Full Paper
2096
Summary: Concurrent tandem catalysis systems have shown
a significant advantage in the convenient synthesis of linear
low-density polyethylene (LLDPE) from a sole ethylene
monomer stock by uniquely coupling the tandem action
between an ethylene oligomerization catalyst and an ethylene copolymerization catalyst in a single reactor. Recently,
we have reported the successful synthesis of ethylene-hexene
derived LLDPE using an effective concurrent tandem
catalysis system comprising (Z5-C5H4CMe2C6H5)TiCl3 (1)/
MMAO and a CGC copolymerization catalyst, [(Z5C5Me4)SiMe2(tBuN)]TiCl2 (2)/MMAO. In this work, we
report the results from an extensive study on the important
rheological properties of LLDPE grades prepared with this
tandem catalysis system. Two sets of LLDPE samples having
different short-chain branching density (SCBD) were prepared with the tandem catalysis system under various catalyst
concentrations and at temperatures of 25 and 45 8C. The melt
rheological properties of these polymers were evaluated using
small-amplitude dynamic oscillation measurements. These
polymers have been found to possess typical rheological
properties found in long-chain branched (LCB) polymers,
such as enhanced zero-shear viscosity (Z0), improved shearthinning, elevated dynamic moduli, and thermorheological
complexity, which indicate the presence of long-chain
branching in the polymers. The long-chain branching density
(LCBD) of the two respective sets of polymers were qualita-
tively compared and correlated to the polymerization conditions including catalyst ratio and temperature. This work
represents the first study on the rheological properties of
LLDPE synthesized with concurrent tandem catalysis, and
it discloses another appealing feature of this unique
approach—its ability to produce LCB LLDPE from a single
ethylene monomer stock.
Synthesis of linear low-density polyethylene (LLDPE) from
ethylene using ethylene oligomerization catalyst and an ethylene copolymerization catalyst.
Long-Chain Branching and Rheological Properties of
Ethylene-1-Hexene Copolymers Synthesized from
Ethylene Stock by Concurrent Tandem Catalysis
Zhibin Ye,*1 Fahad AlObaidi,2a Shiping Zhu,*2 Ramesh Subramanian1
1
School of Engineering, Laurentian University, Sudbury, Ontario, Canada P3E 2C6
E-mail: zye@laurentian.ca
2
Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7
E-mail: zhuship@mcmaster.ca
Received: June 11, 2005; Accepted: August 5, 2005; DOI: 10.1002/macp.200500248
Keywords: catalysis; concurrent tandem catalysis; linear low-density polyethylene (LLDPE); long-chain branching; rheological
properties; structure
Introduction
As an important family of polyethylenes, linear low-density
polyethylene (LLDPE), a copolymer of ethylene with
a-olefins, has been extensively used for a broad range of
a
Current address: SABIC R&T, Polymer Research Department,
Polyolefins Section, Riyadh, Saudi Arabia.
Macromol. Chem. Phys. 2005, 206, 2096–2105
commodity applications, particularly for film applications.
Compared to high-density polyethylene (HDPE), LLDPE
possesses reduced melting point, crystallinity, and
density attributed to the presence of short-chain branches
with controlled length and frequency on the polymer
backbone, which not only facilitates effective polymer
processing but also introduces additional favorable material
properties.[1] Commercial LLDPE is produced by ethylene
DOI: 10.1002/macp.200500248
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Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . .
copolymerization with a-olefin comonomers, such as
1-butene, 1-hexene, and 1-octene, using classical multisite Ziegler-Natta catalysts. More recently metallocene
catalysts, which have tremendously revolutionalized olefin
polymerization in the past two decades, have been used in
some commercial LLDPE processes. This new generation
of homogeneous single-site catalysts has opened up a
unique route to a novel series of LLDPE grades with unprecedented controlled chain structure and superior tailored
properties.[2]
Metallocene LLDPE exhibits some outstanding materials properties compared to Ziegler-Natta polymers like
higher transparency and enhanced mechanical performance
as a consequence of more uniform distribution of shortchain branching (SCB) and narrower molecular weight
distribution (MWD).[2–4] More importantly, LLDPE prepared with a number of metallocene catalyst systems, such
as the constrained geometry catalyst (CGC), has been
shown to possess the most desired long-chain branching
structure, a characteristic structure ubiquitous in LDPE
from conventional radical polymerization processes.[4]
Without compromising other excellent properties, the
presence of a small amount of LCB in metallocene LLDPE
dramatically improves the viscoelastic properties of the
polymer, thereby making the polymer mimic the excellent
processability and high melt strength typically found in
long-chain branched (LCB) LDPE.[5] These excellent processing properties coupled with other superior properties
