Chemistry Reference
In-Depth Information
0
where
T
m
is the equilibrium melting temperature for an infinite molecular weight chain and
T
me
is the
corresponding melting temperature for a fraction that contains
x
repeat units. From the stand point of
thermodynamics,
T
me
is a
first-order transition temperature
[
15
]. The melting points, when
measured very carefully, can in many cases be sharp. On the other hand, melting points of ordinary
crystals may melt over a range (Table
2.3
). Table
1.2
shows some first-order transition temperatures,
commonly designated as
T
m
.
For systems that are polydisperse, with a most probable chain-length distribution, the melting
temperature molecular weight relation is expressed as [
42
]:
=T
m
m
1
1
=T
¼ðR=DH
u
Þð
2
=X
n
Þ
where
X
n
represents the mole fraction of non-crystallizing units. This equation is based on the stipulation for
conditions for phase equilibrium. It is specific to and valid only for polymers that have a most
probable molecular weight distribution. This relationship for the melting temperature of each
polydisperse system has to be treated individually [
42
]. By applying the Clapeyron equation and
from measurements of applied hydrostatic pressure the value of
X
n
is the number average degree of polymerization. In this equation, the quantity 2 ⁄
DH
u
can be determined.
DS
m
applies to very high molecular weight polymers. For polymers that
are medium or low in molecular weight, the degree of polymerization (
This equation,
T
m
¼ DH
m
/
X
) has to be included:
T
m
¼ðDH
0
þ XDH
1
Þ=ðDS
0
þ XDS
1
Þ
Mandelkern points out [
38
] that the experimental data shows that there is no correlation between
the melting temperature of a polymeric crystal and the enthalpy of fusion, as is found in many small
molecules. The
values of polymers generally fall into two classes. They are ether within a few
thousand calories per more or about 10,000 cal/mole. Polymers that fall into the category of
elastomers have low melting temperatures and high entropies of fusion. This reflects the compacted
highly flexible nature of the chains. At the other extreme are the rigid engineering plastics. These
materials possess high melting points and correspondingly lower entropies of fusion [
42
].
DH
2.3.3.2 Kinetics of Crystallization
The rate of crystallization in polymeric materials is of paramount importance. For some polymers,
like atactic polystyrene or some rubbers, rapid cooling can lead to the glassy state without any
formation of crystallites. The amount of crystallinity actually depends very much upon the thermal
history of the material. The amount of crystallinity, in turn, influences the mechanical properties of
the material. Microscopic observation of the growth of the spherulites as a function of time will yield
information of the crystallization rate. The rate is a function of the temperature. As the temperature is
lowered, the rate increases. This growth is usually observed as being linear with time. Presence of
impurities will slow down the growth rate. When the growth rate is plotted against crystallization
temperature, a maximum is observed. This is due to the fact that as the temperature is lowered the
mobilities of the molecules decrease and the process eventually becomes diffusion-controlled.
According to the Avrami equation, the fraction that crystallizes during the time
t
, and defined as
1
l
(
t
), can be written as [
42
]:
Z
t
0
Vðt; tÞNðtÞ
r
c
r
l
1
lðtÞ¼
1
exp
d
t
