Langevin-Poisson-EQT: A dipolar solvent based quasi-continuum approach for electric double layers

Abstract

Water is a highly polar solvent. As a result, electrostatic interactions of interfacial water molecules play a dominant role in determining the distribution of ions in electric double layers (EDLs). Near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Therefore, a detailed description of the structural and dielectric properties of water is important to study EDLs. However, most theoretical models ignore the molecular effects of water and treat water as a background continuum with a uniform dielectric permittivity. Explicit consideration of water polarization and hydration of ions is both theoretically and numerically challenging. In this work, we present an empirical potential-based quasi-continuum theory (EQT) for EDL, which incorporates the polarization and hydration effects of water explicitly. In EQT, water molecules are modeled as Langevin point dipoles and a point dipole based coarse-grained model for water is developed systematically. The space dependence of the dielectric permittivity of water is included in the Poisson equation to compute the electrostatic potential. In addition, to reproduce hydration of ions, ion-water coarse-grained potentials are developed. We demonstrate the EQT framework for EDL by simulating NaCl aqueous electrolyte confined inside slit-like capacitor channels at various ion concentrations and surface charge densities. We show that the ion and water density predictions from EQT agree well with the reference molecular dynamics simulations.

Principles of surface potential estimation in mixed electrolyte solutions: Taking into account dielectric saturation

“…To include the effects of water orientation polarization and variation in dielectric permittivity in a local DOI:10.1063/1674-0068/cjcp1907132 c ⃝2019 Chinese Physical Society electric field on the electrostatic potential, a nonlinear dielectric function is given by [29,30]:…”

Role of ionic polarization and dielectric decrement in the estimation of surface potential of clay particles

“…To include the effects of water orientation polarization and variation in dielectric permittivity in a local electric field on the electrostatic potential, a dielectric function modelled as Langevin point dipoles for an azimuthal symmetry is (Gongadze, van Rienen, Kralj‐Iglič, & Iglič, ; Mashayak & Aluru, ): where D v is the relative dielectric permittivity of a vacuum ( D v = 1), f d is the dipolar fluid of concentration (i.e. water in this study), p d the molecular dipole moment of water, the Langevin function ( u ) = coth u − 1/ u and k is the Boltzmann constant.…”

“…To include the effects of water orientation polarization and variation in dielectric permittivity in a local electric field on the electrostatic potential, a dielectric function modelled as Langevin point dipoles for an azimuthal symmetry is (Gongadze, van Rienen, Kralj-Igli c, & Igli c, 2011;Mashayak & Aluru, 2017):…”

“…The Langevin model is a mean-field approach and it disregards dipole-dipole direct interactions and correlations (Gongadze et al, 2014). However, the Langevin model is an improvement over the uniform permittivity approach (Mashayak & Aluru, 2017). The D 0 calculated from Equation (7) is smaller than D b , which reflects the dielectric decrement.…”

Multiscale modeling of electroosmotic flow: Effects of discrete ion, enhanced viscosity, and surface friction

“…Variations in the ion/solvent densities can be quantified using MD simulations with appropriate spatial binning. Alternatively, one can utilize continuum based theories such as the recently proposed empirical potential based quasi-continuum theory (EQT), [31][32][33][34][35][36][37][38] which a multiscale formulation to compute the density and the corresponding PMF profiles in the nanochannel. The advantages of using EQT over particle-based methods are significant in terms of computing speed since it is orders of magnitude faster.…”