36
2 Filler and Rubber Reinforcement
2.6 Some More Remarks on Rubber Reinforcement
2.6.1 The Payne and the Mullins Effects
Before going to the main parts, Parts 2 and 3, several comments relevant to rubber
reinforcement are disclosed here. Firstly, two stress-softening effects reported on
rubber, i.e., the Payne and Mullins effects are to be differentiated [85, 137–140].
Because Mullins employed filler-loaded rubber samples, his effect was misunderstood: It was often assumed to be due to the presence of CB, or nanofillers in general.
But, the Mullins effect originates from the viscoelastic nature of rubber itself [141].
Accordingly, the effect is observed in wider samples including pure gum stocks [142]
than the Payne effect. For example, in the case of NR [143–145], stress softening
by SIC or template crystallization is observed (see Sect. 2.1 and Chap. 8) and also
observed in thermoplastic elastomer (TPE) [146].
Consequently, the Mullins effect has to be considered more general than the Payne
effect and more complex hysteresis phenomenon. It has to be studied separately from
rubber reinforcement by nanofillers. For this purpose, new approach may be needed
like, e.g., Urayama’s use of biaxial tensile mode [147].
2.6.2 Reinforcement Theory by Sato and Furukawa
A little separate from the discussions described in Sects. 2.4 and 2.5, Y. Sato and J.
Furukawa reported a theoretical interpretation of rubber reinforcement [148, 149].
(Ref. [147] is cited in Chaps. 1, 4, and 5 of Ref. [5], but Payne did not cite it in his
Chap. 3.) In Ref. [148], Sato declared that his aim of the study was to overcome a
dominant trend in rubber industry for developing theory on reinforcement:
Regrettably, the filler mixing technique in rubber industry tends to depend much on the past
experiences and on the accumulation of relevant data so far. Due to this tendency, many
engineers fail to have wide and far-sighted vision on rubber reinforcement, in particular. The
difficulty of extending rubber elasticity theory to the filled rubber seems to be originated
from the same reason.
In line with this objective, he worked with Prof. Furukawa and calculated the free
energy change associated with the deformation of anisotropic rubber–filler composites [148, 149]. After trying the applicability of a few non-Gaussian chain models,
they derived equations of free energy changes for the composite, referencing to the
Boggs’s mathematical treatment on an incompressible material [150]. The derivation was conducted for the perfect adsorption (perfect wetting) and for no adsorption
(no wetting at all) of rubber onto the filler surface. Here, the adsorption is possibly
corresponding to bound rubber formation. The adsorption parameter is 1.0 for the
perfect wetting and zero for no wetting. Zero means no bound rubber on the filler
surface at all, but actually, the value may be between zero and unity.
2 Filler and Rubber Reinforcement
2.6 Some More Remarks on Rubber Reinforcement
2.6.1 The Payne and the Mullins Effects
Before going to the main parts, Parts 2 and 3, several comments relevant to rubber
reinforcement are disclosed here. Firstly, two stress-softening effects reported on
rubber, i.e., the Payne and Mullins effects are to be differentiated [85, 137–140].
Because Mullins employed filler-loaded rubber samples, his effect was misunderstood: It was often assumed to be due to the presence of CB, or nanofillers in general.
But, the Mullins effect originates from the viscoelastic nature of rubber itself [141].
Accordingly, the effect is observed in wider samples including pure gum stocks [142]
than the Payne effect. For example, in the case of NR [143–145], stress softening
by SIC or template crystallization is observed (see Sect. 2.1 and Chap. 8) and also
observed in thermoplastic elastomer (TPE) [146].
Consequently, the Mullins effect has to be considered more general than the Payne
effect and more complex hysteresis phenomenon. It has to be studied separately from
rubber reinforcement by nanofillers. For this purpose, new approach may be needed
like, e.g., Urayama’s use of biaxial tensile mode [147].
2.6.2 Reinforcement Theory by Sato and Furukawa
A little separate from the discussions described in Sects. 2.4 and 2.5, Y. Sato and J.
Furukawa reported a theoretical interpretation of rubber reinforcement [148, 149].
(Ref. [147] is cited in Chaps. 1, 4, and 5 of Ref. [5], but Payne did not cite it in his
Chap. 3.) In Ref. [148], Sato declared that his aim of the study was to overcome a
dominant trend in rubber industry for developing theory on reinforcement:
Regrettably, the filler mixing technique in rubber industry tends to depend much on the past
experiences and on the accumulation of relevant data so far. Due to this tendency, many
engineers fail to have wide and far-sighted vision on rubber reinforcement, in particular. The
difficulty of extending rubber elasticity theory to the filled rubber seems to be originated
from the same reason.
In line with this objective, he worked with Prof. Furukawa and calculated the free
energy change associated with the deformation of anisotropic rubber–filler composites [148, 149]. After trying the applicability of a few non-Gaussian chain models,
they derived equations of free energy changes for the composite, referencing to the
Boggs’s mathematical treatment on an incompressible material [150]. The derivation was conducted for the perfect adsorption (perfect wetting) and for no adsorption
(no wetting at all) of rubber onto the filler surface. Here, the adsorption is possibly
corresponding to bound rubber formation. The adsorption parameter is 1.0 for the
perfect wetting and zero for no wetting. Zero means no bound rubber on the filler
surface at all, but actually, the value may be between zero and unity.