Determining the Dilution Exponent for Entangled 1,4-Polybutadienes Using Blends of Near-Monodisperse Star with Unentangled, Low Molecular Weight Linear Polymers

Abstract

We determine experimentally the "dilution exponent" alpha for entangled polymers from the scaling of terminal crossover frequency with entanglement density from the linear rheology of three 1,4-polybutadiene star polymers that are blended with low-molecular-weight, unentangled linear 1,4-polybutadiene at various star volume fractions, phi(s). Assuming that the rheology of monodisperse stars depends solely on the plateau modulus G(N)(phi(s)) proportional to phi(1+alpha)(s), the number of entanglements per chain M-e(phi(s)) proportional to phi(-alpha)(s), and the tube-segment frictional Rouse time tau(e)(phi(s)) proportional to phi(-2 alpha)(s), we show that only an alpha = 1 scaling superposes the M-e(phi(s)) dependence of the terminal crossover frequency omega(x,t) of the blends with those of pure stars, not alpha = 4/3. This is the first determination of a for star polymers that does not rely on any particular tube model implementation. We also show that a generalized tube model, the "Hierarchical model", using the "Das" parameter set with alpha = 1 reasonably predicts the rheological data of the melts and blends featured in this paper.