The effects of pressure and temperature upon the viscosities of liquids with special reference to polymeric liquids

Abstract

Abstract From a consideration of the work required for expansion of a liquid, the following relationship between viscosity η, pressure P and temperature T is put forward. magnified image For unassociated liquids with molecules which are not too large, V * is taken as the parachor, log 10 (η* in Ns/m 2 ) is −3.88, P * is 8.58 × 10 6 N/m 2 , R is the gas constant, and T * is a constant characteristic of each liquid. The equation can be applied to polymeric liquids if V * and η* are taken as disposable constants. For example, for polystyrene V * is found to be 3 × 10 −3 m 3 mol −1 and log 10 (η* in Ns/m 2 ) to be 3.4 log 10 M̄ w −10.2 where M̄ w is the weight‐average molecular weight (kg/mol) from 5 kg/mol upwards. In the equation, the same constants serve for the variation of viscosity with pressure and with temperature. The viscosity under a high pressure can therefore be estimated from viscosities all measured at normal pressures but at different temperatures. The viscosities of a number of polymers have been measured over a range of temperature and pressure and the results support the equation. Support is found for the view that segments are involved in the flow of polymeric liquids and V * gives a measure of the volume of the segment. The size of the segment seems to increase as the flexibility of the polymer chain decreases. The lowest values for V * are found for polysiloxanes in which the segment seems to be only four atoms long. Larger values of V * are found for polymers with units of the type –CH 2 –CHR‐. Larger values still of V * are given by polymers with units of the type –CH 2 ‐CR 1 R 2 ‐ and even larger V * values are found for those polymers with benzene rings constituting a major part of the main chain. As V * rises the viscosity of the polymeric liquid becomes much more dependent upon pressure and temperature. Thus whilst the polysiloxanes have viscosities which are relatively insensitive to pressure and temperature, the aromatic polysulphones and poly(2,6‐dimethylphenylene oxide) have viscosities which are very sensitive to pressure and temperature.