# Nonlocal Poisson-Fermi model for ionic solvent.

@article{Xie2016NonlocalPM, title={Nonlocal Poisson-Fermi model for ionic solvent.}, author={Dexuan Xie and Jinn-Liang Liu and Bob Eisenberg}, journal={Physical review. E}, year={2016}, volume={94 1-1}, pages={ 012114 } }

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…

## 15 Citations

### Nonlocal Poisson-Fermi double-layer models: Effects of nonuniform ion sizes on double-layer structure.

- PhysicsPhysical review. E
- 2018

Numerical results show that nuNPF can significantly improve the quality of the ionic concentrations and electric fields generated from uNPF, implying that the effect of nonuniform ion sizes is a key consideration in modeling the double-layer structure.

### On the equilibrium of the Poisson–Nernst–Planck–Bikermann model equipping with the steric and correlation effects

- MathematicsCommunications in Mathematical Sciences
- 2023

The Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water molecules are treated as different species with non-uniform sizes and valences with interstitial voids, can describe the…

### Field model for complex ionic fluids: analytical properties and numerical investigation

- MathematicsArXiv
- 2019

In this paper, we consider the field model for complex ionic fluids with an energy variational structure, and analyze the well-posedness to this model with regularized kernels. Furthermore, we deduce…

### An Efficient Finite Element Iterative Method for Solving a Nonuniform Size Modified Poisson-Boltzmann Ion Channel Model

- PhysicsJ. Comput. Phys.
- 2022

### Relative dielectric constants and selectivity ratios in open ionic channels

- Physics
- 2017

It is shown that some properties of open channels are quite insensitive to variation in the relative dielectric coefficient, thereby explaining such effects seen unexpectedly in simulations.

### Dynamics of Current, Charge and Mass

- Physics
- 2017

Abstract Electricity plays a special role in our lives and life. The dynamics of electrons allow light to flow through a vacuum. The equations of electron dynamics are nearly exact and apply from…

### A Flux Ratio and a Universal Property of Permanent Charges Effects on Fluxes

- PhysicsComputational and Mathematical Biophysics
- 2018

Abstract In this work, we consider ionic flow through ion channels for an ionic mixture of a cation species (positively charged ions) and an anion species (negatively charged ions), and examine…

### SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson‐Boltzmann equation

- Computer ScienceJ. Comput. Chem.
- 2017

This work reconstructs SMPBE (Size Modified Poisson‐Boltzmann Solvers) using a new objective electrostatic free energy, clearly showing that the electrostatics and ionic concentrations predicted by S MPBE are optimal in the sense of minimizing the objective electro static free energy.

### Electrodynamics Correlates Knock-on and Knock-off: Current is Spatially Uniform in Ion Channels.

- Physics
- 2020

The electrodynamics of charge guarantee strong correlations between the movements of ions on all time scales, even those of atomic scale thermal motion, so they are present in individual trajectories, not just averages.

## References

SHOWING 1-10 OF 90 REFERENCES

### Nonlocal continuum solvation model with exponential susceptibility kernels

- Physics
- 1998

An algorithm is developed for performing calculations for the nonlocal electrostatic solvation theory of an ion in a cavity, accounting for electrostatic boundary conditions. The latter implies an…

### Efficient Algorithms for a Nonlocal Dielectric Model for Protein in Ionic Solvent

- PhysicsSIAM J. Sci. Comput.
- 2013

It is shown that the solution of the nonlocal dielectric model for protein in ionic solvent is unique, and can be found from solving two well-defined partial differential systems and one Poisson-like boundary value problem.

### Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2014

A nonlocal Poisson-Boltzmann equation (NLPB) is formulated and both linear and nonlinear dielectric response in this model for the case of a single plane geometry is studied to shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

### Correlated ions in a calcium channel model: a Poisson-Fermi theory.

- PhysicsThe journal of physical chemistry. B
- 2013

A continuum model of biological calcium channels designed to deal with crowded systems in which ionic species and side chains nearly fill space is derived, derived from classical hard-sphere lattice models of configurational entropy of finite size ions and solvent molecules.

### A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models

- Physics
- 2013

A nonlocal continuum electrostatic model, defined as integro-differential equations, can significantly improve the classic Poisson dielectric model, but is too costly to be applied to large protein…

### A nonlocal modified Poisson-Boltzmann equation and finite element solver for computing electrostatics of biomolecules

- PhysicsJ. Comput. Phys.
- 2016

### Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The classical Scharfetter-Gummel method for semiconductor devices is extended to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors, and is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation.