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

2014 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 03A6 = 03BB3/03BB03 where 03BB3 is the largest eigenvalue of the interia matrix at equilibrium and 03BB03 is its value when the membrane is perfectly flat. We find that 03A6 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 twodimensional membranes. J. Phys. France 51 (1990) 1415-1430 1 er JUILLET 1990,