Electrochemistry at complex interfacial geometries

Abstract

A study of electrochemical response of interfaces, when one or more of the electrodes assume arbitrary or rough (random) geometries, is of utmost importance but is difficult to analyse. The importance arises from the fact that most real systems have arbitrary geometries and always possess some degree of randomness. The roughness causes various surface?enhancement phenomena and is observed in various contexts. The origin of the difficulty is that the experimentally observable quantity like the current is to be evaluated by solving the boundary?value problem involving geometrically complex boundary profile and, for random geometries, carrying out the ensemble averaging. Our objective here is two?fold: (A) to obtain expressions for the concentration and the electron?transfer flux density as well as the total current observable in terms of (i) the statistics characterising the surface roughness, viz., correlation function and the structure factor, (ii) the local curvature of the surface characterising arbitrary geometries. (B) To analyse the inverse problem, viz., the deduction of statistical information about surface morphology from the knowledge of the measured current transients. Such an analysis is carried out through a Green’s function method. Two approaches, viz., (i) the perturbation method for treating the weakly and gently fluctuating surface about a plane and (ii) the curvature expansion, are adopted for approximating the Green’s function appropriate to the surface with arbitrary surface geometries. Both (i) and (ii) are equivalent to multiple?scattering analysis at the surfaces - the difference being that we solve a diffusion equation here instead of the Helmholtz equation employed in wave?propagation problems. Specific results for the one? and two?dimensional roughness as well as those with Gaussian statistics are derived. Results pertaining to several cases - (i) diffusion?controlled and reversible, (ii) quasi?reversible electron transfer, and (iii) frequency response - are reported. The inverse problem analysed indicates the experimental methodology for deducing surface statistics from measured current. Two other sources of complexity arising in the analysis of electrochemical interfaces are: (a) the non?linear dependence of the electron?transfer current on the potential difference and (b) the coupling of electron transfer with several homogeneous reactions with attendant diffusion of the species involved. This problem for expanding?plane model for DME and planar electrode is handled elegantly.