title: Hybrid Monte Carlo and continuum modeling of electrolytes with concentration-induced dielectric variations.
abstract: The distribution of ions near a charged surface is an important quantity in many biological and material processes, and has been therefore investigated intensively. However, few theoretical and simulation approaches have included the influence of concentration-induced variations in the local dielectric permittivity of an underlying electrolyte solution. Such local variations have long been observed and known to affect the properties of ionic solution in the bulk and around the charged surface. We propose a hybrid computational model that combines Monte Carlo simulations with continuum electrostatic modeling to investigate such properties. A key component in our hybrid model is a semianalytical formula for the ion-ion interaction energy in a dielectrically inhomogeneous environment. This formula is obtained by solving for the Green's function Poisson's equation with ionic-concentration-dependent dielectric permittivity using a harmonic interpolation method and spherical harmonic series. We also construct a self-consistent continuum model of electrostatics to describe the effect of ionic-concentration-dependent dielectric permittivity and the resulting self-energy contribution. With extensive numerical simulations, we verify the convergence of our hybrid simulation scheme, show the qualitatively different structures of ionic distribution due to the concentration-induced dielectric variations, and compare our simulation results with the self-consistent continuum model. In particular, we study the differences between weakly and strongly charged surfaces and multivalencies of counterions. Our hybrid simulations conform particularly the depletion of ionic concentrations near a charged surface and also capture the charge inversion. We discuss several issues and possible further improvement of our approach for simulations of large charged systems.
authors.affiliation: School of Mathematical Sciences, Tongji University, 1239 Siping Road, Shanghai, 200092, China.
authors.forename: Xiaofei
authors.initials: X
authors.lastname: Guan
authors.affiliation: School of Mathematical Sciences and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Manman
authors.initials: M
authors.lastname: Ma
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Zecheng
authors.initials: Z
authors.lastname: Gan
authors.affiliation: School of Mathematical Sciences, Institute of Natural Sciences, and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Zhenli
authors.initials: Z
authors.lastname: Xu
authors.affiliation: Department of Mathematics and Graduate Program in Quantitative Biology, University of California, San Diego, California 92093-0112, USA.
authors.forename: Bo
authors.initials: B
authors.lastname: Li