Anal. Chem. 1987,
2098
(7) (8) (9) (10) (11)
(12) (13)
(14) (15) (16) (17) (18) (19) (20) (21)
vances in Chemistry Series No. 214; American Chemical Society: Washington D.C., 1987; Chapter 27, pp 571-591. Peters, T. L. Anal. Chem. 1982, 5 4 , 1913-1914. Bruchet, A.; Cognet, L.; Malieviaiie, J. Water Res. 1984, 18, 1401- 1409. Suffet, I. H.; Brenner, L.; Coyie. J. T.; Cairo, P. R. Environ. Sci. Techno/. 1978, 12, 1315-1322. Suffet, I . H.; Gibs, J.; Coyle, J. A.; Chrobak, R. S.; Yohe, T. L. J.Am. Water Works Assoc. 1985, 7 7 , 65-72. Coyie, G. T.; Maloney, S. W.; Gibs, J.; Suffet, I. H. I n Water Chlorination: Environmental Impact and Health Effects; Jolley, R. L.. et al., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983: Vol 4, Chapter 30, pp 42 1-443. Gibs, J.; Najar, E.; Suffet, I. H. In. Water Chlorination: Environmental Impact and Health Effects; Jolley, R. L. et ai., Eds.; Lewis Publishers: Chelsea, MI, 1986; Voi. 5, Chapter 88, pp 1099-2008. Brown, D. W.; Ramos, L. S.; Vyeda, M. Y.; Friendman, A. S.; Macleod, W. D.. I n Petroleum in the Marine Environment; Pitrakis, L., Weiss, F. T.. Eds.; American Chemical Society Symposium, Advances in Chemistry Series No. 185; American Chemical Society: Washington, D.C., 1980; Chapter 14, pp 313-326. Oliver, B. G.; Nicoi, K. D. Sci. TotalEnvlron. 1984, 3 9 , 57-70. Aiford-Stevens, A. L.; Budde, W. L.; Beiler. T. A. Anal. Chem. 1985, 5 7 , 2452-2457. Eiceman, G. A.; Clement, R. E.; Karasek, F. W. Anal. Chem. 1979, 5 1 , 2343-2350. Eiceman, G. A.; Clement, R. E.; Karasek. F. W. Anal. Chem. 1981, 5 3 , 955-959. Yu, M.;Hites, R. A. Anal. Chem. 1981, 5 3 , 951-954. Simoneit, B. R. T. Atmos. Environ. 1984, 18. 51-67. Gunther. F.; Biinn, R. C.; Koibezen, M. J.; Barciay, J. H.; Harris, W. D.; Simon, H. S. Anal. Chem. 1951, 2 3 , 1835-1842. Sherrna. J.; Beroza, M. "Manual of Analytical Quality Control for Pes-
59,2098-2101
(22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36)
ticides and Related Compounds in Human and Environmental SamplesFinal Revision;" EPA-600/1-79-008, 1979; 197-198. Goidberg, M. C.; DeLong, L.; Sinciair, M. Anal. Chem. 1973, 4 5 , 89-93. Erickson, M. D.; Giguere, M . T.; Whitacker, D. A. Anal. Lett. 1981, 1 4 , 841-857. Chiba, M.; Moriey, V. J . Assoc. Off. Anal. Chem. 1968, 5 1 , 55-62. Rose, A.; Rose, E. I n Treatise On Analytical Chemistry. farf 1 Voi. 5 , Theory and Practice, 2nd ed.; Interscience: New York, 1982; pp 449-503. Rose, A. I n d . Eng, Chem. I941a, 3 3 , 594-597. Rose, A.; Long, H. H. I n d . Eng. Chem. 1941b, 3 3 , 684-687. Meipoider, F. W.; Headington, C. E. I n d . Eng. Chem. 1947, 3 9 , 763-766. McCabe, . L.; Thieie, E. W. Ind. Eng. Chem. 1925, 17, 605-611. Fensk, M. R. Ind. Eng. Chem. 1932, 2 4 , 482-485. Underwood, A. J. V. Trans. Inst. Chem. Eng. 1932, 10, 112-152. Fensk, M. R . I n Science of Petroleum; Dunstan, Albert Ernest, Ed.; Oxford University Press: New York, 1938. Carney, T. P. Laboratory Fractional Distillation; MacMiilian: New York, 1949. Coulson, E. A.; Herington, E. F. G. Laboratory Distillation Practice Interscience: New York, 1958; Chapter 8. Kreli, E. Handbook of Laboratory Distillation; Elsevier: New York, 1963. Miiier, J. C.; Miller, J. N. Statistics for Analytical Chemistry; Ellis Horwood Series in Analytical Chemistry: Eiiis Horwood Ltd: Chichester, West Sussex, England, 1984.
