Distribution of Interacting Ionic Particles in Disordered Media

Details Distribution of Interacting Ionic Particles in Disordered Media Distribution of Interacting Ionic Particles in Disordered Media

2001-06-08

arxiv.org/abs/cond-mat/0106153v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1209/epl/i2002-00407-y

Equilibrium distribution of interacting ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For an arbitrarily given realization of the disorder, an exact solution of the equation is obtained in one dimension using a mapping of the nonlinear Poisson-Boltzmann equation to a self-consistent Schrodinger equation. The resulting density profile shows that the ions are delocalized, despite what the equivalent Schrodinger formulation in one dimension would suggest. It is shown that the ions are not distributed so as to locally neutralize the background, presumably due to their mutual interactions.

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