Coupling theory for counterion distributions based in Tsallis statistics

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 Moreira and Netz [Europhys. Lett. 52 (2000) 705]. Excellent agreement with these is obtained.