2003/03/31 by Peter Müller · 1 citation
Materials Science · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/36/42/002
published as J. Phys. A 36, 10443-10450 (2003) · 9 pages, slightly extended version, to appear in J. Phys. A
arxiv created 2003/08/28 · openalex publication_date 2003/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 σ and τ of the cluster-size distribution.