RECEIVED for review December 23,1986. Accepted May 11, 1987.
Ohmic Potential Drop at Electrodes Exhibiting Steady-State Diffusion Currents Stanley Bruckenstein Chemistry Department, University at Buffalo, State University of New York, Buffalo, New York 14214
Theory shows that all (m1cro)electrodes exhlblt the same ohmic potential drop provided they are in a steady-state dlffuslonal reglme and the cell geometry would yield the eiectrodes's prlmary reststance. Laplace's equation describes both the steady-state dlffusion and the reslstance in such electrochemical cells. This experlmental sltuatlon can be realized uslng microelectrodeswhose dlmensions are small enough to obtaln dlffuslonal steady state before natural convection occurs. Expressions are derlved for the ohmic potentlal drop occurring durlng vdlammetry. Two IhnMng cases are discussed, the electrolyds of a pure binary electrolyte and a binary electrolyte in the presence of a large excess of supporting electrolyte. The results are Independent of solvent and of the geometry of the microelectrode provlded the diffuse double layer is small compared to the diffusion layer thickness.
One of the advantages of microelectrodes is the low ohmic potential drops that they exhibit between the counter and working electrodes. This fact is well-appreciated. It has led to the use of two-electrode control circuits, rather than the conventional three-electrode potentiostatic circuitry in wide use with electrodes of macrodimensions ( I ) . My purpose is to point out some simple relations describing the ohmic potential drop that apply under certain steady-state diffusion conditions at the working (indicator) electrode in a twoelectrode cell. 0003-2700/87/0359-2098$01.50/0
The results given below apply only to a single microelectrode structure in a cell where only the microelectrode determines the diffusional flux and the primary resistance. The volume of the cell and its dimensions, and the size of the counter electrode and its distance from the working electrode are assumed to be sufficiently large so as to correspond to an infinitely large counter electrode infinitely distant from the microelectrode in a cell of infinite dimensions. Practical cells meeting these requirements are not difficult to devise when working with microelectrodes. At steady state both the diffusion current and the primary resistance can be described by the Laplace equation V 2 0 = 0; n(s) = 0; Q ( a )= 1; grad Q = 0 a t insulating boundaries (1)
with the specified boundary conditions. Q(s) is the value of fi at the electrode surface for the orthogonal coordinate system values x8,y8,and 2,. First, I will show that all electrode systems that can be described by eq 1 exhibit the same ohmic potential drop between the working electrode and a counter electrode at infinity. An example meeting these requirements would be a working electrode that is potentiostated at constant potential in contact with a solution containing a redox couple that (a) is completely reversible or (b) exhibits heterogeneous electron transfer kinetic control. Second, I will show that the ohmic potential drop is independent of solvent for a given electroactive solute in the absence or presence of supporting electrolyte, provided complete 0 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 17, SEPTEMBER 1, 1987
dissociation of all electrolytes takes place and the diffusion layer is not too small. In practice, only microelectrodes can be expected to meet the requirements of eq 1. Only they have physical sizes such that a steady-state flux can be established before natural convection disrupts the diffusion process.
