8.2 Template Crystallization: Dynamic Mechanism …
143
amorphous, oriented and longer network chains can crystallize onto the template.
This process is somewhat similar to the formation of shish kebab crystal, just
described in Sect. 8.2.1.
Including crystallization, all the physical and chemical processes are classified
into either of the two, (1) a stochastic process and (2) a deterministic process, as
follows:
(1) In the former, the various events that make up the process each occur with a
certain probability.
(2) In the latter, each succeeding event is absolutely predetermined by a certain
philosophical consideration.
Formation of nucleus is a stochastic process [36, 60], the first approximation of
which is a random process (zeroth order Markov chain). Depending on the crystallizing system, random, first-order, second-order, or a higher-order Markov may
be applicable to nucleation, yet definitely not described by the deterministic causal
relationship.
From the formal logic viewpoint, formation of a fully extended chain by stretching
of rubber vulcanizates is simply explained by the causal relationship. Namely, the
stretching is a cause and the extended chain (potential template) is its effect or
result, and they are related by the deterministic relation of cause and effect (the
causality in logic), particularly under the condition of the affine deformation. By the
way, the causal relationship was established in Greek by Aristotle (384–322 BCE),
well within a framework of the classical philosophy. In the formation of extended
network chains by stretching the NR vulcanizate, there is no room for probability of
the extended chain formation [11, 36, 60, 61], which is a definitive difference from
nucleation based on density fluctuation. Note that distribution of the network chains
in NR vulcanizates is not monodispersed, and network chains of various lengths are
present there. The present idea of template crystallization by the logical consideration
is the first proposal of the homogeneous crystallization not due to nucleation [39,
40], even though a few eminent crystallographers might have already suggested its
possibility, as mentioned already.
Figure 8.4 shows the changes of crystallization index (CI) and oriented amorphous
index (OAI) with stretching ratio (α) for NR vulcanizates of various network chain
densities based on the experimental results obtained at SPring-8, Hyogo in Japan
[62–73]. Here, CI is equivalent to crystal fraction, OAI is the oriented amorphous
fraction, and α = l/l 0 where l 0 is the initial length of the specimen and l is that of the
stretched. These results are the basis of considering SIC behavior of NR vulcanizates.
OAI began to increase upon stretching and continued to increase linearly with
elongation. The higher is the network chain density (averaged value) of the vulcanizates, the larger is the slope of OAI increase. The observed effects on OAI by
stretching the NR vulcanizates seem to be rational under the assumption of the affine
deformation. On the other hand, CI did not change at all at the initial stage of elongation. Approximately speaking, the crystallization started around α = 4 regardless
of the network chain density of the vulcanizate. This strain, where SIC starts, is
143
amorphous, oriented and longer network chains can crystallize onto the template.
This process is somewhat similar to the formation of shish kebab crystal, just
described in Sect. 8.2.1.
Including crystallization, all the physical and chemical processes are classified
into either of the two, (1) a stochastic process and (2) a deterministic process, as
follows:
(1) In the former, the various events that make up the process each occur with a
certain probability.
(2) In the latter, each succeeding event is absolutely predetermined by a certain
philosophical consideration.
Formation of nucleus is a stochastic process [36, 60], the first approximation of
which is a random process (zeroth order Markov chain). Depending on the crystallizing system, random, first-order, second-order, or a higher-order Markov may
be applicable to nucleation, yet definitely not described by the deterministic causal
relationship.
From the formal logic viewpoint, formation of a fully extended chain by stretching
of rubber vulcanizates is simply explained by the causal relationship. Namely, the
stretching is a cause and the extended chain (potential template) is its effect or
result, and they are related by the deterministic relation of cause and effect (the
causality in logic), particularly under the condition of the affine deformation. By the
way, the causal relationship was established in Greek by Aristotle (384–322 BCE),
well within a framework of the classical philosophy. In the formation of extended
network chains by stretching the NR vulcanizate, there is no room for probability of
the extended chain formation [11, 36, 60, 61], which is a definitive difference from
nucleation based on density fluctuation. Note that distribution of the network chains
in NR vulcanizates is not monodispersed, and network chains of various lengths are
present there. The present idea of template crystallization by the logical consideration
is the first proposal of the homogeneous crystallization not due to nucleation [39,
40], even though a few eminent crystallographers might have already suggested its
possibility, as mentioned already.
Figure 8.4 shows the changes of crystallization index (CI) and oriented amorphous
index (OAI) with stretching ratio (α) for NR vulcanizates of various network chain
densities based on the experimental results obtained at SPring-8, Hyogo in Japan
[62–73]. Here, CI is equivalent to crystal fraction, OAI is the oriented amorphous
fraction, and α = l/l 0 where l 0 is the initial length of the specimen and l is that of the
stretched. These results are the basis of considering SIC behavior of NR vulcanizates.
OAI began to increase upon stretching and continued to increase linearly with
elongation. The higher is the network chain density (averaged value) of the vulcanizates, the larger is the slope of OAI increase. The observed effects on OAI by
stretching the NR vulcanizates seem to be rational under the assumption of the affine
deformation. On the other hand, CI did not change at all at the initial stage of elongation. Approximately speaking, the crystallization started around α = 4 regardless
of the network chain density of the vulcanizate. This strain, where SIC starts, is