Structure‐Property Relationships of Linear and Long‐Chain Branched Metallocene High‐Density Polyethylenes Characterized by Shear Rheology and SEC‐MALLS

26
DOI: 10.1002/macp.200500321
Summary: Linear and long-chain branched high-density
polyethylenes with a molar mass M w between 1 700 and
1 150 000 g mol1 were synthesized using metallocene
catalyst systems. Depending on the polymerization parameters the molar mass distribution reached values ranging
from 2 to 12. The resins were characterized with various
analytical methods. The branch detection took place via two
independent methods, melt rheology and SEC-MALLS. New
relationships between catalyst structure, polymerization
conditions, and the branching content of polyethylenes were
established. Besides the branched materials strictly linear
polymers are presented; for those no long-chain branches
were detected either by light scattering or by rheology. The
viscosity function was observed to be strongly influenced by
the molar mass distribution and the degree of long-chain
branching. The molar mass distribution was affected by the
catalyst type and the polymerization conditions. A dependence of the melting point and the melting enthalpy on the
molar mass was observed.
Full Paper
Z0-M w correlation of the linear and long-chain branched
samples.
Structure-Property Relationships of Linear and
Long-Chain Branched Metallocene High-Density
Polyethylenes Characterized by Shear Rheology
and SEC-MALLS
Christian Piel,1 Florian J. Stadler,2 Joachim Kaschta,2 Sascha Rulhoff,1 Helmut Münstedt,2 Walter Kaminsky*1
1
Institute of Technical and Macromolecular Chemistry, University of Hamburg, Bundesstr. 45, D-20146 Hamburg, Germany
Fax: (þ49) 40 42838 6008; E-mail: kaminsky@chemie.uni-hamburg.de
2
Institute of Polymer Materials, Friedrich-Alexander University Erlangen-Nürnberg, Martensstr. 7, D-91058 Erlangen, Germany
Received: July 15, 2005; Revised: October 31, 2005; Accepted: November 3, 2005; DOI: 10.1002/macp.200500321
Keywords: catalysts; DSC; high-density polyethylene; linear; long-chain branches; metallocene; polymerization; SEC-MALLS;
viscosity function
Introduction
With the advent of metallocene catalysts relatively narrow
distributed and strictly linear as well as long-chain branched
polyethylenes can be obtained in a large range of molar
masses.
Long-chain branches (LCBs) and narrow molar mass
distribution (MMD) (M w =M n ) are a novel structure combination in polyethylene (PE), which has only been possible
to achieve with single-site catalysis. Long-chain branching
in metallocene catalysis is believed to take place via a
Macromol. Chem. Phys. 2006, 207, 26–38
copolymerization route, in which a vinyl terminated PE
chain is incorporated into a growing polymer chain.[1]
Although there was another mechanism observed for
vanadium catalysts and transferred to metallocenes,[2] the
examination of the polymerization behavior of several
metallocene compounds revealed that chain transfer mechanisms were catalyst specific. Depending on the catalyst
structure, the termination of chain growth occurred via b-H
elimination, chain transfer to the monomer, or chain
transfer to the catalyst. Long-chain branching analysis
of PEs produced with different metallocene catalysts
ß 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Structure-Property Relationships of Linear and Long-Chain Branched Metallocene . . .
indicated that the catalysts with high vinyl selectivity and
good copolymerization ability were the most prominent in
producing a polymer with modified rheological properties.
The first single-site catalyst reported to produce LCB-PE
was a constrained geometry catalyst (CGC), which is a halfmetallocene.[3,4] In the early publications, it was only stated
that the open structure of CGC enables LCB formation.
Later it has been possible to use sterically more hindered
dicyclopentadienyl catalysts for the production of LCB-PE.
LCB has been produced with Cp2ZrMe2/B(C6F4)3[5] and
Cp2ZrCl2/MAO,[6–8] but the use of (Me5Cp)2ZrMe2/MAO
catalyst resulted in a linear polymer.[5,9] In addition to these
catalysts, Et[Ind]2ZrCl2/MAO and other ansa-metallocenes
have also been reported to produce LCB-PE.[10–13] In this
work PEs with a defined linear or long-chain branched
topography were synthesized in order to find more relationships between catalyst structure, polymerization conditions, and branch incorporation.
Three different basic methods are used for the detection
of LCB: 13C NMR spectroscopy, size exclusion chromatography with coupled multi-angle laser light scattering
(SEC-MALLS), and rheological measurements. Melt rheological measurements are the most sensitive methods for
detecting very low concentrations of LCB. The LCB
density in single-site catalyzed PEs is typically in the range
of 0.01–0.2 branch points per 1 000 main-chain carbons.[10,12] In many cases, low LCB content is difficult to
detect with 13C NMR spectroscopic methods, even though
nowadays a differentiation between side chains of longer
than six carbons is possible.[14] However, a mixture of shortchain branches and LCBs (usually found in LLDPE) is very
hard or even impossible to characterize with respect to
LCBs because of the similar signals of SCBs and LCBs.[15]
Here SEC-MALLS and melt rheological measurements are
used for branch detection.
Shear rheological measurements are a very sensitive tool
to get an insight into the molecular structure as well as into
the processing behavior of polymers. The dependence of
the zero shear-rate viscosity Z0 on the molar mass M w is
described by
a
Z0 ¼ K1M w
for M w > Mc
ð1Þ
Z0 ¼ K2M w
for M w < Mc
ð2Þ
Mc 2Mc
ð3Þ
and well known for years.[16] a, usually between 3.4 and 3.6,
is the slope of the correlation. K1 and K2 are the parameters
dependent on the polymer type and the temperature, and Mc
is a critical molar mass which is approximately two times
the entanglement molar mass Me. Technically relevant
polymers usually have a weight-average molar mass M w of
more than 5Mc because the polymers with a lower M w are
very brittle.