make LCB metallocene LLDPE a perfect substitute for
conventional LDPE in the market for a broad range of
important applications.[2] The incorporation of in situ
generated vinyl-ended macromonomers into growing
polymer chains by the open-structured homogeneous
catalysts during copolymerization has been believed to
be the mechanism responsible for the formation of LCB
in metallocene LLDPE.[6,7] Given their valuable features
and tremendous technological advance, extensive research
has been undertaken to synthesize, characterize, and
study the viscoelastic properties of LCB metallocene
LLDPE.[6–25]
As an alternative to the conventional two-monomer
(ethylene and a-olefin) approach for LLDPE production,
recently a new synthetic approach, which utilizes concurrent tandem catalysis to produce LLDPE with ethylene
as the sole monomer stock in a single reactor, has attracted a
significant amount of research interest.[26,27] This novel
approach employs the concurrent tandem action between
two catalysts in the system: one catalyst (ethylene oligomerization catalyst) oligomerizes ethylene into 1-alkene,
while the other catalyst (ethylene copolymerization catalyst) concurrently copolymerizes the in situ generated 1alkene with ethylene to produce LLDPE.[26,27] By selecting
suitable catalyst combinations and adjusting catalyst
concentration ratios, LLDPE with controlled SCB length
and density can be effectively produced. Compared to the
Macromol. Chem. Phys. 2005, 206, 2096–2105
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conventional copolymerization approach, this tandem
catalysis approach possesses an appealing advantage of
using ethylene as the only monomer, which avoids the use
of a-olefin and hence precludes the separate ethylene oligomerization process usually required in LLDPE production.[28,29] A number of versatile tandem catalysis
systems,[28–42] particularly systems employing a combination of single-site homogeneous catalysts, have been successfully developed and summarized in recent review
articles.[26,27]
The concurrent tandem catalysis approach is conceptually elegant and virtually successful. It is aimed at a
convenient synthesis of LLDPE. However, the properties of
LLDPE prepared by this novel approach, particularly the
viscoelastic properties critical to the processing and
applications of the polymers, have never been investigated.
From the application point of view, it is also highly
desirable in this approach to introduce the valuable LCB
structure into these polymers to enhance their processing
properties. We speculate that LCB LLDPE can be produced
by this approach as well if we select a unique copolymerization catalyst (such as CGC) in the tandem catalyst
combination, which has the capability of in situ generation
and incorporation of vinyl-ended macromonomers. Recently, we used a tandem catalyst system comprising of an
ethylene trimerization catalyst, (Z5-C5H4CMe2C6H5)TiCl3
(1)/MMAO, and a CGC copolymerization catalyst, [(Z5C5Me4)SiMe2(tBuN)]TiCl2 (2)/MMAO, for the successful
synthesis of LLDPE of n-butyl branches with ethylene as
the only monomer stock.[28,29] In this work, we carried out a
further investigation on the melt rheological properties of
LLDPE prepared with this tandem catalysis system and the
results reported here show convincingly the presence of a
sparse level of LCB in these polymers. This work hence
demonstrates that LCB LLDPE can be obtained from
ethylene as the sole monomer using this unique tandem
catalysis system that comprises a CGC catalyst having high
macromonomer generation and incorporation ability. It
represents another appealing feature of this concurrent
tandem catalysis approach for LLDPE preparation.
Experimental Part
The detailed synthesis of n-butyl branched LLDPE utilizing the
tandem catalysis system, comprising (Z5-C5H4CMe2C6H5)TiCl3 (1)/MMAO and [(Z5-C5Me4)SiMe2(tBuN)]TiCl2 (2)/
MMAO, has been reported in our previous articles.[28,29] The
synthesis was carried out in a 500 mL glass reactor equipped
with a magnetic stirrer under atmospheric pressure of ethylene.
Typical synthesis procedure is as follows:
Toluene and MMAO were introduced into the purged reactor
under nitrogen protection. Subsequently, the reactor was
evacuated, pressurized with ethylene, and then placed into an
oil bath set at the operating temperature. After equilibrium for
10 min, stock solutions in toluene for both catalysts with
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Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian
prescribed amounts were injected simultaneously to initiate the
concurrent ethylene trimerization and copolymerization. The
system temperature and ethylene pressure were kept constant
throughout the reaction. The contents of the reactor were
magnetically stirred. After 1 h, the reaction was quenched by
injecting 20 mL methanol and venting the reactor. The synthesized polymer was collected, washed with an excessive
amount of methanol, and then dried.
