Statistical Thermodynamics of Polyelectrolyte Solutions

Abstract

Since long it has been realized that the electrostatic interactions between charged macromolecules and small ions and eventually the interactions between the charges on a same macromolecule play an important role in the equilibrium properties of polyelectrolyte solutions. It is therefore not surprising that most efforts in the field of the theoretical description of these solutions have been focused on the solution of the Poisson-Boltzmann equation for the electrostatic potential around a polyion, usually in a given fixed conformation, and the subsequent calculation of the electrostatic free energy and its bearing on the thermodynamics of the system. Pioneering work was done by Hermans and Overbeek [1] and Katchalsky and coworkers [2]; many others have followed some of which have been listed in the references [3]. Less numerous papers have been devoted to a more general statistical thermodynamical approach. Some attempts, starting from a Kuhn-like chain of ‘statistical elements’ were made by Katchalsky [4] but these treatments were criticized by Rice and Harris [5] because of inter alia the use of undiminished statistical weight for all conformations of the polyion with the same end-to-end distance. The work of the latter [5, 6] however is also based on an analogous model and includes many specified and unspecified assumptions.