Macromol. Chem. Phys. 2006, 207, 26–38
www.mcp-journal.de
Unfortunately the zero shear-rate viscosity Z0 is not easy
to measure for high-molar mass resins as, among other
problems, the longest relaxation time becomes very high
which leads to very long measurement times. A narrow
MMD limits the width of the relaxation toward long and
short relaxation times and is therefore advantageous for
the determination of the zero shear-rate viscosity as the
necessary measurement time is reduced.
The zero shear-rate viscosity Z0 of LCB polymers
depends not only on the M w but also on the molecular
topography. Thus, no simple equation such as [Eq. (1)]
is valid for non-linear chains. As a general trend
small amounts of LCB will lead to an increased Z0
while large amounts of LCB (e.g., in LDPE) will decrease
Z0.[17–20]
Polyethylene tends to cross-link with increasing time in
the melt, and cross-linking involves the formation of LCBs
as a first step. Thus, it is of great importance to ensure the
thermal stability of the samples. If cross-linking can be
excluded, the deviation of the viscosity function from the
linear function is very sensitive to detect LCB.
LCBs dramatically influence the viscosity function.
Therefore, the knowledge of a linear standard polymer is
important. LCBs will change the relaxation behavior by
introducing additional modes which account for an
s-shaped viscosity function.[19,21,22]
In order to separate the effects of the MMD and longchain branching by shear rheology, the MMD has to be
measured by SEC. A MALLS detector attached to the SEC
apparatus is able to measure the radius of gyration as a
function of the molar mass hr2i0.5 (M) of the samples as an
additional information besides the absolute molar mass.
The presence of LCBs in the polymer leads to a decrease of
the radius of gyration hr2i0.5. By plotting the radius of
gyration as a function of the molar mass hr2i0.5 (M) this
decrease can be detected as the deviation from a linear curve
representative for each class of polymers. Due to physical
limitations the hr2i0.5 cannot be detected below 20 nm.
In this study a broad range of linear and long-chain
branched PEs were synthesized using metallocenes and
CGC. Some catalysts were taken which were studied before
concerning long-chain branching. However, there is a lack
of information available in literature how the catalyst
structure and the polymerization conditions affect the
formation of LCBs. By using also known systems definitely
linear and long-chain branched PEs were obtained. New
structure-property relationships using two independent
detection methods can be established and extended to new
systems based on the results.
Experimental Part
Polymer Synthesis
All operations were performed under a dry argon atmosphere
using standard Schlenk techniques.
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C. Piel, F. J. Stadler, J. Kaschta, S. Rulhoff, H. Münstedt, W. Kaminsky
The solvent toluene and the monomer ethene were purified
passing through two columns with a 4-Å molecular sieve and
BASF copper catalyst R3-11. Methylaluminoxane (MAO,
Crompton) solution was filtered; the toluene was removed in
vacuo, and MAO stored as a solid. Freshly prepared solutions
in dry toluene were used for polymerizations.
The ethene polymers were produced using (CpMe5)2ZrCl2
(A), Cp2ZrCl2 (E), rac-[Et(Ind)2]ZrCl2 (B), [Me2Si(Me4Cp)NtertBu)]TiCl2 (D), [Ph2C(2,7-di-tertBuFlu)(Cp)]ZrCl2 (F),
and [Me2C(Cp)2]ZrCl2 (G) together with MAO as cocatalyst.
Synthesis of the catalyst precursors A, E, F, and G (Figure 1)
was performed according to the general procedure reported in
literature. The metallocene B and the CGC D were purchased
from Boulder Scientific Corp. All precursors were stored under
argon atmosphere, and fresh solutions in dry toluene were
prepared before use.
Polymerizations were carried out in dry toluene in either a 1l
or a 3l Büchi glass reactor equipped with a magnetic stirrer. The
ethene pressure for every run was set and the pressure was kept
constant during the polymerization; ethene was fed and
recorded constantly by a Brooks Mass Flow Controller. The
monomer concentrations were calculated using literature
data.[23] Some polymerizations were done in presence of
hydrogen to reduce the molar mass of the polymer. In these
cases the solution was saturated with hydrogen by setting up a
pressure for 5 min prior feeding ethene. The polymerizations
were started by injecting the catalyst precursor dissolved in
toluene into the ethene-saturated toluene/MAO solution. The
polymerization reaction was stopped by addition of 1 ml of
ethanol. Polymerization details are given in Table 1. The
polymer solution was stirred overnight in an ethanol/HCl/
water solution, filtered, and washed with plenty of ethanol
followed by evaporation of the solvents and drying of the
polymer in vacuo at 60 8C overnight.
Molecular Characterization
Differential Scanning Calorimetry (DSC)
The thermal behavior of the polymers was measured on a
Mettler-Toledo DSC 821e, temperature range from 0 to 200 8C
with a heating and cooling rate of 20 K min1. To determine
the melting temperatures and enthalpies the second heat was
used. The crystallinity was determined from melt enthalpy;
enthalpy of fusion of perfectly crystalline PE was taken to be
290 J g1.[24]
Size Exclusion Chromatography (SEC)
The molecular characterization was carried out on a Waters
150C, equipped with a refractive index (RI) detector and an
additional IR detector (PolyChar, IR4) at 140 8C for column
and sample compartment using 1,2,4-trichlorobenzene (TCB)
as solvent. The high-temperature SEC was coupled with a
MALLS apparatus (Wyatt, DAWN EOS), which was also
operated at 140 8C. The samples (2 g l1) were dissolved
in TCB at 160 8C for 3 h prior to the analysis. Irganox 1035
Figure 1. Catalyst precursors (CpMe5)2ZrCl2 (A), Cp2ZrCl2 (E), rac-[Et(Ind)2]ZrCl2 (B),
[Me2Si(Me4Cp)NtertBu)]TiCl2 (D), [Ph2C(2,7-di-tertBuFlu)(Cp)]ZrCl2 (F), [Me2C(Cp)2]ZrCl2 (G).