The thermal properties of the polymer, including melting
point (Tm), and melting enthalpy (DHm), were measured using
a calibrated TA 2910 MDSC in the standard DSC mode. Ultra
high-purity N2 gas at a flow rate of 30 mL min1 was purged
through the calorimeter. A refrigerated cooling system (RCS)
with the cooling capacity to 220 K was attached to the DSC
cell. The polymer sample (about 5 mg) was first heated to
180 8C at the rate of 10 8C min1 in order to remove any
thermal history. It was then cooled down to 20 8C at the rate of
10 8C min1. A second heating cycle was applied to acquire a
DSC thermogram at the scanning rate of 10 8C min1. The
peak temperature with the highest endotherm was chosen as
the melting point. The molecular weight (MW) and MWD of
the polymer samples were measured at 140 8C in 1,2,4trichlorobenzene using a Waters Alliance GPCV 2000 with
DRI detector coupled with an in-line capillary viscometer. The
polymer MWs were calculated according to a universal calibration curve based on 11 polystyrene standards with MWs
ranging from 2.5 103 to 1.09 106 g mol1. The 75.4 MHz
13
C NMR analyses were conducted using a Bruker AV300
Pulsed NMR spectrometer at 120 8C. The polymer samples
were dissolved in 1,2,4-trichlorobenzene and deuterated
o-dichlorobenzene mixture (weight ratio of 9/4) in 10 mm
NMR tubes with a concentration about 20 wt.-%. Waltzsupercycle decoupling was used to remove 13C-1H couplings.
At least 2 500 scans were applied for each acquisition to obtain
a good signal-to-noise ratio. The polymer chemical shift
assignments and calculations followed the ASTM D5017-91
method.[43]
Rheological measurements of the polymer melts were carried out on an ATS RheoSystem STRESSTECH HR rheometer
in the stress-controlled oscillation mode using 20 mm parallel
plate geometry at a gap of about 1.0 mm. Before the measurements, the polymer samples were conditioned with
1 000 ppm Irganox 1 010 antioxidant supplied from CibaGeigy Canada. The fine polymer reactor powders were mixed
with the antioxidant solution in acetone. The acetone was then
evaporated overnight under vacuum at 75 8C. Subsequently,
the antioxidant-conditioned polymer powders were pelletized
using an ATLAS Laboratory Mixing Molder at 150 8C and
further compression-molded in a carver press at 150 8C into
small disks with 20 mm in diameter and 1.5 mm in thickness.
The rheological measurements were conducted in the frequency range of 0.002–50 Hz. Strain sweeps were performed
at 1 Hz before frequency sweeps in order to establish the linear
viscoelastic region. The experiments were performed at
regular intervals of 10 8C within temperature range from 140
to 200 8C. Temperature was maintained within 0.2 8C using
an ETC-3 (elevated temperature control) temperature control
system and the measurements were all conducted under N2
atmosphere.
Results and Discussion
Polymer Synthesis using Tandem Catalysis System
and Structural Characterization
Two sets of ethylene-1-hexene LLDPE polymers, PE1–
PE4 and PE6–PE8 as shown in Table 1, were prepared from
ethylene stock with the concurrent tandem catalysis system
comprising of the ethylene trimerization catalyst,
(Z5-C5H4CMe2C6H5)TiCl3 (1)/MMAO, which trimerizes
ethylene into 1-hexene, and the copolymerization CGC
catalyst, [(Z5-C5Me4)SiMe2(tBuN)]TiCl2 (2)/MMAO,
which copolymerizes the in situ generated 1-hexene with
Table 1. Synthesis conditions and properties of polymer samples investigated. Other conditions: solvent, toluene; total volume, 150 mL;
Al/Ti ¼ 1 000; ethylene pressure, 1 atm.
Polymer
sample
PE1
PE2
PE3
PE4
PE5
PE6
PE7
PE8
PE9
M w a)
Trimerization CGC Temperature Polymerization
catalyst (1)
(2)
time, t
mmol
mmol
8C
h
kg mol1
30
15
10
5
0
50
25
7.5
0
15
15
15
15
15
25
25
25
25
25
25
25
25
25
45
45
45
45
1
1
1
1
1
1
1
1
1
99
118
160
100
386
40
41
75
147
PDIa)
3.2
2.8
4.3
3.3
11.9
2.6
2.9
3.7
6.7
Tmb)
wb)
Hexene
percentagec)
SCBD
8C
%
mol-%
per 1 000
carbons
60.0, 127.3d)
80.8, 126.1d)
91.8
113.6
135.1
121.7
124.2
127.0
134.1
7.6
18.5
28.0
34.3
56.6
40.6
44.7
56.9
68.9
9.5
6.9
5.1
3.0
0
n.d.e)
n.d.
n.d.
0
40.0
30.3
23.1
14.2
0
n.d.
n.d.
n.d.
0
a)
Determined by GPCV.
Measured by DSC. Crystallinity was calculated based on the melting enthalpy of 290 J g1 for a perfect PE crystal.
c)
1-Hexene molar percentage in the copolymer, determined by 13C NMR.
d)
Higher melting peak is from a small amount of polymer byproduct produced by the trimerization catalyst.
e)
n.d.: not determined.
b)
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Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . .
Complex Viscosity Curve
A detailed investigation on the melt rheological properties
of these polymers was carried out using small-amplitude
dynamic oscillation measurements, and the presence of
sparse LCB in these polymers was elucidated from the
rheological results. The complex viscosity curves obtained
at 190 8C for the set of LLDPE samples (PE1–PE4) and
HDPE sample PE5 prepared at 25 8C are shown in Figure 1.
