Poisson-Nernst-Planck (PNP) equations have been frequently used to describe the distributions of electric potential, and ion concentrations in ionic solutions. However, classic PNP equations treat an ion as a point without volume, which can be inadequate for highly concentrated ionic solutions like ionic liquids. Several modifications on adding finite-size effect into PNP equations have been proposed in the literature. We have developed our own version of that called PNP steric model [1] by adding chemotaxis-like nonlinear intra- and inter-diffusion terms into Nernst-Planck equations with an additional bi-Laplacian diffusion term to suppress high-mode instability. By fixing inter-diffusion coefficient and varying intra-diffusion coefficients, we found the formation of the following electric double layer (EDL) patterns: (1) hexagonal/triangular lattice, (2) straight stripe pattern, (3) curve stripe pattern, (4) curve stripe pattern with dislocations, in cation/anion concentration and electric potential distributions. (1) is a solid-like pattern and (2)-(4) are fluid-like patterns. The involved physical mechanism of phase change (symmetry breaking) will be discussed.

[1] T.L. Horng, T.C. Lin, C. Liu, and B. Eisenberg, PNP equations with steric effects: A model of ion flow through channels, J. Phys. Chem. B, 116(37), 1142211441, 2012.

 

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