Macromol. Chem. Phys. 2006, 207, 26–38
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ß 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Structure-Property Relationships of Linear and Long-Chain Branched Metallocene . . .
Table 1.
#
Polymerization conditions.
Catalyst
A1
A2
A5
A4
A6
A7
A8
A9
A3
E8
E1
E9
E2
E3
E4
E5
E6
E7
B1
B2
B4
B5
B6
B7
B8
B9
D3
D4
D5
F1
F2
F3
G1
G2
A
A
A
A
A
A
A
A
A
E
E
E
E
E
E
E
E
E
B
B
B
B
B
B
B
B
D
D
D
F
F
F
G
G
Temperature
c (ethene)a)
1
p (ethene)b)
n (H2)
Timec)
n (catalyst)
MAO
Toluene
mmol
min
mmol
mg
ml
60
240
240
240
240
300
75
80
75
180
242
60
60
241
215
45
60
60
240
158
90
241
240
218
154
190
240
241
225
243
250
243
93
90
0.20
1.00
1.25
1.00
0.25
4.50
0.20
0.10
0.10
0.50
0.50
0.2
0.20
0.50
0.50
0.25
0.50
0.20
0.50
0.25
0.50
0.25
0.50
0.25
0.25
0.25
3.00
1.00
1.00
0.48
0.32
0.16
2.50
1.50
200
1 000
1 000
1 000
1 000
1 000
400
400
400
1 000
1 000
200
200
600
1 000
200
200
200
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
800
800
200
2 000
2 000
2 000
2 000
2 000
400
400
400
2 000
2 000
200
200
2 000
2 000
200
200
200
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
2 000
1 200
1 200
8C
mol l
bar
30
30
60
60
60
90
90
90
90
30
30
60
60
60
60
90
90
90
60
60
60
60
75
75
75
90
60
60
90
60
60
60
90
90
0.24
0.24
0.23
0.47
0.41
0.24
0.24
0.24
0.24
0.23
0.23
0.13
0.13
0.41
0.41
0.06
0.13
0.13
0.08
0.25
0.41
0.41
0.07
0.22
0.37
0.19
0.41
0.41
0.24
0.24
0.41
0.41
0.05
0.10
2.00
2.00
2.80
5.80
5.00
3.80
3.80
3.80
3.80
2.00
2.00
1.55
1.55
5.00
5.00
1.00
2.00
2.00
1.00
3.00
5.00
5.00
1.00
3.00
5.00
3.00
5.00
5.00
3.80
2.95
5.00
5.00
0.79
1.58
9.0
8.3
8.3
16.6
9.0
9.0
9.0
8.3
9.0
9.0
9.0
9.0
a)
Ethene concentration in toluene.
Ethene pressure in the reactor.
c)
Polymerization time.
b)
(Ciba SC) was added to the solution in a concentration of
1 g l1 to avoid degradation during analysis. The flow rate was
chosen to be 0.5 ml min1 in order to prevent mechanical
degradation of the polymer on the columns. 300 ml of the
solution was injected onto a set of four SEC columns (3 Shodex
columns UT 806, 1 Shodex UT807). Calibration of the SEC
was performed with narrow MMD polystyrene Standards from
Polymer Laboratories of molecular weights ranging from 1 to
11 000kg mol1. The Mark Houwink constants for the universal
calibrations were K ¼ 1.21 104 ml g1 and a ¼ 0.707 for
PS[25] and K ¼ 4.06 104 ml g1 and a ¼ 0.725 for PE.[26]
Rheology
For the rheological measurements several different commercial rheometers were used. Most measurements were carried
out using a 25 mm parallel plate geometry. For the samples with
a smaller viscosity a 25 mm/2.5 cone/plate, 50 mm parallel
Macromol. Chem. Phys. 2006, 207, 26–38
www.mcp-journal.de
plate, and 50 mm/2.5 cone/plate geometry were also used. All
experiments were performed under nitrogen atmosphere. The
materials were stabilized with 0.5 wt.-% Irganox 1010 and
0.5 wt.-% Irgafos 38 or Irgafos 168 (Ciba SC).
To obtain a stability criterion degradation tests were performed under continuous oscillation at a constant frequency o.
A maximum deviation of 5% in the storage modulus G0 at a
low frequency o is considered to the time of stability. The tests
indicate that the time of stability is beyond 15 000 s for most
samples.
As PE is cross-linking without stabilizer, the fact that no
cross-linking is observed for any of the samples (except for A6)
proves that the chosen stabilization is appropriate. A6 starts
cross-linking after a very short measuring time (100 s). Thus,
no further rheological measurements were performed for A6.
Frequency sweeps in the linear viscoelastic regime were
performed with a Malvern/Bohlin CVOR ‘‘Gemini’’ in the
frequency range between 0.01 and 1 000 s1.
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C. Piel, F. J. Stadler, J. Kaschta, S. Rulhoff, H. Münstedt, W. Kaminsky
Samples with a maximum relaxation time, which is high
enough not to reach the zero shear-rate viscosity with a
frequency sweep, were also characterized by creep tests to
reach the zero shear-rate viscosity Z0. Experimental details of
the rheological tests are described in depth elsewhere.[27]
Polymerizations and Results
Polymerization Behavior
When considering long-chain branch formation via the
copolymerization route, the choice of catalyst and polymerization conditions has to play a great role. The importance of catalyst vinyl-group selectivity for formation of
LCB is described by the group of Seppälä for catalysts E, B,
and others.[6,11,28] Another important factor is the polymerization reactor: In a batch polymerization, the macromonomer concentration (here the polymer itself) increases
Table 2.
