Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches

Abstract

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, towards the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

11 pages, 5 figures, version to be published in PRE

References in corpus (14)

• Diffuse-Charge Dynamics in Electrochemical Systems
• Electrostatic correlations: from Plasma to Biology
• Induced-Charge Electro-Osmosis
• Beyond Poisson-Boltzmann: Fluctuations and Correlations
• From Structure to Function in Open Ionic Channels
• Variational charge renormalization in charged systems
• Image charges in spherical geometry: Application to colloidal systems
• Strong Coupling Electrostatics in the Presence of Dielectric Inhomogeneities
• Weak and Strong Coupling Theories for Polarizable Colloids and Nano-Particles
• Charge Fluctuations and Counterion Condensation
• Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction
• Electrostatic correlations in inhomogeneous charged fluids beyond loop expansion
• Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers
• Solving Fluctuation-Enhanced Poisson-Boltzmann Equations

Cited by in corpus (17)

• On the theoretical description of weakly charged surfaces
• A fast spectral method for electrostatics in doubly-periodic slit channels
• Electrostatic correlation induced ion condensation and charge inversion in multivalent electrolytes
• Structure-Preserving and Efficient Numerical Methods for Ion Transport
• Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media
• Inhomogeneous screening near a dielectric interface
• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• A Maxwell-Ampère Nernst-Planck Framework for Modeling Charge Dynamics
• Poisson-Boltzmann theory with non-linear ion correlations
• Hysteresis and Linear Stability Analysis on Multiple Steady-State Solutions to the Poisson--Nernst--Planck equations with Steric Interactions
• Linear-Scaling Selected Inversion based on Hierarchical Interpolative Factorization for Self Green's Function for Modified Poisson-Boltzmann Equation in Two Dimensions
• Stability of equilibria to the model for non-isothermal electrokinetics
• Modeling Concentration Profiles in Electrolytes by Solving 3-D Poisson-Nernst-Planck Equations via Finite Difference Method
• Energetic Stable Discretization for Non-Isothermal Electrokinetics Model
• Modified Poisson-Nernst-Planck model with Coulomb and hard-sphere correlations
• Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System
• Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores