Berlin 2005 – wissenschaftliches Programm
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CPP: Chemische Physik und Polymerphysik
CPP 8: SYMPOSIUM: Polymer networks and beyond: From molecular structure to materials and biological functions III
CPP 8.5: Vortrag
Samstag, 5. März 2005, 15:45–16:00, TU C243
Dielectric relaxation of gelling polymers — •Alice von der Heydt1, Henning Löwe1, Peter Müller2,1, and Annette Zippelius1 — 1Institut für Theoretische Physik, Universität Göttingen — 2Department of Mathematics, University of California, Irvine
Frequency-dependent dielectric relaxation of gelling polymers was investigated within Rouse dynamics for a macroscopic model network with random polar crosslinks of concentration c drawn from a bond percolation ensemble. Averaged over a crosslink-ensemble at concentration c and uncorrelated dipole orientations, the generic dielectric susceptibility χc(ω) is given in terms of the ensemble-averaged density of states Dc(γ) or the resolvent of the network’s connectivity matrix Γ. When the system approaches the 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