Mean-field-theory for polymers in mixed solvents. Thermodynamic and structural properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approache s criticality. Both the single and the many chain problems are examined. Wh en the mixed solvent is near criticality without solute, addition of a smal l amount of polymers shifts the criticality towards either enhanced compati bility or induced phase separation depending upon the value of the paramete r describing the interaction asymmetry of the solvents with respect to the polymer. The polymer-solvent effective interaction parameter increases stro ngly when the solvent mixture approaches criticality. Accordingly, the appa rent excluded volume parameter decreases and may vanish or even become nega tive. Consequently, the polymer undergoes phase transition from a swollen s tate to an unperturbed state or even takes a collapsed configuration. The e ffective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of t ernary mixtures of polymers in mixed solvents are investigated within the E dwards Hamiltonian model. It is shown that the effective potential on a tes t chain in strong solutions could be written as an infinite series expansio n of terms describing interactions via one chain, two chains etc. This summ ation can be performed following a similar scheme as in the Ornstein-Zernik e series expansion.