It can be seen that the four LLDPE samples show very
different complex viscosity curves despite possessing very
similar M w and PDI, which are two important parameters
that dramatically affect complex viscosity and shearthinning nature of the polymer. The Cross equation,[45]
given by Equation (1), was applied to fit the complex
viscosity curves.
Z0
1 þ ðtoÞa
Macromol. Chem. Phys. 2005, 206, 2096–2105
PE1
PE2
PE3
100000
PE4
PE5
10000
1000
0.01
0.1
1
10
100
Angular Frequency (rad/s)
1000
Figure 1. Polymer melt complex viscosity curve at 190 8C for
samples PE1–PE5 prepared at 25 8C.
where Z0 is zero-shear viscosity, t is a characteristic
relaxation time, and a is a dimensionless exponent that is
independent of temperature. The zero-shear viscosity for
each polymer at 190 8C obtained by fitting the Cross model
is listed in Table 2, and it qualitatively increases in the
following order: PE1 < PE2 < PE3 < PE4. Typically comparing PE1 and PE4, which have almost the same M w and
PDI, the zero-shear viscosity for PE4 is more than an order
of magnitude higher than that of PE1.
For linear HDPE, Raju et al.[46] proposed the following
equation to correlate Z0 of HDPE at 190 8C to the weight
average MW of the polymer:
3:6
Z0 ¼ 3:4 1015 M w
ð2Þ
This equation is independent of PDI and has been found
to be valid for conventional linear Ziegler-Natta polyethylenes of PDI ranging from 3 to 35.[18,47,48] Studies have
Rheological Properties and Elucidation of
Long-Chain Branching
Z*ðoÞ ¼
1000000
Complex Viscosity (Pa s)
ethylene. The trimerization catalyst has been shown to
produce 1-hexene of high purity.[28,44] The CGC catalyst
was adopted owing to its well-known outstanding capability in producing LCB polymers.[4,6,7] These polymers
were prepared at two temperature levels (25 and 45 8C) and
with different concentration ratios for the two catalysts
under atmospheric pressure of ethylene to achieve different
short-chain branching density (SCBD) and, therefore,
different melting temperature (Tm) and crystallinity (w).
Table 1 summarizes the polymerization conditions and the
polymer properties, including weight average MW (M w )
and polydispersity index (PDI), Tm and w, and SCBD.
For comparison purposes, two homo-polyethylene samples, PE5 and PE9, were also prepared at the two respective temperatures using the sole CGC catalyst under
equivalent conditions. The synthesis and characterization
of these polymers have been reported in our previous
articles.[28,29]
From Table 1, it can be seen that LLDPE samples prepared at the same temperature possess similar weight
average MWs and PDIs, while their melting temperature,
crystallinity, and SCBD decrease significantly with an
increase in the concentration ratio of catalyst 1/catalyst 2 as
expected. Compared to the set (PE1–PE4) prepared at
25 8C, the samples (PE6–PE8) prepared at 45 8C all have
higher melting temperature and crystallinity, and hence
lower SCBD owing to the pronounced deactivation of
the trimerization catalyst 1 at elevated temperatures.[28,44]
The two homo-polyethylene samples, PE5 and PE9, have
much higher M w and possess broader MWD due to difficulty in monomer diffusion typically observed in the
ethylene homopolymerization system.
ð1Þ
www.mcp-journal.de
Table 2.
190 8C.
Some rheological properties of polymers investigated at
Polymer samples
PE1
PE2
PE3
PE4
PE5
PE6
PE7
PE8
PE9
Z0a)
Estimated Z0b)
Pa s
Pa s
1.4 104
8.4 104
1.1 105
2.3 105
1.8 106
2.0 103
3.7 102
4.4 103
4.8 104
3.3 103
6.2 103
1.8 104
3.4 103
4.4 105
1.3 102
1.4 102
1.2 103
1.4 104
nc)
0.82
0.71
0.68
0.62
0.33
0.82
0.88
0.79
0.71
a)
Zero-shear viscosity obtained by fitting complex viscosity curve
using Equation (1).
b)
Calculated zero-shear viscosity by using Equation (2).
c)
Power-law exponent obtained by fitting complex viscosity curve
using Equation (3).
ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian
also shown that Equation (2) can be applied to linear side
chain branched LLDPE samples with SCBD ranging from
zero to as high as 48.5/1 000 carbons.[18,19] However, this
equation is not valid for LCB polyethylenes, which usually
exhibit much higher Z0 than the value calculated with the
equation.[10,11,18,19] The zero-shear viscosities for the four
samples, PE1–PE4, were estimated using Equation (2) and
listed in Table 2. These estimated values are far lower
(almost an order of magnitude) than the zero-shear
viscosities obtained from the Cross model equation, which
suggests the presence of LCB structure in these four
polymers.
The power-law expression, given by Equation (3), was
used to fit the complex viscosity curves in order to quantify
and compare the shear-thinning behaviors of the four
polymers.
