ar ticle

Materials Focus Vol. 7, pp. 1–9, 2018 (www.aspbs.com/mat)

Copyright © 2018 by American Scientific Publishers All rights reserved. Printed in the United States of America

Thermo-Rheological Complexity of Novel Branch Polyethylene Synthesized by High Performance Bulky -Diimine Nickel (II) Catalysts Saud Hashmi1 , Awan Zahoor1 , and Zafar Khan Ghouri2, ∗ 1 2

Department of Chemical Engineering, NED University of Engineering and Technology, Pakistan Central Laboratories Unit, Qatar University, P.O. Box: 2713, Doha, Qatar

ABSTRACT

KEYWORDS: Hyperbranched Polyethylene, Chain-Walking, Rheology, Crystallization, Short-Chain.

1. INTRODUCTION Rheology is undoubtedly the best tool for the investigation of non-Newtonian fluids in order to have a better understanding of fundamental properties of macromolecules in relation to their structures and superamolecular interactions. Rheological characterization of polymer solution is state of the art techniques that become more popular now a days both academic and application point of view.10 The non-Newtonian flow properties constitute the most essential piece of rheological information as far as designing and optimizing polymer processing operations which they invariably occur in the shear thinning range of flow intensities.4 In these engineering applications, a constitutive relationship representing the material response to the kinematic stimulus is coupled with the pertinent flow geometry. By thus solving the fluid mechanics of the process, estimates may be obtained for its energetic requirements, processing capacities, possible exposure to prohibitive shear or thermal fields.53 The concept of nonNewtonian flow of polymer melts and multi-component fluids (polymeric and colloid solutions as well as other dispersions) is a cornerstone of rheology to the same extent as the linear Newton law and the Navier-Stokes equations as its consequence are the base of the dynamics of viscous fluids. The nonlinear viscoelastic behavior originates from the ability of the moving matter for microstructural ∗

Author to whom correspondence should be addressed. Emails: [email protected], [email protected] Received: xx Xxxx xxxx Accepted: xx Xxxx xxxx

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rearrangements for the purpose of decreasing its energetic requirements for flow. Polyethylene (PEs) is the far most studied polymer because of its tremendous commercial applications. Market development is explained in terms of the innovations that permitted molecular tailoring and expansion in to new applications. Current catalysis and the production processes are keys to explain the molecular features that distinguish the different types of polyethylene, all having essentially same back bone while variation arises from branches that modify the nature of material. The influence of branching on the properties of polyethylenes (PEs) has gained much interest during the last years. Branch architecture of PEs include Short-chain branches (SCBs), Long Chain branch (LCBs), hyper branch and dendrimers. Traditional methods to produce dendrimers and hyperbranched polymers use condensation polymerization of ABx monomers where branching is introduced by the structure of the monomer.6 9 Each addition of monomer increases the number of active sites per chain. In most cases, this conventional approach requires synthesis of a specifically designed monomer. Free radical polymerizations of olefin monomers can have long-chain branching if the catalysts used encourage chain transfer. Gao and Yan,15 but this results in broad molar mass distributions. Brookhart et al. have reported -diimine palladium and nickel (II) complexes that polymerize ethylene with high insertion reaction rates to produce polyethylene with high molecular weight with different types of branches along the polymer chains due to chain walking doi:10.1166/mat.2018.1545

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Hyperbranched polyethylene was synthesized with a high performance bulky -diimine nickel (II) catalyst. The resulting material shows no crystallization, indicating at least 1 branch point per 20 carbons and a rather narrow molar mass distribution with Mw /Mn = 2.6. The rheological behavior is dominated by a thermo rheological complexity, relatively high entanglement molar mass. The flow activation energy is 62.4 kJ/mol, which is a typical value for low density polyethylene (LDPE). Overall, the material has a similar behavior to many LDPEs, while having more short-chain branches in comparison, making it amorphous.

