Charged cylindrical surfaces: effect of finite ion size

A simple statistical mechanical approach is applied to calculate the profile of the density of the number of particles and the profile of the electrostatic potential of an electric double layer formed by a charged cylindrical surface in contact with electrolyte solution. The finite size of particles constituting the electrolyte solution is considered by including the excluded volume effect within the lattice statistics while the electrostatic interactions are considered by means of the mean electrostatic field. It is shown that the excluded volume effect decreases the density of the number of counterions and increases the electrostatic potential near the charged cylindrical surface. The effect is more pronounced for high area densities of charge of the charged surface and for larger counterions. Further, it is shown that the ratio between the density of the number of the counterions near the charged cylindrical surface and the density of the number of counterions far from the charged surface reaches a plateau at large linear charge densities for ions of finite size, while no plateau is reached for dimensionless ions. The effective thickness of the electric double layer in cylindrical geometry is introduced. It is shown that the effective thickness increases with increasing counterion size while its dependence on the area density of charge of the charged surface exhibits a minimum. The theoretical approach presented in this work can be used for description of the electrostatics of the thin cylindrical structures in biological systems such as DNA, protein macromolecules and charged micro and nano tubes.