (0.6 ps) is close to that expected from the calculated resistance (0.53 ps) and clearly indicates that the double layer will be fully charged by 4 ps after the potential step. For the experiment depicted in Figure 7, the iR error is 11 mV at 4 ps, a value which is easily overcome by an increase in potential. Both the iR error and time constant increase at smaller electrode radii are due in part to internal electrode resistance, so nothing is gained by smaller radii for the cylindrical geometry. However, for a disk electrode, the time constant and iR error can be much lower, although the optical arrangement is more complex. For a 5 pm radius disk in 1M H2S04,for example, the time constant is 14 ns, making submicrosecond potential step experiments quite feasible. Such electrodes, associated optics, and signal processing systems are presently under development. The observed absorbance transients shown in Figure 4 agree well with theory, indicating that uncomplicated cylindrical diffusion occurs at least until times exceeding 0.1 s. The maximum value of (Dt)l/z/rofor which theory and experiment agreed was 1.7 (corresponding to 300 ms) for a 6.4pm radius gold electrode, although smaller upper limits on (Dt)'iz/r0were observed as the electrode radius increased. At longer times, a negative deviation of experiment from theory is observed for all electrode sizes except ro = 280 pm. The deviation was strongly dependent on laser power, with good agreement between theory and experiment being observed at fairly low power, below 50 mW/cm2 at the electrode (-0.1 mW beam power). There are at least three possible causes of deviation at high laser power, all of which can be avoided by operating at low power. First, the partial absorption of the beam by the electrode will heat up the fiber and produce thermal convection. A 90% reflective Pt fiber will heat up at a rate of 0.1 "C/s to 10 OC/s for the power range 0.01-1.0 W/cm2, a rate which is large enough to produce local heating a t the higher powers. Second, absorption by electrogenerated chromophore will also heat the solution at a rate of about 2 "C/s at an absorbance of 0.01 and input power of 0.2 W/cm2. Third, high powers can bleach the chromophore if it is photolytically unstable. Whether deviations from theory a t long times originate with thermal or photolytic effects, they can be avoided for all electrode sizes provided the power density is less than 50 mW/cm2 and the experiment is shorter than 300 ms. I t should also be noted that high power densities cause a positive deviation from theory at short times, but a much larger negative deviation as the experiment progresses. Fortunately, laser power effects are negligible at short times,
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
where the microelectrode characteristics are most important for improving transient response. For powers below 50 mW/cm2, theory and experiment agree up to (Dt)li2/roof 1.7. As indicated in the figures, higher powers were used for very fast runs (Figures 6 and 7 ) to provide higher light levels to decrease noise. For fast runs these higher powers were permissable since the run was over before thermal or bleaching effects appeared. For fast experiments which require extensive signal averaging, thermal convection induced by local heating would have beneficial effects, since the solution would be agitated between runs, to restore initial conditions. The high acceptable duty cycle reported earlier (14) is very likely a manifestation of laser-induced thermal convections. The results observed on Au and Pt electrodes are in contrast to those observed on carbon fiber electrodes ( 1 4 ) ,for which absorbance was linear with t1/2up to about 1s, despite theoretical predictions (Figure 4) of 30% deviation from linearity at this point. The linearity of the transients from carbon electrodes remains unexplained, but there are two major differences between carbon fibers and the metals used here. First, the low reflectivity of carbon will greatly increase thermal effects caused b,y electrode absorption. Second, the surface topology of carbon fibers is very different from metals, with highly noncylindrical shapes observed at the microscopic level, and a roughness factor of about 500 (24). Whatever the origin of the disparity, 1% or Au electrodes are superior to carbon for the experiment described here, not only because of agreement with theory but also because of the much lower internal resistance of metals over carbon, decreasing the electrode resistance (andl therefore cell time constant) by at least a factor of 100. An additional advantage of the metal electrodes is much longer life, with the Pt or Au fibers being much more robust in both mechanical and chemical contexts. The presence of thermal effects on all electrodes restricts the measurements to regions of time where the diffusion layer thickness is no more than twice the electrode radius (Dt)li2/r0 < 2). While some effects of cylindrical diffusion such as product dilution and enhanced mass transport will occur in the accessible time scale, they will not be as large as similar effects observed for the spherical case, as with a microdisk (10, 11). The excellent transiend, response of the technique shown in Figure 7 is a direct result of the low time constant and small iR error resulting from the small electrode area. The time resolution and agreement