Dynamic coupling between stress and composition in polymer solutions and blends

Phenomenological hydrodynamic equations are proposed for entangled polymer blends as generalization of those for polymer solutions. They can describe coupling between macroscopic flow and relative diffusion. The key concept we use is the "tube velocity" introduced by Brochard in the problem of mutual diffusion in polymer blends. As applications, (I) we give a general expression for the time-correlation function of the polymer concentration around equilibrium and examine its relaxation in some typical cases. It can be strongly influenced by the viscoelastic effect when the two polymers have different lengths. Our expression can also be used for gelling solutions and explains previous dynamic light scattering experiments at the sol-gel transition. (ii) Detailed calculations are performed for the case of a single rheological relaxation time (the Maxwell model). The steady state structure factor is obtained to Iinear order in macroscopic flow. (iii) We predict that composition inhomogeneity is created in mixtures oflong and short polymers undergoing nonuniform flow. Its origin is that the longer chains support stress more than the shorter ones and the resultant imbalance of stress causes relative motion of the two polymers. These results are applicable both to solutions and blends.