Hashmi et al.

phenomena.18 The microstructure of the produced polymer depends on ligand structure of -diimine complexes. By controlling the kinetic competition between chainwalking and insertion, Guan and co-workers demonstrated that polyethylenes with a continuum of properties can be prepared from homo-polymerization of ethylene and suggested that this involved a range of branching topologies from linear to hyper-branched to dendritic.7 The possibility of producing polymers with a continuum of topologies without changing the chemical structure provides a unique opportunity for fundamental studies of topological effects on polymer rheological properties. SCBs are primarily introduced into PEs in order to modify their mechanical properties in the solid state. Their influence on flow properties is mostly regarded to be negligible. However, it is established that short-chain branches increase the temperature sensitivity of rheological properties.36 Stadler et al. showed that long-chain branched polyethylenes have a significant dependence of the activation energy Ea on the relaxation time. At shorter relaxation times Ea is very close to that of linear PE, but it increases with longer times. The lower Ea values are assumed to be due to linear molecules and the higher ones to different species of long-chain branched molecules.38 Hyperbranched PEs found considerable interest now a days because of new promising area of potential applications for hyperbranched polymers is the field of chemical engineering. The use of hyperbranched polymers in separation processes involving extractive distillation, solvent extraction, absorption, membranes or preparative chromatography might offer considerable potentials for cost savings. In these applications full investigation of mechanical and rheological properties are of great importance. Due to the highly branched, globular structure, the configuration of hyper-branched PEs polymers and dendrimers is coined by a lack of chain entanglements. The non-entangled state imposes poor mechanical properties, resulting in brittle dendritic polymers with limited use as thermoplastics.17 The stress–strain behavior of hyperbranched PEs polymers can be similar to that of ductile metals as observed by Rogunova et al. for hyperbranched PEs. Like ductile metals, hyperbranched PEs do not strain harden.30 In this study we discuss the influence of polymer architecture on rheological behavior of as synthesized hyper-branched polyethylene by using High Performance Bulky -Diimine Nickel (II) Catalysts reported earlier by Vatankhah-Varnoofaderani, et al.56 The rheological properties of this poly-ethylene were conceptually linked with the molecular architecture and show a qualitative assessment of the degree of branching. Dynamic mechanical spectroscopy suggests non-Newtonian flow behavior under shear and high degree of thermo-rheological complexity, induced by novel chain branching. 2

2. EXPERIMENTAL DETAILS 2.1. Materials, Rheology, Principle of Measurement and Oscillatory Test At t = 0 a sinusoidal stress t is applied to the sample with an angular frequency . t = ˆ · sin · t for t ≥ 0

(1)

Where ˆ is the stress amplitude (see Fig. 1). In the steady state the time-dependent deformation t is given as t = ˆ · sin · t −

(2)

Where ˆ is the maximum stress applied (see Fig. 1). The time dependent deformation t is a sinusoidal oscillation of the same frequency as the applied stress. The phase angle (Fig. 1) is the angular difference between t and t. The magnitude of the complex shear modulus G∗ can be calculated from the ratio of the applied stress and the deformation amplitude as G∗ =

ˆ ˆ

(3)

The storage modulus G and the loss modulus G are defined as G = G∗ · cos

(4)

∗

G = G · sin

(5)

The magnitude of the complex viscosity ∗ is defined as G∗ (6) ∗ = In some cases the oscillation data are analyzed in terms of the complex compliance whose magnitude is defined as J ∗ =

1 ˆ = ∗ ˆ G

(7)

δ

stress τ, deformation γ [a.u.]

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Thermo-Rheological Complexity of Novel Branch Polyethylene Synthesized by High Performance

^τ

γ^

γ(t) τ(t) 0π

1π

2π

3π

4π

time×frequency t×ω [rad] Fig. 1. Principle of oscillatory tests. Mater. Focus, 7, 1–9, 2018

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Analogous to the storage modulus G and the loss modulus G the storage compliance J and the loss compliance J are defined as J = J ∗ · cos =

G G∗ 2

(8)

J = J ∗ · sin =

G G∗ 2

(9)

For infinitely small angular frequencies in the linear viscoelastic regime the loss modulus or the loss compliance can be used to determine the zero shear-rate viscosity 0 and the storage compliance equals the linear steady-state elastic compliance Je0 : lim J = Je0

(10)

1 G = lim = 0 →0 · J →0

(11)

