Activation Volume in the Density Scaling Regime: Equation of State and   Its Test by Using Experimental and Simulation Data
  In this paper, a formalism for the activation volume of glass forming materials is suggested. An isothermal equation of state for the activation volume is formulated, which is extended to a generalized equation of state that describes the activation volume as a function of temperature and pressure. Both the equations of state are very successfully validated by using experimental and simulation data collected for supercooled Kob-Andersen binary Lennard-Jones liquid and materials from various material groups such as van der Waals liquids, polymers, protic ionic liquids, and strongly hydrogen bonded liquids. Some predictions based on these equations of state for the activation volume are also very satisfactorily verified in case of each considered system, especially a kind of the activation volume scaling with the scaling exponent that also constitutes the slope of the expected linear pressure dependence of the isothermal bulk modulus for the activation volume is confirmed. The until recently unexpected negative value of the slope are explained in case of the systems that obey the thermodynamic scaling law at least to a good approximation. 
Andrzej Grzybowski, Kajetan Koperwas, Alicja Swiety-Pospiech,   Katarzyna Grzybowska, and Marian Paluch
cond-mat.soft