Thermodynamics of the Laminar Donnan System

Thermodynamic quantities of a polyelectroyte immersed in salt solution are derived modeling the polyelectrolyte by a sequence of charged parallel flat plates. The starting point for the analysis is the derivation of the Gibbs free enthalpy in its canonic variables pressure (p) and temperature (T), i.e., as a thermodynamic potential. From this, further thermodynamic quantities such as Helmoltz free energy, entropy, internal energy, compressibility, isobar and isochor heat capacities, and expansive force are derived in analytical expressions by differentiation. All these formulas contain the parameter plate surface charge density (sigma) that provides a measure of the discontinuity of the polymer charge distribution that can be used to fit the theory to experimental data. Thermodynamic quantities are also known from the classical Donnan equilibrium that treats the polyelectroyte charge network as a charge continuum. A limiting process is used to perform the transition from the laminar Poisson- Boltzmann model to the continuous Donnan equilibrium. In general, the expressions of the Donnan system are recovered for plate charge density sigma-->0, number of plates Z-->infinity, and sigma Z=constant. Copyright 2000 Academic Press.