REPOR7
Stanley Pons
Department of Chemistry University of Utah Salt Lake City, Utah 841 12
Martin Fleischmann Department of Chemistry University of Southampton Southampton SO9 5NH England In the early 1970s a number of research groups exploited the advantages of microelectrodes, which are normally defined as devices with characteristic dimensions smaller than about 20 fim, over conventional electrodes. Because many of the undesirable aspects of electrochemical and electroanalytical techniques can he reduced or eliminated with microelectrodes, their use has grown rapidly. Microelectrodes are advantageous for several reasons. First, very small currents (rates of reaction) as low as A, 10 e-Is, can be measured with relative ease. Second, iR losses in solution are reduced a t small electrodes. This “error” to the applied potential at the electrode-solution interface prevents electrochemical experiments from being performed with “large” electrodes in all but ionically conducting solutions. Third, capacitative charging currents, the limiting factor in all transient electrochemical techniques, are reduced to insignificant proportions at electrodes of sufficiently small area. Fourth, the rate of mass transport to and from the electrodes increases as the electrode size decreases; moreover, steady states of mass transfer are rapidly established. As a consequence of reduced capacitative charging currents and increased mass transport rates, microelectrodes exhibit excellent signal-to-noise (S/N) characteristics. Finally, as the literature indicates, microelectrode systems are easily implemented and involve relatively low costs. The unusual properties of microelectrodes also allow electrochemical measurements to be made on novel systems-those that are not amenable to 0003-2700187/A359- 1391IS0 1.50/0 @ 1987 American Chemical Society
I
A
Flgure 1. Designs of microelectrodes. (a) Side view 01 a microdisk electrode. (b) plane view of a micrwing eiectrcde. (c) plane vlew 01 a micro-
disk-micrwing electrode, (d) side view Of a spherical mercury drop deposited on a disk, (e) side view Of a particle in a dispersion undergoing eIecnolysis by a field applied across the cell.
ANALYTiCAL CHEMISTRY. VOL. 59, NO. 24, DECEMBER 15, 1987
1391 A
tography. The detector in the gas phase is especially sensitive for analytes that have a proton loss involved in chemical reactions following the electron transfer. The increased sensitivity results from the high mobility of the proton. The detectors are species-sensitive because of differences in standard potentials of the analytes, and they are quantitatively more sensitive than thermal conductivity detectors.
PotentialIMlts vs. AglAg+ Flgure 2. Effect of electrolyte addition to acetonitrile when using a plt microelectrode of radius 0.5 wn in oxidation of 1 mM ferrocene.
~
~
I disk
(a) Wimaut electrolyie. (b) with 1 mM Et,NCIO,.
conventional electroanalysis. In this REPORTwe will review some of these systems and comment on some of the more interesting properties of very small electrodes, their application to other types of analytical and physical measurements, and solutions to the problem of mass transport to certain microelectrode geometries. Further information about these areas is available; see the Suggested Reading list. Figure 1 illustrates some of the designs of microelectrodes. The high mass transfer rates allow electroanalytical measurements to be made a t low substrate concentrations (using the chronoamperometric or chronopotentiometric responses as well as stripping voltammetry of preconcentrated species, e.g., using Hg microdrops). Other applications include the measurement of the kinetics of fast electrode reactions (from the kinetically controlled polarization curves) and of the kinetics of fast reactions in solution coupled to electrode reactions (e.g., using the radius dependence of the limiting currents that become kinetically controlled by the reactions in solution). These applications are dependent on three of the special properties because of the spherical (or quasi-spherical) concentration and potential fields surrounding the microelectrode: the reduction of iR losses, decreased capacitative currents, and increased mass transport rates. The reduced iR effect is particularly important to other applications of microelectrodes because it allows measurements to be made on novel systems under unusual conditions such as the following: nonpolar solvents in the presence of appropriate support electrolytes (type 1) polar solvents and mixtures of polar and nonpolar solvents in the absence of purposely added support elec-
trolytes (type 2, Figure Za), low-temperature glasses and eutectics (type 3, Figure Zb), and the gas phase (type 4). Measurements of the first three types have been made with conventional microdisk electrodes (Figure la). Type 2 measurements have also been demonstrated using the bipolar electrolysis of dispersions of metal and semiconductor particles supported in solvents without added support electrolyte (Figure le). It is important that ions be invariably generated (or consumed) in electrode reactions, that is Ox e- a Rdor
+
Oxf
+ e- F? Fkl
so that conditions can be chosen to increase the conductance of the solution in the vicinity of the microelectrodes. Because the bulk of the resistance is in this region (the resistance is proportional to the resistivity and the inverse of the electrode radius), the ohmic lases are small and calculable or measurable, particularly in the kinetically controlled region of the polarization curves. Measurements in the gas phase (type 4) are now made with disk-ring electrodes (Figure IC)where the current will usually, hut not necessarily, flow over the “insulator” surface separating the disk from the surrounding ring electrode while gas-phase species diffuse to the microdisk or, most likely, to the edges of the disk through the quasi-spherical diffusion field. The conditions are therefore somewhat different from those for measurements of types 1,2, and 3. We have previously demonstrated the utility of these devices as sensitive detectors in gas-phase chromatography and for measurements of picogram levels of DNA bases by liquid chroma-