#
A1
A2
A5
A4
A6
A7
A8
A9
A3
E8
E1
E9
E2
E3
E4
E5
E6
E7
B1
B2
B4
B5
B6
B7
B8
B9
D3
D4
D5
F1
F2
F3
G1
G2
and the monomer concentration decreases as the polymerization proceeds. The monomer concentration is constant in
semi-batch polymerization and in the continuous stirred
tank reactor system; both monomer and macromonomer
concentrations are constant after the steady-state conditions
are achieved. The shown polymerizations were performed
in a semi-batch process. The influence of the polymerization time on the amount of branches in the polymer is under
investigation and will be described elsewhere.
The polymerization activities and polymer characteristics are given in Table 2. Catalysts E and B deliver the
highest polymerization activities of all investigated catalysts in this study. It is remarkable that the activity of
catalysts A, D, and F is enormously increased if hydrogen
is used. Hydrogen affects the activity in different ways
depending on the catalyst structure; for catalysts B and E
lower activities are observed.
Polymerization activities and polymer characteristics.
Activitya)
27 100
30 900
17 800
19 900
129 200
2 800
56 200
53 100
47 000
31 300
37 600
193 000
194 500
124 900
45 600
275100
171 500
414 200
130 200
187 900
134 600
76 000
279 900
245 000
268 400
498 300
7 200
16 400
43 000
45 400
22 000
46 300
16 300
25 500
Tmb)
Tcb)
DH
Crystallinityc)
Mw
8C
8C
J g1
%
kg mol1
140
140
142
142
136
135
131
131
129
138
133
138
128
140
133
135
136
126
139
141
138
135
135
138
138
135
140
136
140
140
136
138
113
118
112
112
113
112
117
114
116
115
113
112
116
113
115
109
117
117
115
112
110
109
112
114
113
111
116
114
112
114
109
111
114
112
101
104
174
137
170
176
232
217
227
228
237
152
248
173
244
181
256
208
202
246
179
217
208
202
196
171
196
226
156
199
177
172
151
185
205
214
60
45
53
60
80
74
78
78
81
52
85
59
83
62
88
71
69
84
61
74
71
69
67
58
67
78
53
68
60
59
52
64
70
74
665
923
403
564
72
179
28
19
17
565
12.7
221
6.5
297
15
52
47
4.7
147
93
100
67
106
76
69
66
560
74
365
102
1 150
173
1.7
2.8
MMD
3.0
3.8
2.6
4.3
11.6
4.0
7.8
6.5
10.0
2.2
2.1
2.1
2.2
2.1
2.5
2.0
2.0
2.5
2.2
1.9
2.0
2.1
2.5
1.8
2.0
1.8
2.1
2.0
2.6
2.0
4.0
2.0
2.8
2.9
kgpolymer (molcat h mol l1 ethene)1.
Peak temperature.
c)
Enthalpy of fusion of perfectly crystalline PE was taken to be 290 J g1.[24]
a)
b)
Macromol. Chem. Phys. 2006, 207, 26–38
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Structure-Property Relationships of Linear and Long-Chain Branched Metallocene . . .
Molar Masses
For all polymers made by the catalysts E, B, D, F, and G the
expected MMD of about 2 was found. Catalyst A was found
not to be thermostable for a long time and at higher
temperatures. Especially at 90 8C in the reactor a broadening of the MMD was observed, and if hydrogen was
present, a broad MMD was obtained at 60 8C too. The
highest molar mass of all polymers in this study is produced
by catalyst F at 60 8C and 0.41 mol l1 ethene concentration. The molar masses of a series of comparable polymers
in dependence of catalyst structure and hydrogen presence
are given in Figure 2. The reduction of the molar mass by the
presence of hydrogen is very much catalyst specific; it
depends on the favored termination reaction.
Thermal Behavior
Figure 3. Melting temperatures of all of the investigated
polymers.
The melting temperature of PE depends on the molar mass
of the material up to a certain point. The melting temperature increases with increasing molar mass up to a molar
mass M w of 100 kg mol1. After reaching a Tm of about
140 8C no more increase is observed (Figure 3). This is in
agreement with the constant T0m ¼ 141.5 8C[29] which is
described to be the highest possible melting temperature for
a PE; deviations of our data (A4 and A5) are reflected to
DSC inaccuracy.
The crystallization temperature of the materials investigated is between 101 and 115 8C (see Table 2); it much less
depends on the molar mass than the crystallinity. The melt
enthalpy of the samples decreases with increasing molar
mass of the polymers; it does not depend on the type of
catalyst (Figure 4). A maximum of the enthalpy of melting
is observed at a molar mass of about 10 000 g mol1: Each
linear chain has two end groups which are acting as chain
imperfections and cause crystallization hindrances just like
short-chain branches in LLDPE. These end groups lower
both crystallinity and melting point. However, because the
crystallinity was measured using a heating and cooling rate
of 20 K min1, non-equilibrium conditions are present. As
the melting and crystallization peaks of all samples are
approximately the same, the crystallization time is also very
similar for all samples. Because of the different viscosities
of the samples (Z0 varies in a range of about nine decades for
the linear samples and even more for the LCB-samples) the
time needed for equilibrium crystallization is also very
different. For the samples with a very low molar mass the
crystallization time is probably sufficient to reach a quasiequilibrium state. For the samples with the highest molar
masses the chain movements are much more restrained.
Thus, more time is required for the quasi-equilibrium state
of crystallization.
The DSC results show a strong dependence of the
polymers thermal behavior on the molar mass but there is no
hint of any effect of the catalyst structure on this. It is
Figure 2. Molar masses of the polymers obtained at 60 8C and
0.41 mol l1 monomer concentration.