→0

lim

With aT : shift factor, R: gas constant, T : measurement temperature, T0 : reference temperature (in this work T0 is always 20 C), and Ea : activation energy. For linear PE melts the activation energy is found to be constant in both shear and elongation and in the linear and non-linear regime. This is called a thermorheologically simple behavior. The shift factors aT for the thermorheologically simple samples were determined by (horizontally) shifting G ( and G ( including a vertical density compensation term bT . Many of the long-chain branched samples, however, show an increase in the activation energy Ea with Mater. Focus, 7, 1–9, 2018

2.2. Synthesis of -Diimine Ligand with Nickel Catalyst -Diimine ligand was prepared by condensation reaction of acenaphthenequinone with the 2,6-dialkyl or allyl 4-hydroxy group substituted anilines. Anilines (2.2 equiv), acenaphthenequinone (1 equiv) and ptoluenesulphonic acid monohydrate (0.25 mol%) were dissolved in 75 mL benzene and condensation reaction was performed in a threeneck flask (100 mL) fitted with a Dean-Stark apparatus and a condenser under dried nitrogen atmosphere. The mixture was heated to reflux for three days and water by-product was constantly removed by water and benzene azeotrope. The solvent was removed under dried nitrogen and the product was purified by column chromatography (flash silica, ethyl acetate/hexane = 1:1). In the next step for -diimine nickel (II) complex preparation, NiBr2 (DME) (1 equiv) and -diimine produced above (1 equiv) and 75 mL CH2 Cl2 were added to a Schlenk tube and stirred at room temperature for one day. The resulted suspension was filtered and the solvent was removed under nitrogen flow and the resulted solid was washed with diethyl ether (3 × 20 mL) to give a solid catalyst. For detail see Vatankhah-Varnoofaderani et al.56 2.3. Synthesis of Hyper-Branch Polyethylene Ethylene polymerization was carried out in a Büchi reactor equipped with magnetic stirrer and a thermal mass flow meter for measuring and recording feed streams and a thermocouple that connected to circulator to control reactor temperature. Reactor heating and purging was carried out for 2 h before polymerization to remove poisonous elements. The reactor was then cooled to room temperature and dried hexane (750 mL) was charged to the reactor under nitrogen atmosphere. A desired amount of diluted co-catalyst (ethyl aluminium sesquichloride) in hexane was added into the reactor and stirrer was turned on for five minutes while all lines to reactor were close. The catalyst was weighed 3

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The quantities 0 and Je0 are the same as determined by creep and creep recovery tests. However, the approximation G = 1/J is only valid for G G i.e., in the proximity of the terminal regime ( → 0). In order to perform correct rheological oscillatory measurements it has to be ensured that the oscillation has reached its stationary value. It was found that an oscillation of only one period is already sufficient to measuring correct data. The time-temperature superposition principle states that a change in temperature will change the time dependent material behavior in a way that the curves are very much alike in shape but only differ in their time (or frequency) dependence. Thus the data can be shifted in a logarithmic time or frequency scale onto each other using a shift factor aT to form a so-called master curve. Depending on the distance from the glass transition temperature Tg the temperature dependence of the rheological properties follows either a WLF or an Arrhenius type dependence. Typically, the thermo rheological behavior of PE follows an Arrhenius type dependence defined as 1 1 − Ea = lg aT · 2303 · R (12) T T0

decreasing G and G , i.e., decreasing frequency , which is called thermorheologically complex behavior. The activation energy Ea determined from G exhibits different values from the activation energy Ea determined from G at the same frequency (at the reference temperature T0 . This is a consequence of the change in the phase angle . Oscillatory shear tests were performed using a Malvern Kinexus rheometer in oscillatory mode with 20 mm diameter cone and plate geometry. The angular frequency was varied from 103 to 10−2 rad s−1 , and the temperature ranged from −5 to 90 C. The temperature was increased from −5 to 90 C with the increment of 10 C. The isothermal rheology data at different temperatures were shifted to obtain master curves at the reference temperature 20 C using time-temperature superposition.

