On the pressure dependence of viscosity, especially for fluids that have a tendency to form glasses

Understanding fluid viscosity is crucial for applications including lubrication and chemical kinetics. A commonality of molecular models is that they describe fluid flow based on the availability of vacant space. The proposed analysis builds on Goldstein's idea that viscous transport must involve the concerted motion of a molecular ensemble, referred to as cooperatively rearranging regions (CRRs) by Adam and Gibbs in their entropy-based viscosity model for liquids close to their glass transition. The viscosity data for propylene carbonate reveal a non-monotonic trend of the activation volume with pressure, suggesting the existence of two types of CRR with different compressibility behaviors. This is proposed to result from a change in CRR free volume (<0.2 GPa) and a growth in its size (>0.2 GPa). We use Evans-Polanyi perturbation theory to develop an analytical model for the structural changes of the CRR in function of pressure and temperature and their effect on Eyring viscosity. This analysis shows that the activation energies and volumes scale with the CRR size. Using the compressibility data of propylene carbonate, we show that the activation volume of the CRR at low pressures depends on the compressibility of an ensemble comprised of the first coordination shell around a molecule. At higher pressures, we apply an Adam-Gibbs-type analysis to model the increase in CRR size and its effect on viscosity, where the increase in size is estimated from propylene carbonate's heat capacity. However, this analysis also reveals deviations from the Adam and Gibbs model that will guide future improvements.