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

Abstract

Predicting 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.

On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids

“…A number of examples of the density predictions from ambient pressure up to GPa range with the parameter k fitted empirically within the room range of temperatures can be found in the work [5]. Here, we will consider two more complicated cases related to the predictive capacity of the discussed approach using two principal test substances considered above.…”

“…One of the principal questions is a possible variation of the parameter k with temperature, which was determined in the work [5] as the slope of the linear fit of ln(c 3 ρ) vs. ln(ρ) and may depend on the interval of the fitting. Instead, here we calculated it directly as the derivative (6) using the quantities given by the Span-Wagner fundamental equation of state by the REFPROP.…”

“…The tests of the predictive capacity of the method based on the data determined at ambient pressure and the nonlinearity parameter use the scheme proposed in the work [5] when the target predicted density at high pressures is calculated as…”

“…allows an accurate prediction of the liquid density up to extremely high pressures [5] when considering the initial value problem for the ordinary differential equation along an isotherm obtained within the linear response theory…”

“…Note that except k all terms in Equations ( 4) and ( 5) can be easily determined at ambient pressure (or along the liquid-vapor coexistence curve up to the normal boiling point) and one needs to obtain the value of k , which includes the pressure derivatives, at this condition. In the work [5], it has been shown, referring to the phonon theory of liquids [7,8], that…”