Fluid critical behavior at liquid–gas phase transition: Analytic method for microscopic description

Abstract

The behavior of fluids in the vicinity of the liquid-gas critical point is studied within the cell fluid model framework. The analytic method for deriving the equation of state of a cell fluid model in the low-temperature region (T < T c ) is developed using the renormalization group transformation within the collective variables approach. Mathematical description within the grand canonical ensemble is illustrated by an example of the Morse interaction potential possessing the Fourier transform. A specific feature of the proposed method lies in the possibility to use exclusively microscopic characteristics of a fluid (parameters of the interaction potential) for calculating macroscopic quantities (pressure and other thermodynamic quantities) without involving the hard-spheres reference system. The grand partition function, thermodynamic potential, and equation of state of the model near the critical point are derived taking into account the non-Gaussian (quartic) distribution of order parameter fluctuations. A nonlinear equation, which links the density and the chemical potential, is presented and solved. Graphs of the dependence of the density on the chemical potential are plotted for various values of the relative temperature. The numerical estimates of the critical-point parameters for potassium, obtained in addition to the estimates for sodium, are given. The calculated critical-point parameters for liquid alkali metals (sodium and potassium) are in accord with experimental data. The coexistence curve for sodium is plotted and compared with other authors' data in the immediate vicinity of T c , where theoretical and experimental researches are difficult to carry out. The differences between the obtained results and the earlier published results for T > T c are discussed.

Фазовий Перехід Першого Роду В Рамках Коміркової Моделі Плину: Області Зміни Хімічного Потенціалу Та Відповідні Густини

“…The theoretical and experimental study of the behavior of liquids and their mixtures in a vicinity of their critical point (see, e.g., works [1][2][3][4][5][6][7][8]) is an important and challenging task. In our previous works [9,10], the behavior of fluid was studied in an immediate vicinity of the critical point, and in works [11][12][13] beyond this vicinity. As a result, a wide region near the critical point has been covered.…”

“…In works [9,10], the analysis was performed in the framework of the collective-variables approach and using the renormalization group transformation [14]. An analytical procedure for calculating the grand partition function and the thermodynamic potential in the cell fluid model was developed in works [9,10] using the approximation of a non-Gaussian (quartic) distribution for order parameter fluctuations and without involving the hard-spheres reference system.…”

“…In works [9,10], the analysis was performed in the framework of the collective-variables approach and using the renormalization group transformation [14]. An analytical procedure for calculating the grand partition function and the thermodynamic potential in the cell fluid model was developed in works [9,10] using the approximation of a non-Gaussian (quartic) distribution for order parameter fluctuations and without involving the hard-spheres reference system. The formation of the reference system as a part of the repulsive component of the interaction potential made it possible to take into account all kinds of interaction (both short-and long-range) from the same position of the collective-variables approach.…”

“…The role of interaction potential in this work is played by the Morse potential. The interaction potential parameters, which are given in works [9,10] and are necessary for quantitative estimates, correspond to the data for sodium. They were taken from work [15], which was devoted to the study of vapor-liquid First-Order Phase Transition in the Framework of the Cell Fluid Model equilibrium curves for metals using Monte Carlo simulation and Morse potential.…”

Equation of State of a Cell Fluid Model with Allowance for Gaussian Fluctuations of the Order Parameter

“…The equation of state obtained in this paper is not applicable in an immediate vicinity of the critical point (| | < * ∼ 10 −2 ). Works [15,19] are devoted to the construction of the equation of state in this narrow neighborhood of with regard for the non-Gaussian fluctuations. A significant role in the development of this technique was played by works [20][21][22][23][24] devoted to describing the behavior of a three-dimensional Ising-like system near with the use of the quartic measure density (the 4 model).…”