Analytic Scaling Functions Applicable to Dispersion Measurements
Abstract
Scaling functions,
F
+
(ω/
ω
+
c
)
and
F
−
(ω/
ω
−
c
)
for
ϕ>
ϕ
c
and
ϕ<
ϕ
c
, respectively, are derived from an equation for the complex conductivity of binary conductor-insulator composites. It is shown that the real and imaginary parts of
F
±
display most properties required for the percolation scaling functions. One difference is that, for
ω/
ω
c
<1
,
R
F
−
(ω/
ω
c
)
has an
ω
-dependence of
(1+t)/t
and not
ω
2
as previously predicted, but never conclusively observed. Experimental results on a Graphite-Boron Nitride system are given which are in reasonable agreement with the
ω
(1+t)/t
behaviour for
R
F
−
. Anomalies in the real dielectric constant just above
ϕ
c
are also discussed.