1.2.15) The current rises from zero as the scan starts and attains a steady-state value, vC d (Figure
1.3 FARADAIC PROCESSES AND FACTORS AFFECTING RATES OF ELECTRODE REACTIONS
1.3.4 Electrochemical Cells and Cell Resistance
Consider a cell composed of two ideal nonpolarizable electrodes, for example, two SCEs immersed in a potassium chloride solution: SCE/KC1/SCE. The i-E characteristic of this cell would look like that of a pure resistance (Figure 1.3.8), because the only limitation on current flow is imposed by the resistance of the solution. In fact, these conditions (i.e., paired, nonpolarizable electrodes) are exactly those sought in measurements of solution conductivity. For any real electrodes (e.g., actual SCEs), mass-transfer and charge-trans- fer overpotentials would also become important at high enough current densities.
When the potential of an electrode is measured against a nonpolarizable reference electrode during the passage of current, a voltage drop equal to iR
sis always included in the measured value. Here, R
sis the solution resistance between the electrodes, which, un- like the impedances describing the mass transfer and activation steps in the electrode re- action, actually behaves as a true resistance over a wide range of conditions. For example, consider once again the cell in Figure 1.3.4. At open circuit (/ = 0), the potential of the cadmium electrode is the equilibrium value, £
eq,cd (about —0.64 V vs. SCE). We saw ear-
fcappl
1 Ideal electrodes
• Real electrodes
Hg/Hg2CI2/K+, CI7Hg2CI2/Hg
© 0
Figure 1.3.8 Current-potential curve for a cell composed of two electrodes approaching ideal nonpolarizability.
1.3 Faradaic Processes and Factors Affecting Rates of Electrode Reactions . 25 Her that with £appi = —0.64 V (Cd vs. SCE), no current would flow through the ammeter.
If £a p p l is increased in magnitude to -0.80 V (Cd vs. SCE), current flows. The extra ap- plied voltage is distributed in two parts. First, to deliver the current, the potential of the Cd electrode, Ecd, must shift to a new value, perhaps -0.70 V vs. SCE. The remainder of the applied voltage (-0.10 V in this example) represents the ohmic drop caused by cur- rent flow in solution. We assume that the SCE is essentially nonpolarizable at the extant current level and does not change its potential. In general,
£a p p l (vs. SCE) = ECd(vs. SCE) - iRs = £eq,Cd(™. SCE) + V - iRs (1.3.6) The last two terms of this equation are related to current flow. When there is a cathodic current at the cadmium electrode, both are negative. Conversely, both are positive for an anodic current. In the cathodic case, £a p p l must manifest the (negative) overpotential (£Cd - £eq,cd) needed to support the electrochemical reaction rate corresponding to the cur- rent. (In the example above, r\ = -0.06 V.) In addition £appl must encompass the ohmic drop, iRs, required to drive the ionic current in solution (which corresponds to the passage of negative charge from the cadmium electrode to the SCE).10 The ohmic potential drop in the solution should not be regarded as a form of overpotential, because it is characteristic of the bulk solution and not of the electrode reaction. Its contribution to the measured electrode potential can be minimized by proper cell design and instrumentation.
Most of the time, one is interested in reactions that occur at only one electrode. An experimental cell could be composed of the electrode system of interest, called the working (or indicator) electrode, coupled with an electrode of known potential that ap- proaches ideal nonpolarizability (such as an SCE with a large-area mercury pool), called the reference electrode. If the passage of current does not affect the potential of the reference electrode, the E of the working electrode is given by equation 1.3.6.
Under conditions when iRs is small (say less than 1-2 mV), this two-electrode cell (Fig- ure 1.3.9) can be used to determine the i-E curve, with E either taken as equal to £appi or corrected for the small iRs drop. For example, in classic polarographic experiments in aqueous solutions, two-electrode cells were often used. In these systems, it is often true that / < 10 /x,A and Rs < 100 П, so that iRs < (10~5 A)(100 ft) or iRs < 1 mV, which is negligible for most purposes. With more highly resistive solutions, such as those based on many nonaqueous solvents, a very small electrode (an ultramicr о electrode, Section 5.3) must be used if a two-electrode cell is to be employed without serious complica-
Working electrode
Power supply
^appl
Reference electrode
Figure 1.3.9 Two-electrode cell.
10The sign preceding the ohmic drop in (1.3.6) is negative as a consequence of the sign convention adopted here for currents (cathodic currents taken as positive).
26 : Chapter 1. Introduction and Overview of Electrode Processes
т
Working or indicator Reference Auxiliary or counter electrodes
Figure 1.3.10 Three-electrode cell and notation for the different electrodes.
tions from the ohmic drop in solution. With such electrodes, currents of the order of 1 nA are typical; hence Rs values even in the Mft range can be acceptable.
