Critical behaviour of the Rouse model for gelling polymers

Details Critical behaviour of the Rouse model for gelling polymers Critical behaviour of the Rouse model for gelling polymers

2003-03-11

arxiv.org/abs/cond-mat/0303205v2

J. Phys. A 36, 10443-10450 (2003)

Physics

Condensed Matter

Statistical Mechanics

9 pages, slightly extended version, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/36/42/002

It is shown that the traditionally accepted "Rouse values" for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are related to the return probability of a "blind ant"-random walk on the critical percolating cluster. The resulting scaling relations express the critical exponents of the shear-stress-relaxation function, and hence those of the shear viscosity and of the first normal stress coefficient, in terms of the spectral dimension $d_{s}$ of the critical percolating cluster and the exponents $\sigma$ and $\tau$ of the cluster-size distribution.

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