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T [°C]

107

15.00

10

25.00

6

35.00 45.00 55.00

105

65.00 75.00 85.00 95.00

104

105.0

103

10–2

3. RESULTS AND DISCUSSION

The G∗ -plot, shown in Figure 2, clearly shows that the data at different temperatures does not agree in the range of the phase angle between 30 and 70 . This behavior in polyethylene is typically associated with the presence of long-chain branches, which induce a thermorheological complexity.20 22 23 2829 33–35 38 50 67 A change of the shape of the rheological functions at different temperatures. Furthermore, the shape of the data, especially below 60 C is typical of highly branched materials such as low density polyethylene, while the data above 70 C is rather typical for lightly branched LCB-mPE.34 39–46 48 57–59 60 61 66 68 69 However, due to the limited amount of sample and the difficult nature of the measurements for this sample, in the following, we ignore the thermorheological complexity and try to make a master-curve, which is as good as possible for the data available. The viscosity function at different temperature ∗ , shown in Figure 3, clearly demonstrates the decrease of viscosity with increasing temperature (color coded according to the color bar on the right of the figure). Furthermore, it proves that the material is shear thinning, which is

10–1

100

101

ω

102

103

[s–1]

Fig. 3. Viscosity functions at different temperatures.

a good indicator of the sample being entangled, although highly branched sometimes is not entangled at all and, therefore, shows Newtonian behavior.27 It is also obvious that even at the highest temperatures = 0.01 s−1 is not yet in the terminal regime, which again is a good, prove of the high molar mass and high level of entanglements. The data of G and G show an—at a first glance—normal behavior of a polymer melt for this hbPE (Fig. 4). However, details show quite unusual features for the rheological behavior, which deserve discussion in detail and already give an insight into the structure. First of all, the plateau modulus G0n , which can be estimated from the plateau value of G at −10 C at the highest as well as from the G∗ )-plot (Fig. 2) is slightly below 800000 Pa, which is distinctly below the value of 2300000 Pa, being the commonly accepted value for PE.12 In turn, the entanglement molar mass Me is around 2800 g/mol and not around 800 g/mol, which is the

90 G' G"

106 75 T [ºC]

45

30

15

105

–5.000 5.000 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.0

G', G" [Pa]

60

δ [º]

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–5.000 5.000

|η*|[Pas]

and dissolved in CH2 Cl2 . The solution was injected into the reactor by syringe while the stirrer was turned on. The speed of stirring was adjusted to 400 RPM and the reactor was pressurized by a desired amount of hydrogen (if necessary). Then, the reactor pressure was increased by continuous ethylene charging through the pressure regulator on ethylene cylinder. The reactor temperature was increased and controlled by a circulator at a desired temperature. After 1 h, the reactor was cooled and the reactor pressure was vented. The polymerization was terminated by injection of a 2% HCl/methanol solution into the reactor. The polymer solution or slurry was dried in vacuum oven at 70 C for overnight.

T [ºC] –5.000 5.000 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.0

104

103

102

0 103

104

105

|G*| [Pa] Fig. 2. G∗ -plot of the hbPE at different temperatures.

4

106

10–2

10–1

100

101

ω

102

103

[s–1]

Fig. 4. Functions of G and G at different temperatures. Mater. Focus, 7, 1–9, 2018


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T [ºC] –5.000 5.000 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.0

10–3

J', J'' [Pa]

10–4

10–5

10–6 J' J" –7

10

10–2

10–1

100

ω Fig. 5.

101

102

[s–1]

Functions of J and J at different temperatures.

Stadler and Karimkhani37 and rather resembles the values for LDPE,13 24 although the molar mass distribution is significantly more narrow. Hence, it can be expected that the behavior in this respect is closer to a conventional LDPE than to a catalytic PE. Figure 6 shows the apparent master curve of the viscosity functions. The thermorheological complexity is obvious mainly in the transition region, i.e., between ∗ aT = 0.01–10 s−1 . The apparent mastercurve (Fig. 7) of G aT and G aT demonstrate the typical behavior of a viscoelastic material. What becomes especially interesting is the thermorheological complexity, which is observed as a stacking of the plateau value of G aT at high frequencies, suggesting that the plateau modulus significantly depends on temperature, which was not compensated for by a modulus shift. Furthermore, especially in the crossover region (c aT ≈ 0.1 s−1 the thermorheological complexity is

107

106

105

104

103

T [ºC] –5.000 5.000 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.0

102 10–5 10–4 10–3 10–2 10–1 100

101

102

103

104

105

ω*aT Fig. 6.

