Statistical Thermodynamics of an “Open” Hard Sphere System on the Equilibrium Fluid Isotherm: Study of Properties of the Freezing Transition Without Direct Involvement of the Equilibrium Solid Phase

Abstract

Using several theoretical tools $$\ldots $$ (i) the nucleation theorem, (ii) an equivalent cavity, (iii) the reversible work of adding a cavity to an open hard sphere system, and (iv) the theory of “stability”... the authors estimated the density at which the hard sphere freezing transition occurs. No direct involvement of the equilibrium solid phase is involved. The reduced density $$\uppi a^3\rho _f/6$$ (where a is the hard sphere diameter and $$\rho _f $$ is the actual density at which freezing occurs) is found to be 0.4937 while the value obtained by computer simulation is 0.494. The agreement is good, but the new method still contains some approximation. However, the approximation is based on the idea that at a density just below $$\rho _f $$ the fluid adopts a distorted structure resembling the solid, but different enough so that long-range order vanishes. Initial loss of stability may not be involved in every fluid–solid transition, but it may be an early step in the hard sphere and related systems.