On the microscopic theory of phase transitions in binary fluid mixtures

Abstract

The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order parameter in a binary mixture is discussed. The basic density measure (Ginsburg-Landau-Wilson Hamiltonian) is obtained in the collective variable phase space which contains the variable connected with the order parameter of the system. It is shown that the problem can be reduced to the 3D Ising model in an external field.

Ginzburg-Landau-Wilson Hamiltonian for a Multi-Component Continuous System: A Microscopic Description

“…In a general case only one of the quantities ε 1 (k) and ε 2 (k) is a critical one, no matter whether the system approaches the gas-liquid or mixing-demixing critical point [15,16].…”

“…In order to obtain the effective GLW Hamiltonian we can follow the program proposed in [13,16], namely: (1) to determine the critical branch ε s (k) and the ordering fields χ s, k connected to it; (2) to integrate over the remaining χ s, k (irrelevant variables), using the Gaussian density measure as the basic one; (3) as a result of the integration performed in (2), to construct the functional including higher powers of the ordering fields χ s, k than the second power. As a result, we obtain the GLW Hamiltonian with coefficients which are the known functions of the microscopic parameters, temperature, concentration and density.…”

“…As it was proposed in [13,16], we integrate in (3.17)-(3.18) (taking into account (3.15)-(3.16)) overφ − k with the Gaussian measure density as the basic one.…”

“…As a result, non-classical critical exponents and analytical expressions for thermodynamic functions are obtained [6,9]. More recently this theory has been developed for a binary fluid mixture [12][13][14][15][16][17].…”

Phase diagram of the restricted primitive model: charge-ordering instability

“…Using the method of CVs, developed for a two-component continuous system [34,35] we can rewrite the grand partition function of the RPM in the following form:…”