between theory and experiment compare favorably with the best competitive method, internal reflection spectroscopy, and the present experiment required no adjustable parameters Rather the theoretical absorbance was calculated directly from properties of the chemical system and electrode with no uncertainty about penetration depth, as in IRS (9,251. In addition, the sophisticated potentiostat that is usually required for fast electrochemical or spectroelectrochemical measurements is not required. The trivial two-electrode design is free from electronic stability problems (26) and very little attention need be paid to cell design, since the transient response is dictated by the working electrode itself, and the position of the counterelectrode is fairly unimportant. The peak current required for the experiment depicted in Figure 7 was 6 mA, with a peak power of 1.4 mW, compared to the 200-300 W required for fast IRS (9). When absorbance readings at times less than 200 ks were from 0.8 to 1.1V. desired, it was necessary to increase Eapp Since the first reading at 4 ps is about 6 time constants after the step, and since the iR error at this point is about 11 mV, the extra driving force required is not due to an inaccurate electrode potential. Therefore the charge transfer rate of OD must be retarding the response at 0.8 V and not at 1.1. Finally, it should be noted that the subtraction of a blank run is
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important for fast experiments, or for any case where the absorbance is low. As shown in Figure 6, the "absorbance" caused by the reflectance change for Pt in 1M HzS04is about 7x but this value varies with metal, medium, potential, and wavelength. The reflectance change is composed of the electroreflectance effect (27) combined with surface oxide formation or any other changes in the electrode surface. While background "absorbance" was not a major correction in the present work, it can be quite large compared to the absorbance from weaker chromophores, and blank runs should always be recorded and subtracted if necessary. CONCLUSION External reflection from Pt or Au cylindrical microelectrodes provides excellent transient response, with the time of the first data point being limited by the data acquisition system rather than the spectroelectrochemical apparatus. In addition to speed, the technique allows such transient response without a potentiostat with its accompanying instability at high speed. With a disk rather than cylinder electrode, the RC constant and therefore the transient response should be ca. 40 times better, and experiments examining the submicrosecond time scale are in progress. In addition to improvements in rise time by using a disk, more efficient collection optics for the cylinder should permit the use of a continuum source, allowing a wide wavelength range to be examined. LITERATURE CITED (1) McDonald, D. D. "Transient Techniques in Electrochemistry"; Plenum Press: New York, 1977; Chapter 7. (2) Agarwal, H. P. I n "Electroanalytical Chemistry"; Bord, A. J., Ed.; Marcel Dekker: New York, 1974; Vol. 7, p 161. (3) Bond, A. M.; Smith, D. E. Anal. Chem. 1979, 46, 1946. (4) Reference 1, Chapter 4. (5) Durand, R., et al. Nectrochim. Acta. 1980, 25,399 and references therein. (6) Matsuda, H.; Aoyagui, S. J . Electroanal. Chem. 1978, 87, 155 and reference therein. (7) Perone, S. P. Anal. Chem. 1986, 38, 1158. (8) Brown, E. R.; Smith, D. E.; Booman, G. L. Anal. Chem. 1968, 4 0 , 1411.
(9) Davls, J. E.; Winograd, N. Anal. Chem. 1972, 44, 2152. (IO) Dayton, M. A.; Brown, J. C.; Stutts, K. J.; Wightman, R. M. Anal. Chem. 1980, 52,946. (11) Dayton, M. A.; Ewing, A. G.; Wlghtman, R. M. Anal. Chem. 1980, 52, 2393. (12) Ponchon, J.-L.; Cespuglio, R.; Gonon, F.; Jouvet, M.; Pujol. J.-F. Ana/. Chem. 1979, 51, 1483. (13) Scharifker, F.; Hills, 0. J . Nectroanal. Chem. 1981, 130,81. (14) Robinson, R. S.; McCreery, R. L. Anal. Chem. 1981, 53,997. (15) Carslaw, H. S.;Jaeger, J. C. "Conduction of Heat in Solids"; Oxford University Press: London, 1947; pp 280-282. (16) Abramowitz, M., Stegun, I , Eds. "Handbook of Mathematical Functlons"; U.S. Government Printing Office: Washington, DC, 1964; p 355. (17) Reference 16, p 886. (18) Reference 16, p 253. (19) Wlnograd, N.; Blount, H. N.; Kuwana, T. J . Phys. Chem. 1969, 73, 3456. (20) Pllla, A. Anal. Chem. 1988, 4 0 , 1173. (21) Prulksma, Richard; McCreery, R. L. Anal. Chem. 1981, 53,202. (22) Adams, R. N. "Electrochemistry at Solid Electrodes"; Marcel Dekker: New York, 1969; p 216. (23) Glleadi, E.; Kirowa-Elsner, E.; Pensiner, J. "Interfacial Electrochemistry"; Addison-Wesley: London, 1975; pp 241-242. (24) Jenning, V. J. I n "Analytical Chemistry Symposia"; Smyth, W. F., Ed.; Elsevier: New York 1980; Vol. 2, p 199. (25) Hansen, W. N. I n "Advances in Electrochemical Engineering and Electrochemistry"; Delahay, P., Tobias, C. W., Eds.; Wliey: New York; VOl. 9, p 1. (26) Harrar, J. E.; Pomernacki, C. L. Anal. Chem. 1973, 45, 57. (27) McIntyre, J. D. E. ref 23, p 61.
RECEIVED for review July 6,1982. Accepted August 13,1982. R.L.M. and C.W.M. are Alfred P. Sloan Fellows for 1981-1983, and partial support of this work by the Sloan Foundation is acknowledged. Major support came from the Chemical Analysis Division of the National Science Foundation, and additional support from the Chevron Research Company is acknowledged.
