Calculation of Thermodynamic Properties of Polyelectrolytes

Abstract

Expressions are derived which introduce an appreciable simplification into the calculation of the thermodynamic properties of solutions of polyelectrolytes in certain cases. For example, for a certain class of theoretical models of these systems it is found that the square of the mean ion activity coefficient of a uni-univalent salt in the presence of polymeric ions is V^2/∫e^(-eψ/kT)dV • ∫e^(eψ/kT)dV, the integration of the potential ψ being over a region whose volume is the volume of solution per macro-ion, V, and whose symmetry is that assumed for the polyelectrolyte. The osmotic pressure of a salt-polyelectrolyte system is, ignoring the contribution of the macro-ion, estimated to be Σ_ic_i^skT, where Σ_ic_i^s is the sum of the concentrations of all ions at the surface bounding the previously defined volume V. Other relations and various applications are given. The activity coefficient of salt in the presence of polyelectrolytes, calculated by extending the "parallel rod" picture of polymeric ions, is found to be in reasonable agreement with the experimental data. The use of the Poisson-Boltzmann equation to estimate ψ in these systems is shown not to render inconsistent several alternative expressions for the electrostatic contribution to the free energy.