Molecular dynamics simulations of the structure of gelation/percolation clusters and random tethered membranes

Abstract

We study the equilibrium structure of isolated (diluted) three dimensional percolation clusters and site-diluted tethered membranes using a molecular dynamics simulation. We find that the percolation clusters swell upon dilution and the fractal dimension changes from 2.5 to about 2, in agreement with recent Flory-type theories and neutron scattering experiments on gelation clusters. The equilibrium configuration of the site-diluted membranes is found to be rough on small length scales but flat asymptotically. We measure the ratio Φ = λ3/λ03 where λ 3 is the largest eigenvalue of the interia matrix at equilibrium and λ 03 is its value when the membrane is perfectly flat. We find that Φ decreases linearly with decreasing p, the fraction of sites present in the membrane. The membranes are shown to have anisotropic scattering functions. Only when p → p+ c, where pc is the percolation threshold, do the membranes become isotropic, indicating that random site-dilution is not sufficient to produce a crumpling of two-dimensional membranes