Elementary cuspoid catastrophes as the models of phenomenological equations of state

Abstract

The suggested earlier approach based on the equation of state expressed as the equilibrium surface of cuspoid catastrophes has been expanded and developed. The family of equations of state with arbitrary critical point degeneracy has been obtained. In other words, the order of a partial derivative of pressure with respect to volume at the critical point has become an arbitrary assigned variable. This, in turn, has led to more realistic, as compared to the classic case, behaviour of fluid in the immediate vicinity of the critical point. The critical exponents became functions of the degree of critical point degeneracy. By suitable selection of the degree of degeneracy it is possible to obtain the preset values of critical exponents. A simple nonanalytic equation of state has been obtained. This equation allows us to describe some non-classical phenomena in the vicinity of critical point liquid-gas without using scaling. The same equation holds in the ideal gas area without using crossover. One more implication arising from the suggested approach is a singularity in the equations of state – endpoint of gas-liquid equilibrium at low pressures.