An alternative approach to the phonon theory of liquids: An analytical study of Frenkel frequency and heat capacity as a function of pressure and temperature

Based on the Maxwell relationship and experimental viscosity data, the phonon theory of liquids can provide a temperature-dependent description of liquid heat capacity that is consistent with experimental data. However, since liquid heat capacity also varies with pressure, we present an alternative approach that can be used to calculate the Frenkel frequency in terms of temperature and pressure by applying the concept of chemical potential under the assumption of a diffusive equilibrium. Using this derived Frenkel frequency, we formulate an analytical expression for the liquid heat capacity in terms of both temperature and pressure, without the need for viscosity data, which is consistent with predictions from the phonon theory of liquids. Our model is tested by comparing the calculated heat liquid capacity with experimental data for four noble liquids at various pressures and temperatures, and good agreement is found. Finally, based on our findings, we propose analytical expressions for the Frenkel line and viscosity as a function of pressure and temperature, and discuss the key details and implications of our approach.