5.6 Semiflexible Nanofiller Networks with Bound Rubber …
101
φ ui + φ i = 1
(5.5)
Figure 5.14a presents two-phase parallel model showing G
at 293 K as a function
of φ ui and φ i . In the region of 40 phr CB loading, G
shows nearly a linear
relationship with each volume fraction, indicating that a parallel mechanical model
is applicable in this region. This result implies that the network structure formed in
the high CB loading region of 40 phr or more consisted of CB particles and a layer
of rubber molecular chains, i.e., a rubber layer on the outside of the glassy rubber
layer attached to the CB particle surface. Consequently, the mechanical properties
of the samples followed a parallel mechanical model. Because it is thought that a
stress occurs from a rubber matrix phase and CNIL, G
should be corrected by their
cross-sectional area except for the ingredients in Table 4.4 (see Sect. 4.3.2 of the
present book). It is postulated that as the volume fractions of CB, ZnO, stearic acid,
CBS, and S are very smaller than CB, they do not contribute to G
. Therefore, it
is thought that G
must be corrected by CB volume. The corrected storage moduli
(G
correct ) are expressed in Eq. (5.6):
G
correct = G
/(S NR /S NR + CB )
(5.6)
and
S NR /S NR + CB = (100/ρ NR )
2/3
/[(100/ρ NR ) + (100/ρ CB )]
2/3
(5.7)
where S is the cross-sectional area, and ρ is the density of each component.
Figure 5.14b is plotted the calculated values of G
correct , which approximately form
the straight line.
The value of G
correct at 80 phr CB was 142 MPa, which is approximately a
half of the observed one. The two may be regarded to be comparable, taking both
experimental and theoretical simplifications into account. In this connection, G
i =
140 MPa may be equivalent to the modulus of the second layer of the bound rubber
reported by Nakajima et al. [25]. They elucidated three bound rubber layers by AFM
(atomic force microscopy) and evaluated the moduli of them as 1 GPa (the first layer
contacting CB surface), 60 MPa (the second layer), and 8 MPa (the third layer).
In addition, we have also confirmed that the similar G
i value can be calculated by
another calculation method [49].
Anyway, our hypothesis of the semiflexible nanofiller network involving bound
rubber in rubber matrix is effective only semiquantitatively for a moment, and the
next target is the prediction of the mechanical property at fully quantitative level. For
this purpose, there is much more room for improvement or even for thinking of a
completely different rheological model based on our semiflexible nanofiller network
image.
101
φ ui + φ i = 1
(5.5)
Figure 5.14a presents two-phase parallel model showing G
at 293 K as a function
of φ ui and φ i . In the region of 40 phr CB loading, G
shows nearly a linear
relationship with each volume fraction, indicating that a parallel mechanical model
is applicable in this region. This result implies that the network structure formed in
the high CB loading region of 40 phr or more consisted of CB particles and a layer
of rubber molecular chains, i.e., a rubber layer on the outside of the glassy rubber
layer attached to the CB particle surface. Consequently, the mechanical properties
of the samples followed a parallel mechanical model. Because it is thought that a
stress occurs from a rubber matrix phase and CNIL, G
should be corrected by their
cross-sectional area except for the ingredients in Table 4.4 (see Sect. 4.3.2 of the
present book). It is postulated that as the volume fractions of CB, ZnO, stearic acid,
CBS, and S are very smaller than CB, they do not contribute to G
. Therefore, it
is thought that G
must be corrected by CB volume. The corrected storage moduli
(G
correct ) are expressed in Eq. (5.6):
G
correct = G
/(S NR /S NR + CB )
(5.6)
and
S NR /S NR + CB = (100/ρ NR )
2/3
/[(100/ρ NR ) + (100/ρ CB )]
2/3
(5.7)
where S is the cross-sectional area, and ρ is the density of each component.
Figure 5.14b is plotted the calculated values of G
correct , which approximately form
the straight line.
The value of G
correct at 80 phr CB was 142 MPa, which is approximately a
half of the observed one. The two may be regarded to be comparable, taking both
experimental and theoretical simplifications into account. In this connection, G
i =
140 MPa may be equivalent to the modulus of the second layer of the bound rubber
reported by Nakajima et al. [25]. They elucidated three bound rubber layers by AFM
(atomic force microscopy) and evaluated the moduli of them as 1 GPa (the first layer
contacting CB surface), 60 MPa (the second layer), and 8 MPa (the third layer).
In addition, we have also confirmed that the similar G
i value can be calculated by
another calculation method [49].
Anyway, our hypothesis of the semiflexible nanofiller network involving bound
rubber in rubber matrix is effective only semiquantitatively for a moment, and the
next target is the prediction of the mechanical property at fully quantitative level. For
this purpose, there is much more room for improvement or even for thinking of a
completely different rheological model based on our semiflexible nanofiller network
image.