Figure 4. Melting enthalpy dependence on the molar mass of the
polymers.
Macromol. Chem. Phys. 2006, 207, 26–38
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C. Piel, F. J. Stadler, J. Kaschta, S. Rulhoff, H. Münstedt, W. Kaminsky
Figure 7. Influence of hydrogen on MMD and radius of gyration
for catalyst B (B4, B5).
Figure 5. MMDs of polymers polymerized with different
catalysts but under the same conditions.
In Figure 5, the MMDs of polymers made with the different
catalysts but under the same experimental conditions are
compared. It reveals that the different catalysts produce
polymers which differ in molar mass but have comparable
MMDs. The exception is polymer D3 with a high-molar
mass tailing (see arrow). F2 has a slightly broadened MMD.
The influence of the ethene concentration at a fixed polymerization temperature on the MMD and on the radius of
gyration is discussed with respect to Figure 6 for catalyst B.
The linear reference (A2) shown in Figure 6–8 is described
by Stadler et al.[27]. An increase in ethene concentration
leads to slightly decreasing molar masses but has, in
accordance with the ongoing polymerization mechanism,
no influence on the width of the MMD. From the radius of
gyration as a function of absolute molar mass it is concluded
that all polymers are long-chain branched because of the
coil contraction which is evident from the comparison with
the radius of gyration of linear molecules. The polymers do
not differ in their coil contraction and carry, therefore,
LCBs of a similar topography.
The effect of hydrogen on molar mass and the long-chain
branching is shown in Figure 7 and 8 for catalysts B and E,
respectively. For all conditions studied, the presence of
hydrogen reduces the molar masses. The effect is different
for the different catalysts. While the decrease in molar mass
is moderate for catalyst B it is very much pronounced for
catalyst E. In this case, the MMD is shifted to about 20 times
smaller molar masses resulting in a polymer which is too
brittle for applications.
Together with the change in molar mass a change in longchain branching is observed. While for products from
Figure 6. Influence of ethene concentration on molar mass
and radius of gyration for catalyst B at 75 8C polymerization
temperature.
Figure 8. Influence of hydrogen on MMD and radius of gyration
for catalyst E (E3, E4).
therefore concluded that none of the catalysts incorporates
sizable numbers of short-chain branches by side reactions which would lower the melting temperature and
enthalpy.[30]
Branch Detection by SEC-MALLS
Macromol. Chem. Phys. 2006, 207, 26–38
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33
Structure-Property Relationships of Linear and Long-Chain Branched Metallocene . . .
Table 3.
Rheological properties of the long-chain branched samples.
Z0
Z0/Zlin
0
dc
a)
>4.7 107a)
1.2 103
>108a)
8.7 105
6.6 105
4.2 103
>108a)
4.0 104
1.2 104
6.3 103
>9.0 107
4.5 103
(9.0 106)a)
3.1 104
9.0 107a)
4.5 105
Degree of
branching from
SEC-MALLS
Significant
Very weak
Very significant
Significant
Significant
Very weak
Very significant
Significant
Weak
Weak
Significant
Very weak
Very significant
Weak
Very significant
Significant
High
Low
Very high
High
High
None
Very high
High
Low
High
Low
None
High
High
Low
High
8
Pa
E3
E6
B1
B2
B4
B5
B6
B7
B8
B9
D3
D4
D5
F1
F2
F3
Efficacy of branching
from rheology
>103
2.0
>2 775
126
73
2.0
>9 000
12
4.9
3.1
>20
1.5
>12
3.2
>1.51
6.9
–
–
14
35
37
68
26
51
65
69
–
–
–
72
–
63
Zmax.
catalyst B without hydrogen a long-chain branched structure could be clearly detected, it can hardly be found for
the products of catalyst B polymerized with hydrogen
(Figure 7). The same was found for catalyst E (Figure 8).
For this grade (E4) the radius of gyration was so small due
to the lower molar mass that it could only be detected for
the high-molar masses, showing great scatter. The mean
value of the radius of gyration suggests that the polymer is
linear.
The degrees of branching are listed in Table 3. The degree
of branching is qualitatively estimated by the radius of
gyration. If a deviation from the linear standard is barely
visible, the degree of branching is set ‘‘low’’ while a large
deviation is designated with ‘‘very high.’’
Branch Detection by Melt Rheology
The weight-average molar mass M w and the level of longchain branching determine the zero shear-rate viscosity Z0.
The shape of the viscosity function, viz the dependence of
the viscosity on shear rate or angular frequency, is strongly
influenced by the MMD. Because of the broad range of
molar masses the viscosity functions of several linear and
two long-chain branched samples determined by dynamicmechanical experiments are plotted in Figure 9 in a molar
mass-independent way. Figure 9 shows the complex viscosity jZ*(o)j normalized by the zero shear-rate viscosity as a
function of stress oZ0. The solid lines represent the limiting
values of this plot for low and high frequencies. The
limiting value in this reduced plot for infinitely low
frequencies is 1. The other line at high frequencies has a
double logarithmic slope of 1 representing the limiting
slope of the shear thinning behavior.
Macromol. Chem. Phys. 2006, 207, 26–38
www.mcp-journal.de
The direct measurement of the zero shear-rate viscosity
by the frequency sweeps applied is only possible up to
molar masses of 150 000 g mol1 (for the narrowly
distributed resins) as for higher molar masses no distinct
plateau in the complex viscosity jZ*(o)j can be observed if a
minimum frequency o of 0.01 s1 is used. Such a behavior
was also found for commercial resins.[27] For higher molar
masses or broader MMDs more or less exact extrapolation
methods are applied in literature. A possibility to measure
Z0 directly is the use of creep tests which was done for all
samples presented here.
