Regensburg 2002 – wissenschaftliches Programm
DY 52.3: Vortrag
Freitag, 15. März 2002, 11:45–12:00, H2
Critical behaviour of normal stresses at the gelation transition — •Peter Müller1, Kurt Broderix1,2, and Annette Zippelius1 — 1Institut für Theoretische Physik, Georg-August-Universität, D-37073 Göttingen — 2Deceased
A simple Rouse-type model with randomly distributed harmonic crosslinks is employed to derive a theoretical prediction for the critical behaviour of normal stress coefficients in a gelling polymeric liquid. While the second normal stress coefficient is found to vanish exactly regardless of the statistical ensemble from which crosslinks are drawn—a typical result for these types of models—an additional scaling ansatz establishes the scaling relation ℓ = k+z for the critical exponent ℓ of the first normal stress coefficient. 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. Choosing three-dimensional bond percolation for the crosslink ensemble, this scaling relation yields the value ℓ ≈ 4.9. Alternatively, with the classical mean-field distribution of crosslinks one finds the value ℓ =3, in a accordance with an exact expression for the first normal-stress coefficient based on a replica calculation.