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.
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BibTeX
@misc{rege2026massconserving,
title = {{Mass-conserving growth percolation in polymer gelation}},
author = {Ameya Rege and Lorenz Ratke},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01044},
eprint = {2609.01044},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01044},
}
RIS
TY - UNPB
TI - Mass-conserving growth percolation in polymer gelation
AU - Ameya Rege
AU - Lorenz Ratke
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01044
UR - https://arxiv.org/abs/2609.01044
AB - 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.
ER -