Gelation and critical phenomena View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2005-03-13

AUTHORS

Dietrich Stauffer , Antonio Coniglio , Mireille Adam

ABSTRACT

For the critical exponents near the sol-gel phase transition, classical theories like those of Flory and Stockmayer predict one set of exponents, whereas scaling theories based on lattice percolation predict different exponents. The two groups of theories differ in their treatment of intramolecular loops, space dimensionality and excluded volume effects. In this article, the differences and similarities between the results of the competing theories are reviewed. For example, a gel fraction like (p-pc)β vanishes for conversion factors p very close to the gel point pc, the weight average molecular weight diverges as (pc-p)−γ for p very slightly below pc, and the radius of macromolecules at the gel point p=pc varies as the ϱ-th power of the number of monomers in that macromolecule. Classical theories predict β=γ=1 and ϱ=1/4 whereas the percolation theory gives β ≃ 0.45, γ ≃ 1.74 and ϱ ≃ 0.40. We also generalize the percolation concept to include interaction effects and concentration fluctuations; in this case the sol-gel phase transition may be connected with a phase separation. Some experimental results are reviewed to check whether the percolation theory agrees with reality; no clear answer has been found so far, due to experimental difficulties. For instance, for the viscosity a power law (pc − p)−0.8, which agrees with one of the percolation ideas has been established in several experiments; the shear modulus of the gel vanishes roughly as (p − pc)3 in some experiments, which agrees better with the classical theory. More... »

PAGES

103-158

References to SciGraph publications

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  • Book

    TITLE

    Polymer Networks

    ISBN

    978-3-540-11471-0

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/3-540-11471-8_4

    DOI

    http://dx.doi.org/10.1007/3-540-11471-8_4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1025371885


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