Mathematical Modeling of Nano-Patterns in Electrochemical Processes

Northwestern University, Evanston IL

Investigators

Abstract

Proposal #0204643 PI: Alexander Golovin Institution: Northwestern University Title: Mathematical modeling of nano-patterns in electrochemical processes ABSTRACT This project is devoted to the mathematical modeling of nano-scale self-organization and pattern formation in electrochemical processes. The focus is on (i) electroconvection during anodic dissolution and the growth of anodic oxide layers; (ii) the growth and stability of pores in dielectric and semiconductor layers; (iii) the stability and nonlinear dynamics of pattern formation at solid-solid interfaces in the presence of chemical reactions, electric field, and elastic stresses. Mathematical techniques to be used are linear stability and bifurcation analysis, asymptotic analysis, as well as numerical implementations of boundary integral methods, phase-field models, and level-set methods for free-boundary problems. From the scientific point of view, the research is aimed at understanding the basic physico-chemical mechanisms responsible for the formation of highly regular nano-scale patterns in electrochemical systems. The goal of this project is to develop mathematical models of the most important processes leading to self-organization (pattern formation) on the nano-scale. These mathematical models can be used in numerical simulations and thus enable the creation of a new generation of electronic, opto-electronic, and magneto-electronic devices. From the educational point of view, the proposed project, being essentially interdisciplinary and devoted to the cutting edge of modern science and technology, will attract graduate students who will be able to acquire knowledge and research experience in several interconnecting scientific disciplines and become capable of carrying out interdisciplinary research.