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Topology-Engineered Hyperbranched High-Molecular-Weight Polyethylenes as Lubricant Viscosity-Index Improvers of High Shear Stability Jianli Wang,† Zhibin Ye,*,† and Shiping Zhu‡ School of Engineering, Laurentian UniVersity, Sudbury, Ontario, Canada P3E 2C6, and Department of Chemical Engineering, McMaster UniVersity, Hamilton, Ontario, Canada L8S 4L7
Chain walking polymerization provides a novel strategy to synthesize highly branched high-molecular-weight polyethylenes with controllable chain topologies ranging from linear to hyperbranched dendritic structure. In this work, we report the performance of this novel series of polyethylenes as lubricant viscosity-index improvers. By examining a range of such model polymers possessing various tailor-designed chain topologies, we report the first systematic study on the unique effects of chain topology on the polymers’ viscosity thickening ability and shear stability. It is demonstrated that hyperbranched polyethylenes we prepared possess extremely high shear stability with almost zero shear degradation regardless of their high molecular weight. Our study shows that these hyperbranched polymers have great potential for formulating high-performance lubricants with superior properties. Introduction The viscosity index (VI) of a lubricant, which evaluates the lubricant’s viscosity dependency on temperature, is a critical parameter that defines the quality and application temperature range of a lubricant. Lubricants of high VI value possess better maintained viscosity constancy in a broad temperature range and are preferred in most mechanical systems. Polymers are widely used as viscosity index (VI) improvers for lubricant formulation.1,2 The addition of a small quantity of polymerbased VI improver, which possesses viscosity thickening power as a result of its high molecular weight, is able to minimize viscosity variation over a wide temperature range, increase the VI, improve the quality, and broaden the application temperature range of lubricants.2 The molecular weight and macromolecular chain architecture of a polymer are the key parameters that govern its ability to thicken lubricants. A polymer with higher molecular weight and narrower molecular weight distribution usually possesses stronger thickening powers.3 In addition to the viscosity thickening power, the shear stability (often revealed by using the shear stability index, SSI, determined by the Kurt Orbahn (KO) test of the formulated lubricants) is the other primary characteristic of a polymer-based VI improver. It reflects the polymer’s ability to resist shear-induced macromolecular degradation under high-shear conditions ubiquitous in most mechanical systems.1,2,4 Polymers with high shear stability (i.e., low SSI value) coupled with excellent thickening power are often required for formulating lubricants used in mechanical systems where high shear stress is applied. Like the viscosity thickening power, the shear stability of a polymer is also governed by its molecular weight and macromolecular chain architecture. Polymers of higher molecular weight usually possess lower shear stability.4 Although increasing the molecular weight improves the viscosity thickening power, a linear polymer of high molecular weight suffers tremendously from its poor shear stability due to a drastic molecular weight drop caused by irreversible chain breakage under high-shear conditions, which cuts down tremendously the * To whom correspondence should be addressed. E-mail: zye@ laurentian.ca. Fax: (705) 675-4862. † Laurentian University. ‡ McMaster University.
polymer’s viscosity thickening power and shortens greatly the lifetime of lubricants.1 In contrast, star-shaped polymers, one type of topology-controlled polymers, exhibit much higher shear stability owing to the insensitivity of their molecular weight toward chain breakage. In the past few decades, star-shaped polymers (such as polystyrene, hydrogenated polyisoprene, poly(1,4-butadiene), and their copolymers) have been intensively studied as VI improvers with significantly enhanced shear stability, and some have been commercialized.1,2,5-7 Compared to star-shaped polymers, other topology-controlled polymers, such as hyperbranched polymers and dendrimers, have seldom been studied for applications as lubricant VI improvers, although extensive research8,9 on their novel synthesis and applications in such areas as drug delivery and nanotechnology has been carried out in the past decade, and they are