Critical Dynamics of Gelation

Kurt Broderix; Henning Loewe; Peter Mueller; Annette Zippelius

doi:10.1103/physreve.63.011510

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Critical Dynamics of Gelation

Kurt Broderix·Henning Loewe·Peter Mueller·Annette Zippelius

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Abstract

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=ϕ-β$ for the critical exponent of the shear viscosity. Here $β$ is the thermal exponent for the gel fraction and $ϕ$ 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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Kurt Broderix, Henning Loewe, Peter Mueller, Annette Zippelius. 2000-09-05. Critical Dynamics of Gelation. https://doi.org/10.1103/physreve.63.011510

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