Apparent mastercurve of the viscosity function.

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literature value for PE.12 It is well established that branching lowers the plateau modulus due to two effects. Firstly, atoms in the side chains don’t contribute to the main chain and, therefore, the number of carbons between two entanglements must be higher than for a molecule without any carbons in the side chain. Secondly, side chains are more bulky than hydrogens as the normal atoms branching from the PE-main chain. This additional bulkiness makes the chain stiffer and, thus, increasing the number of main chain carbons between two entanglements. Chen et al.,5 for example, found that the number of monomer units between two entanglements depends significantly on the length of the side chain at constant molar content of side chains (= constant molar comonomer content nc . Increasing the length of the short-chain branch from 10 to 24 C increased the number of monomer units between two entanglements from 47.2 to 68.6 at constant nc ≈ 3 mol%. Considering that on the average only around 1.5–2 SCBs are between two entanglements, it clearly shows the second effect mentioned above (for pure PE, only about 33 monomer units are between two entanglements). A further untypical feature is that G is almost constant and around 140000 Pa, while for most normal polymer melts, a clear minimum should be observed.25 49 Long-chain branched polymer melts, however, are clearly established to have a very diverse G when G is in the rubbery regime, i.e., with many peaks and valleys, which can be attributed to different molecular motions.25 31 54 55 62 However, as clearly established as well. Dealy and Larson,8 polydispersity smears out these individual processes and, thus, leads to less identifiable processes. For this reason, it is safe to assume that the constant G in the rubbery regime is related to polydispersity and statistical long-chain branching, although typical LDPE does not show this behavior, as this regime is inaccessible due to crystallization. The functions of the complex compliance J and J are mainly important for the terminal regime. It is obvious from Figure 5 that J reaches a power slope close to −1 for the highest temperatures at low . However, J is not even close to a plateau value, which would correspond to Je0 .11 64 As the terminal regime is not reached with respect to the viscous properties, it is not surprising that the same is not true for the elastic properties, which is reached at even lower frequencies (= longer relaxation times).40 It is important to note that the maximum value of J is around 6 ∗ 10−4 Pa−1 , which is about the value expected for Je0 for linear PE of the molar mass distribution Mw /Mn . However, it is also clear that Je0 of the hbPE is significantly above this value. Based on the slope of J for the lowest and highest T , one can expect that Je0 lies at least factor 5 higher than 6 ∗ 10−4 Pa−1 . This value is significantly beyond the values found for long-chain branched metallocene PE.

|η*|/aT [Pas]

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T [ºC]

G' G''

90

G',G''[Pa]

105

T [ºC] –5.000 5.000 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.0

104

103

102 10–5 10–4 10–3 10–2 10–1

100

101

102

103

104

105

70

60

50

40

30

20

10

0

–10 –20

101

101

100

100

10–1

WLF-temperature dependence

10–2

10–2

Ea = 62.4±1.4 kJ/mol 2.75

3.00

3.25

3.50

10–1

3.75

4.00

1000/T [1/K]

Fig. 7. Apparent mastercurve of the function of G aT and G aT .

Fig. 9. Arrhenius plot.

severe, which is already quite visible in the G∗ plot (Fig. 2). In general, the lower the temperature, the more visible is the double bend nature of G aT , typical for long-chain branched PE.44–46 It is also visible that in the terminal region, i.e., at the lowest frequencies G aT and G aT run almost parallel to each other, again a typical sign of long-chain branching or gel-like nature.8 The apparent master curve of the function of J aT and J aT (Fig. 8) basically shows this information again. Here, the fact that Je0 —the plateau of J aT for aT − > 0 is clearly not reached yet becomes even better visible than in Figure 5. As in G aT and G aT , the thermorheological complexity is clearly visible. The temperature dependence was assessed by an Arrhenius plot (Fig. 9), showing that the temperature dependence can be nicely described with an Arrhenius law for T >50 C, which leads to an activation energy Ea of

