Chemistry Reference
In-Depth Information
Figure 4.
GPC-IR representation using five site types. The table lists the mass fractions (m), number average molecular
weights (M
n
), and 1-olefin fraction (F) of polymer made on each site type.
Notice that for the low molecular weight
region, one may have to account for the
effect of methyl end groups on the experi-
mental IR data.
This simple representation of GPC-IR
profiles permit a systematic interpretation
of results observed in several academic and
industrial polyolefin analytical laboratories.
averaging of the chemical compositions per
chain as the chains get longer. Samples with
infinite length would all have comonomer
fractions exactly equal to the average
comonomer fraction of the polymer.
The other important property of
Stockmayer's distribution is shown in
Figure 6: the CCD component broadens
steadily when the reactivity ratio product
increases, that is, as the copolymer passes
from alternating to random and, finally, to
block comonomer sequences. This is also
an intuitive concept, since all chains of a
perfectly alternating copolymer have the
same composition (F
¼
0.5), while a tende-
ncy to form long blocks of one of the
comonomer will necessary increase inter-
molecular heterogeneity.
We can apply our Modeling Principle 1
to Stockmayer's distribution to describe
the bivariate distribution of chain length
(or molecular weight) and chemical com-
position of polyolefins made with multiple
site catalysts. In this case, the following
generic expression applies,
Wðr; FÞ¼
X
Chemical Composition
Distribution of Linear Chains
The bivariate distribution of chain length
and chemical composition of linear poly-
olefins is given by Stockmayer's distribu-
tion, Equation (4). A short description of
its main features is useful to clarify several
properties of binary copolymers such as
LLDPE and propylene/ethylene copoly-
mers.
Figure 5 shows Stockmayer's distribu-
tions for four model single-site polyolefins
with the same reactivity ratio product
(
1, random
co
polymers) and average
ethylene fraction (
F ¼
0
:
8), but with differ-
ent average chain lengths. Notice that, as
the number average chain lengths of the
samples increase, their distributions become
narrower on the chemical composition
dimension. This trend is also observed for
each sample individually: shorter chains
have a broader chemical composition distri-
bution (CCD) than longer chains. This is a
well known effect, caused by the statistical
r
1
r
2
¼
n
m
j
w
j
ðr; FÞ
(16)
j
¼
1
where
) for each site is given by
Equation (4). It should be clear that this
equation can be transformed into a mole-
cular weight distribution and expressed in
either linear or log scale, using the trans-
formations demonstrated above for Flory's
distribution.
w
j
(
r
,
F