hypothesized to possess superior shear stability owing to their highly branched dendritic chain structure. We recently synthesized and characterized a novel range of highly branched polyethylenes with controllable chain topologies by chain walking ethylene polymerization using a palladium diimine catalyst.10,11 The topology of these polymers can be conveniently engineered between linear and hyperbranched dendritic structure by simply controlling the polymerization conditions.12 In this work, we present the first study on the performance of these polymers as lubricant VI improvers and systematically investigate the unique effects of chain topology on their viscosity thickening power and shear stability. We demonstrate that hyperbranched highmolecular-weight polyethylenes we prepared possess extremely high shear stability, with SSI approaching zero, and these advanced materials have great potential for formulating lubricants with superior shear stability. Experimental Section Materials. The preparation of highly branched polyethylene samples of various chain topologies by ethylene polymerization with palladium diimine catalyst has been reported in detail in our previous papers.10,11 The materials used and the synthetic procedure adopted for polymer synthesis are described in the previous papers. A paraffinic type base oil, which has a density of 0.8649 g/mL (15 °C), kinematic viscosities (KVs) of 30.06 cSt (40 °C) and 5.18 cSt (100 °C), and a VI of 101, was obtained
10.1021/ie0613624 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/17/2007
Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1175 Table 1. Polymerization Conditions and Polymer Properties
polym
ethylene pressure (atm)
temp (°C)
brancha per 1000 C
Mwb (kg/mol)
PDIb
[η]b (dL/g)
Tgc (°C)
η0d (Pa s)
HBPE1 HBPE2 HBPE3 HBPE4 HBPE5
0.2 1.0 1.0 6.5 30.0
35 35 25 25 25
118 112 111 109 102
94 161 149 165 140
2.3 2.1 2.2 2.7 2.4
0.093 0.14 0.35 0.54 0.82
-67 -65 -65 -64 -63
25 43 196 8.0 × 104 9.1 × 104
a Short-chain branching density determined using 1H NMR in CDCl . b The weight-average molecular weight (M ), polydispersity index (PDI), and 3 w intrinsic viscosity ([η]) were determined using GPC-VIS in 1,2,4-trichlorobenzene at 140 °C. c Glass transition temperature determined using DSC at 10 °C/min. d Zero-shear viscosity at 25 °C determined using small-amplitude dynamic oscillation rheometry.
Scheme 1. Schematic Trend of the Topology Change in the Five Polymers
from Imperial Oil Ltd. (Sarnia, Ontario) and was used as received for all lubricant formulations. Polymer Characterization. The highly branched polyethylene samples were extensively characterized for their structural and physical properties. Characterization techniques used include differential scanning calorimetry (DSC) for the glass transition temperature, gel permeation chromatography (GPC) with a dual detector array (differential refractive index concentration detector and viscometer detector) for the molecular weight and distribution together with the intrinsic viscosity, 13C and 1H nuclear magnetic resonance (NMR) for the branching structure and density, and dynamic oscillatory rheometry for the rheological properties. Detailed characterization procedures and instruments used are described in our previous papers.10,11 Lubricant Formulation. Prescribed amounts of each highly branched polyethylene sample were blended into a base oil to prepare lubricants formulated with different polymers at various concentrations. The formulated lubricants were homogenized overnight using a mechanical shaker at 50 °C to obtain a uniform polymer dispersion in the lubricants. No additional additives other than the polymers were used in the lubricant formulation. Lubricant Performance Testing. The KVs of the lubricants (both sheared and unsheared) at 40 and 100 °C were tested according to ASTM D445. Kurt Orbahn testing of the viscosity loss of the lubricants under shear was performed according to ASTM D7109-04 using a European diesel injector apparatus. Data were recorded after 30, 60, and 90 cycles. The shear stability index was calculated after 30 cycles on the basis of ASTM D6022. Results and Discussion Five highly branched polyethylene samples (HBPE1HBPE5) differing in chain topology were synthesized by ethylene polymerization with a chain walking palladium diimine catalyst, [(ArNdC(Me)C(Me)dNAr)Pd(CH3)(NCMe)]SbF6 (Ar ) 2,6-iPr2C6H3). The control and tuning of the polymer chain topology in this unique synthetic strategy was achieved conveniently by simply choosing different combinations of ethylene pressure and polymerization temperature during chain walking ethylene polymerization. Combinations of lower temperature and higher pressure generally tend to linearize the polymer chain topology.12 Table 1 lists the polymerization conditions and structural properties of the five polymers produced. The synthesis and characterization of these polymers have been reported in our previous papers.10,11