THEORETICAL SECTION Diffusion Problem. Assume that a microelectrode of arbitrary shape and size is in contact with a solution containing a binary electrolyte AysZaBy:b (AB) of bulk concentration C". A is electrolyzed at the working electrode and its diffusion coefficient, D , is assumed constant in the diffusion layer. Furthermore, assume (a) that no supporting electrolyte is present, in which case D ( = D A B ) represents the coupled diffusion coefficient of A'. and its counterion BZBand, in this case only, Aza is reduced to the metal, (b) or that there is supporting electrolyte, DyPGy? (DG) present in large excess. Then D represents the single ion diffusion coefficient of A, Dk Also, assume that a steady-state current has been reached at the working electrode and that the concentration of A at infinity is C" and its concentration everywhere on the electrode surface is Cs.Laplace's equation is valid in these circumstances (2). For this diffusion problem it is
DV2C = 0, C(s) = C8;C(m) = C" grad C = 0 a t insulating boundaries (2) Defining the variable Q = [C - CB]/[Cm- Cs]transforms eq 2 into eq 1. The current density at any point on the electrode surface is then given by
io = -nFD(1 - t,j-'(grad CIS= -nFD(C" - Cs)(l- t,)-l(grad Qla(3) In eq 3, t A is the transport number of species A's. In the presence of excess supporting electrolyte, t A is zero. The total current, I, at the electrode is obtained by integrating over the entire electrode surface
I = -nFD(C"
-
Cs}(l- t J ' j ( g r a d Qls d S
(4)
This result is completely general and does not depend on the shape of the electrode. Conductance Problem. For the diffusion problem considered above, the potential distribution in the cell is described bY v29 = 0, 9(s) = 9 s ; @(a) = 9" grad 9 = 0 a t insulating boundaries
(5)
where asis the potential just outside the diffusion layer at the microelectrode where all concentrations are uniform and 0" is the potential at the infinitely large counter electrode. Defining the variable Q = [a - PI/[@" - an]transforms eq 5 into eq 1. The current density at any point on the electrode surface, the primary current distribution, is then given by
io = -ulgrad 91,= -a(@" - Wjlgrad
Qls
(6)
where u is the specific conductance of the solution in the cell. The total current, I, at the electrode is obtained by integrating over the entire electrode surface.
Hence the cell resistance, R, is
This result is completely general and does not depend on the shape of the electrode.
2099
Table I. Limiting Current and Primary Resistance at Electrodes limiting current/nFDC" or 1/(Ra) *
geometry sphere of radius = a disk of radius = a in an infinite insulating plane oblate spheriod of semiaxes a and c, a > c prolate spheriod of semiaxes a and c, c, > a two spheres of radius a in
47ra 4a (a2@ 4a(a2- c2)1/z/tan-1 47r(a2- c2)1/2/tanh-1(1 - b2a-2)1/2 8 r a In 2
contact cube of side a
-8.224a
elliptic disk of semiaxes a and 47ra(K[(1- b2a-2)1/2])-1 b, a > b'
"Taken from ref 3. The relationship between the steady-state limiting current and the capacitance for the various cases is Z = (nFDC")C/c, where C is the capacitance expression given in ref 4 and c is the dielectric constant. bTaken from ref 4. The relationship between the primary resistance and the capacitance given for the various cases is R = c/Cu. Obviously, the product ZR = nFDC"/u for these specific cases. The various formulas are given for the convenience of the reader. " ( k ) is the complete elliptic integral of modulus k .
Ohmic Potential Drop. The dimensionless forms of the Laplace equation for the diffusion problem and the conductance problem are identical and have the same solutions for R. The boundary conditions become identical in the case where the diffusion layer thickness is large compared to the double layer thickness. This condition will always be met in the presence of a large excess of supporting electrolyte. Under both these circumstances, the product, IR, is obtained by multiplying eq 4 and 8.
I R = nFD(C"- C 8 ) / ~ (-1t a )
(9)
This result demonstrates that the ohmic potential drop between an infinitely distant, infinitely large counter electrode and a working electrode does not depend upon the geometry of the working electrode. Table I presents analytical expressions for I and R for various electrode geometries. They were obtained from static-field formulas for the capacitance of an isolated body(ies) (3)and static-current formulas (4)for the same geometries as described in the footnotes to Table I. The first two entries are familiar ones, the case of the sphere and the disk electrode imbedded in an infinite plane. To the best of my knowledge the others have not been considered previously from the electrochemical viewpoint. This listing is not intended to be inclusive but is given primarily to point out that in addition to the familiar heat transfer literature, there is a rich literature in other fields that can provide approaches to diffusion problems of interest in electrochemistry. The product of I and R agrees with eq 9 in all cases shown in Table I. In the absence of added supporting electrolyte, it is possible to estimate the ohmic potential drops in a way that requires no knowledge of the specific conductivity of the solution being studied, the concentration of the diffusing species, or the solvent. In the presence of supporting electrolyte the ratio of the concentration of the supporting electrolyte to that of the diffusing species must be known. First consider the case of the electroactive species A diffusing in the absence of supporting electrolyte. Defining yz = y&,I = y&bl, the specific conductance in terms of the limiting ionic conductances of A and B is = yz(xao