1392A * ANALYTICAL CHEMISTRY, VOL. 59. NO. 24. DECEMBER 15, 1987
The problem ol the analysis of mass transport to finite dkks and rhgs It is well known that closed-form simple solutions can be obtained for most types of electrochemical experiments using hemispherical or spherical microelectrodes, provided that any coupled reaction kinetic terms are first order or pseudo first order. For a spherical electrode of any radius r, under conditions of constant flux Q, the concentration distribution is
with a steady-state mass transfer coefficient Dlr, (compare with the mass transport coefficient to a large planar electrode, DI6c; the minimum value of 6c 5 0.001 em for marked forced convection). Definitions of these and other symbols used in equations throughout this REPORTare provided in the glossary of symbols (see box). Unfortunately, the applicability of such types of microelectrodes has thus far been somewhat restricted to the electrodeposition of ensembles or single mercury droplets, the electrolysis of dispersions, or the dropping mercury microelectrode, to name a few examples. Disk and the recently introduced ring microelectrodes are more easily constructed, but the necessary mathematical analysis has thus far proved to be rather intractable. A related problem, the capacitance of a disk, was investigated experimentally by Cavendish in the mid-lll(lOs. The mathematical difficulties of analyzing problems in the cylindrical coordinate system result from discontinuities at the edges of the electrodes where the diffusion-limited flux for a reversible system becomes infinite. The combined effects of the finite rates of the surface reactions and of the distribution of potential and concentration (i.e., the “tertiary current distribution”), however, limit the electron transfer rates at the edges for real systems. Microdisk and microring geometries, however, share the advantage of spherical microelectrodes; quasi-spherical diffusion fields are established in relatively short amounts of time. These spherical diffusion fields give high rates of mass transfer to the surfaces of
the microelectrodes so that the kinetics of fast electrode reactions and of fast reactions in solution can be studied under steady-state conditions. Complicated transient techniques at microelectrodes then may not be required, because it is now easy to build electrodes with very small dimensions. It is therefore always useful to examine whether the steady-state behavior can be predicted directly. The steady-state behavior is described by the diffusion equation in the cylindrical coordinate system
the surface of a disk, the discontinuous integrals
[exp
ra
satisfy the boundary conditions provided f(X) = (2ls)AC sin(Xa). That is, we obtain the solution
lo-
j(X) exp(-hz)J,(Xr)dX
where Jo is a Bessel function of the fust kind of order zero. The f ( X ) are sought so that the equation satisfies the appropriate boundary conditions for any particular electrode geometry. For instance, for a reversible reaction under constant concentration conditions a t
c = C" - - (2sC " - CS) x with flux F = 4D(C- - C*)a and mass transfer coefficient (km), = 4DIsa. For the constant flux condition a t a disk, the concentration distribution is
Glossary of symbols used c" a
Bulk concentration,mol ~ r n - ~ Radius of disk, inner radius
ring, om Coordlnate normal to plane of disk, cm &,J, bssei functions Q Flux, mol cm-2 s-' 0 Surface wncentration, mi cmm3 Outer radius of ring. cm b r Radial coordinate, em D Diffusion coefficient. cm2s-l km Mass transport coefficient, cm s-' 2FI Hypergeometric function F Faraday constant, coulomb equivalent-' I Current, amperes 6 Exchange current density. amperes cm-2 2' Real part, impedance Z" imaginary part, impedance Gas constant. J mi-' K-' R CAW Average concentration,mol cm-3 o Angular frequency, M a Transfer coefficient (in exp) z
with mass transfer coefficient (km)Q= 3rD/8a, where we take the average surface concentration to be equal to zero, and where we have made use of another discontinuous integral. For the ring geometry under the same conditions, we
and mass transfer coefficients, with average concentration a t the surface equal to zero: (km)Q=
3s
8 6c
xp(w)]/
+
exp
exp
(-)I
Numerical evaluation of the integrals is straightforward. Many of the equations may be expressed in terms of hypergeometric functions, which are convenient as these series generally converge rapidly and their propagation is simple and well-suited to representation by efficient algorithms. A complete development of these equations, as well as expressions for several other experiments, are found in the literature cited in the Suggested Reading list. This approach can be extended to predict the non-steady-state behavior of disk electrodes for a variety of electrochemical experiments. Although experiments with very small electrodes will usually be carried out in the steady state (or under quasi-steady-state conditions), the measurement of transient responses with readily available instrumentation becomes feasible for electrodes having somewhat larger dimensions. For instance, the concentration distribution at a disk for the simple case of chronopotentiometry is C=C"-
%1
Jo(ar)J,(ola)erf(D112at 112) & OL
and the chronopotentiometric response for simple Butler-Volmer kinetics is
v -
-Q-C"
D(b2 - a')
n T
-e
associated with
After separating variables, we find a general solution of the form
-
(s) + (s)
r >a
'r
