Dynamic relaxations of polymers in mixed solvents

Dynamic relaxations of ternary solutions-of polymers in mixed solvents are investigated theoretically. The formalism is based on a combination of the Edwards Hamiltonian method and the Langevin equation with a random white noise. Two parameters play a crucial role in defining the mechanism of relaxations. The first parameter is the interaction dissymmetry of the solvent vis-avis the polymer. This parameter describes the difference in affinity of the polymer on the one hand and the two solvents on the other hand. The second parameter is the interaction between the two solvents and their degree of compatibility. The theory predicts two modes. One reflects the polymer concentration fluctuations and the other describes the solvent composition fluctuations. If the interaction dissymmetry parameter is small, these two modes are decoupled and reflect classical results of polymer solution dynamics and solvent dynamics. If the dissymmetry parameter is large, the two relaxation modes are coupled. The extent of coupling depends upon the interaction between the two solvents. If this interaction is small, only slight numerical differences are obtained with respect to the case of decoupled modes. If the interaction between the two solvents is large, then one observes a strong coupling between the modes reflecting polymer concentration fluctuations and solvent composition fluctuations. The frequencies and amplitudes of these modes are studied here in terms of polymer size, concentration, polymer-mixed solvent interaction dissymmetry parameter and the solvent-solvent interaction parameters.