Chemistry Reference
In-Depth Information
of the crystalline stems during the rapid solid-state transformation from the mesophases to the crystal
forms. As a result, over long distances, on molecular scale, and short times, the stems are kinetically
constrained to be close to the lateral position that is maintained as they grew in the mesophase. At the
same time, the local packing now favors the more stable crystal phase with a higher lateral density.
The constraints on the chain ends favoring the lateral density of the mesophases, and forces
competition with the density of the thermodynamically favored crystal structures. This causes the
crystal to break up into domains. Sirota then suggests that the granular structures observed in many
polymer crystals are fingerprints of the transitions from the transient intermediates from which the
crystals have formed [
49
].
It was reported recently, that polymeric can also form quasicrystals. Hayashida et al. [
50
]
demonstrated that certain blends of polyisoprene, polystyrene, and poly(2-vinylpyridine) form star-
shaped copolymers that assemble into
quasicrystals
. By probing the samples with transmission
electron microscopy and X-ray diffraction methods, they conclude that the films are composed of
periodic patterns of triangles and squares that exhibit 12-fold symmetry. These are signs of quasi-
crystalline ordering. Such ordering differ from conventional crystals lack of periodic structures yet
are well-ordered, as indicated by the sharp diffraction patterns they generate. Quasi-crystals also
differ from ordinary crystals in another fundamental way. They exhibit rotational symmetries (often
five or tenfold). There are still some basic questions about their structure.
2.3.3.1 Thermodynamics of Crystallization
The free energy change of a polymer from liquid to crystal is
DF ¼ DH TDS
At the melting point
T
m
the crystals and the liquid polymer are at equilibrium. The change in free
energy, therefore,
DF ¼
0. That means that at the melting point:
T
m
¼ DH=DS
If the heat of fusion is large, then the melting temperature of the polymer crystals will be high (due
to high intermolecular attraction) or if the entropy of fusion is small.
Mendelkern [
42
] noted that there are three different interfacial free energies that are characteristic
of crystallites. One,
s
e
, is for the equilibrium extended chain crystallite, a second one
s
ec
represents
the mature, but non-equilibrium crystallite, and the third one is
s
en
is the interfacial free energy
involved in forming a nucleus. These quantities cannot be identified with one another. Because only
portions of the polymeric chains participate in the formations of crystallites, the section or sections of
the chains of
x
length that participate in crystallite formation can be designated as
z
e
0
and the sections
of the chains that remain in disorder and amorphous, as
x z
e
0
.
The dependence of the melting temperature of such a system upon chain length is [
42
]:
0
1
=T
m
1
=T
m
¼ðR=DH
u
Þf½ð
1
=xÞþð
1
=x z
e
0
þ
1
Þg
where,
z
e
is the equilibrium crystalline length. The
effective interfacial free energy associated with the basal plane of an equilibrium crystalline length
z
e
00
designated as
s
e
is [
42
]:
DH
u
is the enthalpy of fusion per repeat unit and
2
s
e
¼ RT
me
f½z
e
=ðx z
e
þ
1
Þ þ
ln
½ðx z
e
þ
1
Þxg
