General Concepts of Crystallization: Some Recent …
17
on such cases also on the degree of deviation of the liquid state from the respective metastable equilibrium state. The principal features how such dependence can
be incorporated into the theory have been described in [49–51]. However, its implementation as a regular tool into the theory of crystal nucleation and growth is very far
from a comprehensive realization. Accounting for the dependence of the relaxation
time on the structural order parameter, in [50, 51] a possible origin of stretched exponential relaxation was described. In addition, it is shown that particular relaxation
mechanisms distinguished already by Kauzmann [11] and recently reconfirmed to
be of particular significance for dielectric relaxation can be explained in such model
terms. Some more information and the discussion of some other topics related to
crystallization of oxide glasses can be found in monographs [5, 6] and reviews [40,
52]. A detailed theoretical analysis of the effects of interplay of deviations of the
liquid from metastable equilibrium and stress development and stress relaxation in
crystal nucleation is presently in preparation.
5 Polymer Crystallization: Some Specific Features
Above described spectrum of achievements and problems is of interest independently
on the particular system where crystallization is studied. Some specific problems of
polymer crystallization will be described below. Generally, also polymer crystallization can be subdivided in primary nucleation and growth, similar to the systems
described above. But due to the chain structure of the polymer molecules, particular situations exist for nucleation, growth, and for the crystalline morphologies
developing.
From a thermodynamic point of view, the equilibrium configuration of a polymer
chain in the crystalline state should be the extended chain. Commonly, this configuration is not realized for long-chain polymers because of entropic penalties. Polymer
crystals generally represent non-equilibrium states usually referred to as folded chain
crystals [53–56]. Only crystals containing fully stretched chains can be regarded as an
equilibrium thermodynamic state. The occurrence of non-equilibrium folded states
has its origin in the high internal conformational entropy of individual chains in
the melt. Sommer et al. [57] made an estimate for the time needed to create a fully
stretched chain made of 100 monomers by spontaneous fluctuations. The required
time of 10
58 s is obviously behind any practical relevance. As a consequence of chain
folding lamellar, plate-like crystals with thickness of the order of 10 nm and lateral
dimensions up to several ten µm are often formed. The lamellae are further arranged
in lamellae stacks where the crystals are separated by amorphous layers of a few nm
thickness and the stacks may form 100 µm sized spherulites.
Regarding the dielectric relaxation behavior, the lamellae stack morphology is
of particular interest. Lamellae stacks comprise crystalline lamellae and amorphous
layers in between [58]. The amorphous layer is often subdivided into a fraction
participating in the segmental relaxation (glass transition) and another fraction not
17
on such cases also on the degree of deviation of the liquid state from the respective metastable equilibrium state. The principal features how such dependence can
be incorporated into the theory have been described in [49–51]. However, its implementation as a regular tool into the theory of crystal nucleation and growth is very far
from a comprehensive realization. Accounting for the dependence of the relaxation
time on the structural order parameter, in [50, 51] a possible origin of stretched exponential relaxation was described. In addition, it is shown that particular relaxation
mechanisms distinguished already by Kauzmann [11] and recently reconfirmed to
be of particular significance for dielectric relaxation can be explained in such model
terms. Some more information and the discussion of some other topics related to
crystallization of oxide glasses can be found in monographs [5, 6] and reviews [40,
52]. A detailed theoretical analysis of the effects of interplay of deviations of the
liquid from metastable equilibrium and stress development and stress relaxation in
crystal nucleation is presently in preparation.
5 Polymer Crystallization: Some Specific Features
Above described spectrum of achievements and problems is of interest independently
on the particular system where crystallization is studied. Some specific problems of
polymer crystallization will be described below. Generally, also polymer crystallization can be subdivided in primary nucleation and growth, similar to the systems
described above. But due to the chain structure of the polymer molecules, particular situations exist for nucleation, growth, and for the crystalline morphologies
developing.
From a thermodynamic point of view, the equilibrium configuration of a polymer
chain in the crystalline state should be the extended chain. Commonly, this configuration is not realized for long-chain polymers because of entropic penalties. Polymer
crystals generally represent non-equilibrium states usually referred to as folded chain
crystals [53–56]. Only crystals containing fully stretched chains can be regarded as an
equilibrium thermodynamic state. The occurrence of non-equilibrium folded states
has its origin in the high internal conformational entropy of individual chains in
the melt. Sommer et al. [57] made an estimate for the time needed to create a fully
stretched chain made of 100 monomers by spontaneous fluctuations. The required
time of 10
58 s is obviously behind any practical relevance. As a consequence of chain
folding lamellar, plate-like crystals with thickness of the order of 10 nm and lateral
dimensions up to several ten µm are often formed. The lamellae are further arranged
in lamellae stacks where the crystals are separated by amorphous layers of a few nm
thickness and the stacks may form 100 µm sized spherulites.
Regarding the dielectric relaxation behavior, the lamellae stack morphology is
of particular interest. Lamellae stacks comprise crystalline lamellae and amorphous
layers in between [58]. The amorphous layer is often subdivided into a fraction
participating in the segmental relaxation (glass transition) and another fraction not