Carbon Nanotube Reinforced Composites: Metal and Ceramic ...

where p is volume fraction of the filler and pc the percolation threshold. The critical
exponents s, s 0 and t are assumed to be universal. The conductivity exponent t reflects
the dimensionality of the system with values about 1.3 and 2.0 for two and three
dimensional random percolation system, respectively [17]. However, the experimental
conductivity exponent t value can deviate from the universal value as a result of
electron tunneling from conducting fillers above the percolation threshold [18].
According to the literature, the measured percolation threshold in CNT–ceramic
composites is very low, typically in the range of 0.64–4.7 vol%, depending on the type
of ceramic matrix and processing technology employed [19, 20].
In terms of a.c. properties, the experimental conductivity and dielectric constant
display a pronounced frequency-dependent behavior. The frequency dependence of
effective conductivity and dielectric constant of a conductor-insulator composite near
the percolation threshold can be described by the following universal power law
relation [16]:
s / u x
e / u y
6.3 Percolation Concentrationj173
ð6:5Þ
ð6:6Þ
where u is frequency. The critical exponents x and y must satisfy the following
relation:
x þ y ¼ 1: ð6:7Þ
Peigney and coworkers investigated the percolation behavior of in situ MgAl2O3/
CNT nanocomposites having 0.2–25 vol% CNT [19]. The nanocomposites were
prepared by catalytic chemical vapor deposition followed by hot pressing at 1300 C.
Figure 6.2(a) and (b) shows the variation of electrical conductivity with CNT content
for the MgAl2O3/CNTnanocomposites. The inset in Figure 6.2(a) represents a log-log
plot of the conductivity as a function of p-pc. From least-square analysis, a linear fit can
be obtained according to Equation 6.2, yielding an exponent t ¼ 1.73 0.02. and
percolation threshold p c ¼ 0.64 0.02 vol% (about 0.31 wt%). At the percolation
threshold, the electrical conductivity increases over seven orders of magnitude from
10 8 to 0.4 S m 1 . Comparing with the ultralow value of pc (0.0025 wt%) for MWNT/
epoxy nanocomposites [7], the percolation threshold is two orders of magnitude
higher for the MgAl2O3/CNT nanocomposites. This is attributed to the degradation
of CNTs during hot-pressing at 1300 C.
Very recently, Ahmad et al. studied the electrical conductivity and dielectric
behavior of Al2O3/MWNT nanocomposites prepared by SPS at 1350 C [20]. A
percolation threshold of 0.79 vol% was found for such nanocomposites. Further,
the dielectric constant can reach as high as 5000 in the low frequency region by
adding 1.74 vol% MWNT. Shi and Liang [21] also investigated the percolation and
dielectric behavior 3Y-TZP (3 mol% yttria-stabilized tetragonal polycrystalline zirconia)
filled with various MWNT contents. The 3Y-TZP/MWNT nanocomposites were
fabricated by ball milling constituent materials followed by SPS at 1250 C under a
pressure of 60 MPa. Figure 6.3 shows the effective d.c. conductivity vs CNT concentration
for the 3Y-TZP/MWNT nanocomposites. Using the least square fit, the