J. Phys. France 51, 1415-1430 (1990)
DOI: 10.1051/jphys:0199000510130141500

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

Gary S. Grest et Michael Murat

Corporate Research Science Laboratories, Exxon Research and Engineering Company, Annandale, NJ 08801, U.S.A.

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.

PACS
8270G - Gels and sols.
0540 - Fluctuation phenomena, random processes, noise, and Brownian motion.
0550 - Lattice theory and statistics (Ising, Potts, etc.).

Key words
fractals -- gels -- membranes -- molecular dynamics method -- percolation