Free Volume Approach to Polystyrene Melt Viscosity

Abstract

The Doolittle approach to Newtonian viscosity assumes η=A expB/f, where A and B are constants independent of temperature and f, the relative free volume, is (v−v0)/v0. Here v is the specific volume and v0 is the occupied volume. Using machine computations, this equation was applied to published data on polystyrene, replacing v by its equivalent vg+(dv/dT)(T−Tg), where vg is the specific volume at the glass temperature Tg. The agreement between calculated and observed viscosities is at least as good, and perhaps better, than that afforded by other existing empirical expressions. The constant B is independent of molecular weight and temperature while v0 depends slightly on molecular weight. A log-log plot of A against molecular weight M produces two straight lines intersecting at M=35 000. At higher values of M, the slope is 3.4; at lower values, it is slightly greater than one. This treatment separates the melt viscosity of polystyrene into two factors, A, dependent only on structural parameters, and f, which is determined by the specific volume and is a function of temperature.