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. (C) 2000 The Electrochemical Society. All rights reserved.