Free volumes in polystyrene and polyisobutylene

This is the authors' abstract. We don't add key points for this paper.

The melt viscosities of polystyrene and polyisobutylene fractions are expressed by a modified Arrhenius (M.A.) temperature equation, η = A exp {B/(T − T0)}, and by a free volume equation, η = A exp 1/{f}, in which f = vf/v, the free volume fraction. Thus, it is assumed that f, as defined, is a linear function of temperature, since f = (T − T0)/B. By this method, the derived “occupied” volume, vs = v −vf, has a temperature dependence which is determined by the temperature coefficients of f and v (i.e., 1/B and αl) and is not related to the experimental αg value for the glass. For polyisobutylene, the temperature coefficient of vs is positive, while for polystyrene it is slightly negative. Possible effects of liquid structure in determining the temperature behavior of vs are suggested. Calculated viscosities and free volume fractions at the glass point, Tg, over a wide range of molecular weight, M, in both polymers lead to the conclusion that the glass transition is primarily an “iso‐viscosity” (ηg ≃ 1013 poise), rather than an “iso‐free volume”, state. However, in the two polymers, both conditions can exist simultaneously for similar values of M. Thus at equal M,fg = (Tg = T0/B) is about the same for both polymers. For M ≃ 100,000, fg ≃ 0.031. These observations support the view that the glass transition is primarily a kinetic, rather than a thermodynamic, phenomenon. The estimated time dependence of Tg is found to differ in the two polymers at equal M and to vary with M in each case.