Percolation threshold parameters of fluids

Extensive Monte Carlo simulations on three qualitatively different model supercritical fluids (square-well fluid, Lennard-Jonesium, and primitive water) have been performed to examine percolation threshold parameters for continuum (correlated) models and their relation to general results valid for random lattice models; random-site percolation simple-cubic lattice has therefore been considered as well. Two different bond criteria, the configurational and self-bound ones, defining a cluster have been used. In addition to the percolation threshold occupation probability $p_c$ and the percolation threshold fluid density ${\rho }_c$, the correlation length exponent $\nu$ and the wrapping probability at the percolation threshold $R_{w,c}$ have also been evaluated. It is found that parameters $\nu$ and $R_{w,c}$ exhibit not only strong temperature dependence but also, unlike the case of lattice systems, dependence on the nature of the system considered and the employed definition of the cluster.

Figure 1

The wrapping probability $R_w$ as a function of probability $p$ for a given site to be occupied in a simple-cubic lattice of linear dimension $L$ (the upper graph) and as a function of density for the Lennard-Jones fluids and Hill clusters at temperature $T=1.6$ and different number of particles $N$ (lower graph). The thick solid line represents the probability $R_w$ in the limit $L\to \infty$.

Figure 2

The same as Fig. 1 for $R_w$ as a function of the scaling variable. The solid line corresponds to the fit by Eq. (7)

Figure 3

The standard error of the mean of the probability $R_w$ for the simple-cubic lattice with $L=32$ for which $n=8\times {10}^5$ configurations was generated and investigated for the presence of the wrapping cluster. The full circles are simulation results and the solid line represents results obtained using Eq. (6).

Figure 4

An example of two configurational clusters (overlap of disks defines the bond) in a continuous 2D system. Filled disks represent a three particle, not percolating cluster. Disks connected by lines represent a wrapping cluster.