2.5 Reinforcing Factors of Particulate Nanofiller
33
It is needless to say that this compliment has to be equally shared with Smallwood
on the ‘isomorphism.’ However, the Guth–Gold, Eq. (2.2), and two Guth equations,
Eqs. (2.4) and (2.5), have had questions since his disclosure, and the problem seems
to remain unsolved still now. This problem will be detailed later in 2.6.4.
Anyway Einstein (not directly), Smallwood and Guth (both directly), have contributed to establishing the hydrodynamic volume effect in rubber reinforcement
from the theoretical arena. Experimental study on this reinforcement effect was first
appeared in 1947 [125] and was followed by quite a number of reports up to now.
The majority of the experimental results of CB or silica reinforcement have not been,
however, explained by hydrodynamic volumes calculated by Eqs. (2.3), (2.4), and
(2.5). Generally, the modulus or stress values were much smaller than the observed
ones. By using the modified Guth equation, Eq. (2.5), some experimental results
were reported to be explained, but even in these cases, the shape factor (the aspect
ratio) f was too big a value for the filler. Figure 2.6 by Payne clearly suggests that
the hydrodynamic volume effect is at the base, not much covering the main part of
reinforcement effect. Payne also wrote [85]:
… the hydrodynamic effect, well-known to be dependent on the shape factor, f, of the filler
particles or agglomerates…
Therefore, the failure of the three equations mentioned above is reasonably estimated
due to the structuring of nanofillers. Namely, very large shape factors are assumed
to be those of the aggregates or agglomerates.
Payne explained the second factor ‘Strong links’ as follows [85]:
A second factor for which evidence is given suggesting that it arises from a few strong likages
which are known to link filler to the matrix.
Payne might think of F. Bueche’s Fig. 1.20 in Chap. 1 of Ref. [5], which was originally
appeared in Ref. [81]. Some of the ‘bound rubber’ supporters interpret this statement
as the direct influence of bound rubber on reinforcement effect via chemical bonding between filler and rubber matrix [82, 83]. Those two factors, hydrodynamic and
bound rubber effects, constitute G ∞ value as shown in Fig. 2.6. Since the value is
constant, they may be of use for explaining static properties, e.g., tensile mechanical behaviors. However, Payne needed the third effect, structuring of nanofiller, for
explaining the strain dependence of dynamic modulus, i.e., the Payne effect.
Next subsection and Parts 2 and 3 of the present book have started from this point
and are describing the structuring of nanofiller and the relationship between the bound
rubber and the structuring. The two factors are apparently in confrontation, but they
would be unified in a manner that preserves them (‘aufheben’ per German philosopher
Georg Wilhelm Friedrich Hegel [126]) finally into a semi-flexible nanofiller network.
2.5.5 Structure Formation of Nanofiller: Filler Networks
Though Fig. 2.6 is a qualitative expression in nature, it still suggests that Payne
has assumed the structuring of filler being the most influential factor to the Payne
effect. However, to draw the image of structuring of filler was not possible then.
33
It is needless to say that this compliment has to be equally shared with Smallwood
on the ‘isomorphism.’ However, the Guth–Gold, Eq. (2.2), and two Guth equations,
Eqs. (2.4) and (2.5), have had questions since his disclosure, and the problem seems
to remain unsolved still now. This problem will be detailed later in 2.6.4.
Anyway Einstein (not directly), Smallwood and Guth (both directly), have contributed to establishing the hydrodynamic volume effect in rubber reinforcement
from the theoretical arena. Experimental study on this reinforcement effect was first
appeared in 1947 [125] and was followed by quite a number of reports up to now.
The majority of the experimental results of CB or silica reinforcement have not been,
however, explained by hydrodynamic volumes calculated by Eqs. (2.3), (2.4), and
(2.5). Generally, the modulus or stress values were much smaller than the observed
ones. By using the modified Guth equation, Eq. (2.5), some experimental results
were reported to be explained, but even in these cases, the shape factor (the aspect
ratio) f was too big a value for the filler. Figure 2.6 by Payne clearly suggests that
the hydrodynamic volume effect is at the base, not much covering the main part of
reinforcement effect. Payne also wrote [85]:
… the hydrodynamic effect, well-known to be dependent on the shape factor, f, of the filler
particles or agglomerates…
Therefore, the failure of the three equations mentioned above is reasonably estimated
due to the structuring of nanofillers. Namely, very large shape factors are assumed
to be those of the aggregates or agglomerates.
Payne explained the second factor ‘Strong links’ as follows [85]:
A second factor for which evidence is given suggesting that it arises from a few strong likages
which are known to link filler to the matrix.
Payne might think of F. Bueche’s Fig. 1.20 in Chap. 1 of Ref. [5], which was originally
appeared in Ref. [81]. Some of the ‘bound rubber’ supporters interpret this statement
as the direct influence of bound rubber on reinforcement effect via chemical bonding between filler and rubber matrix [82, 83]. Those two factors, hydrodynamic and
bound rubber effects, constitute G ∞ value as shown in Fig. 2.6. Since the value is
constant, they may be of use for explaining static properties, e.g., tensile mechanical behaviors. However, Payne needed the third effect, structuring of nanofiller, for
explaining the strain dependence of dynamic modulus, i.e., the Payne effect.
Next subsection and Parts 2 and 3 of the present book have started from this point
and are describing the structuring of nanofiller and the relationship between the bound
rubber and the structuring. The two factors are apparently in confrontation, but they
would be unified in a manner that preserves them (‘aufheben’ per German philosopher
Georg Wilhelm Friedrich Hegel [126]) finally into a semi-flexible nanofiller network.
2.5.5 Structure Formation of Nanofiller: Filler Networks
Though Fig. 2.6 is a qualitative expression in nature, it still suggests that Payne
has assumed the structuring of filler being the most influential factor to the Payne
effect. However, to draw the image of structuring of filler was not possible then.