Poisson–Nernst–Planck Systems for Ion Flow with Density Functional Theory for Hard-Sphere Potential: I–V Relations and Critical Potentials. Part I: Analysis

摘要: We consider a one-dimensional steady-state Poisson–Nernst–Planck type model for ionic flow through membrane channels. Improving the classical models where ion species are treated as point charges, this includes interaction due to finite sizes of modeled by hard sphere potential from Density Functional Theory. The resulting problem is singularly perturbed boundary value an integro-differential system. examine and investigate size effect on current–voltage (I–V) relations numerically, focusing case two oppositely charged involved only components excess chemical potentials included. Two numerical tasks conducted. first one approach solving obtaining I–V curves. This accomplished implementation analytical strategy introduced Ji Liu in [Poisson–Nernst–Planck systems with density functional theory hard-sphere potential: critical potentials. Part I: Analysis, J. Dyn. Differ. Equ. (to appear)]. second task numerically detect values V c .The existence these realized relatively simple setting approximations obtained above mentioned reference. propose algorithm detection without using any formulas but based defining properties curves directly. For reference, our agree well predictions. including nonzero permanent charge which no analytic formula relation available now, algorithms can still be applied find numerically.