The Poisson-Nernst-Planck (PNP) theory is one of the most widely used analytical methods to describe electrokinetic phenomena for electrolytes. The model, however, considers isolated charges and thus is valid only for dilute ion concentrations. The key importance of concentrated electrolytes in applications has led to the development of a large family of generalized PNP models, and in particular a class of steric PNP models which account for finite size effect via an approximate Lennard-Jones interaction between the ionic species.

In this talk, I consider high-order steric PNP models which are derived by taking into account high-order approximations of the Lennard-Jones kernels. Particularly, I will show that the model gives rise to pattern formation. Accordingly, a mapping of the parameter regimes of distinct self-assembly behaviors and the relevant bifurcation associated with them will be shown, and their effect on electrostatic screening and transport will be considered. In particular, we reveal a novel mechanism of under-screening, and consider relevance to gating phenomena.