Critical Dynamics of Gelation

Details Critical Dynamics of Gelation Critical Dynamics of Gelation

2000-07-06

arxiv.org/abs/cond-mat/0007088v2

Phys. Rev. E, vol. 63, 011510 (2001)

Physics

Condensed Matter

Statistical Mechanics

34 pages, 2 figures (revtex, amssymb); revised version (minor changes)

Scientific paper

10.1103/PhysRevE.63.011510

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation $ k=\phi-\beta$ for the critical exponent of the shear viscosity. Here $\beta$ is the thermal exponent for the gel fraction and $\phi$ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.

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