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

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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 B2 and for the first two salt distribution coefficients A1 and A2. The effect of electric interactions is represented as an increased effective diameter dB or dA of the colloidal cylinder. This yields the simple excluded volume expressions B2 = πdBL2/4 and A1 = πdA2L/4 for hard cylinders of length L and diameter dB and dA, 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 dB is found to vary from 29 Å to about 220 Å, and dA 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.