Thermodynamics of a model for flexible polyelectrolytes in the binding mean spherical approximation

We discuss our previous solution of the mean spherical approximation (MSA) for flexible polymers made of arbitrarily charged spheres of arbitrary diameter. Closed form analytical results for some particular cases are presented, in particular thermodynamic excess functions and an equation for the MSA screening parameter ΓT. It is found that the ideal chain approximation does not satisfy the exact Debye–Hückel limiting law since the polymer term appears with an effective charge squared that is 8.5 instead of 9 for a trimer, 14 instead of 16 for the tetramer, and 7n−16 instead of n2 for very large n. We propose a new chain approximation that takes three-body hard core exclusion into account. We show that this triplet exclusion chain approximation satisfies explicitly the Debye–Hückel limiting law for all lengths n, and also for all charge combinations.