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Novel Theoretical Self‐Consistent Mean‐Field Approach to Describe the Conductivity of Carbon Fiber Filled Thermoplastics—PART I—Theory
Author(s) -
Schubert Dirk W.
Publication year - 2018
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201700104
Subject(s) - volume fraction , materials science , percolation (cognitive psychology) , fiber , composite number , percolation theory , composite material , electrical resistivity and conductivity , exponent , percolation threshold , conductivity , mean field theory , nonlinear system , statistical physics , mathematical analysis , thermodynamics , mathematics , physics , condensed matter physics , linguistics , philosophy , quantum mechanics , neuroscience , biology
A novel theoretical approach is shown which yields a nonlinear differential equation for the resistivity of carbon fiber filled composites below the percolation threshold as a function of the volume fraction of the filler and the fiber orientation. The solution of the equation is given analytically and a particular value for the exponent predicted. The theoretical concept can be transferred to other composite properties.