Correlation Length and Entanglement Spacing in Concentrated Hydrogenated Polybutadiene Solutions

The concentration correlation length, ξ, and the entanglement spacing, d, have been determined in solutions of hydrogenated polybutadiene in n-alkane solvents at 140 °C by small-angle neutron scattering and rheology, respectively. The former varies as ξ ∼ φ^-0.76 over the range 0.04 < φ < 0.7. This result is in agreement with scaling predictions for semidilute solutions in a good solvent, but interestingly this dependence extends to concentrations well beyond the regime where the scaling law should be valid. The entanglement spacing was obtained via measurements of the dynamic loss modulus, G″, as a function of frequency, ω, from φ = 0.2 to φ = 1. The maximum value of G″ in the terminal dispersion regime varies as φ^1.9, implying that d ∼ φ^-0.45. The shape of G″(ω) was independent of φ and M, and d was independent of M, as expected for well-entangled solutions. These results indicate that the entanglement spacing and the correlation length need not have the same concentration dependence in concentrated solutions in a good solvent. The ratio ξ/d, termed the constraint porosity parameter in the polymer mode-coupling theory, varies from 0.09 in the melt to 0.15 when φ = 0.2, which may have important implications for the concentration dependence of the molecular weight exponent for chain diffusion.