Statistical geometry of cavities in a metastable confined fluid.

The statistical geometry of cavities in a confined Lennard-Jones (LJ) fluid is investigated with the focus on metastable states in the vicinity of the stability limit of the liquidlike state. For a given configuration of molecules, a cavity is defined as a connected region where there is sufficient space to accommodate an additional molecule. By means of grand canonical Monte Carlo simulations, we generated a series of equilibrium stable and metastable states along the adsorption-desorption isotherm of the LJ fluid in a slit-shaped pore of ten molecular diameters in width. The geometrical parameters of the cavity distributions were studied by Voronoi-Delaunay tessellation. We show that the cavity size distribution in liquidlike states, characterized by different densities, can be approximated by a universal log-normal distribution function. The mean void volume increases as the chemical potential &mgr; and, correspondingly, the density decreases. The surface-to-volume relation for individual cavities fulfills the three-dimensional scaling S(cav)=gV(2/3)(cav) with the cavity shape factor g=8.32-9.55. The self-similarity of cavities is observed over six orders of magnitude of the cavity volumes. In the very vicinity of the stability limit, &mgr;-->&mgr;(sl), large cavities are formed. These large cavities are ramified with a fractal-like surface-to-volume relation, S(cav) approximately V(cav). Better statistics are needed to check if these ramified cavities are similar to fragments of a spanning percolation cluster. At the limit of stability, the cavity volume fluctuations are found to diverge as (<V(2)(cav)>-<V(cav)>(2)) approximately (&mgr;-&mgr;(sl))/kT with the exponent gamma(c) approximately 0.93. This exponent can be referred to as the cavity pseudocritical exponent, in analogy with the other pseudocritical exponents characterizing the divergence of thermodynamic quantities at the spinodal point.