15 research outputs found
Anomalous stress relaxation in random macromolecular networks
Within the framework of a simple Rouse-type model we present exact analytical
results for dynamical critical behaviour on the sol side of the gelation
transition. The stress-relaxation function is shown to exhibit a
stretched-exponential long-time decay. The divergence of the static shear
viscosity is governed by the critical exponent , where is
the (first) crossover exponent of random resistor networks, and is the
critical exponent for the gel fraction. We also derive new results on the
behaviour of normal stress coefficients.Comment: 13 pages, 6 figures; contribution to the proceedings of the Minerva
International Workshop on Frontiers In The Physics Of Complex Systems (25-28
March 2001) - to appear in a special issue of Physica
Critical Dynamics of Gelation
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 for the critical exponent of the shear
viscosity. Here is the thermal exponent for the gel fraction and
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.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor
changes