Two Simple Approaches to Sol-Gel Transition

Details Two Simple Approaches to Sol-Gel Transition Two Simple Approaches to Sol-Gel Transition

2000-08-10

arxiv.org/abs/cond-mat/0008161v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, LaTeX

Scientific paper

We represent a theory of polymer gelation as an analogue of liquid-glass transition in which elastic fields of stress and strain shear components appear spontaneously as a consequence of the cross-linking of macromolecules. This circumstance is explained on the basis of obvious combinatoric arguments as well as a synergetic Lorenz system, where the strain acts as an order parameter, a conjugate field is reduced to the elastic stress, and the number of cross-links is a control parameter. Both the combinatoric and synergetic approaches show that an anomalous slow dependence of the shear modulus on the number of cross-links is obtained.

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