Nonlocal Poisson-Fermi model for ionic solvent

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

Figure 1

The correlation length parameter $\lambda$ predicted by formula (16) as a decreasing function of $I_s$.

Figure 2

A comparison of a nonlocal Poisson model solution $\mathrm{\Phi }$ (top plot) with a nonlocal Poisson-Fermi model solution $W$ of $\mathrm{\Phi }$ (bottom plot) in a view using $\mathbf{r}=(x,0,z)$ for a test model with a dielectric unit ball containing 488 charges from a protein (PDB ID: 2LZX).