Critical behavior of a three-dimensional kinetic gelation model.

Abstract

We present extensive results from a computer-simulation study of a kinetic growth model for radical-initiated irreversible gelation. Lattices as large as 100\ifmmode\times\else\texttimes\fi{}100\ifmmode\times\else\texttimes\fi{}100 were used to examine polymerization of a system of tetrafunctional and bifunctional monomers with initiator concentrations ${c}_{I}$, ranging from 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ to 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$. The cluster-size distribution shows unexpected oscillations which become increasingly pronounced as ${c}_{I}$\ensuremath{\rightarrow}0. The scaling properties of the cluster-size distribution cannot be described by simple droplet scaling theory, and we propose a generalized form for the scaling. The bulk properties show critical exponents which are independent of ${c}_{I}$ and identical to percolation values within the errors. The amplitude ratio ${C}^{\mathrm{\ensuremath{-}}}$/${C}^{+}$ is not independent of ${c}_{I}$. The backbone of the largest cluster at the gel transition is also investigated and its fractal dimension is found to be distinctly larger than that of a random percolation cluster at ${p}_{c}$.