Samples with a narrow MMD (e.g., E5) show a small
transition region. A broader MMD (e.g., A7 and A5) leads
to a wider transition zone between the shear thinning regime
at high frequencies and the limiting zero shear-rate
viscosity Z0. The angular frequency is linked to the shear
rate, the complex viscosity to the shear viscosity, by the
Cox-Merz rule which is valid for unfilled polymer melts.
Therefore, from measurements of this kind conclusions
with respect to aspects of processing can be drawn.
In addition to the linear samples the normalized viscosity
functions of the long-chain branched PEs F3 and a
commercial LDPEa are plotted. As can be seen the shear
thinning of F3 is similar to that of the LDPE but more
pronounced than that for the linear sample with the broadest
MMD. It is obvious that viscosity functions are not the most
appropriate rheological functions to get an insight into
the branching structure. Broadening of the MMD and the
introduction of LCBs do have a similar effect on shear
thinning.
a
The LDPE is Lupolen 1840D from Basell company. The data
were taken from Schwetz et al.[31]
ß 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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C. Piel, F. J. Stadler, J. Kaschta, S. Rulhoff, H. Münstedt, W. Kaminsky
LCBs. The ratio Z0/Zlin
0 is used as a characteristic number for
further discussions. Zlin
0 is the zero shear-rate viscosity of a
corresponding linear sample with M w equal to that of the
branched counterpart. In some cases the zero shear-rate
viscosity could not be reached due to extremely long
retardation times. These measurements are marked by an
arrow, which indicates that Z0 is still higher than the value
Zmax measured. For such samples the quotient Zmax/Zlin
0 is
discussed as a qualitative quantity.
Phase Angle as a Function of Complex Modulus
Figure 9. Normalized viscosity functions of several linear and
two long-chain branched PEs obtained from dynamic mechanical
measurements at 150 8C.
Zero Shear-Rate Viscosity
Zero shear-rate viscosity as a function of the mass average
molar mass M w determined by SEC-MALLS is a very
sensitive correlation for the detection of long-chain branching. The zero shear-rate viscosities of the samples are
plotted in Figure 10 as a function of M w . All linear samples
come to lie onto a line described by Z0 ¼ 9 1015 M w 3.6
(Z0 in Pa and M w in g mol1). This means that no LCBs
were detected for any of the samples either by SECMALLS or by rheology. For the samples listed in Table 3, a
clear deviation of Z0 (M w ) from Z0 M w 3.6 toward higher
viscosities is found which clearly indicates the existence of
Figure 10. Z0-M w correlation of the linear and long-chain
branched samples (open symbols, linear samples; filled symbols,
branched samples).
Macromol. Chem. Phys. 2006, 207, 26–38
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The plot of the phase angle d as a function of the complex
modulus jG*j (sometimes called van Gurp-Palmen plot)
can often be found in literature as it is sensitive with respect
to LCBs and MMDs. The drawback of this plot is that it does
not allow to clearly discriminate between the influence of
the MMD and branching. This fact is obvious from
Figure 11 in which d(jG*j) is plotted for four linear PEs
and one long-chain branched product (B4). The linear
samples A5 and A7 which possess a narrower MMD than
E1 and E5 significantly deviate from the curves for these
products. LCBs can have an additional effect on d(jG*j) as
demonstrated by the curve for sample B4 in Figure 11. Its
shape is distinguished by a minimum of the corresponding
phase angle dc which is used in literature to characterize
branching. Despite the ambiguity of d(jG*j) with respect to
molecular characterization, dc is discussed in this article for
all samples whose curves do exhibit a distinct minimum
of d.
Comparison of the Rheological Data
The rheological data characteristic for long-chain branched
samples are given in Table 3. The zero shear-rate viscosities, the ratios Z0/Zlin
0 , and the minima of the phase angle dc
are listed and evaluated for an assessment of branching.
Figure 11.
d(jG*j) plot for some of the PEs.
ß 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
35
Structure-Property Relationships of Linear and Long-Chain Branched Metallocene . . .
From Table 3 it becomes obvious that the determination
of dc is rather limited. It is well established from literature
that a stronger efficacy of LCBs is reflected in a higher
viscosity ratio[19,21,22] and a smaller dc.[32] It follows from
Table 3 that lower the dc larger is the viscosity ratio in all
cases for which dc could be determined.
Based on this qualitative agreement of the two rheological quantities an assessment on the efficacy of the LCBs
is also given in Table 3. For comparison, the qualitative
evaluation of the degree of branching from SEC-MALLS is
listed in the last column of Table 3. There is an agreement
between the two methods concerning branching for most of
the samples. For B9, D3, F1, and F2 obvious discrepancies
exist, however.
For D3 and F2 it was found that these samples are highly
branched according to the rheological measurements but
almost linear according to SEC-MALLS.b An explanation
is as follows: The polymers possess an extremely highmolar mass (cf. Table 2). Therefore, very few but extremely
long branches can account for the behavior observed in the
rheological measurements, which were not detectable by
SEC-MALLS.
The products B9 and F1, which exhibit a high degree of
branching but only a small difference from the rheological
behavior of a linear sample, are of quite low molar mass M w .
Therefore, the LCBs have to be relatively short. As a
consequence they are not efficient with respect to the
rheological quantities but are still long enough to produce a
significant coil contraction in solution.
Interesting is the fact that for the two samples (B5 and
D4), for which branching could not be detected by SECMALLS, a small but measurable viscosity ratio Z0/Zlin
0 in the
range of about 2 could be observed. This finding gives a hint
of the very high sensitivity of the zero shear-rate viscosity
with respect to long-chain branching.
E (E3), and F (F2) using no hydrogen show very high-molar
masses and viscosities. For those samples it was not
possible to reach the zero shear-rate viscosity because of the
very long relaxation times. Therefore, the values Zmax/Zlin
0 in
Figure 12 are marked by arrows. For catalyst B (sample B4)
it was possible to determine the zero shear-rate viscosity
which leads to a zero shear-rate viscosity increase Z0/Zlin
0 of
53. All the catalysts (B, D, E) produce polymers which
show a more than tenfold increase of the zero shear-rate
viscosity Z0 over the value of a linear sample of equal M w .
