Mass-conserving growth percolation in polymer gelation

Abstract

Polymer gelation involves the emergence of a system-spanning network from growing polymer-rich domains, yet conventional percolation models typically prescribe particle size independently of material consumption. We formulate gelation as a locally mass-conserving growth-percolation process in which Voronoi capture zones define finite material reservoirs for individual nuclei. Local depletion determines the evolving supersaturation and limiting particle size, while particle contacts generate a dynamic network whose first spanning cluster defines the gel point. Three mechanisms, namely, interface-, diffusion-, and polymer-blob-controlled growth produce distinct gelation kinetics while sharing the same accessible final state. Spatial fluctuations in nucleation further generate a distribution of gelation times. The framework separates gelation from saturation and naturally captures post-gel aging as continued growth and topological maturation.