+ Xbo)CABm
(10) where y is the number of ions of the indicated charge into
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ANALYTICAL CHEMISTRY, VOL. 59, NO. 17, SEPTEMBER 1, 1987
which a molecule of electrolyte dissociates. Then, making use of eq 10 and the Nernst relationship which applies at infinite dilution for the coupled diffusion of a salt D A B = (lZa1-'
+ ~ Z ~ ~ - ' ) ( R ~ / ~ ) [ ~ , +" ~Ah")] ~ " / ( (11) ~,"
yields, on substitution in eq 9, with the definition of tA = X,"/{Xao + X h o ] and the requirement that n = za because A's is reduced to the metal
IR = ffka/TZ)(\za\-' + Izb\-'>(RT/F)(Xa")/(Xa'
-t 'bo)
(12) where CY = I/Ib and Ih is the limiting diffusion current. With the exception of hydrogen and hydroxyl ions, most other ions have very similar limiting equivalent conductances, so I assume A," = Abo and obtain
IR =
+
( Q Z ~ / ~ T Z ) ( [ Z ~ ~ - ' Iz,l-')(RT/F)
(13)
as the result that will be used to predict ohmic potential drops. If the diffusion salt is a uni-univalent salt, z, = 1 and I R = aRT/F = 2 5 . 6 ~mV a t 25 "C (14) The predicted voltage drop is significant in the S-shaped region of the I-E curve, e.g., for CY = 0.5, IR = 12.8 mV. Thus I-E curves obtained by the two-electrode technique in the absence of supporting electrolyte must be corrected for IR effects before thermodynamic or kinetic analyses are attempted. Ohmic potential drops will be even greater when non-steady-state electrochemical techniques such as cyclic voltammetry are used. The use of a three-electrode potentiostat comes to mind. However, this solution is not practical with a microelectrode as it will not be feasible to place the Luggin capillary tip close enough to the electrode surface to eliminate a significant fraction of the ohmic potential drop. Most of the IR drop occurs within a distance comparable to the characteristic dimension of the microelectrode. I have not discussed other cases of which there are a myriad of variations. Obviously larger values of z, and z b produce smaller values of IR. It should be noted that multiply charged ions often undergo acid-base reactions with the solvent water or complex or form ion pairs with their counterion. So it would be unrealistic to use eq 13 to calculate the IR drop arising during the reduction of ferric chloride in the absence of supporting electrolyte. Three assumptions were made in arriving a t eq 12. First limiting law expressions that strictly apply only at zero ionic strength were assumed valid (eq 10 and 11). Second DAB was assumed constant in the diffusion layer (use of DC2C = 0 rather than 0.DOC = 0). Third, the dimensions of the diffuse double layer were assumed to be smaller than the steady-state diffusion layer (use of Laplace's equation to describe the diffusion process.) The first two assumptions are good ones for voltammetric situations where CABm is usually less than a few millimolar, and CABmfrequently approaches micromolar levels. The third one is the most restrictive under typical voltammetric conditions at microelectrodes having very small dimensions and is most serious since the electroactive species is plated out, rather than converted to another ionic species. This problem has been discussed by Ibl ( 5 ) who predicted significant effects in the case of the reduction of cupric ion to copper metal from a 0.1 mM copper sulfate solution if the diffusion layer thickness was 1 wm and CY = 0.95. In view of the fact that lower solute concentrations are likely to be used at microelectrodes whose dimensions are smaller than 1 pm, appropriate care should be used in applying eq 12. In the presence of a bulk concentration, CDGm,of supporting electrolyte DG, it is possible to estimate the ohmic potential drop by making only a slight modification in the previous treatment. I assume that it is valid to neglect the presence of AB to estimate the specific conductance of the solution
provided CDGm >> CAB-. Then the equivalent ionic conductance given by eq 10 may be written as (7
= Tz(Xdo
where yz = Td(Zgl = then given by
yglZd)
+ Xgo)CDGm
(15)
The diffusion coefficient of A is
DA = (RT/lzalF)Xa"
(16)
Proceeding as before and assuming all equivalent conductances are the same, the expression
IR = ff ( n / Z , T Z ) (CABrn/CDGm)(RT/F)(Xao / Ado 4= /2z ,YZ)(CAB"/ Cm-1 (RT/F)
