152
6 Micromechanical Models of PVA-Based Bionanocomposite Films
polymeric molecular chains can be absorbed by the hydrogen bonding or electrostatic forces, resulting in the formation of interphase layers in nanocomposites. As
such, these interphase layers behave like solid transitional material phases to restrict
the mobility of other molecular chains of matrices with a positive contribution to
the total volume of reinforcements [11, 14]. As a result, actual volume fractions
of fillers in composite theoretical models should be reconsidered by using effective
volume fraction instead. Wan and Chen [13] and other co-workers [11, 14] have
reported that when nanoparticles are fully embedded within polymer matrices, the
layers of absorbed polymeric chains in nanoparticles have a thickness xR g of the
polymer, in which the layer thickness is increased to x times of the radius of gyration
of polymer R g . The total volume fraction of nanoparticle is increased with the additional term of kxR g A T ρ p , which is defined by the effective volume fraction according
to Eqs. (6.10)–(6.13).
The parameters of PVA-based bionanocomposite films in Table 6.1 were used to
estimate effective volume fraction, and subsequently predicted results obtained from
Halpin–Tsai model and Mori–Tanaka model were determined in terms of effective
volume fraction of nanofillers, as illustrated in Figs. 6.1, 6.2 and 6.3. The predictions
on the basis of effective volume fraction of nanofillers appear to be in better agreement with experimental data, as opposed to those corresponding to nominal volume
fraction, which have also been confirmed by the previous findings [13, 14]. With
respect to PVA/Cloisite 30B clay bionanocomposite films at the low volume fraction
of 0.085 vol%, experimental data coincide more closely with predicted results based
on effective volume fraction and exfoliated clay structures, while better agreement
is manifested for those predicted in terms of effective volume fraction and intercalated clay structures at high volume fraction levels. Such a phenomenon suggests
that a majority of Cloisite 30B clays tend to be exfoliated at low volume fractions, as
confirmed by the AFM evaluation in Chap. 4, while intercalated clay structures are
manifested with increasing the volume fraction of Cloisite 30B clays. Consequently,
the predicted results cannot unanimously fit well with experimental data based on
effective volume fraction and intercalated clay structures.
According to above-mentioned results, the use of effective volume fraction can
lead to more accurate prediction to experimental data in comparison with nominal
volume fraction in PVA-based bionanocomposites. However, the layer thickness of
polymeric molecules absorbed on nanofiller surfaces (kx) is even in the same grades
of polymers with different molecular structures and polarities. As noted earlier in
Chap. 5, interphase features do not possess uniform layer thickness, and their dimensions and properties vary greatly when embedded with heterogeneous nanoparticles
by altering particle sizes/dimensions, as well as nanomechanical properties associated with particle/filler interactions. As a result, it is suggested that a new and simple
formula in Eq. (6.14) should be utilised to calculate nanofiller volume fraction from
both interphase volume and volume fraction, in which interphase volume fraction
∅ Interphase is estimated in two different systems, namely uniform particle monodispersion and particle polydispersion. Modelling parameters in Table 6.2 are substituted
into Eqs. (6.37) and (6.29), respectively, to estimate associated ∅ Interphase values in
6 Micromechanical Models of PVA-Based Bionanocomposite Films
polymeric molecular chains can be absorbed by the hydrogen bonding or electrostatic forces, resulting in the formation of interphase layers in nanocomposites. As
such, these interphase layers behave like solid transitional material phases to restrict
the mobility of other molecular chains of matrices with a positive contribution to
the total volume of reinforcements [11, 14]. As a result, actual volume fractions
of fillers in composite theoretical models should be reconsidered by using effective
volume fraction instead. Wan and Chen [13] and other co-workers [11, 14] have
reported that when nanoparticles are fully embedded within polymer matrices, the
layers of absorbed polymeric chains in nanoparticles have a thickness xR g of the
polymer, in which the layer thickness is increased to x times of the radius of gyration
of polymer R g . The total volume fraction of nanoparticle is increased with the additional term of kxR g A T ρ p , which is defined by the effective volume fraction according
to Eqs. (6.10)–(6.13).
The parameters of PVA-based bionanocomposite films in Table 6.1 were used to
estimate effective volume fraction, and subsequently predicted results obtained from
Halpin–Tsai model and Mori–Tanaka model were determined in terms of effective
volume fraction of nanofillers, as illustrated in Figs. 6.1, 6.2 and 6.3. The predictions
on the basis of effective volume fraction of nanofillers appear to be in better agreement with experimental data, as opposed to those corresponding to nominal volume
fraction, which have also been confirmed by the previous findings [13, 14]. With
respect to PVA/Cloisite 30B clay bionanocomposite films at the low volume fraction
of 0.085 vol%, experimental data coincide more closely with predicted results based
on effective volume fraction and exfoliated clay structures, while better agreement
is manifested for those predicted in terms of effective volume fraction and intercalated clay structures at high volume fraction levels. Such a phenomenon suggests
that a majority of Cloisite 30B clays tend to be exfoliated at low volume fractions, as
confirmed by the AFM evaluation in Chap. 4, while intercalated clay structures are
manifested with increasing the volume fraction of Cloisite 30B clays. Consequently,
the predicted results cannot unanimously fit well with experimental data based on
effective volume fraction and intercalated clay structures.
According to above-mentioned results, the use of effective volume fraction can
lead to more accurate prediction to experimental data in comparison with nominal
volume fraction in PVA-based bionanocomposites. However, the layer thickness of
polymeric molecules absorbed on nanofiller surfaces (kx) is even in the same grades
of polymers with different molecular structures and polarities. As noted earlier in
Chap. 5, interphase features do not possess uniform layer thickness, and their dimensions and properties vary greatly when embedded with heterogeneous nanoparticles
by altering particle sizes/dimensions, as well as nanomechanical properties associated with particle/filler interactions. As a result, it is suggested that a new and simple
formula in Eq. (6.14) should be utilised to calculate nanofiller volume fraction from
both interphase volume and volume fraction, in which interphase volume fraction
∅ Interphase is estimated in two different systems, namely uniform particle monodispersion and particle polydispersion. Modelling parameters in Table 6.2 are substituted
into Eqs. (6.37) and (6.29), respectively, to estimate associated ∅ Interphase values in