All five samples are highly branched amorphous polymer materials with a high branching density of ∼110 per 1000 carbons and a glass transition temperature of ∼-65 °C. HBPE1-HBPE3 are oil-like liquids, and HBPE4 and HBPE5 are sticky elastic solids. On the basis of our prior reports,10,11 the short chain branching type and distribution should be very close in these polymers regardless of their chain topology. Owing to their highly branched nature, all five polymers are highly soluble in many polar and nonpolar solvents, including tetrahydrofuran, dichloromethane, chloroform, ether, toluene, alkanes, etc. They are all high-molecular-weight polymers and have close average molecular weight and polydispersity. The topological differences among the polymers can be elucidated using rheological analysis and GPC measurement with a GPC system having a dual concentration and viscosity detector array. Parts a and b of Figure 1 show, respectively, the dependence of the intrinsic viscosity on the polymer fraction molecular weight from GPC measurement in 1,2,4-trichlorobenzene (TCB) at 140 °C and the complex viscosity of the polymer melt at 25 °C as a function of the angular frequency from small angle dynamic oscillation measurement. From Figure 1a, both increasing the ethylene pressure and reducing the polymerization temperature lead to a significant increase in the intrinsic viscosity of polymer fractions having the same molecular weight owing to a change of the chain topology from a hyperbranched to a linear structure. From Figure 1b, with an increase of the ethylene pressure and/or a decrease of the polymerization temperature, the zero-shear viscosity of the polymer melt increases dramatically and non-Newtonian shear thinning appears and becomes more obvious. On the basis of these results, in this series of polymers, the chain topology changes from hyperbranched to linear in order from HBPE1 to HBPE5, with HBPE1 and HBPE2 being typically hyperbranched as evidenced from their extremely low viscosity and Newtonian flow behavior in the whole frequency range. Scheme 1 shows schematically the trend of the topology change in these five polymers. The performance of a polymer as a VI improver is governed by its chain structural parameters including its molecular weight and distribution, chain topology, and branching density and type.1 Though having different chain topologies, this range of highly branched polyethylenes possess very similar average molecular weights and distributions and short branching densities and types. Therefore, these polymers comprise an excellent model system for us to systematically study the prime effect of chain topology on their performance. One paraffinic type base
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Table 2. KV and VI of Lubricants Formulated with Highly Branched Polyethylene at Different Concentrations KV (cSt) and VI of lubricants formulated at different polym concns polym
0.2 wt %
0.5 wt %
1 wt %
31.59 (KV, 40 °C) 5.439 (KV, 100 °C) 107 (VI) 33.71 (KV, 40 °C) 5.778 (KV, 100 °C) 113 (VI) 41.9 (KV, 40 °C) 7.065 (KV, 100 °C) 129 (VI) 39.55 (KV, 40 °C) 6.673 (KV, 100 °C) 124 (VI)
32.25 (KV, 40 °C) 5.534 (KV, 100 °C) 108 (VI) 33.38 (KV, 40 °C) 5.722 (KV, 100 °C) 112 (VI) 37.86 (KV, 40 °C) 6.432 (KV, 100 °C) 121 (VI) 59.43 (KV, 40 °C) 9.782 (KV, 100 °C) 150 (VI) 50.9 (KV, 40 °C) 8.408 (KV, 100 °C) 140 (VI)
HBPE1 HBPE2 HBPE3
30.5 (KV, 40 °C) 5.272 (KV, 100 °C) 104 (VI) 31.4 (KV, 40 °C) 5.41 (KV, 100 °C) 107 (VI)
HBPE4 HBPE5
33.48 (KV, 40 °C) 5.735 (KV, 100 °C) 112 (VI)
Table 3. Kurt Orbahn Test of the Shear Stability of Base Oils Formulated with Highly Branched Polyethylenea KV of formulated lubricants at percentage 100 °C (cSt) KV loss concn after 30 after 60 after 90 after 30 SSI after polym (wt %) fresh cycles cycles cycles cycles 30 cycles HBPE2 HBPE3 HBPE4 HBPE4 HBPE4 OCP a
3 3 0.5 1 3
6.83 6.895 6.889 6.898 9.695 9.643 9.622 9.609 6.976 6.158 6.117 6.103 9.09 7.265 7.156 7.098 20.91 14.43 13.71 13.38 8.232 6.742 6.616 6.598
-0.95 0.54 11.7 20.1 31.0 18.1
-3.9 1.1 45.3 46.6 41.2 48.7
The Kurt Orbahn test was performed according to ASTM D7109.