Ago)
(17) is obtained. If n / z , = 1, and the supporting electrolyte is a uni-univalent salt, a t the half wave potential
IR =
(ff /2)
( CAB-/ C,,")(RT/F) = f f ( c ~ ~ ~ / C D G ) 1 mV 2 . 8 at 25
"c (18)
At the half-wave potential, eq 18predicts an ohmic potential drop of 6.4 pV for a 1000-fold excess of DG over AB. A 50-fold excess of DG over AB would lead to an ohmic potential drop of 0.13 mV, a negligible quantity in even the most exacting electroanalytical studies. For most studies a 10-fold excess with an estimated IR of -0.6 mV would be acceptable. Larger n values would increase the ohmic potential drop. It is not too realistic to consider this case for n > 2, as the problem solved applies only if the electron transfer reaction is reversible or obeys heterogeneous electron transfer kinetics. The beneficial effects of larger normal concentrations of supporting electrolyte and values of z, > 1 are obvious. The presence of significant excess supporting electrolyte is required if the two-electrode technique is used with rapid scanning triangular wave voltammetry. The currents using cyclic voltammetry will always be very much larger than those in the steady-state case. In the absence of any other information, I suggest an approximate estimate of IR can be made by redefining a in any of the preceding equations as =I(t)/Il, where I ( t ) is the instantaneous current in the cyclic voltammetric experiment and I , is the limiting current in the steady-state potentiostatic experiment. Effect of Solvent. The ohmic potential drops predicted by both eq 12 and 17 are independent of solvent. However, there are two solvent-dependent effects that have not been considered. First, the possibility of ion pair formation in low dielectric constant solvents complicates the diffusion process in that the ion pair between A and B or A and G diffuses simultaneously with the separate ions. Bockris and Reddy (6) estimate that this coupled diffusion coefficient is within 20% of the one free of ion pair formation (6). Hence, the ion-pair effect should introduce errors only modestly larger than those expected from concentration effects in aqueous solution. Second, the thickness of the double layer is proportional to (Cc)-'/*, where C is the concentration of the electrolyte and e is the solvent's dielectric constant. The increase in the size of the diffuse double layer will limit the lower concentration limit of application of eq 12 and 17 in many low dielectric constant solvents. Thus predictions of ohmic potential drops made in nonaqueous solutions containing supporting electrolytes are likely to be more reliable than those made in the absence of supporting electrolyte. This statement is equally valid in water, although the magnitude of the problem is smaller.
CONCLUSION The ohmic potential drop introduced by using a two-electrode electrochemical technique does not depend upon the geometry of the working electrode provided its dimensions
Anal. Chern. 1987, 59,2101-2111
are small enough to permit establishment of a diffusional steady state. In a 1:1,univalent binary electrolyte solution, ohmic potential drops as large as 25 mV may occur near the top of the S-shaped region of a steady-state I-E curve. They should be taken into account prior to any thermodynamic or kinetic analysis. This ohmic potential drop is independent of the concentration of electroactive species. In the presence of supporting electrolyte, the ohmic potential drop is proportional to the ratio of concentrations of the electroactive species to supporting electrolyte but remains independent of electrode geometry. A 50-fold excess of supporting electrolyte reduces the ohmic potential drop to a negligible amount under steady-state potentiostatic conditions. Substantially more supporting electrolyte is required in a rapid scanning triangular wave experiment using a two-electrode technique. The analysis, which is based upon classical limiting law electrochemical transport theory in water, yields a result which does not depend upon the solvent. The latter conclusion is only a first approximation.
2101
ACKNOWLEDGMENT S.B. thanks J. G. Osteryoung for her valuable and stimulating discussions.
LITERATURE CITED (1) Wightman, R. M. Anal. Chem. 1981, 5 3 , 1125A. (2) Marchiano, S. L.; Arvia, A. J. Comprehensive Treatise of Electrochemistry; Yeager, E., Bockris, J. O'M., Conway, B. E., Sarangapani, S., Eds.; Plenum: New York, 1983; Vol. 6, Chapter 2, pp 74-77. (3) Smythe, W. R. American Institute of Physics Handbook, 3rd ed.; Gray, D. E.,Ed.; McGraw-Hill: New York, 1972; p 5-12. (4) Smythe, W. R. American Institute of Physics Handbook, 3rd ed.; Gray, D. E., Ed.; McGraw-Hill: New York, 1972; p 5-24. ( 5 ) Ibl, N. Comprehensive Treatise of Electrochemistry;Yeager, E., Bockris, J. O M ,Conway, B. E., Sarangapani, s., Eds.; Plenum: New York, 1983; Vol. 6, Chapter 1, pp 42-43. (6) Bockris, J. O'M.; Reddy, A. K. N. Modern €lectrochemistry; Plenum: New York. 1972; p 383.
