Towards an exact theory of polyelectrolytes

Abstract Within the framework of the gas approximation an exact method is developed for calculating the electric potential distribution around a polyion. The polyion is modelled as an infinitely long impermeable cylinder and the mobile ions are assumed to be impermeable spheres. Equations are derived for two potentials ψ min and ψ max so that the genuine potential ψ lies in between. The equations are numerically solved for different parameter values. The results are compared with data obtained on the basis of the standard Poisson-Boltzmann equation.