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 im pedance at the Formal potential for a redox-active monolayer assembly consi sting of multiple independent populations of redox sites, each exhibiting t he same formal potential but a unique electron-transfer rate constant. The model is sufficiently flexible to allow for consideration of any rate distr ibution that can be represented as a table of rate constants and weighting factors. The model was implemented in the spreadsheet program Microsoft Exc el and used to simulate the ac voltammetry behavior for several redox-activ e monolayer assemblies with square rate-constant distributions (i.e.. all w eighting factors are equal) in linear and log frequency space. The assumpti on of a broadened rate-constant distribution always yields a broadened I-pe ak/I-background vs. log(frequency) plot from the simulated variable-frequen cy ac voltammetry data set. The broadening is asymmetric about the median r ate 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 e xponential rate distribution (i.e., a distribution in which the values of l og(rate constant) are evenly spaced). implications for interpreting experim ental data in terms of dispersed kinetics are discussed. (C) 2000 The Elect rochemical Society. All rights reserved.