Chemistry Reference
In-Depth Information
where,
N
(
t
) is the nucleation frequency per untransformed volume,
V
(
t
,
t
) is the corresponding
volume of the growing center, and
r
l
represent the densities of crystalline and liquid phases.
Based on that, the rate constant for crystallization kinetics can be described [
42
]:
r
c
and
=w
c
Þkt
n
ln
½ðV
1
V
t
Þ=ðV
1
V
0
Þ ¼ ð
1
where,
V
1
,
V
t
, and
V
0
are specific volumes at the times shown by the subscripts, and
w
c
is the weight
fraction of the polymer crystallized.
is the rate constant for crystallization It was found, however,
that crystallization continues in polymeric materials for much longer periods of time than the Avrami
equation predicts.
For all homopolymers the rate of crystal growth increases linearly with time, or
k
G ¼
d
r
/d
t
.
Mandelkern defines the steady-state nucleation rate,
N
as follows [
42
]:
ðE
D
T=RT DG
=RTÞ
N ¼ N
0
exp
where
E
D
is the energy of activation for transporting the chain segments across the crystal-liquid
interface.
If the crystallization takes place over an extended temperature range, most if not all homopolymers
display a maxima in rates of spherulitic growth and in the overall crystallization. The equation for
spherulitic growth is written as follows [
42
]:
0
exp
ðU
=ðT T
1
Þ
0
G ¼ G
exp
ðKT
m
=T
c
DG
u
TÞ
where
T
1
is the temperature at which all molecular and segmental motion stops.
2.4 The Mesomorphic State, Liquid Crystal Polymers
The state of mesomorphism is a spontaneously ordered liquid-fluid crystalline state. Liquid crystals
were discovered as early as 1888. They are materials that exhibit order in one or two dimensions but
not in all three. By comparison, the amorphous materials lack any order, while the crystalline ones
exhibit order in three dimensions. All liquid crystalline polymers exhibit some degree of fluidity.
They were investigated extensively in the 1900s and became commercially important in 1960s.
These are macromolecules that can align into crystalline arrays while they are in solution (
lyotropic
)
or while in a molten state (
thermotropic
). Such liquids exhibit
anisotropic
behavior [
51
,
52
]. The regions
of orderliness in such liquids are called
mesophases
. Molecular rigidity found in rigid rod-shaped
polymers, for instance, is the chief cause of their liquid crystalline behavior. It excludes more than one
molecule occupying a specific volume and it is not a result of intermolecular attractive forces. Some
aromatic polyesters or polyamides are good examples, like polyphenylene terephthalate:
O
O
O
n
O
Because the molecules posses anisotropy, they are aligned while still in a fluid form. This differs
from ordinary liquids, that are
isotropic
, where the molecules lack any kind of arrangement.
