High-temperature flow behavior of glass-forming liquids: A free-volume interpretation

High-temperature viscous flow data are reported for three relatively simple organic liquids: o-terphenyl, salol, and α-phenyl-o-cresol. The results are combined with previous flow data on the same liquids to obtain viscosity-temperature relations over some 15 orders of magnitude. For each liquid, as well as for tri-α-naphthylbenzene, the free-volume theory of Turnbull and Cohen is found to provide a close representation of the data for viscosities between 10^-2 P (the high-temperature limit of the data) and about 10⁴ P. Over this range, even the pre-exponential factors derived from fitting the experimental results are in close agreement with those predicted by the theory. At lower temperatures, the free-volume expression overestimates the difficulty of flow. For all four organic liquids, the fractional free volumes at the points of departure, T, of the experimental data from the free volume predictions are close to 0.015. An empirical high-temperature flow relation of the free-volume form is suggested as η≈s[(MkT)1/2/a²₀] exp{0.25/[0.015 + Δα(T - T_B)]}, where M is the mass of the molecule, a ₀ is its diameter, and Δα is the difference in thermal expansion coefficient between liquid and glass. It is suggested again that free-volume theories be used to represent flow behavior in the fluid range rather than in the high-viscosity region as the glass transition is approached.