On the Effect of the Ir Drop on Chronoamperometric Measurements Involving Irreversibly Adsorbed Redox Active Species on Electrode Surfaces

Potential step chronoamperometry has been often used to determine rate constants for electron transfer in systems involving redox active species covalently linked to electrode surfaces. As has been amply discussed in the literature,^1,3 the current following the potential step yields a single exponential transient allowing the sum of the forward and reverse rate constants for electron transfer to be obtained from a linear fit of the log i vs time plots. One of the problems associated with this approach relates to the ohmic drop, a factor that must be properly accounted for in order to extract reliable kinetic parameters from the data. Not surprisingly, both theoretical and experimental strategies have been proposed to overcome these difficulties. This contribution presents the results of a theoretical study aimed at gaining insight into the electrical response of such a system.  

The equivalent circuit often used to represent electrochemical systems of interest in this work is shown in Scheme 1, where R_s and C_d are voltage-independent elements that account for the resistance of the electrolyte and the double layer, respectively, and R_p a voltage dependent element that simulates the redox or faradaic process associated in this case with species irreversibly adsorbed on the electrode surface (see below). As indicated in the diagram V_app and V_c are the potentials applied to the entire circuit and across R_p, respectively, where the latter is referred to as the overpotential. The dynamic response of the equivalent circuit will be governed by the set of coupled differential equations [1] and [2], wherein θ(t) is the time dependent coverage of the reduced form of the redox couple, Q is the total number of redox active species expressed in terms of charge assuming a one-electron transfer process, f = F/RT, where F is Faraday’s constant, R the universal gas constant, T the absolute temperature, α is the transfer coefficient, and k_bv is the potential independent heterogeneous rate constant for electron transfer. As indicated, the kinetics associated with the electron transfer process have been assumed without loss of generality to be of the Butler-Volmer type. The initial conditions of interest here assume the coverages of both the reduced and oxidized forms of the redox species to be equal, i.e. θ(0) = 0.5, for which V_c, i.e. the overpotential, would be identically zero (see Eqs. [3] and [4]). 

Shown in Fig. 1, (center panel) are plots of the total current (solid lines) as a function of time for the circuit shown in Scheme 1 following a potential step for various overpotential values as specified. The dotted lines represent the faradaic contribution to the total current. The same data expanded in the short time regime is given in the upper panel. Also shown in the lower panel is the data in the center panel but as a semilog plot in the lower panel to better illustrate that at low overpotential the faradaic component dominates the decay. As the overpotential is increased, however, the capacitor is responsible for the changes in the actual decay. 

It is common practice to display the kinetic parameters as a function of the overpotential, which for processes governed by Butler Volmer kinetics, would yield a straight V-shaped curve. Deviations from this behavior have been explained by invoking Marcus-type as opposed to Butler-Volmer kinetics. Care must be exercised, however, to properly account for contributions to the transient derived from the solution resistance. In fact for the parameters selected in this study, such plots indeed show a bending to reach limiting values for the rate constants. Although schemes have been reported in the literature to correct for this ohmic drop their full range of applicability still remains to be determined. 

ACKNOWLEDGEMENTS

This work was supported by NSF. 

REFERENCES

1. Chidsey C. E. D. Science, 251, 4996, 919

2. Henstridge, M. C.; Laborda, E.;Rees, N. V.;Compton, R.G. Electrochim. Acta 2011, 84, 12

3. Robinson, D. B.; Chidsey, C. E. D. J. Phys. Chem. B. 2002, 106, 10706