液体声子理论的另一种方法：Frenkel频率和热容随压力和温度变化的解析研究
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
AI总结：
本文提出一种无需黏度数据、基于化学势和扩散平衡计算Frenkel频率的新方法，推导出液体热容随温度和压力变化的解析表达式，并在四种惰性液体中验证了模型准确性。
摘要：
基于麦克斯韦关系和实验黏度数据，液体声子理论能够提供与实验数据一致的液体热容随温度变化的描述。然而，由于液体热容还随压力变化，我们提出一种替代方法，通过在扩散平衡假设下应用化学势概念，来计算作为温度和压力函数的Frenkel频率。利用这一推导得到的Frenkel频率，我们建立了液体热容作为温度和压力函数的解析表达式，无需黏度数据，且与液体声子理论的预测一致。我们通过将计算得到的液体热容与四种惰性液体在不同压力和温度下的实验数据进行比较来检验该模型，结果吻合良好。最后，基于我们的发现，我们提出了Frenkel线和黏度作为压力和温度函数的解析表达式，并讨论了该方法的关键细节和意义。
英文摘要：
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.
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