A new approach to the lennard-jones potential and a new model: PNP-steric equations
Journal
Communications in Mathematical Sciences
Journal Volume
12
Journal Issue
1
Pages
149-173
Date Issued
2013
Author(s)
Eisenberg, B.
Abstract
A class of approximate Lennard-Jones (LJ) potentials with a small parameter is found whose Fourier transforms have a simple asymptotic behavior as the parameter goes to zero. When the LJ potential is replaced by the approximate LJ potential, the total energy functional becomes simple and exactly the same as replacing the LJ potential by a delta function. Such a simple energy functional can be used to derive the Poisson-Nernst-Planck equations with steric effects (PNP-steric equations), a new mathematical model for the LJ interaction in ionic solutions. Using formal asymptotic analysis, stability and instability conditions for the 1D PNP-steric equations with the Dirichlet boundary conditions for one anionic and cationic species are expressed by the valences, diffusion constants, ionic radii, and coupling constants. This is the first step to study the dynamics of solutions of the PNP-steric equations. © 2014 International Press.
Type
journal article