Dynamics in blends of long polymers with unentangled short chains

Scaling ideas for dynamics of polymer solutions are extended to the case of a solution of long chains (of N monomers) in unentangled short chains (of P monomers). The P chains can be sufficiently short to make the long chains partially swell (P < TV1'2). While the configurational statistics of the partially swollen long chains are perfectly analogous to the case of a long chain in marginal solvent, the dynamics are qualitatively different because of differences in the screening of hydrodynamic interactions. When the long chains are dilute and partially swollen (N > P2), hydrodynamic interactions control their terminal relaxation. When N < P2, excluded volume is fully screened, and the dilute long chains relax by Rouse motion (with hydrodynamic interactions fully screened). The assumptions about hydrodynamic screening in dilute solution have consequences in the semidilute regimes of unentangled and entangled behavior, where we calculate the viscosity and the tracer diffusion coefficients. We end with a discussion of assumptions about hydrodynamic screening, and experiments are suggested to test those assumptions using binary blends with one unentangled component.