Interactions of highly charged colloidal cylinders with applications to double‐stranded DNA

Abstract This paper presents new applications of the McMillan‐Mayer solution theory to dispersions of highly charged colloidal cylinders in monovalent salt solutions. The thermodynamic solution properties are given in terms of the virial expansions relating to a Donnan membrane equilibrium. General expressions are derived for the second Donnan pressure virial coefficient B 2 and for the first two salt distribution coefficients A 1 and A 2 . The effect of electric interactions is represented as an increased effective diameter d B or d A of the colloidal cylinder. This yields the simple excluded volume expressions B 2 = π d B L 2 /4 and A 1 = π d A 2 L /4 for hard cylinders of length L and diameter d B and d A , respectively. The coefficient A 2 is derived from the dependence of B 2 on the salt concentration. Computations are made for double‐stranded DNA in sodium chloride solutions with the DNA model developed in the preceding paper: a uniformly charged cylinder, with size and charge consistent with transport experiments, and surrounded by a Gouy double layer. In 1–0.005 M sodium chloride solutions d B is found to vary from 29 Å to about 220 Å, and d A from 30 Å to about 170 Å, with little sensitivity to the uncertainties in the kinetic diameter d ≈ 24 Å and the experimental ζ potentials of DNA. Corresponding results predicted by the classical Donnan theory are 6–167 times too high for B 2 . Values of A 2 are relatively small, in line with the expected rapid convergence of the virial expansion for the salt distribution. This is consistent with a phase transition from random to parallel orientation of the cylinders predicted first by Onsager for hard cylinders on the basis of B 2 , but not yet observed for DNA in simple salt solutions.