Journal of the Electrochemical Society, Vol.147, No.12, 4584-4588, 2000
A generalized equivalent-circuit model for electroactive monolayers exhibiting a fixed redox potential and a distribution of electron-transfer rate constants - I. Square distributions
An equivalent-circuit model is presented that enables calculation of the impedance at the Formal potential for a redox-active monolayer assembly consisting of multiple independent populations of redox sites, each exhibiting the same formal potential but a unique electron-transfer rate constant. The model is sufficiently flexible to allow for consideration of any rate distribution that can be represented as a table of rate constants and weighting factors. The model was implemented in the spreadsheet program Microsoft Excel and used to simulate the ac voltammetry behavior for several redox-active monolayer assemblies with square rate-constant distributions (i.e.. all weighting factors are equal) in linear and log frequency space. The assumption of a broadened rate-constant distribution always yields a broadened I-peak/I-background vs. log(frequency) plot from the simulated variable-frequency ac voltammetry data set. The broadening is asymmetric about the median rate fur a linear rate distribution (i.e.. a distribution in which the rate constant values are evenly spaced), but symmetric about the median for an exponential rate distribution (i.e., a distribution in which the values of log(rate constant) are evenly spaced). implications for interpreting experimental data in terms of dispersed kinetics are discussed.