Phase Transitions in Fluid State of Systems of Purely Repulsive Potentials

ABSTRACT

Phase behaviors in fluid state of systems of purely repulsive potentials (PRPs) are investigated with a recently proposed 3rd-order thermodynamic perturbation theory (TPT) (Phys. Rev. E. 2006, 74, 031119). It is found that a usual gas-liquid transition (GLT) always happen to several investigate PRPs, whose perturbation part as a function of particle separation holds a discontinuous point, or an indifferentiable point, or is differentiable, but with an additional length scale besides the hard sphere diameter. Other findings to include that 1: a longer range of the repulsive perturbation tail, or a bigger jump of the repulsive perturbation tail at an interrupted point, can stabilize the GLT more easily; 2: all of the GLTs resulting from the investigated PRPs is accompanied with a density anomaly, in contrast to the traditional GLTs due to a hard core plus an attractive tail. Finally, contrary to the previous findings in literature due to conventional 1st-order TPT, and 2nd-order TPT based on a macroscopic compressibility approximation (MCA), the present investigation does not discover for a square shoulder (SS) potential in any periodic phase behavior of critical temperature as a function of the repulsive step radius and high density liquid-low density liquid transition (HDL-LDL). A convergence analysis of the 3rd-order TPT indicates that the previously found SS potential phenomenology (Phys. Rev. E. 2003, 67, 010201(R); Phys. Rev. E. 2006, 74, 041201), should be an artifact originating from the insufficiency of the employed 1st-order TPT and 2nd-order MCA-TPT. The counter examples are found to a liquid-liquid transition hypothesis (Nature, 1992, 360, 324) of the density anomaly.