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Percolation threshold for Bruggeman composites.

A V Goncharenko1, E F Venger

  • 1Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 41 Nauki avenue, 03028 Kyiv, Ukraine. avg@isp.kiev.ua

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
Summary

This study calculates the percolation threshold for Bruggeman composites with Beta-distribution-shaped spheroids. Results show thresholds vary based on spheroid orientation, ranging from 0 to 1 for aligned spheroids and 0 to 1/3 for random mixtures.

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Area of Science:

  • Materials Science
  • Statistical Physics
  • Complex Systems

Background:

  • Percolation theory is crucial for understanding material properties.
  • Bruggeman composites offer a model for heterogeneous materials.
  • Spheroidal microgeometries influence composite behavior.

Purpose of the Study:

  • To calculate the percolation threshold for two types of Bruggeman composites.
  • To investigate the impact of Beta distribution on spheroid shape.
  • To analyze how orientation affects percolation in these composites.

Main Methods:

  • Phenomenological approach for percolation threshold calculation.
  • Analytical derivation using Gauss hypergeometric functions.
  • Numerical calculations for varying Beta distribution parameters.

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Main Results:

  • For aligned spheroids, the percolation threshold matches that of identical spheroids with the most probable shape, ranging from 0 to 1.
  • For random mixtures, the percolation threshold is expressed via the Gauss hypergeometric function, ranging from 0 to 1/3.
  • Thresholds are dependent on the Beta distribution parameters.

Conclusions:

  • The orientation of spheroids significantly impacts the percolation threshold in Bruggeman composites.
  • Analytical and numerical methods provide a comprehensive understanding of these composite systems.
  • The Beta distribution offers a flexible model for spheroid shapes in percolation studies.