38
2 Filler and Rubber Reinforcement
In this citation, ‘the fused carbon chains forming the persistent structure’ is meaning the primary aggregate of high structure carbon blacks such as ISAF and HAF.
Their primary aggregates are not decomposed even by the mechanical mixing, while
the higher aggregates of them might be disaggregated depending on the mechanical
mixing conditions. A paper claimed free radical formation by the decomposition of
CB aggregates, which induced further aggregation [159]. However, this claim was
negated because the radical formation was at very high CB loading (150 phr) only
[160]. Namely, at the end of the rubber mixing stages, the clustering of CB (and
nanofiller in general) may fundamentally be assumed to be at the primary aggregate level. The presence of bound rubber is not considered above. More detailed
discussions are given later in 5.4.
It is noteworthy, however, that the rubber mixing is not the finishing step of
processing. At the vulcanization step, the rubber compound is maintained at a high
temperature (maybe higher than 130 °C and below 220 °C) for minimal a few min at
220 °C or up to 30 min at 130 °C. During the vulcanization, both decomposition and
clustering are possible, and the resultant aggregation states might be different from
those at the end of mixing. The aggregation state of nanofillers in the vulcanizates is
focused in Part 2.
2.6.4 Reconsideration of Hydrodynamic Volume Effect
At 2.5.4, hydrodynamic volume effect is historically introduced. More modern considerations are presented in this subsection. Firstly, the index of the third term in
the Guth–Gold equation, Eq. (2.2), is to be checked. Stockmayer already suggested
that the numerical value 14.1 was bigger than expected [100]. Assuming f = 0.1,
the second term gives 0.25, and the third term 0.141, which means the two are of
comparable magnitude. It is not ordinary if the higher-order term is larger than the
lower one. Not larger, but being comparable had induced a doubt. In spite of this
concern, use of the Guth equation has been popular among rubber researchers and
engineers.
For example, Y. Fukahori et al. proposed an extension of the Guth equation as
follows [161]:
G = G 0 (1 + 2.5 ϕ eff + 14.1 ϕ
2
eff + 0.20
√
S
3 ϕ
3
eff )
(2.6)
where S stands for surface area by the BET (Brunauer–Emmett–Teller) method. They
assumed that the third term was related to bound rubber. However, the bound rubber
is the result of filler-to-rubber interactions and within the assumption of wetting of
the filler by rubber. Guth’s understanding might be the effect of bound rubber being
included in the second term. If the third term is expressing the three-body interactions
among the particles, it may be corresponding to the effect of occluded rubber (see
2.4.2 and 2.5.3 for the occluded rubber). However, this effect may better be evaluated
2 Filler and Rubber Reinforcement
In this citation, ‘the fused carbon chains forming the persistent structure’ is meaning the primary aggregate of high structure carbon blacks such as ISAF and HAF.
Their primary aggregates are not decomposed even by the mechanical mixing, while
the higher aggregates of them might be disaggregated depending on the mechanical
mixing conditions. A paper claimed free radical formation by the decomposition of
CB aggregates, which induced further aggregation [159]. However, this claim was
negated because the radical formation was at very high CB loading (150 phr) only
[160]. Namely, at the end of the rubber mixing stages, the clustering of CB (and
nanofiller in general) may fundamentally be assumed to be at the primary aggregate level. The presence of bound rubber is not considered above. More detailed
discussions are given later in 5.4.
It is noteworthy, however, that the rubber mixing is not the finishing step of
processing. At the vulcanization step, the rubber compound is maintained at a high
temperature (maybe higher than 130 °C and below 220 °C) for minimal a few min at
220 °C or up to 30 min at 130 °C. During the vulcanization, both decomposition and
clustering are possible, and the resultant aggregation states might be different from
those at the end of mixing. The aggregation state of nanofillers in the vulcanizates is
focused in Part 2.
2.6.4 Reconsideration of Hydrodynamic Volume Effect
At 2.5.4, hydrodynamic volume effect is historically introduced. More modern considerations are presented in this subsection. Firstly, the index of the third term in
the Guth–Gold equation, Eq. (2.2), is to be checked. Stockmayer already suggested
that the numerical value 14.1 was bigger than expected [100]. Assuming f = 0.1,
the second term gives 0.25, and the third term 0.141, which means the two are of
comparable magnitude. It is not ordinary if the higher-order term is larger than the
lower one. Not larger, but being comparable had induced a doubt. In spite of this
concern, use of the Guth equation has been popular among rubber researchers and
engineers.
For example, Y. Fukahori et al. proposed an extension of the Guth equation as
follows [161]:
G = G 0 (1 + 2.5 ϕ eff + 14.1 ϕ
2
eff + 0.20
√
S
3 ϕ
3
eff )
(2.6)
where S stands for surface area by the BET (Brunauer–Emmett–Teller) method. They
assumed that the third term was related to bound rubber. However, the bound rubber
is the result of filler-to-rubber interactions and within the assumption of wetting of
the filler by rubber. Guth’s understanding might be the effect of bound rubber being
included in the second term. If the third term is expressing the three-body interactions
among the particles, it may be corresponding to the effect of occluded rubber (see
2.4.2 and 2.5.3 for the occluded rubber). However, this effect may better be evaluated