Diffusivity and Viscosity of Concentrated Hydrogenated Polybutadiene Solutions

Abstract

We report measurements of diffusion (D) and viscosity (η) in hydrogenated polybutadiene (hPB)/alkane solutions. The volume fractions (φ) extend from 0.20 up to the melt and the molecular weights (M) from 4900 up to 440 000; the number of entanglements per chain, M/Me, ranges up to about 450. The temperature dependences of both D and η are similar, consistent with literature values, and independent of φ and M. We thus conclude that the monomeric friction factor is also independent of φ and M. For all samples with M/Me ≥ 3 the data are consistent with the scaling relations D ∼ M-2.4±0.1φ-1.8±0.2 and η ∼ M3.4±0.1φ3.8±0.2; within the precision of the data the M exponents do not depend on φ, and the φ exponents do not depend on M. The M exponent for D in solution is consistent with previously reported studies for φ ≤ 0.4 but apparently conflicts with the reptation value of −2.0 in the melt. However, by comparing with the literature melt self-diffusion data for hPB and six other polymers, it is clear that the exponent is, in fact, universally stronger than −2.0. Furthermore, if a single universal exponent is assumed, the best value based on all the data is −2.28 ± 0.05. Our hPB data resolve the longstanding anomaly that the longest relaxation times τ1 based on translation (∼Rg2/D) and orientational relaxation (∼η) appeared to have different M dependences. The data also indicate that for both solutions and melts the dynamics are determined primarily by the number of entanglements per chain. The data are compared with current models of polymer dynamics, both reptative and nonreptative. In the former case it is clear that a self-consistent theory incorporating both “constraint release” and “contour length fluctuations” is required.