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

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 B₂ and for the first two salt distribution coefficients A₁ and A₂. 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 B₂ = πd_BL²/4 and A₁ = πd_A²L/4 for hard cylinders of length L and diameter d_B and d_A, respectively. The coefficient A₂ is derived from the dependence of B₂ 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 1–0.005M 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 B₂. Values of A₂ 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 B₂, but not yet observed for DNA in simple salt solutions.