Theoretical Analysis of the Relative Significance of Thermodynamic and Kinetic Dispersion in the dc and ac Voltammetry of Surface-Confined Molecules

© 2015 American Chemical Society. Commonly, significant discrepancies are reported in theoretical and experimental comparisons of dc voltammograms derived from a monolayer or close to monolayer coverage of redox-active surface-confined molecules. For example, broader-than-predicted voltammetric wave shapes are attributed to the thermodynamic or kinetic dispersion derived from distributions in reversible potentials (E$^{0}$) and electrode kinetics (k$^{0}$), respectively. The recent availability of experimentally estimated distributions of E$^{0}$ and k$^{0}$ values derived from the analysis of data for small numbers of surface-confined modified azurin metalloprotein molecules now allows more realistic modeling to be undertaken, assuming the same distributions apply under conditions of high surface coverage relevant to voltammetric experiments. In this work, modeling based on conventional and stochastic kinetic theory is considered, and the computationally far more efficient conventional model is shown to be equivalent to the stochastic one when large numbers of molecules are present. Perhaps unexpectedly, when experimentally determined distributions of E$^{0}$ and k$^{0}$ are input into the model, thermodynamic dispersion is found to be unimportant and only kinetic dispersion contributes significantly to the broadening of dc voltammograms. Simulations of ac voltammetric experiments lead to the conclusion that the ac method, particularly when the analysis of kinetically very sensitive higher-order harmonics is undertaken, are far more sensitive to kinetic dispersion than the dc method. ac methods are therefore concluded to provide a potentially superior strategy for addressing the inverse problem of determining the k$^{0}$ distribution that could give rise to the apparent anomalies in surface-confined voltammetry.