Thus, it can be concluded that the polymers carry LCBs of
high-molar mass.
When the synthesis is carried out using hydrogen for
molar mass control, the ratio Z0/Zlin
0 is significantly decreased for samples B5, D4, and E4. While for E4 a viscosity was
not measurable, a value of Z0/Zlin
0 of 1.5 is found for D4 and
of 2.0 for B5, respectively. These results indicate that only
few LCBs have been formed and that hydrogen does
decreases not only the molar mass but also the incorporation
of macromers in the branching step (by chain termination
with saturated endgroups).
For the products of catalyst F no conclusions on the effect
of hydrogen with respect to the level of long-chain
branching can be drawn, as due to the ultra-high-molar
mass of F2 no estimate of Z0 could be obtained, while for F3
the zero shear-arte viscosity could be measured. It is
interesting to note that the catalyst F produces more LCBs
in the presence of hydrogen compared to the catalysts B, D,
and E as the ratio Z0/Zlin
0 for F3 is 7, which is much higher
than the values obtained for D4, E4, and B5.
Influence of Ethene Concentration
Besides the influences of the type of catalyst and of
hydrogen on the rheological properties of PEs the effect
of monomer concentration was investigated. For these
measurements the catalyst B was used and the ethene
Effect of Various Polymerization
Conditions on Branching
Making use of the correlations between rheological
properties and branching obtained from the foregoing
investigations it can be tried to get an insight into the effect
various polymerization conditions have on branching.
Influence of Hydrogen
In Figure 12 the increase of the zero shear-rate viscosity
over a linear sample of equal M w Z0/Zlin
0 is compared for
samples synthesized under the same experimental conditions but with and without hydrogen used for molar mass
control. The resins produced with the catalysts D (D3),
b
No gelled portion was detected for this resin by SEC-MALLS,
i.e., the injected mass was completely recovered in the detectors.
A very small cross-linked gel fraction which could not be
detected by SEC-MALLS would explain the behavior too.
Macromol. Chem. Phys. 2006, 207, 26–38
www.mcp-journal.de
Figure 12. Influence of hydrogen on the zero shear-rate
viscosity increase Z0/Zlin
0 of LCB-PEs (all synthesized at 60 8C
and 0.41 mol l1 ethene). Arrows indicate that Z0 is not reached
and, therefore, Zmax/Zlin
0 is plotted.
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36
C. Piel, F. J. Stadler, J. Kaschta, S. Rulhoff, H. Münstedt, W. Kaminsky
increase in ethene concentration. Therefore, the ratio of the
monomer concentration to the concentration of vinyl
terminated macromers increases resulting in a decreasing
probability of macromer incorporation, i.e., long-chain
branch formation.
Influence of Polymerization Temperature
Figure 13. Effect of the ethene pressure on the viscosity
functions for PEs synthesized with catalyst B (Tpoly ¼ 75 8C,
ccat ¼ 2.5 107 g mol1).
concentration was varied by the ethene pressure. All other
conditions were kept constant.
The viscosity functions obtained for the polymers
synthesized with pressures of 1, 3, and 5 bar are shown in
Figure 13. Only for the product B8 the zero shear-rate
viscosity is approached at o ¼ 0.01 s1. For the other two
samples it could not be reached in the dynamic-mechanical
measurements. The zero shear-rate viscosities of the linear
equivalents to B7 and B6 should be 3 350 and 11 000 Pa,
respectively, taking their molar masses (cf. Table 2) into
account. At o ¼ 0.01 s1 the difference in viscosity between
B8 (5 bar) and B6 (1 bar) is a factor of 70 while B7 (3 bar)
lies in between. All three polymers show a viscosity ratio
Z0/Zlin
0 which is distinctly larger than 1 as can be derived
using the values of Zlin
0 given in Figure 13. Thus, it can be
concluded that all these polymers are long-chain branched.
With increasing pressure the ratio of Z0/Zlin
becomes
0
smaller indicating a decreasing influence of long-chain
branching.
Besides the ratio of Z0/Zlin
0 the shapes of the viscosity
functions are completely different. The polydispersity
index of the polymers described by M w =M n is similar (cf.
Table 2) but the shear thinning is more pronounced for
B6 than for B7 and B8. This finding gives a hint of the
increasing efficacy of branching if the ethene pressure is
lowered.
Surprisingly, in SEC-MALLS a similar contraction of the
radius of gyration in the overlapping ranges of molar masses
was found for all three polymers in the overlapping ranges
of molar masses (cf. Figure 6). As B6 possesses a significantly higher molar mass, this sample will contain longer
branches compared to the two other polymers giving rise to
the distinct differences in the viscosity functions.
The pressure dependence of Z0/Zlin
0 can be explained
as follows: The increase in pressure is equivalent to an
Macromol. Chem. Phys. 2006, 207, 26–38
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Figure 14 shows the results of a variation of polymerization
temperature at the ethene pressures used for the catalyst B
series. Z0/Zlin
0 decreases with increasing temperature. For all
three pressures a similar trend is found.
A growing polymerization temperature leads to an
increase in the probability of termination reactions. Therefore, the molar masses of the main chains are decreased as
well as the molar mass of macromers. This is distinctly
reflected by the M w values given in Table 2. Even if the
macromers would be incorporated at a similar concentration their effect on rheological quantities (e.g., Z0) was
less pronounced due to the shorter length of the branches.
Discussion and Conclusion
A variety of linear and long-chain branched polymers
covering a vast range of molar masses and MMDs were
synthesized using metallocene catalysts. The formation of
LCB comparing catalyst structures and polymerization
conditions was studied.
