8.1 Low-Temperature Crystallization of NR
135
One of the most fundamental techniques of suggesting and determining crystal
structures is wide-angle X-ray diffraction (WAXD) method, and its fundamental base
is the Bragg condition,
2d sinθ = nλ
(8.1)
where d is the distance between the crystal lattices, θ is an angle of incident X-ray
to the lattice face, λ is the wavelength of X-ray (for CuK α ray, λ = 1.542 nm),
and n is the ordinal number of the reflection (zero or a positive integer). When the
reflections from lattice faces are in the same phase (the Bragg reflection), diffraction
is observed in accord with the Bragg condition, which allows us to determine the
internal lattice distance d. WAXD of amorphous materials displays isotropic ringshaped halo, which suggests the presence of amorphous fractions and their random
orientation. When not halo but clear ring is observed, crystallization is suggested,
but the orientation of the crystallites is random. For X-ray and neutron diffraction
and scattering in general, refer to a concise book [12].
In understanding the crystallization of polymers, degree of crystallization is one
of the key concepts [13, 14]. A polymer is apparently consisting of one long linear chain of high molar mass and exists in a randomized coil-like conformation not
only in solution but also in bulk. The random coil is stochastically and thermodynamically a natural state. Hence, it is geometrically entangled with each other in
bulk. The high molar mass and the randomized state are factors not favorable for
crystallization. In fact, the optimal degree of crystallization among the crystallizing polymers is between 20 and 70%, and the rest remains amorphous. In the specific case of polyethylene (PE), single crystal (an almost perfect crystal, i.e., nearly
100-% crystallinity) has been prepared, which is due to its simple chemical structure
–(CH 2 CH 2 )– and to the fact that its range of possible crystallization temperature
is wide, i.e., (T m −T g ) is approximately wider than 200 ˚C. Thus, crystallites are
generally coexisting with surrounding amorphous regions in polymers. Based on
this fact, a structural study on the coexisting ordered and disordered states is an
important subject in polymer science, which is often called polymer morphology.
Determination of degree of crystallization (the first step of the morphological study
of polymers) has been done by several methods. Among them, four popular ones
are from specific volume, X-ray diffraction, differential scanning calorimetric, and
infrared absorption measurements [14, 15]. It is highly advisable to use at least two
methods for determining the degree of crystallization, preferably including WAXD
measurement as one of them.
Generally speaking, some specific conditions are mandatory for a polymer to
attain a high degree of crystallization: In the preparation of PE single crystal, a dilute
solution of PE is kept under a very mild stirring for long to evaporate the solvent.
This example may suggest that amorphous might be a normal state of polymers
in general, since the macromolecularity (being of high molar mass [1]) is not a
favorable condition for crystallization. When rubber is chemically cross-linked, the
entanglements are trapped in network chains. Upon elongation, some of the trapped
entanglements are expected to function as a movable yet permanent cross-liking
135
One of the most fundamental techniques of suggesting and determining crystal
structures is wide-angle X-ray diffraction (WAXD) method, and its fundamental base
is the Bragg condition,
2d sinθ = nλ
(8.1)
where d is the distance between the crystal lattices, θ is an angle of incident X-ray
to the lattice face, λ is the wavelength of X-ray (for CuK α ray, λ = 1.542 nm),
and n is the ordinal number of the reflection (zero or a positive integer). When the
reflections from lattice faces are in the same phase (the Bragg reflection), diffraction
is observed in accord with the Bragg condition, which allows us to determine the
internal lattice distance d. WAXD of amorphous materials displays isotropic ringshaped halo, which suggests the presence of amorphous fractions and their random
orientation. When not halo but clear ring is observed, crystallization is suggested,
but the orientation of the crystallites is random. For X-ray and neutron diffraction
and scattering in general, refer to a concise book [12].
In understanding the crystallization of polymers, degree of crystallization is one
of the key concepts [13, 14]. A polymer is apparently consisting of one long linear chain of high molar mass and exists in a randomized coil-like conformation not
only in solution but also in bulk. The random coil is stochastically and thermodynamically a natural state. Hence, it is geometrically entangled with each other in
bulk. The high molar mass and the randomized state are factors not favorable for
crystallization. In fact, the optimal degree of crystallization among the crystallizing polymers is between 20 and 70%, and the rest remains amorphous. In the specific case of polyethylene (PE), single crystal (an almost perfect crystal, i.e., nearly
100-% crystallinity) has been prepared, which is due to its simple chemical structure
–(CH 2 CH 2 )– and to the fact that its range of possible crystallization temperature
is wide, i.e., (T m −T g ) is approximately wider than 200 ˚C. Thus, crystallites are
generally coexisting with surrounding amorphous regions in polymers. Based on
this fact, a structural study on the coexisting ordered and disordered states is an
important subject in polymer science, which is often called polymer morphology.
Determination of degree of crystallization (the first step of the morphological study
of polymers) has been done by several methods. Among them, four popular ones
are from specific volume, X-ray diffraction, differential scanning calorimetric, and
infrared absorption measurements [14, 15]. It is highly advisable to use at least two
methods for determining the degree of crystallization, preferably including WAXD
measurement as one of them.
Generally speaking, some specific conditions are mandatory for a polymer to
attain a high degree of crystallization: In the preparation of PE single crystal, a dilute
solution of PE is kept under a very mild stirring for long to evaporate the solvent.
This example may suggest that amorphous might be a normal state of polymers
in general, since the macromolecularity (being of high molar mass [1]) is not a
favorable condition for crystallization. When rubber is chemically cross-linked, the
entanglements are trapped in network chains. Upon elongation, some of the trapped
entanglements are expected to function as a movable yet permanent cross-liking