Microscopic basis of free-volume concept as studied by quasielastic neutron scattering and positron annihilation lifetime spectroscopy.

Abstract

We have reexamined the free-volume concept presented by Cohen and Turnbull on the basis of two microscopic quantities: the excess mean-square displacement <u(2)>(f) and the total free volume V(PA,t), of poly- butadiene evaluated from the quasielastic neutron scattering and the positron annihilation lifetime spectroscopy (PALS) data, respectively. Comparing with the viscosity eta we found two relations, eta=eta(0) exp u( 2)(0)/<u(2)>(f) and eta=eta(0) exp V(*)(PA,0)/V(PA,t)=eta(0) exp V(*)(PA,0)/v(PA,f), where u(2)(0), V(*)(PA,0) and v(*)(PA,0) are the critical values for the mean-square displacement, the total PALS free volume, and the PALS free volume per molecule, respectively, and further v(*)(PA,0)=V(*)(PA,0)/N, N being the total number of molecules or segments. On the basis of these relations, we discuss the microscopic basis of the free-volume theory. The experimentally evaluated critical values u(2)(0) and v(*)(PA,0) are much larger than the average values of <u(2)>(f) and v(PA,f) calculated from the distributions. This has been explained from the low probability of escaping motions from a molecular cage. The free volume per monomer and the free-volume fraction were calculated from the excess mean-square displacement <u(2)>(f). The former was compared with the free-volume hole obtained by PALS, suggesting that 22 monomers are required for one PALS free-volume hole. The free-volume fraction obtained from the excess mean-square displacement was found to be 6.4% at 250 K, which is in reasonable agreement with that evaluated from the rheological data (9.0%).