A model for gelation with explicit solvent effects: Structure and dynamics

TL;DR

This paper introduces a two-component gelation model with explicit solvent effects, analyzing the percolation transition and divergence of shear viscosity as the gel forms, revealing new critical exponents.

Contribution

It presents a novel two-component gelation model incorporating solvent effects and characterizes the unique percolation transition with nonuniversal critical exponents.

Findings

Percolation occurs at a critical crosslink density p_c.

Shear viscosity diverges as p approaches p_c.

Critical exponents are nonuniversal and concentration-dependent.

Abstract

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 crosslinked to each other until the desired number of crosslinks has been attained. At a critical crosslink 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 crosslink density $p$ approaches its critical value $p_c$, the shear viscosity diverges: $\eta(p)\sim (p_c-p)^{-s}$ with $s$ a nonuniversal concentration-dependent exponent.