THE CONCENTRATION-DEPENDENT COOPERATIVE FRICTION COEFFICIENT OF DILUTE POLYMER-SOLUTIONS AT THE THETA-POINT

We combine multiple scattering and renormalization group methods to ca lculate the leading order dimensionless virial coefficient k(s) for th e friction coefficient of dilute polymer solutions under conditions wh ere the osmotic second virial coefficient vanishes (i.e., at the theta point T-theta). Our calculations are formulated in terms of coupled k inetic equations for the polymer and solvent, in which the polymers ar e modeled as continuous chains whose configurations evolve under the a ction of random forces in, the velocity field of the solvent. To lowes t order in epsilon=4-d, we find that k(s) = 1.06. This result compares satisfactorily with existing experimental estimates of k(s), which ar e in the range 0.7-0.8. It is also in good agreement with other theore tical results on chains and suspensions at T-theta. Our calculated k(s ) is also found to be identical to the leading order virial coefficien t of the tracer friction coefficient at the theta point. We discuss po ssible reasons for the difficulties encountered when attempting to eva luate k(s) by extrapolating prior renormalization group calculations f rom semidilute concentrations to the infinitely dilute limit. (C) 1996 American Institute of Physics.