Z* ¼ mon1
ð3Þ
where m is the consistency and n is the power-law exponent,
which indicates the degree of shear-thinning. Improved
shear-thinning, i.e., higher degree of non-Newtonian
behavior and lower n value, is usually observed in LCB
polymers and polymers of high PDI and it becomes more
pronounced with the increase in long-chain branching
density (LCBD) and PDI.[9,22] The power-law exponents
for the four polymers at 190 8C are listed in Table 2, and they
decreased in the following order: PE1 > PE2 PE3 > PE4.
Since the four polymers have fairly similar M w and PDI, the
different n value thus reflects the different LCBD in this set
of polymers, which increases in the following manner:
PE1 < PE2 PE3 < PE4. This suggests that LCBD tends to
decrease with an increase in SCBD of the polymer, i.e.,
LCBD decreases with an increase in the concentration ratio
of catalyst 1 to catalyst 2 during polymerization.
For the set of LLDPE polymers prepared at 45 8C, PE6–
PE8, Figure 2 compares their complex viscosity curves at
190 8C. The values of Z0 and n for these polymers listed in
Complex Viscosity (Pa s)
100000
10000
1000
100
PE6
PE7
PE8
0.1
1
10
PE9
10
0.01
100
1000
Angular Frequency (rad/s)
Figure 2. Polymer melt complex viscosity curve at 190 8C for
samples PE6–PE9 prepared at 45 8C.
Macromol. Chem. Phys. 2005, 206, 2096–2105
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Table 2 were obtained using Equation (1) and (3), respectively. For each polymer, particularly PE6, the Z0 value is
much higher than the estimated one calculated using
Equation (2) based on the MW of the polymer M w, thus
indicating a certain degree of LCB present in the polymers.
Comparing samples PE6 and PE7 having very similar M w
and PDI, PE6 exhibits a much higher Z0 (2.0 103 Pa s for
PE6 and 3.7 102 Pa s for PE7) but a lower n (0.82 for PE6
and 0.88 for PE7) than PE7, which suggests PE6 has higher
LCBD than PE7.
The two homo-polyethylene samples, PE5 and PE9, also
exhibit significantly higher Z0 (about three times higher)
than their respective estimated value using Equation (2),
suggesting the presence of LCB. In Table 2, lower n values
can be found for these two homopolymers compared to their
corresponding LLDPE counterparts prepared at the same
temperature. As well as LCB, the higher PDI of these two
polymers can contribute to the reduced n values. Therefore,
no comparison in LCBD between the homopolymer and
LLDPE samples can be made from their shear-thinning
behaviors.
Dynamic Moduli, G0 (o) and G00 (o)
Figure 3(a) shows and compares the dynamic modulus
[G0 (o) and G00 (o)] curves measured at 170 8C for the set
of LLDPE samples, PE1–PE4. A noticeable deviation
in the frequency of the crossover point of the storage
modulus (G0 ) and loss modulus (G00 ) curves for each
polymer can be clearly identified, which decreases in the
following manner: PE1 > PE2 PE3 > PE4. The modulus
crossover point reflects the viscoelasticity of polymers and
its frequency is virtually dependent on the polymer chain
structural parameters, including M w , PDI, LCBD, and chain
topology. For the LCB polymers of similar M w and PDI,
numerous studies[10,11,14,15,49] have shown that the frequency of the crossover point decreases sensitively with an
increase in the polymer LCBD owing to the greater
enhancement of polymer elasticity. Given the similar M w
and PDI for the four polymers (PE1–PE4), the different
locations of the crossover points in Figure 3(a) provide
additional evidence of the presence of LCB structure.
Furthermore, one can derive that LCBD increases qualitatively in the following order: PE1 < PE2 PE3 < PE4,
which is consistent with our finding in the previous
section based on the shear-thinning behavior for the four
polymers.
A plot of log G0 versus log G00 has been proven to be a
useful tool to investigate the effects of LCB and PDI on
polymer rheological properties.[9,18,19,49] For high-MW
polymers with narrow MWD, the log G0 versus log G00 curve
does not depend on MW but it is a weak function of temperature. Hence, all the data measured at various temperatures and MWs can be described by a single master curve.
For linear polyethylenes of narrow MWD, the correlation
ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . .
