MODIFIED POISSON-NERNST-PLANCK MODEL WITH COULOMB AND HARD-SPHERE CORRELATIONS

We develop a modified Poisson-Nernst-Planck model which includes both the long-range Coulomb and short-range hard-sphere correlations in its free energy functional such that the model can accurately describe the ion transport in complex environment and under a nanoscale confinement. The Coulomb correlation including the dielectric polarization is treated by solving a generalized Debye-Huckel equation which is a Green's function equation with the correlation energy of a test ion described by the self Green's function. The hard-sphere correlation is modeled through the modified fundamental measure theory. The resulting model is available for problems beyond the mean-field theory such as problems with variable dielectric media, multivalent ions, and strong surface charge density. We solve the generalized Debye-Huckel equation by the Wentzel-Kramers-Brillouin approximation, and study the electrolytes between two parallel dielectric surfaces. In comparison to other modified models, the new model is shown to be more accurate in agreement with particle-based simulations and capturing the physical properties of ionic structures near interfaces.

Automated summary

The study develops a modified Poisson-Nernst-Planck model that accurately describes ion transport in complex environments by including both long-range and short-range correlations. The Coulomb correlation is handled by solving a generalized Debye-Huckel equation, while hard-sphere correlation is modeled using modified fundamental measure theory. The resulting model is capable of addressing problems beyond mean-field theory, such as variable dielectric media, multivalent ions, and strong surface charge density, showing improved accuracy compared to other modified models in capturing physical properties near interfaces.