RECEIVED for review February 26, 1987. Accepted April 27, 1987. This work was supported by the Air Force Office of Scientific Research under Grant No. 870037.
Digital Simulation of Homogeneous Chemical Reactions Coupled to Heterogeneous Electron Transfer and Applications at Platinum/Mica/Platinum Ultramicroband Electrodes Theresa Varco Shea and Allen J. Bard* Department of Chemistry, University of Texas, Austin, Texas 78712
DigHal slmulatlon of generatlon-collection, shleldlng, and feedback experiments was carrled out for palred ultramicroband electrodes wlth homogeneous chemical reactions following the heterogeneous electron transfer step, Le., the EC' and EC mechanlsms. Closely spaced mlcroband electrode palrs were constructed by sputter deposition of Pt onto both sides of 2 to 12 pm thlck mlca sheets that were mounted between glass slldes. The band electrodes thus formed had effective thlcknesses of 0.01-6 pm and were 0.5 to 1.2 cm long. Results of cyclk vdtammetrlc and chronoamperometric step, generation-collection, feedback, and shleldlng experiments with several redox couples agreed wlth theoretical predlctlons based on digital slmulatlon of the system at quasl steady state. The applkatlon of these band electrodes to the detemlnatlon d the secondorder rate constant for a following catalytlc reactlon between Fe(CN):and ascorbic acid or aminopyrine was demonstrated.
We describe here the fabrication of a pair of closely spaced (ca. 2-12 pm) Pt ultramicroband electrodes 0.01-6.0 pm wide by sputter depositing Pt films on mica (1-3) and the electrochemical characterization of such electrodes. The application of these electrodes to studies of chemical reactions coupled to a heterogeneous electron transfer reaction, i.e., a following catalytic reaction, by generation-collection experiments under pseudo-first- and second-order reaction conditions is demonstrated. The effects of coupled homogeneous reactions, i.e., the EC' and EC mechanisms, were studied by digital simulation (4)and are reported for two electrode arrays. In particular, generation-collection, shielding, and feedback experiments were simulated.
Ultramicroelectrodes are of interest for several reasons. Steady-state or quasi-steady-state currents are rapidly attained because the small dimensions (less than 10 pm) promote nonlinear mass transport (5-7). Moreover, small areas result in low currents allowing the use of microelectrodes in highly resistive media without appreciable iR drops through the solution (8-11). Ultramicroelectrodes can also be employed with very fast scan rates in linear sweep voltammetry (12,13) to study nucleation phenomena in electrodeposition (14-16) and as electrochemical detectors ( 17,18). Ultramicroelectrodes of various geometries have been fabricated, including disk electrodes prepared by sealing a fine metal wire or carbon fiber in a glass capillary (12, 19,20),microsphere (21),microring (22, 23), microband (24-28), microcylinder (29-34), and vibrating wire electrodes (35). Microband electrodes, which consist of a metal film sandwiched between insulators, have been constructed with a metal bandwidth in the nanometer to micrometer range and lengths of 50 pm to several centimeters (3, 24-28). Wightman and co-workers describe the construction of a single microband by coating a glass slide with Pt or Au films, sealing this with epoxy cement to a second slide, and using the exposed edge as the electrode (24, 27). While single ultramicroelectrode systems are useful for many types of electrochemical experiments, arrays of two or more closely spaced and independently contacted microelectrodes have also been of interest and can be employed in additional electroanalytical modes. For example, photolithographic techniques can be employed to produce arrays of microband electrodes ( 4 ,26, 28, 29), which can be used for electrochemical detectors and in electrogenerated chemiluminescence and electrochemical generation-collection experiments of the type carried out at rotating ring-disk electrodes (RRDE) (36a, 37), e.g., with generation of a species at one electrode and subsequent detection of the generated
0003-2700/87/0359-2101$01.50/0 0 1987 American Chemical Society
