D.S. McLachlan, C. Chiteme, W.D. Heiss, and Jungie Wu

University of the Witwatersrand

PO WITS 2050

Johannesburg

South Africa

In the last 30-40 years the most widely used and
probably successful approach in the modeling of
experimental results for the dc and first order ac
conductivity (dielectric constant) results of good
conductor-bad conductor (Metal-Insulator) media,
near the second order Metal-Insulator Transition at
the critical volume fraction, has been percolation
theory. Recent experiments will be presented that
will show that the standard percolation equations
(which are actually power laws with an unspecified
constant) are unable to, in some cases not even
qualitatively, model the second order terms of the
complex ac conductivity of continuum percolation
composites. It will then is shown that a
phenomenological equation, which has the same
parameters as the percolation equations and reduces
to them in some ideal cases, can usually accurately
but always qualitatively, fit all the experimental
results (first and second order) as a function of
volume fraction and frequency. The second order
terms are the dielectric loss (conductivity) below
the critical volume fraction and a hump, as seen in
water-oil emulsions, in the real dielectric
constant, which often peaks beyond the critical
volume fraction. New results show that 1/f noise,
just above the critical volume fraction, is
characterized by two exponents, and not one as has
previously been observed. A qualitative model for
this behaviour in granular conductor--insulator
media is presented. This model helps explain the
difficulty in the exact modeling of the conductivity
results, just above the critical volume fraction,
near the percolation threshold in granular systems.