Chemistry Reference
In-Depth Information
A Mathematical Model for the Kinetics of
Crystallization in Crystaf
Siripon Anantawaraskul,
*
1
Joa˜o B.P. Soares,
2
Preechathorn Jirachaithorn
1
Summary: A series of ethylene homopolymers and ethylene/1-hexene copolymers
with different molecular weight distributions (MWD) and chemical composition
distributions (CCD) was analyzed by crystallization analysis fractionation (Crystaf) at
several cooling rates to investigate the effect of MWD, CCD, and cooling rate on their
Crystaf profiles. Using these results, we developed a mathematical model for Crystaf
that considers crystallization kinetic effects ignored in all previous Crystaf models
and can fit our experimental profiles very well.
Keywords: chemical composition distribution; crystallization analysis fractionation
(Crystaf); modeling; molecular weight distribution; polyethylene
Introduction
ing level) are often required to fully des-
cribe commercial polyethylene. Despite the
fact that understanding chain microstruc-
ture and structure-property relationships
is crucial for developing new generations
of polymers, establishing reliable structure-
property relationships remain a challenging
task for polymer engineers.
Crystallization analysis fractionation
(Crystaf) is an important polyolefin char-
acterization technique because it can ana-
lyze crystallizability distribution of semi-
crystalline polymers and this distribution
can be used to infer the molecular weight
distribution (MWD) of homopolymers, the
chemical composition distribution (CCD)
of binary copolymers, and the tacticity
distribution (TD) of stereoregular poly-
mers.
[1-3]
Quantitative distributions can
be obtained using a calibration curve, a
relationship between chain crystallizability
and chain microstructure for each case.
Crystaf involves the non-isothermal crys-
tallization of polymer chains from a dilute
solution. During crystallization, the concen-
tration of polymer remaining in solution is
monitored as a function of crystallization
temperature (integral Crystaf distribution).
The first derivative of the integral Crystaf
distribution (differential Crystaf distribution)
represents the weight fraction of polymer
that crystallizes at each temperature.
Consisting of simple monomeric units,
polyethylene and its analog, hydrogenated
polybutadiene, have been viewed as simple
model polymers. This is partly true for
some specially synthesized samples having
chain microstructures that allow us to draw
several conclusions on the effect of chain
microstructure and topology on physical
properties. However, the notion that we
have thoroughly understood this polymer
is far from the true. In fact, the chain
microstructure and topology of commercial
polyethylene are far from simple, but rather
extremely complex.
Average microstructural properties such
as number average molecular weight and
average comonomer content are insuffi-
cient to describe the physical properties of
such complex polymers. Details on both
intra- and intermolecular heterogeneity
(e.g., molecular weight distribution, che-
mical composition distribution, sequence
length distribution, and long chain branch-
