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

Fingerprint

Gelation
Agglomeration
Kinetics
Polymers
Phase transitions
Joining
Phase equilibria
Monomers
Polymerization
Thermodynamics
Molecules

All Science Journal Classification (ASJC) codes

  • Software
  • Computational Mechanics
  • Artificial Intelligence

Cite this

Matsoukas, T. (2018). Kinetic Gelation. In Understanding Complex Systems (pp. 289-323). (Understanding Complex Systems). Springer Verlag. https://doi.org/10.1007/978-3-030-04149-6_9
Matsoukas, Themis. / Kinetic Gelation. Understanding Complex Systems. Springer Verlag, 2018. pp. 289-323 (Understanding Complex Systems).
@inbook{5ad9d993f3bb45078dabb66b4f98889a,
title = "Kinetic Gelation",
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.",
author = "Themis Matsoukas",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/978-3-030-04149-6_9",
language = "English (US)",
series = "Understanding Complex Systems",
publisher = "Springer Verlag",
pages = "289--323",
booktitle = "Understanding Complex Systems",
address = "Germany",

}

Matsoukas, T 2018, Kinetic Gelation. in Understanding Complex Systems. Understanding Complex Systems, Springer Verlag, pp. 289-323. https://doi.org/10.1007/978-3-030-04149-6_9

Kinetic Gelation. / Matsoukas, Themis.

Understanding Complex Systems. Springer Verlag, 2018. p. 289-323 (Understanding Complex Systems).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Kinetic Gelation

AU - Matsoukas, Themis

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85065822537&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065822537&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04149-6_9

DO - 10.1007/978-3-030-04149-6_9

M3 - Chapter

AN - SCOPUS:85065822537

T3 - Understanding Complex Systems

SP - 289

EP - 323

BT - Understanding Complex Systems

PB - Springer Verlag

ER -

Matsoukas T. Kinetic Gelation. In Understanding Complex Systems. Springer Verlag. 2018. p. 289-323. (Understanding Complex Systems). https://doi.org/10.1007/978-3-030-04149-6_9