Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Statistical physics II (general)

DY 7.3: Vortrag

Dienstag, 24. März 2009, 10:15–10:30, HÜL 386

Theory of anisotropic electric conductivity of random resistor network on a Bethe lattice — •Fyodor Semeriyanov, Marina Saphiannikova, and Gert Heinrich — Leibniz-Institut für Polymerforschung, Hohe Str. 6, 01069, Dresden, Germany

We propose a theory of anisotropic electric conductivity of composites filled by particles of anisometric shape. This theory is a generalization of the model of random resistor network proposed by Stinchcombe [1]. Using the Bethe lattice approach, we obtained an analytical solution and verified it by means of computer simulations. Namely, we performed a Monte Carlo simulation for the random resistor network on regular 2D and 3D lattice with resistors of orientation-dependent value and computed electrical conductivity in the parallel and the normal direction of applied voltage. The simulation time increased dramatically as the resistor concentration p approached the percolation threshold pc. The advantage of the analytical approach is that it allows to access this critical region by means of e-expansion, e=p-pc. We obtained the first term to be independent of direction, whereas the second was found to be anisotropic. These results are important in connection with experimental data for carbon-filled systems. Finally, we present a dynamic model for shear-induced effects based on a kinetic equation controlling resistor concentration.

This work was supported by the BMBF grant CarboNet No. 03X0504E.

[1] R.B. Stinchcombe, J. Phys. C 7, 179, 1974.