Biomedical Engineering Reference
In-Depth Information
mechanical and transport properties of composites (Surve
et al
. 2006b). The affect of
a percolating network on the mechanical properties depends on a number of variables,
primarily the size (and aspect ratio) of the particles making the dispersed phase (Garboczi
et al
. 1995; Surve
et al
. 2006b), the interaction energy between particles relative to the
matrix (and relative to
k
T) (Prasad
et al
. 2003), and the volume fraction (Surve
et al
.
2006a).
The high reinforcing effect of CNXL-reinforced nanocomposites has been well
predicted by applying the percolation concept to the classical phenomenological
series-parallel model of Takayanagi
et al
. (1964). In this model, all the interactions,
including matrix-matrix, matrix-filler and filler-filler interactions, that hold the perco-
lating CNXLs network are considered. The use of this model to CNXLs-containing
composites and details of the calculation are reported by Favier
et al
. (1997). In this
approach, the elastic tensile modulus E
c
of the composite is given by the following
equation:
−
v
R
)ψE
2
(
1
−
2
ψ
+
ψv
R
)E
S
E
R
+
(
1
R
E
c
=
(
1
−
v
R
)E
R
+
(v
R
−
ψ)E
S
where the subscripts S and R refer to the soft and rigid phase, respectively, i.e. polymeric
matrix and filler.
ψ
and E
R
correspond to the volume fraction and modulus of the stiff
percolating network, respectively.
ψ
can be written as:
ψ
=
0
for V
R
<
V
Rc
V
R
V
R
b
−
V
Rc
ψ
=
for V
R
≥
V
Rc
−
1
V
Rc
where v
R
and v
Rc
correspond to the volume fraction of the filler and the critical volume
fraction at the percolation threshold, respectively and
b
is the corresponding critical
exponent which is 0.4 in a three-dimensional network.
The model assumes the formation of an infinite network of cellulose whiskers and
this gives rise to unexpectedly large composite stiffness.
The effect of surface chemistry can also be important. For example, as the size of the
filler becomes similar to that of the polymer molecule in the matrix, polymer bridging can
occur. These bridges, depending upon the attractive forces between matrix and filler, can
have a dramatic effect on the ability of the percolating structure to withstand imposed
stresses (Surve
et al
. 2006b; Surve
et al
. 2006a). This effect is especially apparent
in the rubbery phase of the polymer matrix where the modulus can rise by orders of
magnitude at filler volumes less than 10% (Azizi Samir
et al
. 2004b). However, these
large effects have generally only been reported in very soft polymer matrices (Azizi Samir
et al
. 2004b). The percolation effect is thus dependent upon the interaction between
matrix and filler, and can therefore be modified by altering the surface chemistry of the
nanoparticles (Zhang and Archer 2002).
Due to the hydrophilic character of CNXLs, the simplest polymer systems to incor-
porate CNXLs are water-borne systems. In this case films can be formed via solution
casting, i.e. simply allowing the water to evaporate. However, these systems suffer
from limited utility and are only appropriate for niche markets where susceptibility to
moisture is not an issue.
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