(Research Award of the Electrodeposition Division) Mathematical Modeling in Electrodeposition Studies

Mathematical modeling has a long history in electrodeposition.   The modeling may range from current distribution simulations for the design of electrochemical cells to molecular modeling for the design of next-generation additives.  In other instances, modeling is used for data analysis, for troubleshooting, and for more efficient design of experiment.  In some cases, models create value by providing a framework to communicate in interdisciplinary or industrial settings, as a means of protecting intellectual property or as means of explaining to the uninitiated the role of plating-bath constituents.

            While models of the impact of transport phenomena on current distribution, may be quite straightforward, models involving reaction mechanisms can be highly controversial.  Because of the inherent complexity of electrodeposition processes, modeling efforts are often tightly coupled to experiments, and it is rare that a model can explain all or even most experimental observations.  Crafting a model requires a deep understanding of which experimental observations are most relevant to the business or technological goals.

            We discuss some of our past experience in modeling electrodeposition systems.  We briefly discuss work and practical uses of modeling additives in Cu electrodeposition, a process in which a tremendous understanding is available due to its commercial importance.  We then discuss multi-scale modeling of electrochemical nucleation and its impact on current distributions on resistive substrates.  As a final example, we discuss the role of relatively primitive modeling in understanding the co-deposition of nanoparticles and microparticles with nickel.