Electric field of a charged dielectric cylinder with counterions: Application to B-DNA

An analytical model, based on the full nonlinear Poisson-Boltzmann equation, for the electric field and the space distribution of the counterions around a rod with a surface charge density a function of the polar angle is presented. The model is applied for dissolved B-DNA, which is modelled as a dielectric cylinder with a surface charge density consisting of ten vertical line charges. The counterions of the solvent are treated via the two-dimensional nonlinear Poisson-Boltzmann equation. The exact solution of this equation satisfying the boundary conditions has been found. The space distribution of the counterions and the electric field inside and outside the cylinder are determined. The region in which the charge neutrality condition is fulfilled is a concentric cylinder with radius ρ0. This radius is the only parameter in the analytical expressions obtained for the electric field. It is an inherent parameter of the presented theory and the expression for it is derived. Numerical estimations for B-DNA show that the value of ρ0 is near the experimentally measured value for the radius of the Manning cloud.