Theory for Radii and Second Virial Coefficients. 1. Highly Charged Polyelectrolytes

We develop a theory for the dependence of the radii of gyration and second virial coefficients of highly charged polyelectrolytes on molecular weight and ionic strength. The theory is based on using (i) the Flory-Fisk¹ distribution of chain conformations to describe the elastic entropy and (ii) a charged rod model of local intrachain repulsions based on the full Poisson-Boltzmann equation. To describe the overlap between two approaching chains, we go beyond the rigid sphere model of Orofino and Flory2 and assume the chains can change coil size and can deform as elastic ellipsoids to avoid unfavorable interchain repulsions. Added salt weakens electrostatic repulsions, leading to reduced radius of gyration and second virial coefficients. Without adjustable parameters this approach gives reasonable agreement with data on T7 DNA, Col E1 DNA, and poly(styrenesulfonate)s over two decades of ionic strength.