Chemistry Reference
In-Depth Information
Table 1.
Properties of polyethylene and poly(ethylene-co-hexene) samples.
Sample (Trade Name)
Polymer Type
Number average
molecular weight (M
N
)
Polydispersity
Index (PDI)
Mol percent
of 1-hexene
PE8
Ethylene homopolymer
7,900
3.20
0
PE16 (SRM1475)
Ethylene homopolymer
15,400
3.51
0
PE32 (SRM1483)
Ethylene homopolymer
31,600
1.31
0
PE48
Ethylene homopolymer
47,900
2.15
0
EH06
Ethylene/1-hexene copolymers
36,100
2.5
0.68
EH15
Ethylene/1-hexene copolymers
35,200
2.35
1.51
EH31
Ethylene/1-hexene copolymers
34,300
2.18
3.14
Several attempts have been made to
model Crystaf profiles. The models pro-
posed in the literature can be divided into
two groups: models based on Stockmayer's
bivariate distribution,
[4-6]
and models based
on Monte Carlo simulation.
[7-9]
Although
these models can describe Crystaf profiles
for a certain set of samples and fractiona-
tion conditions, they suffer from a major
conceptual flaw because they assume that
the fractionation occurs at, or near to, ther-
modynamic equilibrium. We have recently
shown that this is not the case and that
crystallization kinetic effects influence
Crystaf analysis.
[10]
For a typical operation
condition (a cooling rate of 0.1
8
C/min),
Crystaf is far from thermodynamic equili-
brium, because using slower cooling rates
broaden Crystaf peaks and shift them to
higher crystallization temperatures.
In this paper, we propose a new semi-
empirical mathematical model that accounts
for the effect of crystallization kinetics
during Crystaf analysis. The model was
validated by fitting experimental Crystaf
profiles measured at several cooling rates
for a series of ethylene homopolymers and
ethylene/1-hexene copolymers. Good agre-
ement between the experimental data and
the model was obtained for all the samples
investigated.
(PE16 and PE32, with trade names
SRM1475 and SRM1483, respectively)
were purchased from the National Institute
of Standards and Technology (NIST, USA).
The other polyethylene samples were
synthesized in the olefin polymerization
laboratory at University of Waterloo in a
300 mL Parr autoclave reactor operated in
semi-batch mode. A detailed description of
the polymerization procedure can be found
in a previous publication.
[11]
Crystaf
Crystaf analysis was performed using a
Crystaf model 200 manufactured by Poly-
merChar S.A. (Valencia, Spain). The poly-
mer was dissolved in 1,2,4 trichlorobenzene
(TCB) in a 60 mL, stirred crystallization
vessel at a concentration of 0.1 mg/mL. The
polymer solution was held at 160
C for
60 min to ensure the complete dissolution
of the polymer. Then, the temperature of
the solution was decreased to 110
8
C and
kept at that temperature for 45 min for
stabilization before starting the fractiona-
tion. During analysis, the temperature of
the crystallization vessel was reduced to
30
8
C under constant cooling rates (0.02-
1.0
8
C/min). The decrease in polymer con-
centration in TCB solution with tempera-
ture was monitored using an in-line infrared
detector. The amount of polymer crystal-
lized at each temperature was obtained by
numerical differentiation.
8
Experimental Part
Materials
Seven polyethylene samples (four ethylene
homopolymers and three ethylene/1-hexene
copolymers) were used in this investigation.
Table 1 summarizes some average proper-
ties of these samples. Two of the samples
Crystaf Model
Model Formulation for Homopolymers
For isothermal polymer crystallization, the
relationship between crystallinity, X(t), and
