Universality of Density Scaling

Abstract

Investigations of the sought after complete and commonly accepted theory of the glass transition and related phenomena have recently gained an essential support from a very promising idea of the density scaling of molecular dynamics in viscous liquids. This idea, often known as the thermodynamic scaling concept, has been initiated by many phenomenological observations, which have shown that dynamic quantities (e.g., viscosity, structural relaxation time, or segmental relaxation time in case of polymers) measured in different thermodynamic conditions (e.g., along different isobars and isotherms) can be scaled onto one master curve well described by a function of the single variable that is a product of the inverse temperature and the density power with the scaling exponent considered as a material constant independent of thermodynamic conditions. However, a crucial advantage of the phenomenological description has become its theoretical grounds relied on an effective short-range intermolecular potential, which has been derived from the well-known Lennard-Jones potential and satisfactorily verified by computer simulations. A relation suggested between the scaling exponent and the exponent of the dominant repulsive part of the effective intermolecular potential gives a tempting opportunity to study the macroscopic properties of materials by using the underlying intermolecular potential and vice versa to determine the intermolecular potential parameters based on measurements of macroscopic quantities. It opens new perspectives for our better understanding of complex physicochemical phenomena occurring near the glass transition . In this chapter, we present the density scaling concept as the idea that bears hallmarks of universality in case of both various materials and different quantities. We show that the density scaling law may concern not only dynamic but also thermodynamic quantities, constituting a convenient tool to explore relationships between molecular dynamics and thermodynamics based on the effective short-range intermolecular potential. We demonstrate predictive capabilities of the density scaling law that implies several rules for activation quantities and fragility parameters defined in different thermodynamic conditions, which enable to discover and verify physically well-defined invariants. We also discuss some nontrivial cases of the thermodynamic scaling for which the power density scaling law with a constant scaling exponent is not sufficient, but we can find density or timescale-dependent counterparts of the exponent. The exceptions to the standard power density scaling law delimit further challenges in making progress toward the development of the density scaling idea and its applicability range.