Correlation length and entanglement spacing in concentrated hydrogenated polybutadiene solutions

The concentration correlation length, xi, and the entanglement spacing, d, have been determined in solutions of hydrogenated polybutadiene in n-alkane solvents at 140 degrees C by small-angle neutron scattering and rheology, respectively. The Former varies as xi similar to phi(-0.76) over the range 0.04 < phi < 0.7. This result is in agreement with scaling predictions for semidilute solutions in a good solvent, but interestingly this dependence e xtends to concentrations well beyond the regime where the scaling law shoul d be valid. The entanglement spacing was obtained via measurements of the d ynamic loss modulus, G ", as a function of frequency, omega, from phi = 0.2 to phi = 1. The maximum value of G " in the terminal dispersion regime var ies as phi(1.9), implying that d similar to phi(-0.45). The shape of G "(om ega) was independent of phi 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 dep endence in concentrated solutions in a good solvent. The ratio xi/d, termed the constraint porosity parameter in the polymer mode-coupling theory, var ies from 0.09 in the melt to 0.15 when phi = 0.2, which may have important implications for the concentration dependence of the molecular weight expon ent for chain diffusion.