Poisson-Boltzmann theory with non-linear ion correlations

Abstract

The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems. As a mean-field theory, the PB theory neglects the correlation effect in the ionic atmosphere and leads to deviations from experimental results as the concentration or charge valance increases. A modified PB theory including ion correlation effect while retaining its simplicity is critical for many important applications in which ion correlation effect can be significant. In this paper, we present a new model to incorporate ion correlations into the original PB equation by utilizing the Green's function with a non-linear form of the self-energy, which is different from the linear self-energy equation obtained by the Field-Theoretic (FT) approach. Both equations are solved numerically and compared with our molecular dynamics (MD) simulation. The co-ion distribution calculated by the FT approach deviates significantly from the MD simulation, while our results for both counter-ion and co-ion distributions are justified by the MD simulation.

arXiv comment8 pages, 5 figures

References in corpus (11)

• Electrostatic correlations: from Plasma to Biology
• Screening of a macroion by multivalent ions: Correlation induced inversion of charge
• Beyond Poisson-Boltzmann: Fluctuations and Correlations
• Variational charge renormalization in charged systems
• Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores
• On the theoretical description of weakly charged surfaces
• Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches
• Continuous Self Energy of Ions at the Dielectric Interface
• Solving Fluctuation-Enhanced Poisson-Boltzmann Equations
• Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory
• A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores