Coupling theory for counterion distributions based in Tsallis statistics

TL;DR

This paper extends the Poisson-Boltzmann framework using Tsallis q-exponentials to model counterion distributions across all coupling regimes, achieving analytical solutions that align well with Monte Carlo simulations.

Contribution

It introduces a generalized coupling theory for counterion distributions using Tsallis statistics, unifying weak and strong coupling limits with analytical expressions.

Findings

Analytical expressions match Monte Carlo simulations well.

The approach reproduces known limits of weak and strong coupling.

Provides a unified framework for counterion distribution modeling.

Abstract

It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB approach to account for coupling of arbitrary strength by making use of Tsallis q-exponential distributions. Both the weak coupling and the strong coupling limits are reproduced. For arbitrary coupling we also provide simple analytical expressions which are compared to recent Monte Carlo simulations by A. G. Moreira and R. R. Netz [Europhys. Lett. 52 (2000) 705]. Excellent agreement with these is obtained.