5.4 Toward Nanofiller Networking in Rubber Matrix …
89
cluster formation process of nanofiller particles in rubber matrix by physical interaction, followed by the cross-linking of the clusters to form the filler networks again
by the filler-to-filler interaction, basically in accordance with polymer gelation.
By applying the C* theorem by de Gennes to their system, f, f
+ , and f* are
defined as the filler concentration, the critical concentration of aggregate formation, and the gelation concentration of filler to form a network, respectively. Their
conclusions are as follows:
(1) At f
+ > f and at f* > f > f
+ , the reinforcement is due to the hydrodynamic
volume effect
(2) At f > f*, the reinforcement is due to the filler network formation.
These conclusions seem to be quite acceptable, except the introduction of the
hydrodynamic effect, here, without any comments (see Sect. 2.6.4).
Further, two more studies are referenced [33, 34]. Beaucage et al. reported another
theoretical treatment, which mainly applied the fractal theory to filler systems. However, it seemed to fail to cover the rubber processing including the filler mixing [33].
Gerspacher et al. published a paper entitled ‘Flocculation in Carbon Black-Filled
Rubber Compound’ [34]. They noted that the higher aggregate was decomposed to
primary CB aggregates at the mixing stage, but at the processing after the mixing step
flocculation occurred. In other words, the primary aggregates of CB again aggregated
to form a higher aggregate or even an agglomerate, which was named flocculation.
They mentioned CB networks at the reaggregation. Although they highlighted on
the role of bound rubber, the importance of bound rubber within the CB networks
(to be described next) was not recognized at all. It is suggested that all these papers
have seemed to come just near to the CB networks as an ultimate product of the CB
aggregation.
Under such a situation, a 3D-TEM study on nanofillers in rubber matrix, which is
the main topic of the present book, was started in 2000 by us. The first communication
was reported in 2004 [35], and a review paper was published in Progress in Polymer
Science in 2008 [36]. A concise treatment of the topics is given in a textbook of
rubber science, too [4]. On the working model of nanofiller dispersion in rubber,
the original one which we assumed at the beginning (see Fig. 2.6 in Chap. 2) has
been modified in accordance with the progress of our 3D-TEM study as described
in Chap. 4 [4, 35–56]. Our final schemata are shown in the four figures (Figs. 5.3,
5.4, 5.5 and 5.6). The schemata are to be explained as follows:
First, Fig. 5.3 is shown the bound rubber formation onto the surface of primary
aggregates of CB. The primary particle shown in Fig. 2.6 at the left is a perfect
sphere which Einstein assumed in his calculation of the viscosity (see Sect. 2.5.4).
In practice, the nanoparticle is aggregated at the time of its manufacturing by van
der Waals force (dispersion force by quantum mechanical notation, to result in fillerto-filler interaction) to form the primary aggregate (see Figs. 2.3 and 2.4). When
available CB (at the left of Fig. 5.3, which is a reproduction of Fig. 2.5) is mixed
with rubber (i.e., at the mixing stage of rubber processing in Fig. 2.1), it becomes
encircled by rubber layer due to physical adsorption and chemisorption (filler-torubber interaction) as shown at the middle of Fig. 5.3. How much is the contribution
89
cluster formation process of nanofiller particles in rubber matrix by physical interaction, followed by the cross-linking of the clusters to form the filler networks again
by the filler-to-filler interaction, basically in accordance with polymer gelation.
By applying the C* theorem by de Gennes to their system, f, f
+ , and f* are
defined as the filler concentration, the critical concentration of aggregate formation, and the gelation concentration of filler to form a network, respectively. Their
conclusions are as follows:
(1) At f
+ > f and at f* > f > f
+ , the reinforcement is due to the hydrodynamic
volume effect
(2) At f > f*, the reinforcement is due to the filler network formation.
These conclusions seem to be quite acceptable, except the introduction of the
hydrodynamic effect, here, without any comments (see Sect. 2.6.4).
Further, two more studies are referenced [33, 34]. Beaucage et al. reported another
theoretical treatment, which mainly applied the fractal theory to filler systems. However, it seemed to fail to cover the rubber processing including the filler mixing [33].
Gerspacher et al. published a paper entitled ‘Flocculation in Carbon Black-Filled
Rubber Compound’ [34]. They noted that the higher aggregate was decomposed to
primary CB aggregates at the mixing stage, but at the processing after the mixing step
flocculation occurred. In other words, the primary aggregates of CB again aggregated
to form a higher aggregate or even an agglomerate, which was named flocculation.
They mentioned CB networks at the reaggregation. Although they highlighted on
the role of bound rubber, the importance of bound rubber within the CB networks
(to be described next) was not recognized at all. It is suggested that all these papers
have seemed to come just near to the CB networks as an ultimate product of the CB
aggregation.
Under such a situation, a 3D-TEM study on nanofillers in rubber matrix, which is
the main topic of the present book, was started in 2000 by us. The first communication
was reported in 2004 [35], and a review paper was published in Progress in Polymer
Science in 2008 [36]. A concise treatment of the topics is given in a textbook of
rubber science, too [4]. On the working model of nanofiller dispersion in rubber,
the original one which we assumed at the beginning (see Fig. 2.6 in Chap. 2) has
been modified in accordance with the progress of our 3D-TEM study as described
in Chap. 4 [4, 35–56]. Our final schemata are shown in the four figures (Figs. 5.3,
5.4, 5.5 and 5.6). The schemata are to be explained as follows:
First, Fig. 5.3 is shown the bound rubber formation onto the surface of primary
aggregates of CB. The primary particle shown in Fig. 2.6 at the left is a perfect
sphere which Einstein assumed in his calculation of the viscosity (see Sect. 2.5.4).
In practice, the nanoparticle is aggregated at the time of its manufacturing by van
der Waals force (dispersion force by quantum mechanical notation, to result in fillerto-filler interaction) to form the primary aggregate (see Figs. 2.3 and 2.4). When
available CB (at the left of Fig. 5.3, which is a reproduction of Fig. 2.5) is mixed
with rubber (i.e., at the mixing stage of rubber processing in Fig. 2.1), it becomes
encircled by rubber layer due to physical adsorption and chemisorption (filler-torubber interaction) as shown at the middle of Fig. 5.3. How much is the contribution