# Regensburg 2002 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 52: Weiche Materie

### DY 52.3: Vortrag

### Freitag, 15. März 2002, 11:45–12:00, H2

**Critical behaviour of normal stresses at the gelation transition** — •Peter Müller^{1}, Kurt Broderix^{1,2}, and Annette Zippelius^{1} — ^{1}Institut für Theoretische Physik, Georg-August-Universität, D-37073 Göttingen — ^{2}Deceased

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.