Numerical Studies on Electrostatic Interaction Forces and the Free Energy between Parallel Colloidal Rods of Finite...

Formulas for interaction forces F(s) and the free energy G(s) between two parallel charged prismatic rods of various scaled values of d, ψ_s, and L in skewed configurations are obtained, where s is the lengthwise positional difference between the front-end faces of the respective rods, and d is the minimal distance between the opposing faces of the rods, ψ_s is the electric surface potential, L is the length of the rods. To obtain the free-energy function G(s), (i) 3D spatial distributions of the electric potential ψ around two rods were determined by numerically solving the nonlinear Poisson-Boltzmann equation with a finite element method, (ii) with the ψ distributions so determined, the lengthwise interaction electrostatic Maxwell stress tangential to the midplane between the rods was calculated to obtain the (discrete) s dependence of the stress, and (iii) by introducing two different fitting functions, the discrete s dependence was transformed into a continuous force function, F(s), which was then lengthwise integrated to derive G(s). It was found that the curves of G(s) linearly decreased with increasing s between 1 and L + 1 due to a localization of the stress. Although natural, it is of interest that the values of G(0) calculated for rods of various values of d, ψ_s, and L were in good agreement with those of the interaction free energy obtained in our preceding work by the widthwise integration of repulsive electrostatic forces normal to the midplane between the parallel rods in nonskewed configurations.