Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.73: Poster
Donnerstag, 30. März 2006, 16:00–18:00, P1
Relaxation dynamics of gelling polymers — •Alice von der Heydt1, Henning Löwe2, Peter Müller1,3, and Annette Zippelius1 — 1Institut f. Theoretische Physik, Universität Göttingen, Germany — 2Eidgen. Institut f. Schnee- und Lawinenforschung SLF, Davos, Switzerland — 3Fakultät f. Mathematik, Universität Bielefeld, Germany
Frequency-dependent dielectric relaxation of a gelling macromolecular liquid was investigated within Rouse dynamics for a macroscopic model network with quenched disorder: random permanent polar crosslinks of concentration c were drawn from a bond percolation ensemble. Disorder-averages with respect to the ensemble of crosslinks and uncorrelated dipole orientations yield the generic dielectric susceptibility χc(ω) in terms of the ensemble-averaged density of eigenvalues Dc(γ) or the resolvent of the network’s connectivity matrix Γ. When approaching the c-driven sol-gel transition at the critical concentration ccrit, the growing impact of small relaxation rates is clearly visible in χc(ω): A crossover in the low-frequency domain from asymptotic Debye behavior at small c to e.g. a cusp for Re χc(ω) at ω=0 and criticality can be deduced from the known scaling of Dc(γ). For a mean field ensemble, the critical change in the exponents is confirmed by an approach which does not assume scaling. In this case the frequency dependence can be obtained via the resolvent of Γ by numerically solving an exact integral equation which arises in the replica formulation of the disorder average [1].
[1] K. Broderix, T. Aspelmeier, A. K. Hartmann and A. Zippelius, Phys. Rev. E 64 (2001), 021404