Chemistry Reference
In-Depth Information
An Overview of Important Microstructural
Distributions for Polyolefin Analysis
Joa˜o B.P. Soares
Summary: Polyolefins with complex microstructures are becoming increasingly
common in academic and industrial applications. Polyolefin analytical techniques
are evolving to provide a more detailed picture of these microstructures, with the
development and improvement of hyphenated-techniques and cross-fractionation
methods. These modern analytical techniques provide a wealth of information on
polyolefin microstructure and, despite being extremely useful, they can also be hard
to interpret without the help of mathematical models that link polymerization
kinetics to chain microstructure and polymer characterization results. In this paper
we review some of the most important distributions for polyolefin microstructure
and derive a few new expressions that help understand the results obtained with
several polyolefin characterization techniques.
Keywords: polyethylene; polymer characterization; polymer fractionation; polymer
microstructure; polyolefins
Introduction
Distribution of Chain Length,
Chemical Composition, and
Long Chain Branching
The remarkable versatility of polyolefins
come from the fact that ethylene, propylene
and
-olefins can be copolymerized to
create polymer chains with microstruc-
tures that lead to very different physical
properties.
Polyolefin properties are ultimately
defined by the way the monomers are con-
nected to form linear and branched poly-
mer chains with different degrees of regu-
larity. It is, therefore, very important to
characterize the microstructure of polyole-
fins and to quantify this microstructure
using fundamental models.
In this short overview, we will present
some important equations that describe
polyolefin microstructure and discuss
some modeling principles that can be used
to help understand the results obtained
with several polyolefin characterization
techniques.
a
The most general distribution for the micro-
structure of polyolefins made with coordi-
nation catalysts is given by the equation:
[1,2]
1
ð
2
i þ
1
Þ!
r
2
iþ
1
2
iþ
2
wðr; F; iÞ¼
t
"
#
r
r
(1)
2
r
ð
F
F
Þ
ð
r
tÞ
exp
exp
2
pb
2
b
) is the height of
the weight distribution for chains of length
r, comonomer fraction F, and i long chain
branches (LCB) per chain. This equation
has only two parameters,
b
and
t
,definedas:
In Equation (1),
w
(
r
,
F
,
i
b ¼
q
1
4
Fð
1
FÞð
1
r
1
r
2
Þ
(2)
Fð
1
FÞ
rate of transfer
þ
rate of LCB formation
rate of propagation
t ¼
(3)
Finally,
F
is the average fraction of
comonomer in the copolymer (as calculated
