Molecular origins of the pressure and temperature dependences of fluid viscosity and the glass transition

Abstract

This work examines the origin of the curious variation in the pressure activation volume with increasing pressure, where it initially decreases to a minimum before rising again. It has been shown that the initial decrease arises from compression of the fluid until it reaches a jamming packing fraction, at which point the system starts to exhibit elastic behavior, resulting in an increase in activation volume with further pressure. This regime is analyzed using a modification of the so-called shoving model, in which the extra volume required for molecular rearrangement is accommodated by elastic deformation of the surrounding material. This approach yields an equation in which the viscosity depends on the instantaneous shear modulus, G∞. If G∞ is assumed to be independent of pressure and temperature, the model reduces to Arrhenius and Barus equations. The pressure and temperature dependence of G∞ is calculated using a non-affine Zaccone model for disordered fluids that results in an expression that accurately reproduces the experimental temperature dependence of viscosity across a range of materials. The model also predicts the “fragility” of glass-forming materials as well as the dependence of the glass-transition temperature on pressure. Furthermore, we confirm Zaccone’s conjecture that fragility depends strongly on the strength of the repulsive component of the intermolecular potential.