Analysis of the melt viscosity and glass transition of polystyrene

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Abstract
The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann‐Hesse viscosity equation: log η = log A + B/(T − T0). Evidence that the glass transition is an isoviscosity state (log ηg ≃ 13) for lower molecular weight fractions (M < Mc) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ≃ 19,000; tg = 89°C.), it is shown that B is independent of the p–v–T state of the polymer liquid and that dT0/dP = dTg/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero‐pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔVg* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3ϕ, is reexamined. For polystyrene and polyisobutylene, ϕg/b = 0.03, but ϕg and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ϕ, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dTg/dP, one an exact derivation and the other an empirical correlation, are presented.

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