The melting temperature and melt enthalpy show a strong
dependence on the molar mass in a sense that the crystallization temperature is nearly constant over the whole
range of PEs, and it is remarkable that there is no influence
of the catalyst structure, although the polymer microstructure strongly depends on polymerization conditions
and catalyst type.
Figure 14. Increase of the zero shear-rate viscosities Z0/Zlin
0 for
the series polymerized with catalyst B at different temperatures
Tpoly and ethene pressures. The arrows indicate that the zero shearrate viscosity could not be reached and Zmax/Zlin
0 is represented.
ß 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
37
Structure-Property Relationships of Linear and Long-Chain Branched Metallocene . . .
The molecular characterization of the samples by SECMALLS showed that the molar masses and MMDs as well
as the branching topography are influenced by the catalyst
and the synthesis conditions. Strictly linear samples as well
as highly branched ones were found. For the long-chain
branched samples an increasing contraction of the molecules in solution with growing molar mass was measured
indicating that the long-chain branched molecules are
mainly found in high-molar mass fractions of the MMD.
The number of LCBs in these polymers vary between 0.1
and 3 branches per 10 000 monomers.
The rheological characterization was carried out using
dynamic-mechanical experiments and creep tests. The zero
shear-rate viscosities Z0 of the linear samples were found to
fulfill the power-law function Z0 ¼ K M w 3.6 established by
Stadler et al.[27] All long-chain branched PEs investigated
deviate from this correlation toward significantly higher
zero shear-rate viscosities. Therefore, the ratio Z0/Zlin
0 correlating the measured zero shear-rate viscosity to the one of
its linear counterpart of equal molar mass M w is used as a
rheological measure for the presence of LCBs. The ratio Z0/
Zlin
0 is found to vary by more than three orders of magnitude
showing the sensitivity of this rheological quantity to LCBs.
The shape of the viscosity curves as well as the dependence of the phase angle d on the absolute value of the
complex modulus G* are influenced by branching and
MMD. Thus, these quantities were used only as an additional indicator for the presence of LCBs in cases of similar
MMD, only.
The formation mechanism of the LCB has been described
as a reincorporation of a vinyl unsaturated polymer chain
into a differently growing polymer chain. However, this
reincorporation mechanism requires that the growing
polymer chain is terminated by b-hydrogen abstraction
and that the catalyst is able to incorporate the large vinyl
unsaturated polymer chain. By its influence as chain
termination agent on the molar mass hydrogen also lowers
the amount of LCBs.
Catalyst A forms exclusively linear PEs while catalyst E
is also able to produce LCB-PE especially without hydrogen (see materials E3, E6, E8, and E9) under certain
conditions. At 90 8C polymerization temperature a certain
monomer concentration is necessary to form a very low
amount of LCBs; at 60 8C the highest amount of branches
was observed and at 30 8C also some branches were
detected. For catalyst G a similar behavior can be expected,
when the monomer concentration is higher and the
polymerization temperature is lower than that used here,
LCBs will most likely occur. Comparing the catalysts A and
E the substitution pattern destines if LCBs can be formed.
We explain this with a more open aperture gap size for
catalyst E, and therefore we expect LCBs to be formed by
catalyst G in even larger numbers. In general the more open
the active side is, the better higher a-olefins can be incorporated into the growing chain. With hydrogen no LCBs
Macromol. Chem. Phys. 2006, 207, 26–38
www.mcp-journal.de
were observed and an increase in polymerization temperature decreases the amounts of LCBs.
Catalysts B and D produce only a few or no LCBs, when
hydrogen is present. Under all other conditions the polymers are long-chain branched. Using catalyst B the LCB
content decreases with growing polymerization temperature, although here the degree of branching is higher at
lower monomer concentrations. With catalyst D at 90 8C
even a higher amount of branches is detected than at 60 8C.
Catalyst B shows much higher activities than catalyst
D; therefore, a higher reactivity ratio for ethene can be
assumed and a lower branching degree will be reached.
Catalyst F produces LCB in a remarkable amount
although hydrogen is present. This catalyst gives the
highest degree of branching in this series in the presence
of H2. Higher monomer concentration leads to more
branches. The influence of hydrogen is less distinct than
for the other catalyst systems. The chain termination mechanism via b-hydrogen elimination is believed to be so
pronounced that the vinyl content of the polymer is still high
enough even with hydrogen present in the reactor.
The results of this study underline the widely accepted
mechanism for the formation of LCBs via the copolymerization route.
Generally, the agreement between SEC-MALLS and
rheology concerning the branch detection is quite good.
However, for sample F2 a contrary result was found. This
may be due to very small amounts of chains with ultra-long
branches which influence the rheological quantities very
sensibly, but whose concentration is too low to be detected
by SEC-MALLS.
As final conclusion for the catalysts the following order
of affinity to create LCBs in PEs can be given: F, D, B, E, A.
Catalyst G cannot be classified in this series because the
molar masses were too low obtained.
The differences in electron density and aperture gap size
among the active center depend on the ligand systems and
strongly affect the comonomer incorporation behavior and
the formation of LCB. Besides that the polymerization
conditions are so important that by changing these the
formation of LCB can be controlled, too. The influence of
monomer concentration, polymerization temperature, and
hydrogen is very specific to the catalyst systems.
Acknowledgements: The authors thank the Deutsche
Forschungsgemeinschaft (German Research Foundation, DFG)
for the financial support of this project. They would also like to
thank Mr. I. Herzer for the SEC-MALLS measurements and Mr.
K. Klimke (Max Planck Institute of Polymer Science, Mainz), and
Mr. J. Stange and Mr. D. Auhl (University Erlangen-Nürnberg)
for their scientific input to this project.
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