Density functional theory for the nonspecific binding of salt to polyelectrolytes: Thermodynamic properties

The thermodynamics of the nonspecific binding of salt to a polyelectrolyte molecule is studied using a density functional approach. The polyelectrolyt e molecule is modeled as an infinite, inflexible, and impenetrable charged cylinder and the counterions and co-ions are modeled as charged hard sphere s of equal diameter. The density functional theory is based on a hybrid app roach where the hard-sphere contribution to the one-particle correlation fu nction is evaluated nonperturbatively and the ionic contribution to the one -particle correlation function is evaluated perturbatively. The advantage o f the approach is that analytical expressions are available for all the cor relation functions. The calculated single ion preferential interaction coef ficients, excess free energy, and activity coefficients show a nonmonotonic variation as a function of polyion charge in the presence of divalent ions . These properties display considerable departure from the predictions of t he nonlinear Poisson-Boltzmann (NLPB) equation, with qualitative difference s in some cases, which may be attributed to correlation effects neglected i n the NLPB theory.