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 quantit ies such as Helmoltz free energy, entropy, internal energy, compressibility , isobar and isochor heat capacities, and expansive force are derived in an alytical expressions by differentiation. All these formulas contain the par ameter plate surface charge density (sigma) that provides a measure of the discontinuity of the polymer charge distribution that can be used to fit th e theory to experimental data. Thermodynamic quantities are also known from the classical Donnan equilibrium that treats the polyelectroyte charge net work as a charge continuum. A limiting process is used to perform the trans ition from the laminar Poisson-Boltzmann model to the continuous Donnan equ ilibrium. In general, the expressions of the Donnan system are recovered fo r plate charge density sigma --> 0, number of plates Z --> infinity, and si gma Z = constant. (C) 2000 Academic Press.