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Carbon Nanotube Reinforced Composites: Metal and Ceramic ...

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Figure 6.3 Effective d.c. electrical conductivity (s DC) vs MWNT<br />

concentration for 3Y-TZP/MWNT nanocomposites.<br />

Reproduced with permission from [21]. Copyright Ó (2006)<br />

John Wiley & Sons, Inc.<br />

zirconia material near the percolation threshold, the charge carrier can be transported<br />

across the fillers by tunneling through insulating zirconia. This behavior can<br />

be described by the fluctuation induced tunneling model which takes into account<br />

tunneling through potential barriers of varying height due to local temperature<br />

fluctuations [23]:<br />

where<br />

s exp½ T1=ðT þ T0ÞŠ ð6:8Þ<br />

T1 ¼ wAe 2 =8pk ð6:9Þ<br />

T0 ¼ 2 T1=pcw ð6:10Þ<br />

c ¼ð2 mV0=h 2 Þ 1=2<br />

6.3 Percolation Concentrationj175<br />

ð6:11Þ<br />

e ¼ 4 V0=ew ð6:12Þ<br />

where m <strong>and</strong> e are electron mass <strong>and</strong> charge k the Boltzman constant, V0 the potential<br />

barrier height, w the internanotube distance (gap width), <strong>and</strong> A the area of the<br />

capacitance formed by the junction. At constant temperature, Equation 6.8 can be<br />

further simplified to [24]:<br />

ln s w: ð6:13Þ<br />

Assuming the nanotube dispersion in the insulating matrix is homogeneous, the<br />

composite conductivity at a given temperature can be described by the behavior of a<br />

single tunnel junction where the gap width is w p 1/3 [25]. Accordingly, the d.c.<br />

conductivity should follow the following rule [24]:<br />

ln s p 1=3 : ð6:14Þ

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