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Gelation and critical phenomena

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Polymer Networks

Part of the book series: Advances in Polymer Science ((POLYMER,volume 44))

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.

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Author notes

  1. Dietrich Stauffer

    Present address: Institut für Theoretische Physik, Universität, D-5000, Köln 41, West Germany

Authors and Affiliations

  1. Departement de Physique des Systemes Desordonnes, Université de Provence, Centre St-Jerome, F-13397, Marseille Cedex 13, France

    Dietrich Stauffer

  2. Instituto di Fisica Teorica, Universita di Napoli, Mostra d'Oltremare, pad. 19, I-80125, Napoli, Italy

    Antonio Coniglio

  3. DPh-G/PSRM, CEN Saclay, B.P. No. 2, F-91190, Gif-sur-Yvette, France

    Mireille Adam

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  1. Dietrich Stauffer
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  2. Antonio Coniglio
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Karel Dušek

Additional information

Dedicated to Prof. Manfred Gordon on the occasion of his 65th birthday, who discussed critical phenomena at the gel point as early as in 1974, see Ref. 1.

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Stauffer, D., Coniglio, A., Adam, M. (1982). Gelation and critical phenomena. In: Dušek, K. (eds) Polymer Networks. Advances in Polymer Science, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11471-8_4

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