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

摘要

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,V-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(0)(2)/[u(2)](f) eta=eta(0)exp V-PA,V-0*/V-PA,V-t= eta(0) exp V-PA,V-0*/v(PA,f) where U-0(2),V-PA,V-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,V-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 u(0)(2) 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%). [S1063-651X(99)00308-6]. [References: 27]