2001/07/31 by Kurt Broderix, Peter Müller, Annette Zippelius
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.soft #physics.chem-ph
paper · pdf · doi:10.1103/physreve.65.041505
published as Phys. Rev. E, vol. 65, 041505 (2002) · RevTeX4, 6 pages, 2 figures; changes: explanatory comments expanded
arxiv created 2001/11/08 · arxiv updated 2009/11/30
A simple Rouse-type model, generalised to incorporate the effects of chemical crosslinks, is used to obtain a theoretical prediction for the critical behaviour of the normal-stress coefficients Ψ1 and Ψ2 at the gelation transition. While the exact calculation shows Ψ2≡ 0, a typical result for these types of models, an additional scaling ansatz is used to demonstrate that Ψ1 diverges with a critical exponent ℓ = k+z. Here, k denotes the critical exponent of the shear viscosity and z the exponent governing the divergence of the time scale in the Kohlrausch decay of the shear-stress relaxation function. For crosslinks distributed according to mean-field percolation, this scaling relation yields ℓ =3, in a accordance with an exact expression for the first normal-stress coefficient based on a replica calculation. Alternatively, using three-dimensional percolation for the crosslink ensemble we find the value ℓ ≈ 4.9. Results on time-dependent normal-stress response are also presented.