CRITICAL PHENOMENA AND RENORMALIZATION GROUP

The properties of condensable classical fluid systems near the critical region and in the intermediate region were considered. The extended renormalization group theory, capable of taking into account the effect of density fluctuations on the thermodynamic functions, developed by Dr. White, was applied to a type of pressure potential that consists of two terms: one due to the repulsive interactions and another one due to averaged attractive interactions. A set of recursion relations for incorporating effects of fluctuations were evaluated from the theory for the thermodynamic functions. The theory was applied to the Percus-Yevick pressure potential derived from the compressibility equation and the Carnahan-Starling equation for the pressure of a hard sphere gas. The mentioned potentials were considered with the addition of a mean field attraction term. The recursion relations for these two potentials were evaluated numerically for several isotherms. Theoretical coexistence curves derived from the numerical values of isothermal pressures and chemical potentials were compared with experimental data summarized in the paper by Guggenheim (1945). The theoretical isothermal pressure curves were compared to the experimental data of Pitzer (1955). Numerical values of exponents (beta) and (gamma) resulting from the theory were compared to Moldover's experimental data (1976). Numerical results in terms of the two different potentials used were almost the same except for small changes in the values of the parameters. The theoretical coexistence curve, isothermal pressure curves, and critical compressibility factor Z(,c) are consistent with the experimental data considered. The theoretical values of exponents (beta) and (gamma) agree with experimental values close to the critical point and vary consistently with experimental results when one gets away from the critical point.