In experiments where iRs may be high (e.g., in large-scale electrolytic or galvanic cells or in experiments involving nonaqueous solutions with low conductivities), a three-electrode cell (Figure 1.3.10) is preferable. In this arrangement, the current is passed between the working electrode and a counter (or auxiliary) electrode. The auxil- iary electrode can be any convenient one, because its electrochemical properties do not
Vacuum
Capillary
N2 or H2 inlet
Hg Saturated KCI
Hg2CI2 + KCI Hg
Medium-porosity sintered-Pyrex
disc
4% agar /saturated potassium chloride
29/26
Auxilliary electrode 14 cm
Coarse-porosity, sintered-Pyrex gas-dispersion cylinder
Reference electrode
Solution level Medium frit Stirring bar
Figure 1.3.11 Typical two- and three-electrode cells used in electrochemical experiments, (a) Two- electrode cell for polarography. The working electrode is a dropping mercury electrode (capillary) and the N2 inlet tube is for deaeration of the solution. [From L. Meites, Polarographic Techniques, 2nd ed., Wiley- Interscience, New York, 1965, with permission.] (b) Three-electrode cell designed for studies with nonaqueous solutions at a platinum-disk working electrode, with provision for attachment to a vacuum line.
[Reprinted with permission from A. Demortier and A. J. Bard, /. Am. С hem. Soc, 95, 3495 (1973). Copyright 1973, American Chemical Society.] Three-electrode cells for bulk electrolysis are shown in Figure 11.2.2.
1.3 Faradaic Processes and Factors Affecting Rates of Electrode Reactions 27 affect the behavior of the electrode of interest. It is usually chosen to be an electrode that does not produce substances by electrolysis that will reach the working electrode surface and cause interfering reactions there. Frequently, it is placed in a compartment separated from the working electrode by a sintered-glass disk or other separator. The potential of the working electrode is monitored relative to a separate reference elec- trode, positioned with its tip nearby. The device used to measure the potential differ- ence between the working electrode and the reference electrode has a high input impedance, so that a negligible current is drawn through the reference electrode. Conse- quently, its potential will remain constant and equal to its open-circuit value. This three-electrode arrangement is used in most electrochemical experiments; several prac- tical cells are shown in Figure 1.3.11.
Even in this arrangement, not all of the iRs term is removed from the reading made by the potential-measuring device. Consider the potential profile in solution between the working and auxiliary electrodes, shown schematically in Figure 1.3.12. (The po- tential profile in an actual cell depends on the electrode shapes, geometry, solution conductance, etc.) The solution between the electrodes can be regarded as a poten- tiometer (but not necessarily a linear one). If the reference electrode is placed any- where but exactly at the electrode surface, some fraction of iRs, (called iRu, where Ru
is the uncompensated resistance) will be included in the measured potential. Even when the tip of the reference electrode is designed for very close placement to the working electrode by use of a fine tip called a Luggin-Haber capillary, some uncom- pensated resistance usually remains. This uncompensated potential drop can some- times be removed later, for example, from steady-state measurements by measurement of Ru and point-by-point correction of each measured potential. Modern electrochemi- cal instrumentation frequently includes circuitry for electronic compensation of the iRu
term (see Chapter 15).
If the reference capillary has a tip diameter d, it can be placed as close as 2d from the working electrode surface without causing appreciable shielding error. Shielding denotes a blockage of part of the solution current path at the working electrode surface, which causes nonuniform current densities to arise at the electrode surface. For a planar elec- trode with uniform current density across its surface,
Ru = X/KA (1.3.7)
Working electrode
fl)
Auxiliary electrode
soln
Wk•ЛЛЛЛМЛЛЛЛЛЛЛЛЛЛЛ^^
Ref
(b)
Figure 1.3.12 (a) Potential drop between working and auxiliary electrodes in solution and iRu measured at the reference electrode.
(b) Representation of the cell as a potentiometer.
28 Chapter 1. Introduction and Overview of Electrode Processes
where x is the distance of the capillary tip from the electrode, A is the electrode area, and к is the solution conductivity. The effect of iRu can be particularly serious for spherical microelectrodes, such as the hanging mercury drop electrode or the dropping mercury electrode (DME). For a spherical electrode of radius r0,
In this case, most of the resistive drop occurs close to the electrode. For a reference elec- trode tip placed just one electrode radius away (x = r0), Ru *s already half of the value for the tip placed infinitely far away. Any resistances in the working electrode itself (e.g., in thin wires used to make ultramicroelectrodes, in semiconductor electrodes, or in resistive films on the electrode surface) will also appear in Ru.