# 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…

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## References

SHOWING 1-10 OF 90 REFERENCES

### Generalized Poisson-Fermi formalism for investigating size correlation effects with multiple ions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

A generalized Poisson-Fermi formalism is established to compute the electrostatic potential next to charged surfaces in the presence of multiple ion species with different sizes, anticipated to be useful for interpreting electrophoretic mobility measurements and for computing the electro static potential over the surface of biomolecules in ionic solutions.

### 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.

### Novel formulation of nonlocal electrostatics.

- PhysicsPhysical review letters
- 2004

This work proposes a novel formulation allowing for numerical solutions for the nontrivial molecular geometries arising in the applications mentioned before, based on the introduction of a secondary field psi, which acts as the potential for the rotation free part of the dielectric displacement field D.

### 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.

### Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels.

- PhysicsThe Journal of chemical physics
- 2014

The PNPF model provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore, and numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to study a variety of physical mechanisms.

### 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…