oil, which has a density of 0.8649 g/mL (15 °C), kinematic viscosities of 30.06 cSt (40 °C) and 5.18 cSt (100 °C), and a VI of 101, was chosen in this work for lubricant formulation. The five polymers were blended into the base oil to prepare formulated lubricants. Six polymer concentration levels at weight percentages of 0.2%, 0.5%, 1%, 3%, 5%, and 10% in the formulated lubricants were applied. Owing to their high branching density, all five polymers showed good solubility in the base oil at room temperature within the whole investigated concentration range. However, for lubricants formulated with 10 wt % HBPE4 and HBPE5, which have relatively more linear chain topology, polymer precipitation can appear after a long standing period at room temperature, but after thorough mixing and shaking, the precipitated polymer will redissolve completely in the lubricants. Besides the polymers, no other additives were applied in the lubricant formulations. In an effort to evaluate the polymers’ viscosity thickening power, the KV of each formulated lubricant at 40 and 100 °C was determined and is listed in Table 2. In Figure 2, the dependence of the kinematic viscosity at both 40 and 100 °C on the polymer concentration in the formulated lubricants is compared. At both temperatures, an increase in polymer concentration results in an increase in the kinematic viscosity of the formulated lubricants owing to the increase in polymer chain entanglements and the interaction between the base oil and macromolecules. Such a viscosity increase is more significant in lubricants formulated with HBPE4 and HBPE5, which have more linear chain topology. Comparing lubricants formulated with different polymers at the same concentration, one can conclude a polymer having more linear chain topology gives the formulated lubricant higher kinematic viscosity owing to the enhanced chain entanglements in these polymers. The VI value of each formulated lubricant was calculated using the kinematic viscosity data at 40 and 100 °C according to ASTM D2270 and is listed in Table 2 as well. In Figure 3,
3 wt %
5 wt %
44.28 (KV, 40 °C) 7.09 (KV, 100 °C) 129 (VI) 59.06 (KV, 40 °C) 9.713 (KV, 100 °C) 149 (VI) 139.6 (KV, 40 °C) 21.74 (KV, 100 °C) 183 (VI) 116.7 (KV, 40 °C) 17.98 (KV, 100 °C) 172 (VI)
44.52 (KV, 40 °C) 7.379 (KV, 100 °C) 130 (VI) 53.22 (KV, 40 °C) 8.742 (KV, 100 °C) 142 (VI) 87.75 (KV, 40 °C) 14.03 (KV, 100 °C) 165 (VI) 273.5 (KV, 40 °C) 40.79 (KV, 100 °C) 204 (VI) 238.4 (KV, 40 °C) 29.87 (KV, 100 °C) 165 (VI)
10 wt %
95.7 (KV, 40 °C) 14.86 (KV, 100 °C) 163 (VI) 194.3 (KV, 40 °C) 29.48 (KV, 100 °C) 193 (VI)
720.9 (KV, 40 °C) 94.82 (KV, 100 °C) 225 (VI)
the dependence of the VI value on the polymer concentration for each polymer is compared. For all polymers, the VI value increases with polymer concentration. However, at a given polymer concentration, polymers with more linear chain topology generally give higher VI values, and hence, they possess higher viscosity thickening powers. At a 5 wt % polymer concentration, among the five polymers, HBPE4 yields the highest VI value of 204, which far exceeds the VI requirements in many lubricant applications. At the same concentration, however, hyperbranched HBPE2 gives a VI value of 142, although it has almost the same average molecular weight and polydispersity as HBPE4. From Figures 2 and 3, we can conclude that the viscosity thickening power increases in the order HBPE1 < HBPE2 < HBPE3 < HBPE5 < HBPE4; i.e., it increases when the chain topology changes from a hyperbranched dendritic to a linear structure. However, one exception is observed with HBPE5, which is supposed to have a higher thickening power than HBPE4 on the basis of its more linear chain topology from Figure 1a. We propose that this exception should be attributed to the lower molecular weight of HBPE5 compared to HBPE4, which offsets the effect of the chain topology. The viscosity thickening power of a polymer as a VI improver is directly related to the hydrodynamic volume occupied by the randomly coiled polymer chain.1,4 The coil size is related to the polymer molecular weight, chain topology, and temperaturedependent solubility. A polymer improves the VI value of the lubricant by better enhancing the lubricant viscosity at higher temperature than at lower temperature owing to its improved solubility and expansion of the coil dimension at higher temperature.4 Due to their more compact chain structure, hyperbranched polyethylenes (such as HBPE1 and HBPE2) have a reduced hydrodynamic volume compared to more linearly structured polymers (such as HBPE4 and HBPE5) having the same molecular weight, which can be evidenced from their differences in intrinsic viscosity data shown in Table 1. In addition, the coil dimension of the hyperbranched polymer is much more restricted compared to the linear analogue, which inhibits the expansion of the polymer coil and limits the viscosity improving power. Therefore, the polymer viscosity thickening ability improves with a change of the chain topology from a hyperbranched to a linear structure. To examine the effect of the chain topology on the shear stability of the polymers as VI improvers, the Kurt Orbahn test, which is commonly used for the shear stability testing of VI improvers, was conducted on some selected lubricant samples according to the procedure outlined in ASTM D 7109-04. The tested lubricants were subjected to high shear flow through a
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Figure 3. Viscosity index of formulated lubricants as a function of polymer concentration.
