MeanField Description of Ionic Size Effects: A Numerical Approach
Mr. Shenggao Zhou
Department of Mathematics, Zhejiang University, China
Department of Mathematics and Center for Theoretical Biological Physics
University of California, San Diego, USA
ABSTRACT
Ionic size effects are significant in many biological systems. Meanfield descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the
electrostatic potential, i.e., there are no explicit, Boltzmann type distributions. This work begins with variational formulations of the continuum electrostatics of an ionic solution with such nonuniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. Extensive numerical tests demonstrate that the meanfield model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valencetovolume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical PoissonBoltzmann theory, or the generalized PoissonBoltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization to molecular solvation are discussed. This is joint work with Zhongming Wang and Bo Li.
