A simplified molecular-thermodynamic model of a microphase-separated ionic gel swollen in salt solution

A molecular-thermodynamic model [A.I. Victorov, C.J. Radke, J.M. Prausnitz, Mol. Phys., 2004, submitted for publication] of diblock copolymer ionic gels swollen in brine is simplified by deriving asymptotic expressions for electrostatic terms. This model derived recently from the self-consistent field theory in the limit of strong segregation gives thermodynamic functions for gels of lamellar, bicontinuous, cylindrical and spherical morphologies and details the gel structure including equilibrium microdomain spacing, distribution of mobile ions, polymer segments, and the electric potential across the microdomains. The model reflects the copolymer chain composition, length, rigidity, ionization degree and the effective polymer–polymer and polymer–solvent interactions. Several asymptotic regimes are considered that lead to simple formulae for the solvent chemical potential. Applicability of asymptotic relations is tested. Equilibrium uptakes of salt are calculated for gels of varying ionic charge over a wide range of solution salinity.