Spatio-temporal organization in alloy electrodeposition: a morphochemical mathematical model and its experimental validation

Abstract

This paper proposes a novel mathematical model for the formation of spatio-temporal patterns in electrodeposition. At variance with classical modelling approaches that are based on systems of reaction–diffusion equations just for chemical species, this model accounts for the coupling between surface morphology and surface composition as a means of understanding the formation of morphological patterns found in electroplating. The innovative version of the model described in this work contains an original, flexible and physically straightforward electrochemical source term, able to account for charge transfer and mass transport: adsorbate-induced effects on kinetic parameters are naturally incorporated in the adopted formalism. The relevant non-linear dynamics is investigated from both the analytical and numerical points of view. Mathematical modelling work is accompanied by an extensive, critical review of the literature on spatio-temporal pattern formation in alloy electrodeposition: published morphologies have been used as a benchmark for the validation of our model. Moreover, original experimental data are presented—and simulated with our model—on the formation of broken spiral patterns in Ni–P–W–Bi electrodeposition.