Interaction between Charged Cylinders in Electrolyte Solution; Excluded Volume Effect

Electrostatic interactions govern the physical properties of charged cylindrical structures in electrolyte solutions. Besides the surface charge on the cylinders, another factor influencing the electrostatic interactions are the mobile ions. The finite size of the mobile ions is included by the excluded volume effect within the lattice statistics, while the electrostatic interactions are considered by means of the mean electrostatic field. In this article we consider charged parallel cylinders embedded into an electrolyte solution of mobile monovalent ions. A modified nonlinear Poisson-Boltzmann equation is proposed via variational procedure, and we implement the finite element method to solve it numerically. Excluded volume effect of the system containing two and multiple charged parallel cylinders are taken into account. Numerical results show that the excluded volume effect decreases the concentration of counterion and increases the electrostatic potential near the charged cylinders. The angular distribution of counterion around the particular cylinder is asymmetric. The study of the electrostatic interaction between two parallel equally charged cylinders reveals that an increase in the free energy is seen when the ionic strength is decreased. The free energy decreases as a function of the cylinders separation distance. On the contrary for two oppositely charged cylinders, the free energy increases with increasing cylinder separation distance, while for two cylinders with different charged density it shows nonmonotonic variation with the increasing cylinders separation distance. (Graph Presented).