TITLE:
Statistical Mechanics of Phase Transitions
AUTHORS:
Jan Helm
KEYWORDS:
Phase Transition, Partition Function, Equation-of-State, Radial Distribution Function, Landau Theory, Intermolecular Potential, Van-der-Waals Equation, Lennard-Jones Substance, Dipole Substance
JOURNAL NAME:
Journal of Modern Physics,
Vol.16 No.10,
October
27,
2025
ABSTRACT: This paper presents the mathematical models and calculation of states of matter dynamics (gasses, fluids, solids) and phase transitions from statistical viewpoint, with new calculation methods and results. We introduce here a new ansatz for the partition function, based on the generalized Landau theory, and apply it to two intermolecular potentials: Lennard-Jones and dipole-dipole. For these two potentials, we derive the basic thermodynamic variables, and compare the results with experimental data for Lennard-Jones substance (fluid argon) and for dipole substance (ethanol). This approach allows to derive the thermodynamic properties solely from its intermolecular potential. The paper introduces two novel methods. (1) Landau theory applied to solid-fluid-gas (fgs) systems; (2) Analytic expression for the partition function. The paper is structured as follows. Chapters 2 and 3 introduce the basics of phase transitions, and partition function. Chapter 4 describes the generalized Landau theory and its classical formulation for magnetic systems. Chapter 5 gives a detailed description of the van-der-Waals theory. Chapters 6 and 7 present the two representative substances with model and phase transitions: the Lennard-Jones substance and the dipole substance. Chapters 8 and 9 introduce the ansatz and the formulation of the partition function for fgs systems. Chapters 10 and 11 are the calculation of the radial distribution function and the partition function for the two chosen substances. Chapters 12 and 13 present the results: calculated pressure profiles, equation-of-state and characteristic points for the two substances.