D C Vernon | PubMed Health

PubMed2003

Model for gelation with explicit solvent effects: structure and dynamics.

We study a two-component model for gelation consisting of f-functional monomers (the gel) and inert particles (the solvent). After equilibration as a simple liquid, the gel particles are gradually cross linked to each other until the desired number of cross links have been attained. At a critical cross-link density, the largest gel cluster percolates and an amorphous solid forms. This percolation process is different from ordinary lattice or continuum percolation of a single species in the sense that the critical exponents are new. As the cross-link density p approaches its critical value p(c), the shear viscosity diverges: eta(p) approximately (p(c)-p)(-s) with s a nonuniversal concentration-dependent exponent.

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PubMed1999

Entropic rigidity of randomly diluted two- and three-dimensional networks.

In recent work, we presented evidence that site-diluted triangular central-force networks, at finite temperatures, have a nonzero shear modulus for all concentrations of particles above the geometric percolation concentration p(c). This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles p(r)>p(c). In the present paper we report on analogous simulations of bond-diluted triangular lattices, site-diluted square lattices, and site-diluted simple-cubic lattices. We again find that these systems are rigid for all p>p(c) and that near p(c) the shear modulus mu approximately (p-p(c))(f), where the exponent f approximately 1.3 for two-dimensional lattices and f approximately 2 for the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class as the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion.

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