Kinetic Gelation

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Binary aggregation usually leads to stable populations whose mean size increases indefinitely as aggregation advances, but under special conditions it is possible to observe a phase transition that produces a giant cluster of macroscopic size. In the polymer literature this is known as gelation and is observed experimentally in some polymer systems. Polymerization is perhaps a standard example of aggregation: starting with monomers, polymer molecules of linear or branched structure are formed by joining smaller units together, one pair at a time. The aggregation kernel in this case is determined by the functionality and reactivity of the chemical sites where polymers can join by forming bonds. A kernel that is known to lead to gelation is the product kernel, Ki,j=ij, The classical symptom of gelation is the breakdown of the Smoluchowski equation: within finite time the mean cluster size diverges and the Smoluchowski equation ceases to conserve mass. Gelation has the qualitative features of a phase transition and is often discussed qualitatively in the thermodynamic language of phase equilibrium.

Original languageEnglish (US)
Title of host publicationUnderstanding Complex Systems
PublisherSpringer Verlag
Pages289-323
Number of pages35
DOIs
StatePublished - Jan 1 2018

Publication series

NameUnderstanding Complex Systems
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840

All Science Journal Classification (ASJC) codes

  • Software
  • Computational Mechanics
  • Artificial Intelligence

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