Chemistry Reference
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structure. Finally, if the conditional prob-
ability and molar fraction are equal, the
copolymer is random.
In the discussion below, we chose to
express the mole fraction of ethylene as P,
with the understanding that it is only
equivalent to the conditional probability,
p
crystallizable homopolymer,
. The equa-
tion is similar to the experimentally deter-
mined relationship for the natural loga-
rithm of the mole fraction of ethylene as a
function of the reciprocal of the ATREF
elution temperature or melting point (
T
0
m
K)
as shown in Figure 7 for various homoge-
neously branched copolymers of ethylene.
Note: The ATREF Elution Temperature-NMR
calibration depicted in
8
, described above when the copolymer is
random. From this point forward, we will
consider the measured mole fraction of
ethylene (X) from NMR or other technique
for a polymer as an estimate of
is not intended
to be ''universal'' in that ATREF instrumenta-
tion and methodology varies considerably in
the literature. The calibration in this paper is
therefore to be considered to be unique and
must be repeated for each ATREF instrument.
Also, the preparative TREF fractions or homo-
geneous random copolymers that were chosen
have weight average molecular weights of at
least 100,000 daltons and polydispersity
values of no greater than about 2.5.
Figure 7
the
conditional probability.
Having now proposed a ''blocky'' struc-
ture for the OBC, we are in a position to
validate the proposed structure on the basis
of Flory's equilibrium melting theory as
extended to the ATREF elution tempera-
ture. The key relationship of Flory's theory
is:
[8]
ln
P
1
T
m
1
T
m
ΒΌ
R
D
H
u
Preparative TREF fractions of nearly all
random copolymers and their blends fall on
this line, except for the small, predictable
effects of molecular weight. According to
Flory's definition, if one observes a differ-
ence between the measured (X) and pre-
dicted value (P) of the mole fraction of
(1)
In Equation (1) the mole fraction of
crystallizable monomers,
, is related to the
melting temperature, T
m
, of the copolymer,
and the melting temperature of the pure
P
Figure 7.
The relationship of ethylene mole fraction to ATREF peak elution temperature (
) and DSC melting temperature
^
(
) for various homogeneously branched copolymers can be interpreted on the basis of Flory's equation.
^
