Combining the Tait equation with the phonon theory allows predicting the density of liquids up to the Gigapascal range

Abstract

AbstractPredicting the density of liquids at ultrahigh pressures in the case when only the data measured at ambient pressure are available is a long-standing challenge for thermodynamic research. In this work, we archived this goal for molecular liquids by applying the half-sum of the Tait equation and the Murnagnan equation in the form coordinated with Tait’s at low pressure for predicting the density of molecular liquids up to the pressures more than 1 GPa with uncertainty comparable with the experimental one. It is shown that the control parameter, which is needed in addition to the initial density and the isothermal compressibility can be found using the speed of sound and the density at ambient pressure and has a clear physical interpretation in terms of the characteristic frequency of intermolecular oscillation mimicking the limiting frequency of Debye’s theory of heat conductivity of solids. This fact is discussed as arguing in favour of the modern phonon theory of liquid thermodynamics and expands it range of applicability to the volumetric properties of liquids at temperatures far below the critical one. The validity of the model is illustrated with the case study of classic Bridgman’s dataset as well as with some examples of ultrahigh-pressure data obtained by the diamond anvil cell and shock wave compression methods.