1000000
(a)
1000000
(a)
PE3
PE4
100000
PE1
G', G" (Pa)
G', G" (Pa)
100000
PE2
10000
PE1-G'
PE1-G"
PE2-G'
PE2-G"
PE3-G'
PE3-G"
PE4-G'
PE4-G"
1
10
100
Angular Frequency (rad/s)
10
1
0.01
1000
1000000
1000
100
1000
0.1
10000
0.1
PE6-G'
PE6-G"
PE7-G'
PE7-G"
PE8-G'
PE8-G"
PE9-G'
PE9-G"
1
10
100
Angular Frequency (rad/s)
1000
1.0E+6
(b)
(b)
PE6
1.0E+5
100000
PE7
PE8
G' (Pa)
G' (Pa)
1.0E+4
10000
PE1
1000
PE2
PE9
linear PE
1.0E+3
1.0E+2
PE3
1.0E+1
PE4
100
Linear PE
1.0E+0
10
1.0E+1
100
1000
10000
G" (Pa)
100000
1000000
between G0 and G00 was found to be:[18,19]
G0 ¼ 0:00541ðG Þ
ð4Þ
Short-chain branched linear polyethylenes have been
found to obey the above correlation. However, for polymers
with LCB and/or broad MWD, a deviation from the
correlation with an up-shift of the curve is usually observed
in the terminal region and it becomes more pronounced with
the increase of LCBD and PDI.[9,18,19,49]
Figure 3(b) compares the log G0 versus log G00 master
curves for samples PE1–PE4 with the curve for linear PE
obtained using Equation (4). An obvious up-shift of the
master curves from the linear PE behavior, particularly in
the low-modulus region, can be observed for the four
polymers, thereby suggesting a more elastic nature of the
polymer melts and the presence of LCB. Also, a very minor
yet discernible difference in the degree of up-shift of the
four master curves can be seen. The degree of up-shift
becomes more pronounced in the following sequence:
PE1 < PE2 PE3 < PE4. Considering their similar PDI,
we obtain the same sequence for LCBD difference in the
four polymers.
Macromol. Chem. Phys. 2005, 206, 2096–2105
1.0E+3
1.0E+4
1.0E+5
1.0E+6
G" (Pa)
Figure 3. (a) G0 and G00 curves for the set of LLDPE samples,
PE1–PE4, measured at 170 8C. (b) Log G0 versus log G00 master
curves for polymers PE1–PE4. The solid line is for linear
polyethylene based on Equation (4).
00 1:42
1.0E+2
www.mcp-journal.de
Figure 4. (a) G0 and G00 curves for the set of LLDPE samples,
PE6–PE9, measured at 170 8C. (b) Log G0 versus log G00 master
curves for polymers PE6–PE9. The solid line is for linear
polyethylene based on Equation (4).
Figure 4(a) shows the dynamic modulus curves for
samples PE6–PE9 measured at 170 8C. With the exception
of PE9, the polymers do not have the modulus crossover
point within the experimental frequency window because of
low M w. Figure 4(b) compares the log G0 versus log G00
curves for the four polymers. The obvious up-shift of the
curves from the solid line for linear PE of low PDI suggests
the deviation of the four polymers from linear polymers
with narrow MWD. Although the difference in the deviation degree for the four polymers is very small, one can still
see a discernible deviation that becomes more significant as
follows: PE9 PE8 < PE7 < PE6. Taking the MWD into
consideration, which has a similar effect in up-shifting the
curve as LCB, we can conclude that LCBD increases in the
following manner: PE9 PE8 < PE7 < PE6.
Phase Angle
Phase angle is an even more sensitive indicator of the
presence of LCB.[22] In a plot of phase angle versus angular
frequency, the presence of LCB will not only lead to
reduced phase angles of the polymer but also change the
ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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90
90
80
80
Phase Angle (degree)
Phase Angle (degree)
Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian
70
60
PE1
50
PE2
increasing LCBD
PE3
40
PE4
70
60
PE6
PE7
50
PE8
PE9
40
30
0.001
0.1
10
Angular Frequency (rad/s)
1000
0.01
Figure 5. Phase angle versus angular frequency for polymers
PE1–PE4 measured at 190 8C.
shape of the phase angle curve due to the added long-time
relaxation mode in the viscoelastic behavior. Such effects
on the phase angle curve will become more pronounced
with the increase of LCBD.[9,22] Figure 5 shows the phase
angle curves for the four polymers, PE1–PE4, measured at
190 8C. It should be noted that polymer PE5 was not
included in this comparison due to its much higher M w and
broader MWD. From Figure 5, it can be seen that the phase
angle at a given frequency decreases in the following
manner coupled with a change of the shape of the curves:
PE1 > PE2 PE3 > PE4. The phase angle difference
between PE2 and PE3 is minor compared to those between
other polymer pairs. In general, PE3 has slightly lower
phase angle than PE2. In addition to LCB, the slightly
higher PDI of PE3 can also be seen as a factor contributing
to this difference. Therefore, from the phase angle behavior
in Figure 5 we can conclude the LCBD increases in the
order: PE1 < PE2 PE3 < PE4, which is again consistent
with our findings obtained in previous sections.
It has been reported in many investigations[9,13–15,22,49]
that when the LCBD is high enough in LCB polymers, a
plateau in the phase angle curve can be usually identified
and the frequency width of the plateau increases with the
LCBD. In Figure 5, the change in the shape of the curves can
be clearly observed. However, no obvious plateau in the
curves can be found even for PE4, which has the highest
LCBD among the four polymers, suggesting a comparatively low level of LCBD in these polymers.
