Theory of inhomogeneous polymers in presence of solvent

A theory is developed to predict the free energy and microdomain size of block copolymer systems, taking into account solvent-polymer interactions. The mean-field equations for the polymer probability densities are derived from fundamental statistical mechanics, starting from the total interaction energy of the system, and making use of functional integral techniques. We introduce the constraint of no volume change upon mixing directly into the derivation of the mean-field equations, and thereby eliminate the need to add an indeterminate function to the free energy density to suppress density fluctuations for systems with small compressibility. We solve the mean-field equations numerically for the lamellar block copolymer microdomain structure, and we investigate the effec of the solvent on the size of the microdomains. For the Polystyrene-polyisoprene toluene system we find a first-order “melting” transition for the periodic structure when the block copolymer becomes saturated with solvent.