PERCOLATIVE CONDUCTION IN-2-COMPONENT STRONGLY NONLINEAR COMPOSITES

The effective-medium approximation (EMA) is developed to study the bulk effective response of a class of strongly nonlinear conducting composite media which obey a current-field (J-E) relation of the form J=χE2βE, where χ is the nonlinear coefficient of the medium and β>0. First, a variational approach is invoked for solving the electrostatic boundary-value problem of a spherical inclusion embedded in a host medium. Explicit asymptotic behaviors of the field distribution are derived at both large and small ratios between the coefficients of the constituents. Second, in an attempt to extend the approximation to the vicinity of a percolation threshold, we formulate the EMA for a two-component strongly nonlinear composite from the asymptotic behaviors of the field distribution. Scaling forms of the effective response are extracted and compared to a general scaling theory and an excellent agreement is found. © 1995 The American Physical Society.