Figure 6 shows the phase angle curves for PE6–PE9
measured at 190 8C. Compared to PE7, PE6 exhibits significantly reduced phase angle in the frequency range
although the two polymers possess very similar M w
and PDI. Therefore, it can be inferred again that PE6
has higher LCBD than PE7. However, a similar
comparison with PE8 and PE9 in LCBD cannot be made
from the phase angle curves due to their higher MW
and PDI.
Macromol. Chem. Phys. 2005, 206, 2096–2105
30
www.mcp-journal.de
0.1
1
10
100
Angular Frequency (rad/s)
1000
Figure 6. Phase angle versus angular frequency for polymers
PE6–PE9 measured at 190 8C.
Activation Energy and Thermorheological
Complexity
Linear polymers are considered thermorheologically
simple because their rheological properties obey the timetemperature superposition principle. However, the superposition principle is not valid for LCB polymers because of
constraints imposed by branching points on chain relaxation, and the polymers are termed thermorheologically
complex.[23] The temperature dependence of modulus shift
factor, aT, for rheologically simple polymers often follows
the Arrhenius relation at temperatures well above polymer
glass transitional temperature (Tg). The flow activation
energy Ea, which is a measure of temperature sensitivity, is
given by
Ea 1
1
ð5Þ
aT ¼ exp
R T T0
Thermorheologically complex LCB polymers, however,
do not follow this simple relation. These polymers do not
have single activation energy but exhibit modulus-dependent temperature sensitivity.[23]
Figure 7 shows the activation energy spectra for the set of
samples PE1–PE5 at a reference temperature of 190 8C.
These spectra were plotted on the basis of the experimental
loss modulus data (G00 vs. o) according to the method
summarized by Wood-Adams et al.[23] For these five
polymers, with the increase in angular frequency, the
activation energy gradually decreases and reaches a plateau
value at the high-frequency end, which indicates the
thermorheological complexity of the polymers and the
presence of LCB structure. The plateau activation energy
values, which are dependent on SCBD of the polymers, are
different for the five polymers with PE1 and PE5 having
the highest and lowest values, respectively. This reflects the
difference in SCBD of the polymers. In the high-frequency
region, the stress relaxation behavior of a LCB polymer is
ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . .
PE1
PE3
PE5
Ea from G" (kJ/mol)
40
40
PE2
PE4
Ea from G" (kJ/mol)
44
36
32
28
35
30
PE6
PE7
PE8
PE9
25
24
20
20
0.01
0.1
1
10
100
o
Angular Frequency at 190 C (rad/s)
Figure 7. Activation energy spectra from G00 (reference temperature ¼ 190 8C) for polymers PE1–PE5.
dominated by the repetition of linear chains. Hence, the
activation energy in this region should converge to approximately the same activation energy for a purely linear
polymer of equivalent microstructure.[23] For linear polyethylenes, the activation energy is dependent on the SCBD.
Conventional HDPE has an activation energy of approximately 27 kJ mol1.[23] For conventional linear LLDPE,
activation energy increases with SCBD and activation
energy values up to 45 kJ mol1 has been reported for
highly short-chain branched ethylene-hexene copolymers,[18] and various correlations have been established in
the literature to correlate the effect of SCBD on activation
energy.[9,18,23] From Figure 7, a clear general trend of the
increase of the plateau activation energy with SCBD can
be observed from 26 kJ mol1 for PE5 (SCBD ¼ 0) to
35 kJ mol1 for PE1 (SCBD ¼ 40/1 000 carbons).
Unlike the SCBD-dependent plateau activation energy,
the activation energy in the low-frequency region of the
spectrum is related more to the LCBD of the polymers as
the stress relaxation behavior in this region is dominated by
the LCB molecules that are more sensitive to temperature.
Higher LCBD generally leads to higher activation energy
in the low-frequency range and larger changes in the
activation energy from low frequency to high frequency.[23]
However, owing to the experimental difficulty in obtaining accurate viscoelastic data in the extremely lowfrequency range, activation energy at frequency lower than
0.04 rad s1 could not be accurately determined. Therefore, a comparison of the LCBD of the five polymers based
on the activation energy difference in the low frequency end
could not be performed.
Figure 8 shows the activation energy spectra for
polymers PE6–PE9 at a reference temperature of 190 8C.
Surprisingly, these polymers exhibited an almost constant
activation energy within the studied frequency range,
although other rheological evidences, such as enhanced Z0
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0.01
0.1
1
10
100
1000
o
Angular Frequency at 190 C (rad/s)
Figure 8. Activation energy spectra from G00 (reference temperature ¼ 190 8C) for polymers PE6–PE9.
and up-shifted log G0 versus log G00 curve, have indicated
the presence of LCB in these polymers. This discrepancy
might be due to an even lower level of LCBD in these
polymers and the relative insensitivity of Ea toward LCB
compared to other rheological properties. In addition, the
activation energy values for these polymers are very close
(33–35 kJ mol1), suggesting that the LCBD and SCBD
are very low and close to each other.
