Electrostatic Contributions to Thermodynamic Functions of Systems Containing Polymeric Ions

The electrostatic free energy of systems containing polymeric ions has been evaluated using a model which preserves the inhomogeneous charge distribution of the polyion. The method used includes solution of the Poisson‐Boltzmann equation with largely the Debye‐Huckel approximations. Allowance has been made for the finite volume occupied by the polymer chain, for the ion atmospheres about both fixed and mobile ions, and for the removal of counter ions from the solution by ``site binding.'' A main conclusion of the work is the verification of the previously used postulate that the screened Coulomb potential is a valid first approximation to the potential of mean force between two charges in salt solution. However, it is found that the screening constant differs from that defined in the ordinary Debye‐Huckel theory. It is also shown that a polyelectrolyte model using the screened Coulomb potential implicitly includes all ``osmotic'' forces arising from concentration gradients due to the charges. In salt solutions it is found that the small ions are ordinarily distributed in such a manner that the volume of a polyion is nearly electrically neutral, so that the main interactions between polyions are governed by their spatial dimensions rather than by their charge state. The small ions within the coil, referred to as ``volume bound,'' are distinct from the ``site bound'' counter ions introduced previously, and are trapped within the kinetic unit of a polymer only when it is solvent entrapping.