Figure 1. (a) Polymer intrinsic viscosity ([η]) as a function of molecular weight from GPC-VIS measurement in 1,2,4-trichlorobenzene at 140 °C. (b) Polymer complex viscosity spectra at 25 °C from small-angle dynamic oscillation measurement. Figure 4. Kinematic viscosity of sheared lubricants as a function of the number of Kurt Orbahn cycles.
function of the number of KO cycles is compared for the tested lubricants. For a comparison purpose, a lubricant with the same base oil formulated with a commercial VI improver based on a linear olefin copolymer (OCP) was also tested, and the data are shown in Table 3 and Figure 4 as well. Two commonly used parameters, the percentage kinematic viscosity loss and shear stability index, are used to quantify the macromolecular shear degradation. The percentage kinematic viscosity loss is calculated according to the following equation:
KV loss (%) )
ηf - η s × 100 ηf
(1)
where ηf is the kinematic viscosity of the fresh unsheared lubricant and ηs is the kinematic viscosity of the sheared lubricant. The shear stability index, which removes the effect of variations in the viscosity of fresh lubricant and allows direct comparison of the polymer shear stability,4 is calculated according to eq 2, where η0 is the kinematic viscosity of the base oil. These two parameters were calculated on the basis of 30-cycle KO testing results and are shown in Table 3.
SSI ) Figure 2. Lubricant kinematic viscosity as a function of polymer concentration at (a) 40 °C and (b) 100 °C.
diesel fuel injector after 30, 60, and 90 cycles at 100 °C, and their kinematic viscosities at 100 °C were monitored after these cycles to investigate shear degradation of the polymers. Shear degradation leads to a drop of the polymer molecular weight and, hence, results in a loss in lubricant kinematic viscosity. In Table 3, the kinematic viscosity data of both fresh and sheared lubricants are listed. In Figure 4, the kinematic viscosity as a
ηf -ηs × 100 ηf -η0
(2)
For the lubricants formulated with relatively linearly structured HBPE4 at three different concentrations (0.5, 1, and 3 wt %), significant KV loss after 30 KO cycles can be observed, with the percentage KV loss increasing significantly with the polymer concentration. With the main shear degradation occurring within the first 30 KO cycles, the polymer displayed continuous though minor degradation in the next 30 and 60 KO cycles. Even though at three different polymer concentrations, the SSI values of the three lubricants having different polymer
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concentrations after 30 KO cycles are quite close (∼45). This is consistent with the results found with many lubricant packages using various polymers as VI improvers and reflects the relative independence of the SSI value on the polymer concentration.4 The degradation behavior of this linearly structured HBPE4 sample is very similar to that of the linear commercial OCP polymer, which has a commercial SSI rating of 50. Dramatically different from HBPE4 formulated lubricants, the lubricants formulated with HBPE2 and HBPE3 of more hyperbranched topologies at 3 wt % showed extraordinarily high shear stability in the KO test. From Table 3, even after 90 KO cycles, no obvious shear degradation was observed for the hyperbranched HBPE2 formulated lubricant. Its negative percentage KV loss and SSI values after 30 KO cycles shown in Table 3 are probably due to the slight experimental error in the KV measurement. For the HBPE3 formulated lubricant, the percentage KV loss after 30 cycles is only 0.54% and the SSI value is as low as 1.1. These results convincingly prove that the shear stability of this range of highly branched polyethylenes of high molecular weight can be tremendously enhanced when the chain topology is tuned from a linear to a hyperbranched structure with a constant molecular weight. The hyperbranched structure imparts the polymers with tremendously improved insensitivity of their molecular weight toward shear-induced chain scission, which gives them constant viscosity thickening power throughout the shearing operations. By engineering the polymer chain topology by simply tuning the polymerization condition of chain walking ethylene polymerization, we can therefore conveniently prepare various highly branched polyethylene-based VI improvers for different applications. Owing