Biomedical Engineering Reference
In-Depth Information
with silica (Cho et al., 2011, de Andrade et al., 2008, Guo et al., 2007a, Ning
et al., 2003a, 2004), borosilicate (Boccaccini et al., 2007), aluminoborosi-
licate (Mukhopadhyay et al., 2010), barium aluminosilicate (Ye et al., 2006)
and mullite (Wang et al., 2007) matrices. Improvements in inorganic matrix
CNT composite toughness are usually attributed to conventional fiber
mechanisms, such as crack deflection, CNT bridging and CNT pull-out, as
characteristic features are often observed by fractography (Figs 7.4 and 7.6).
However, scaling considerations, discussed in a recent study (Cho et al.,
2011), highlight the lower absolute performance expected for nanofibers
compared to microfibers, if only these conventional mechanisms operate. It
may, therefore, be most useful to consider the possibility of enabling
fundamentally new toughening mechanisms such as shear banding of hollow
nanostructures or pull-out of flexible SWNTs over convoluted contour
lengths.
7.6.3 Functional properties
The incorporation of CNTs in glass/glass-ceramic matrices also influences
their functional properties, including both electrical and thermal conductiv-
ities. For completeness, a brief account of these properties is given below.
Electrical conductivity
The incorporation of CNTs in glass/glass-ceramic matrices tremendously
increases the electrical conductivity of otherwise insulating glasses and glass-
ceramics (Fig. 7.15). At very low CNT contents, electrical conductivity is
not increased significantly (Gavalas et al., 2001) but the formation of a
conducting percolating network of CNTs rapidly increases electrical
conductivity by several orders of magnitude following the scaling law
according to percolation theory (Kovacs et al., 2007):
t
s
c
¼ s
CNT
ðf f
c
Þ
½
7
:
4
where
σ
c
and
σ
CNT
are the conductivities of composites and CNTs,
respectively,
Φ
c
is the
critical volume fraction (percolation threshold) and the exponent t is the
dimensionality of the system. Most of the systems in Fig. 7.15 had a
percolation threshold between 1wt% and 3wt% and dimensionality
constant between 1 and 3 (Cho, 2010, Mukhopadhyay et al., 2011,
Thomas et al., 2009, Xiang et al., 2007). These values of percolation
threshold are consistent with the excluded volume theory for high aspect
ratio particles (i.e. CNTs of typical aspect ratio of 100-1000). Low
percolating thresholds represent agglomeration of CNTs (de Andrade
Φ
is the volume fraction of CNTs in composites,