Effect of Catalyst Ratio in Tandem
Catalysis on LCBD
The above investigation and analysis of the rheological
properties of the two sets of polymers prepared with
concurrent tandem catalysis have provided strong evidences for the presence of sparse LCB in these polymers.
We believe the mechanism for the LCB formation in this
concurrent tandem catalysis system is no different from that
in the single CGC catalyst system, which has been well
studied for producing LCB polymers. During LLDPE
preparation with the concurrent tandem catalysis system,
the trimerization catalyst 1 trimerizes ethylene to 1-hexene
and the CGC catalyst 2 copolymerizes ethylene with
1-hexene and in situ generates vinyl-ended poly(ethyleneco-hexene) macromonomers, which are further incorporated by catalyst 2 into growing chains to form LCB
polymers.
In several studies[7,10–12,14,15] on the preparation of LCB
LLDPE by ethylene-olefin copolymerization with a single
metallocene catalyst, it has been found that olefin concentration within the copolymerization system greatly affects
LCBD of the polymers. The incorporation of a small
amount of olefin comonomer at low olefin concentrations
can improve the solubility and flexibility of the macromonomer and thus facilitate its reincorporation to generate
LCB LLDPE with enhanced LCBD. However, at high olefin
ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian
contents, excessive olefin incorporation leads to significant
undesirable chain terminations generating unincorporable
vinylidene-terminated chains and thus produce polymers
with reduced LCBD and even linear polymers.[14,15]
From the above rheological results, we can observe a
similar phenomenon with the LLDPE prepared here with
concurrent tandem catalysis. For the set of polymers
prepared at 45 8C (PE6–PE9), we can summarize from
the above rheological data that LCBD increases qualitatively according to the order: PE9 PE8 < PE7 < PE6, i.e.,
LCBD increases with the molar ratio of catalyst 1/catalyst 2
during preparation. The concentration level of 1-hexene
remains to be very low in the polymerization system at
45 8C[28,29,44] due to a significant deactivation of trimerization catalyst 1 at this temperature. An increase in the molar
ratio of catalyst 1/catalyst 2 leads to higher 1-hexene
concentration and increased solubility and flexibility for
the macromonomer without causing excessive undesirable
chain termination. Hence, LCBD tends to increase with an
enhancement in the catalyst ratio at this elevated temperature. However, for the polymer set prepared at 25 8C
(PE1–PE5), the above rheological properties suggest that
LCBD increases in the following sequence: PE1 < PE2
PE3 < PE4, i.e., LCBD increases with a decrease in the
molar ratio of catalyst 1/catalyst 2 during preparation. At
this reduced temperature, the trimerization catalyst 1 does
not experience pronounced deactivation and retains high
activity toward ethylene trimerization.[28,29,44] 1-Hexene
concentration in the polymerization system is thus high
enough to lead to significant undesirable chain terminations, thereby producing unincorporable macromonomers.
Therefore, at this temperature lowering the ratio of catalyst
1/catalyst 2 will suppress such undesirable chain terminations and increase LCBD in the polymer.
Conclusion
In this study, we have examined for the first time the
rheological properties of LLDPE prepared using concurrent
tandem catalysis system with ethylene as the sole monomer
stock. Two sets of ethylene-hexene derived LLDPE (PE1–
PE5 and PE6–PE9) were prepared with binary tandem
catalysis system comprising (Z5-C5H4CMe2C6H5)TiCl3
(1)/MMAO and [(Z5-C5Me4)SiMe2(tBuN)]TiCl2 (2)/
MMAO catalysts with various catalyst ratios and at two
temperature levels (25 and 45 8C). The melt rheological
properties of these polymers were extensively evaluated
and compared utilizing small-amplitude dynamic oscillation measurements. These polymers have been found to
possess some typical rheological properties characteristic
of LCB polymers, such as enhanced zero-shear viscosity,
improved shear-thinning, elevated dynamic moduli, and
thermorheological complexity, which suggest the presence
of LCB in the polymers. The LCBD of the two respective
Macromol. Chem. Phys. 2005, 206, 2096–2105
www.mcp-journal.de
sets of polymers were qualitatively compared and correlated to the polymerization conditions including catalyst
ratio and temperature. At the lower temperature of 25 8C for
various catalyst concentration ratios, LCBD increases with
a decrease in the ratio of catalyst 1/catalyst 2 owing to the
excessive production of unincorporable macromonomers
resulted from high 1-hexene concentration level at this
temperature. At the higher temperature of 45 8C, the LCBD
tends to increase with an increase in the ratio of catalyst
1/catalyst 2 due to the enhancement of flexibility and
solubility of incorporable macromonomers without producing excessive undesirable chain terminations.
Acknowledgements: Z. Y. thanks Natural Science and
Engineering Research Council (NSERC) of Canada for the
financial support of this research.
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