62.4 kJ/mol. Below this threshold, a positive curvature is found, which is typical for a transition to the WLF-regime. Williams, et al.,63 suggesting that the free volume is no longer sufficient so that it can be ignored for explaining the temperature dependence. Typically, this transition is found to be 100–200 K above the glass transition temperature Tg , which is reasonable as amorphous PE was found to have a Tg around −65 C.26 The value of the activation energy Ea = 62.4 kJ/mol is significantly above the value for linear PE (27 ± 3 kJ/mol).36 When using the established scaling laws for the influence of short-chain branching on the activation energy. Stadler, et al.,36 explaining the found Ea would require a side chain content sc of 85%, which clearly is not a reasonable value. When comparing the Ea to corresponding values of long-chain branched PE, one finds that the value lies in the typical range for LDPE, but significantly above the values found for LCB-mPE.1 19 21 22 24 28 33 38 39 67 70 This again suggests to see this hbPE as a close cousin of an LDPE rather than a catalytic PE. When using these data, it is possible to calculate an estimate for the zero shear-rate viscosity 0 at 150 C— the reference temperature for the 0 − Mw -plot. The maximum viscosity found at 90 C is ∗ = 0.01 s−1 = 49400 Pas. The shift factor between 90 C and 150 C for Ea = 62.4 kJ/mol is approximately 17, which means that

0 (150 C)>2900 Pas. Based on the established value for the correlation between zero shear-rate viscosity 0 and weight average molar mass Mw , the expected 0 -value for Mw = 115.9 kg/mol is 10000 Pas,44–47 which is factor 3.5 higher than the minimum value extrapolated. Considering that 0 (150 C) >2900 Pas is a minimum value and that the shape of the viscosity function suggests that 0 is a factor of 2–5 away and, furthermore, that the extrapolation is accompanied by rather large experimental uncertainties, it can only be stated that the zero shear-rate viscosity

T [ºC] –5.000 5.000 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.0

10–3

J', J'' [Pa–1]

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ω*aT [s–1]

80

aT[–]

106

10–4

10–5

10–6 J' J'' 10–7 10–5 10–4 10–3 10–2 10–1

100

ω*aT

101

102

103

104

105

[s–1]

Fig. 8. Apparent mastercurve of the function of J aT and J aT .

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4. CONCLUSIONS In conclusion, we have successfully synthesized hyperbranched polyethylene with a high performance bulky -diimine nickel (II) catalyst. The resultant hyperbranched polyethylene exhibits no crystallization, indicating at least 1 branch point per 20 carbons and a rather narrow molar mass distribution with Mw /Mn = 2.6. The rheological properties are dominated by a thermo rheological complexity, relatively high entanglement molar mass. The introduced polymeric material naked 62.4 kJ/mol of flow activation energy, which is a typical value for low density polyethylene (LDPE). Overall, the material has a Mater. Focus, 7, 1–9, 2018

comparable behavior to many LDPEs, while having more short-chain branches in contrast, making it amorphous.

