A unifying mode-coupling theory for transport properties of electrolyte solutions. I. General scheme and limiting laws

Abstract

We develop a general method for calculating conduction-diffusion transport properties of strong electrolyte mixtures, including specific conductivities, steady-state electrophoretic mobilities, and self-diffusion coefficients. The ions are described as charged Brownian spheres, and the solvent-mediated hydrodynamic interactions (HIs) are also accounted for in the non-instantaneous ion atmosphere relaxation effect. A linear response expression relating long-time partial mobilities to associated dynamic structure factors is employed in our derivation of a general mode coupling theory (MCT) method for the conduction-diffusion properties. A simplified solution scheme for the MCT method is discussed. Analytic results are obtained for transport coefficients of pointlike ions which, for very low ion concentrations, reduce to the Deby-Falkenhagen-Onsager-Fuoss limiting law expressions. As an application, an unusual non-monotonic concentration dependence of the polyion electrophoretic mobility in a mixture of two binary electrolytes is discussed. In addition, leading-order extensions of the limiting law results are derived with HIs included. The present method complements a related MCT method by the authors for the electrolyte viscosity and shear relaxation function [C. Contreras-Aburto and G. Nägele, J. Phys.: Condens. Matter 24, 464108 (2012)], so that a unifying scheme for conduction-diffusion and viscoelastic properties is obtained. We present here the general framework of the method, illustrating its versatility for conditions where fully analytic results are obtainable. Numerical results for conduction-diffusion properties and the viscosity of concentrated electrolytes are presented in Paper II [C. Contreras Aburto and G. Nägele, J. Chem. Phys. 139, 134110 (2013)].

A unifying mode-coupling theory for transport properties of electrolyte solutions. II. Results for equal-sized ions electrolytes

“…are the projectors on the charge-density fluctuations and ion total number density fluctuations subspaces, respectively, which we have introduced already in Paper I. 30,85 In the MSA, c HS (q) is given analytically by the Percus-Yevick (PY) solution for monodisperse hard spheres, 31 whereas the electric direct correlation function part, c EL (q), is obtained from Fourier transforming the analytic solution for c El (r) obtained by Waisman and Lebowitz. 32 The analytic Attard expressions are discussed further down.…”

“…As we have explained in Paper I, 85 the effect of the HIs on the short-time dynamic correlations of the partial concentration fluctuations in an m-component PM system is described by the m × m hydrodynamic function matrix, H(q). According to Eq.…”

“…Our results are obtained using a simplified solution scheme of a versatile MCT method for linear transport properties of electrolyte mixtures, referred to as the simplified MCT-HIs scheme. For conduction-diffusion properties, this scheme has been developed in Paper I, 85 and for viscoelastic properties in a previous publication by the authors. 30 In Paper I, 85 analytic MCT expressions have been derived for pointlike ions with HIs included.…”

“…For conduction-diffusion properties, this scheme has been developed in Paper I, 85 and for viscoelastic properties in a previous publication by the authors. 30 In Paper I, 85 analytic MCT expressions have been derived for pointlike ions with HIs included. These expressions reduce, for very low ion concentrations, to the corresponding DFOF limiting law results.…”

Modeling of Ion and Water Transport in the Biological Nanopore ClyA

“…Moreover, even though the well-known Nernst-Einstein (NE) relation µ i = D i /k B T is strictly speaking only valid at infinite dilution and a good approximation at low concentrations (<10 mM), it significantly overestimates the ionic mobility at higher salt concentrations. [86][87][88][89] In an empirical approach, Baldessari and Santiago formulated an ionic-strength dependency of the ionic mobility based on the activity coefficient of the salt 60 and showed excellent correspondence between the experimental and simulated ionic conductance of long nanochannels over a wide concentration range. 90 Alternatively, Burger et al used a microscopic lattice-based model to derive a set of PNP equations with non-linear, ion density-dependent mobilities and diffusion coefficients that provided significantly more realistic results for ion channels.…”