to their extremely high shear stability, the hyperbranched polyethylenes produced at lower ethylene pressure and higher temperature can be applied in many high-end applications which involve high shear stress and require a highly shear stable VI improver. However, though highly shear stable, these hyperbranched polymers have compromised viscosity thickening powers owing to their compact structure as well, which can be evidenced from their relatively lower VI values at a given polymer concentration in the lubricants. To formulate a lubricant of high VI (for example, 200) with these hyperbranched polymers, a higher polymer concentration (for example, ∼10 wt % for HBPE3) would therefore be needed. On the contrary, the relatively linearly structured polymers (HBPE4 and HBPE5) can be applied at a low concentration dosage in regular applications without a strict requirement on the shear stability of the VI improver. Conclusion We have systematically investigated in this work the unique effects of the chain topology on the performance of a novel range of high-molecular-weight highly branched polyethylenes (HBPE1-HBPE5) having various chain topologies prepared by chain walking ethylene polymerization as lubricant VI improvers. It is demonstrated that, when the chain topology changes
from a linear to a hyperbranched dendritic structure, the shear stability of the polymer as a VI improver can be significantly improved, however compromising its viscosity thickening power. Hyperbranched polyethylenes (HBPE2 and HBPE3) we prepared possess extremely high shear stability with almost zero shear degradation. However, enhancing their viscosity thickening power by increasing their molecular weight is a further research task to reduce their concentration dosage in lubricant formulation. Acknowledgment This work was supported by a University Research Award (URA) Grant from Imperial Oil Ltd. and a Collaborative Research and Development (CRD) Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC). We thank Dr. Aileen R. Wang at Imperial Oil Ltd. (Sarnia, Ontario) for conducting the lubricant performance testing. Z.Y. also thanks the Canadian Foundation for Innovation (CFI) and NSERC for funding the research infrastructure. Literature Cited (1) Ver Strate, G.; Struglinski, M. J. In Polymers as Lubricating-Oil Viscosity Modifier; Schultz, D. N., Glass, J. E., Eds.; ACS Symposium Series 462; American Chemical Society: Washington, DC, 1991; Chapter 15, p 256. (2) Mishra, M. K.; Saxton, R. G. Polymer additives for engine oils. CHEMTECH 1995, 25, 41. (3) Lashkhi, L.; Fuks, I. G. Polymer-Compounded OilssProperties and Specific Features of Application. Chem. Technol. Fuels Oils 1988, 24, 492. (4) Hyndman, C. W.; Kinker, B. G.; Placek, D. G. The Importance of Shear Stability in Multigraded Hydraulic Fluids. In Hydraulic Failure Analysis: Fluids, Components, and System Effects; ASTM STP 1339; Totten, G. E., Wills, D. K., Eds.; American Society for Testing and Materials: West Conshohocken, PA, 2001. (5) Eckert, R. J. A. Hydrogenated star-shaped polymer. U.S. Patent 4116917, 1978. (6) Xue, L.; Agarwal, U. S.; Lemstra, P. J. Shear Degradation Resistance of Star Polymers during Elongational Flow. Macromolecules 2005, 38, 8825. (7) Wang, T.-Y.; Tsiang, R. C.-C.; Liou, J.-S.; Wu, J.; Sheu, H.-C. Preparation and characterization of a star-shaped polystyrene-b-poly(ethylene-co-propylene) block copolymer as a viscosity index improver of lubricant. J. Appl. Polym. Sci. 2001, 79, 1838. (8) Bosman, A. W.; Janssen, H. M.; Meijer, E. W. About Dendrimers: Structure, Physical Properties, and Applications. Chem. ReV. 1999, 99, 1665. (9) Gao, C.; Yan, D. Hyperbranched polymers: from synthesis to applications. Prog. Polym. Sci. 2004, 29, 183. (10) Ye, Z.; Zhu, S. Newtonian flow behavior of high-molecular-weight hypebranched polyethylenes produced with a Pd-diimine catalyst and its dependence on chain topology. Macromolecules 2003, 36, 2194. (11) Ye, Z.; AlObaidi, F.; Zhu, S. Melt Rheological Properties of Branched Polyethylenes Produced with Pd- and Ni-Diimine Catalysts. Macromol. Chem. Phys. 2004, 205, 897. (12) Guan, Z.; Cotts, P. M.; McCord, E. F.; McLain, S. J. Chain Walking: A New Strategy to Control Polymer Topology. Science 1999, 283, 2059.
ReceiVed for reView October 23, 2006 ReVised manuscript receiVed December 7, 2006 Accepted December 11, 2006 IE0613624