References and Notes 1. B. Arikan, F. J. Stadler, et al., Synthesis and characterization of novel ethene-graft-ethene/propene copolymers. Macromolecular Rapid Communications 28, 1472 (2007). 2. F. Beer, G. Capaccio, et al., High molecular weight tail and longchain branching in low density polyethylene. Polymer 80, 2815 (1999). 3. F. Beer, G. Capaccio, et al., High molecular weight tail and longchain branching in SRM 1476 polyethylene. Journal of Applied Polymer Science 73, 2807 (1999). 4. R. B. Bird, Citation Classic-Dynamics of Polymeric Liquids, Vol 1, Fluid-Mechanics, Vol 2, Kinetic-Theory, Cc/Phys Chem Earth(34), 18-18 (1988). 5. X. Chen, F. J. Stadler, et al., Method for obtaining tube model parameters for commercial ethene/alpha-olefin copolymers. Journal of Rheology 54, 393 (2010). 6. S. Z. D. Cheng, C. Y. Li, et al., Polymer helical self-assembly: From asymmetric chemistry to asymmetric physics. Abstr. Pap Am. Chem. S 226, U467 (2003). 7. P. M. Cotts, Z. B. Guan, et al., Novel branching topology in polyethylenes as revealed by light scattering and C-13 NMR. Macromolecules 33, 6945 (2000). 8. J. Dealy and R. G. Larson, Structure and Rheology of Molten Polymers-From Structure to Flow Behavior and Back Again, Hanser, Munich (2006). 9. M. Doi, Challenge in polymer physics. Pure Appl. Chem. 75, 1395 (2003). 10. X. Feng, D. Taton, et al., Janus-type dendrimer-like poly(ethylene oxide)s. J. Am. Chem. Soc. 130, 11662 (2008). 11. J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley and Sons, New York (1980). 12. L. J. Fetters, D. J. Lohse, et al., Chain Dimensions and Entanglement Spacings, Springer, Heidelberg (2007). 13. C. Gabriel, J. Kaschta, et al., Influence of molecular structure on rheological properties of polyethylenes I. Creep recovery measurements in shear. Rheologica Acta 37, 7 (1998). 14. C. Gabriel and D. Lilge, Molecular mass dependence of the zero shear-rate viscosity of LDPE melts: Evidence of an exponential behaviour. Rheologica Acta 45, 995 (2006). 15. C. Gao and D. Yan, A(2) + CBn approach to hyperbranched polymers with alternating ureido and urethano units. Macromolecules 36, 613 (2003). 16. J. Hepperle, H. Münstedt, et al., Rheological properties of branched polystyrenes: Linear viscoelastic behavior. Rheologica Acta 45, 151 (2005). 17. A. Hult, M. Johansson, et al., Hyperbranched polymers. Adv. Polym. Sci. 143, 1 (1999). 18. L. K. Johnson, C. M. Killian, et al., New Pd(Ii)-based and Ni(Ii)based catalysts for polymerization of ethylene and alpha-olefins. J. Am. Chem. Soc. 117, 6414 (1995). 19. U. Keßner, J. Kaschta, et al., Determination of method-invariant activation energies of long-chain branched low-density polyethylenes. Journal of Rheology 53, 1001 (2009). 20. U. Kessner, J. Kaschta, et al., Determination of methodinvariant activation energies of long-chain branched low-density polyethylenes. Journal of Rheology 53, 1001 (2009). 21. U. Kessner, J. Kaschta, et al., Thermorheological behavior of various short- and long-chain branched polyethylenes and their correlations with the molecular structure. Macromolecules 43, 7341 (2010). 22. U. Kessner and H. Münstedt, Thermorheology as a method to analyze long-chain branched polyethylenes. Polymer 51, 507 (2010).

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of this hbPE is—surprisingly—roughly around the value of a linear material. The reason why this is surprising is that normal hbPE typically lies significantly below the

0 − Mw -line and is often almost unentangled.27 However, when considering this material as an LDPE-like material, Gabriel and Lilge14 found that some LDPE are distinctly above the 0 − Mw -relation. In addition, one has to consider that the real molar mass might be higher than the one measured by GPC, as longchain branches lead to coil contraction, which is not compensated for in a standard PE calibrated GPC.2 3 52 Only a light scattering setup would allow doing it, which was not used, however. For this reason, most probably Mw is somewhat higher and thus the 0 -value for this hbPE lies somewhat below the 0 − Mw -relation. The data suggests that a highly branched PE was synthesized, which is so much branched that it does not crystallize anymore. GPC-analysis shows that the material is rather low in polydispersity and intermediate in molar mass. However, due to the high degree of branching it is difficult to say how much the molar masses are underestimated due to coil contraction. The rheological data show that the material has clearly a thermorheological complexity, which is typical for light and medium long-chain branched PE (and other semicrystalline materials.35 50 It is unusual, however, that the thermorheological complexity is already visible in the WLF-behavior dominated temperature range.16 The activation found suggests a significant concentration of long-chain branching-the level of which is typical for LDPE. It has to remain open; however, what is the exact structure, as the polydispersity of the material does not allow for an exact distinction of the types of branching and its concentration as a function of molar mass. In comparison to LDPE, it is clear, however, that this hbPE has many more short-chain branches, which prevent crystallization, while it is estimated that the LCB-concentration and probably also the topography is LDPE-like.32 This clearly shows the differences between this catalytic hbPE and conventional LDPE, which also features a significantly wider molar mass distribution.

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