2.5 Reinforcing Factors of Particulate Nanofiller
31
94]. Perrin managed to visualize the Brownian movement in order to substantiate the
atomism, which led him to author the famous publications [95, 96]. Establishment of
the real presence of atom is therefore looked upon one of the Einstein’s achievements
as well as that of Perrin [87–89, 93, 97, 98].
As Einstein noted in his papers, Eq. (2.1) is derived based on two hypotheses: (1)
the surface of rigid sphere particle is fully wetted by the liquid and (2) no chemical
interactions between the surface and the liquid. The obtained equation suggests that
viscosity of the suspension depends only on volume fraction of the particle, not
on its size. Uniqueness of Einstein’s calculation is his use of statistical fluctuation
idea, which is said to have heralded P. Langevin’s fluctuating force (1908) and the
fluctuation–dissipation theorem by L. Onsager and R. Kubo.
Applicability of Eq. (2.1) is limited to the dilute concentration region (where
the rigid sphere particle is isolated, not interacting each other), and thus, trials to
expand the equation were repeated. Among them, most used has been the Guth–Gold
equation [99];
η = η 0
1 + 2.5 ϕ + 14.1 ϕ
2
(2.2)
On the coefficient of the quadratic term 14.1, it is very strange that how it
was obtained has not been much questioned. An interesting story was disclosed
by W. H. Stockmayer in Recollections of Eugene Guth printed in the book
[100] with his footnote,
The writer’s memory is not to be regarded as infallible as follows:
Full details of the derivation of this extension of Einstein’s result seem not to have been
published in a standard journal, possibly because of the political disruptions and personal
dangers attending the imminent invasion by Hitler’s troops. In later happier years in the
United States, the story was current that the authors had done the calculations on a tablecloth
during a long evening in a Vienna café and had forgotten to take them home. They allegedly
returned on a soberer morrow only to learn that the laundry had already obliterated everything.
(As a matter of fact, the details were given in Gold’s 1937 doctoral thesis in Vienna.)
Guth seemed to have conducted the calculation with O. Gold (his Ph.D. student at
University of Vienna) in the presence of R. Simha (his guest from the USA), and Gold
surely submitted his thesis in 1936 [101]. However, a few months later Guth fled to the
USA. He was a theoretical physicist, and with H. Mark, he had written the pioneering
paper on statistical theory of rubber elasticity [102]. They emphasized there that the
restoring force, being proportional to absolute temperature, was entropic in origin.
This paper enjoyed the most favorable evaluation among several early papers on
rubber elasticity [103].
To the same book [100], H. Mark also contributed his recollections of his earliest collaborations with Guth in the 1930s. In this short recollection, Mark wrote
that the discovery by I. R. Katz, namely, rubber upon stretching develops a certain
degree of crystallinity that disappears again upon relaxation [13], stimulated him to
collaborate with Guth on rubber elasticity. Then, the discovery of Katz was named
the ‘Katz effect.’ It is now called strain-induced crystallization or template crystallization of NR, as described in Chap. 8. Ten years later Guth, who remembered his
31
94]. Perrin managed to visualize the Brownian movement in order to substantiate the
atomism, which led him to author the famous publications [95, 96]. Establishment of
the real presence of atom is therefore looked upon one of the Einstein’s achievements
as well as that of Perrin [87–89, 93, 97, 98].
As Einstein noted in his papers, Eq. (2.1) is derived based on two hypotheses: (1)
the surface of rigid sphere particle is fully wetted by the liquid and (2) no chemical
interactions between the surface and the liquid. The obtained equation suggests that
viscosity of the suspension depends only on volume fraction of the particle, not
on its size. Uniqueness of Einstein’s calculation is his use of statistical fluctuation
idea, which is said to have heralded P. Langevin’s fluctuating force (1908) and the
fluctuation–dissipation theorem by L. Onsager and R. Kubo.
Applicability of Eq. (2.1) is limited to the dilute concentration region (where
the rigid sphere particle is isolated, not interacting each other), and thus, trials to
expand the equation were repeated. Among them, most used has been the Guth–Gold
equation [99];
η = η 0
1 + 2.5 ϕ + 14.1 ϕ
2
(2.2)
On the coefficient of the quadratic term 14.1, it is very strange that how it
was obtained has not been much questioned. An interesting story was disclosed
by W. H. Stockmayer in Recollections of Eugene Guth printed in the book
[100] with his footnote,
The writer’s memory is not to be regarded as infallible as follows:
Full details of the derivation of this extension of Einstein’s result seem not to have been
published in a standard journal, possibly because of the political disruptions and personal
dangers attending the imminent invasion by Hitler’s troops. In later happier years in the
United States, the story was current that the authors had done the calculations on a tablecloth
during a long evening in a Vienna café and had forgotten to take them home. They allegedly
returned on a soberer morrow only to learn that the laundry had already obliterated everything.
(As a matter of fact, the details were given in Gold’s 1937 doctoral thesis in Vienna.)
Guth seemed to have conducted the calculation with O. Gold (his Ph.D. student at
University of Vienna) in the presence of R. Simha (his guest from the USA), and Gold
surely submitted his thesis in 1936 [101]. However, a few months later Guth fled to the
USA. He was a theoretical physicist, and with H. Mark, he had written the pioneering
paper on statistical theory of rubber elasticity [102]. They emphasized there that the
restoring force, being proportional to absolute temperature, was entropic in origin.
This paper enjoyed the most favorable evaluation among several early papers on
rubber elasticity [103].
To the same book [100], H. Mark also contributed his recollections of his earliest collaborations with Guth in the 1930s. In this short recollection, Mark wrote
that the discovery by I. R. Katz, namely, rubber upon stretching develops a certain
degree of crystallinity that disappears again upon relaxation [13], stimulated him to
collaborate with Guth on rubber elasticity. Then, the discovery of Katz was named
the ‘Katz effect.’ It is now called strain-induced crystallization or template crystallization of NR, as described in Chap. 8. Ten years later Guth, who remembered his