Abstract
We report on extensive molecular dynamics (MD) simulations of a model for gels in both two and three dimensions. The model consists of randomly cross-linked monomers with a concentration p of cross-links above the percolation concentration so that the system is in the amorphous solid phase. As the concentration of cross-links approaches the percolation concentration, the entropic shear modulus vanishes as G approximately(p-p(c))(t) with t approximately 1.9 in three dimensions and t approximately 1.3 in two dimensions. These results hold whether or not the background fluid consisting of finite clusters is retained in the system. These results are also consistent with our previous calculations and with a conjecture of de Gennes but not with recent analytical results and another body of simulations.
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