Carbon Nanotube Reinforced Composites: Metal and Ceramic ...
Carbon Nanotube Reinforced Composites: Metal and Ceramic ...
Carbon Nanotube Reinforced Composites: Metal and Ceramic ...
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172j 6 Physical Properties of <strong>Carbon</strong> <strong>Nanotube</strong>–<strong>Ceramic</strong> Nanocomposites<br />
Table 6.1 Effect of sintering temperature on the electrical<br />
conductivity of Al2O3/CNT nanocomposites.<br />
Materials SPS conditions<br />
temperature (1500 C) destroys the structural integrity of CNTs. Consequently, the<br />
electrical conductivity of these nanocomposites is rather low (Table 6.1).<br />
6.3<br />
Percolation Concentration<br />
Percolation theory is commonly used to describe <strong>and</strong> analyze the behavior of connected<br />
clusters in a r<strong>and</strong>om structure, in order to predict whether a system is<br />
macroscopically connected or not. This macroscopic connectivity is of primarily<br />
importance to many physical phenomena such as fluid flow, electric current flow,<br />
heat flux, diffusion, <strong>and</strong> so on [4, 5]. Broadbent <strong>and</strong> Hammersley introduced lattice<br />
models for the flow of fluid particles through a r<strong>and</strong>om medium. They reported that<br />
the fluid would not flow if the concentration of active medium is smaller than a<br />
threshold value or percolation probability [12]. For the resistor network medium, the<br />
flow of electrons across resistors is analogous to the spread of fluid particles in a<br />
r<strong>and</strong>om medium. Kirkpatrick extended this concept into a r<strong>and</strong>om resistor network<br />
consisting of conducting <strong>and</strong> nonconducting materials [13, 14]. The corresponding<br />
expression for d.c. electrical conductivity (s) is given by:<br />
s /ðP PcÞ t<br />
ð6:1Þ<br />
where P <strong>and</strong> Pc are the occupied probability <strong>and</strong> percolation probability of the lattice,<br />
<strong>and</strong> t is the conductivity exponent.<br />
In continuum percolation theory, the s <strong>and</strong> dielectric constant (e) of the composite<br />
containing conducting fillers generally follow the power law relation [15, 16]:<br />
s /ðp pcÞ t<br />
s /ðpc pÞ s<br />
e /jp pcj s 0<br />
Relative<br />
density (%)<br />
Electrical<br />
conductivity<br />
(S m 1 )<br />
Al 2O 3 Ref [11] 1150 C, 3 min 100 10 12<br />
Al2O3/5.7vol% SWNT Ref [11] 1150 C, 3 min 100 1050<br />
Al 2O 3/10 vol% SWNT Ref [11] 1200 C, 3 min 99 1510<br />
Al2O3/15 vol% SWNT Ref [11] 1150 C, 3 min 99 3345<br />
Al 2O 3 Ref [5.71] 1500 C, 10 min 98.6 10 10 –10 12<br />
Al2O3/0.9vol% MWNT [Chap. 5, Ref. 71] 1500 C, 10 min 99.2 1.3 · 10 3<br />
Al 2O 3/1.9vol% MWNT [Chap. 5, Ref. 71] 1500 C, 10 min 98.9 1.3<br />
Al2O3/3.7vol% MWNT [Chap. 5, Ref. 71] 1500 C, 10 min 97.7 65.3<br />
for p>pc ð6:2Þ<br />
for p>pc ð6:3Þ<br />
for p < pc; p>pc ð6:4Þ