146
6 Micromechanical Models of PVA-Based Bionanocomposite Films
In a PVA-based bionanocomposite system, V p represents the nominal volume
fraction of nanofillers (∅ p-nominal ). As such, Eq. (6.28) can be rewritten as:
∅ Interphase =
1 − ∅ p-nominal
1 − exp
−
6∅ p-nominal
D 3
eq
e
t + d
t
3
+ g
t
3
(6.29)
e
=
D
2
eq
S
1 − ∅ p-nominal
(6.30)
d
=
2
D eq
1 − ∅ p-nominal
+
3∅ p-nominal
D
2
eq
2
S 2
1 − ∅ p-nominal
2
D 3
eq
(6.31)
g
=
4
3
1 − ∅ p-nominal
+
4∅ p-nominal D eq
D
2
eq
S
1 − ∅ p-nominal
2
D 3
eq
+
4m∅ p-nominal
D
2
eq
3
3S 3
1 − ∅ p-nominal
3
D 3
eq
2
(6.32)
S =
(1 + 1.5α)
2/3
1 + α
(6.33)
In a typical nanocomposite system, nanoparticles can be dispersed uniformly with
relatively similar sizes, which are known as monodispersed nanoparticles [23]. On
the contrary, when nanoparticles with different sizes and diameters are dispersed
randomly, they are called polydispersed nanoparticles [23].
In case of a monodispersed particle system, the parameters e
, d
and g
are
expressed as:
e
=
D
2
eq
S
1 − ∅ p-nominal
(6.34)
d
=
2D eq
1 − ∅ p-nominal
+
2 +
3∅ p-nominal
S 2
1 − ∅ p-nominal
(6.35)
g
=
4
3(1 − ∅ p-nominal )
+
1
3
+
∅ p-nominal
S
1 − ∅ p-nominal
+
m∅
2
p-nominal
3S 3
1 − ∅ p-nominal
2
(6.36)
By substituting Eqs. (6.34)–(6.36) into Eq. (6.29), and then letting λ =
t
D eq
where
λ and t
are the geometric size factor of anisotropic particles and the interfacial
dimension, respectively, one can obtain