相关论文: On Exact Solutions to the Cylindrical Poisson-Bolt…
The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric…
The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving…
The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric elecrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this…
We present theoretical and numerical studies on stiff, linear polyelectrolytes within the framework of the cell model. We first review analytical results obtained on a mean-field Poisson-Boltzmann level, and then use molecular dynamics…
Using Poisson-Boltzmann equation and linear response theory, we derive an effective interaction potential due to a fixed charge distribution in a solution containing polyelectrolytes and point salt. We obtain an expression for the effective…
We solve the nonlinear Poisson-Boltzmann equation for two parallel and likely charged plates both inside a symmetric elecrolyte, and inside a 2 : 1 asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we…
The two-dimensional generalization of the Polyelectolite model of DNA is proposed. It is reduced to the boundary problem for nonlinear completely integrable equation $\sh$-Gordon. In the linearisible version the exact solution is…
We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer [EPL 111, 28002 (2015)]. We formulate a modified Poisson-Boltzmann theory,…
The structure of cylindrical double layers is studied using a modified Poisson Boltzmann theory and the density functional approach. In the model double layer, the electrode is a cylindrical polyion that is infinitely long, impenetrable,…
We consider the non-linear Poisson-Boltzmann theory for a single cylindrical or spherical macro-ion in symmetric 1:1, together with asymmetric 1:2 and 2:1 electrolytes. We focus on the regime where $\kappa a $, the ratio of the macro-ion…
A Poisson-Boltzmann approach is used to determine the double-layer integral and differential capacitances in a finite-length situation for an electrolytic cell. By means of simple analytical calculations, it is shown how these quantities…
The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and…
We study the adsorption-desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the…
1. Introduction 2. Charged chains at infinite dilution - asymptotic properties 2.1 Definition of the model and Flory-like calculation 2.2 Variational approaches 2.3 Renormalization group calculations 2.4 Screening of electrostatic…
A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson-Boltzmann equation is…
Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for…
In this paper within a field-theoretical approach taking into account explicitly a co-solvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann…
A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its…
Exact single-wave and two-wave solutions of systems of equations of Newell-Whitehead type are presented. The Painleve test and calculations in the spirit of Hirota are used to construct these solutions.
Within the Poisson-Boltzmann (PB) approach electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance $C$ on the surface charge density $\sigma$ and the ionic…