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Synthesis of Ultrahigh Molecular Weight Polyethylene Using Traditional Heterogeneous Ziegler-Natta Catalyst Systems Sudhakar Padmanabhan,* Krishna R. Sarma, and Shashikant Sharma Research Centre, Vadodara Manufacturing DiVision, Reliance Industries Limited, Vadodara, India, 391 346
Ultrahigh molecular weight polyethylene was synthesized from traditional Ziegler-Natta type catalysts (ZN), namely, TiCl4 anchored on MgCl2 support. This, upon activation with AlRR′2 (where R, R′ ) isoprenyl or isobutyl), gave precatalysts (C-2 to C-5) having 16, 21, 25, and 32% trivalent titanium, respectively. The reduction in oxidation states also accompanies the reduction in particle size of the catalysts, which in turn gets reflected in the resulting polymer properties under specified operating conditions. We have demonstrated the effect of process conditions that can surmount the catalyst dependency over the polymer characteristics, and hence, it can result in polymer with consistent polymer properties, which is an important need of the polymer industries. The polymer characteristics such as particle size distribution, average particle size, bulk density, reduced specific viscosity, and concentration of fine and coarse particles were determined and were dependent on various process parameters. Under identical reaction conditions, the polymerization with larger scale yield polymer with different characteristics. The fine-tuning of process conditions yielded polymer with consistent quality. Introduction Ultrahigh molecular weight polyethylene (UHMWPE) belongs to the specialty polymer grade, having unique properties and hence finding applications in areas requiring less abrasion, excellent impact strength, good chemical resistance, etc.1–3 UHMWPE has excellent wear resistance, outstanding impact strength, and very good chemical resistance. Consequently, it finds applications in diversified areas with unique requirements.3 More than two-thirds of the commercial processes involved are based on Hostalen’s continuous stirred tank using conventional ZN catalysts.4 A couple of processes are also based on metallocene catalyst systems with very limited capacities.5 The initial patents on catalysts relating to UHMWPE date back to the early 1970s and still continue to dominate the scene, even after a span of 4 decades. The concept of anchoring TiCl4 on supports like Mg(OR)2/MgCl2 followed by treatment with aluminum alkyls has been fully exploited through diverse process variations.6 Major players in this field arranged chronologically include Ruhrchemie, Hoechst, Himont, and Ticona.4 Petrobras aimed at improved morphology of the polymer through spherical catalyst systems involving supporting and spray-drying techniques.7 Phillips’ novelty was in the use of modified alumina and silica supports to immobilize metals like Ti, V, Cr, Zr, and Hf.8 Equistar derived their strengths through the use of quinolinoxy-containing single site catalysts through a nonalumoxane route.9 Besides, there are numerous examples available in the literature pertaining to the use of homogeneous single-site catalysts involving metals like Ti, V, and Zr for the synthesis of UHMWPE.10 Among the various grades of UHMWPE, the grade with molecular weight 4-5 million g/mol is unique because of its optimum abrasion resistance, impact strength, chemical resistance, etc.3 Hence the 4-5 million molecular weight grade has maximum business volume. At higher molecular weights, though the abrasion resistance was slightly better than that of the lower molecular weight polymers, the impact strength dropped down * To whom correspondence should be addressed. Tel.: +91 265 669 6260. Fax: +91 265 669 3934. E-mail: Sudhakar.padmanabhan@ zmail.ril.com.
considerably. Considering this, it is imperative that we have special grades with unique properties for unique applications.2 Most of the polyethylene produced based on the market needs are manufactured using traditional Ziegler-Natta catalysts, which typically comprise titanium halides (TiX4 where X is generally Cl) supported on magnesium chloride (MgCl2) through various chemical modifications.6 Olefin polymerizations involving such ZN catalysts involve a catalyst preactivation step involving aluminum alkyls, aluminoxanes, or borate compounds (generally known as cocatalysts) wherein, apart from reduction of oxidation states of the titanium, there is also a vacant coordination site created on the titanium. It is on this vacant site that the olefin coordinates, and through a series of transformations, the polymer chain grows. The activity of these catalysts not only depends on the total titanium present in the system but also depends on the percentage of the reduced titanium. The production of UHMWPE using these catalyst systems is again a big task, taking in to account of the possible termination reactions that can kill the propagating active species. The presence of excess aluminum alkyls can bring about the termination via transfer of polymer chain to aluminum. This can reduce the length/molecular weight of the polymer chain and also broaden the molecular weight distribution.11 Experiments on a slightly larger scale in a 5 L laboratory-scale reactor poses a vigorous threat because of the usage of less catalyst, which can easily be killed by the presence of a small amount of impurities in the reaction medium. Hence, process optimization studies play a bigger role in these reactions. In this paper we have demonstrated the capability of using hydrocarbon as a polymerization solvent for producing UHMWPE having desired bulk density (BD), average molecular weight, and average particle size (APS) with controlled fine (250 µm) material and also developed laboratory process for making UHMWPE of 4-6 million g/mol molecular weight with consistent productivities. Experimetal Section The required catalyst, C-1 with 20% titanium content (80% magnesium and chlorides), was synthesized by adopting a well-
10.1021/ie802000n CCC: $40.75 2009 American Chemical Society Published on Web 04/14/2009
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Scheme 1. Process Overview
known procedure:6 10 g of magnesium ethoxide is added to 120 mL of varsol, a high boiling kerosene fraction, under an atmosphere of nitrogen and mechanical stirring. The temperature is increased to 85 °C and maintained. Subsequently, about 35 g (20 mL) of TiCl4 is added to the magnesium ethoxide suspension under a gentle atmosphere of nitrogen slowly over a period of 5-6 h. The molar ratio of Mg:Ti is about 1:2. After the completion of TiCl4 addition, the temperature is increased to 120 °C and maintained for about 60 h to temper the catalyst. The solvent contains the precatalyst as a pale yellow to white suspension. The catalysts were stored under nitrogen atmosphere as a slurry in hexane. The slurry concentration was maintained at 12-15% for easy handling. The slurry was homogenized completely and was transferred using standard syringe techniques. The slurry concentration of the catalysts was determined before each experiment to calculate the amount of the catalyst added. All manipulations like handling and transfer of catalysts and pyrophoric aluminum alkyls were carried out in a nitrogen glovebox/bag. The actual catalyst for UHMWPE is prepared from C-1 (white catalyst) by reducing the same using AlRR′2. The molar ratio employed between the titanium catalyst and the aluminum alkyl varied on the basis of the Ti3+ content intended. The aluminum alkyl is gently added at about 25 °C to the white catalyst slurry under a stream of nitrogen and with mechanical agitation over a period of 3-5 h. The color of the slurry changes to grayish black, and hence, the catalyst is also referred to as the “black catalyst”. Here the titanium is present as a mixture of quadrivalent and trivalent titanium (predominantly) with traces of divalent titanium. Polymerizations were carried out in laboratory Buchi reactors of 1, 5, and 19 L capacity using well-established and validated procedures in hexane as the medium. The hexane used in the runs is dry distilled under a nitrogen atmosphere after refluxing it over sodium hydride as the desiccant, and the moisture content was around 5-8 ppm. The prereduced catalyst slurry in hexane was homogenized and a suitable amount was transferred out for a run. The agitation has been standardized around 500 rpm and the temperature was maintained at 75 °C over the period of 2 h. Hydrogen dosing was done through a precalibrated bomb hooked to the reactor for controlling the molecular weight. The polymer was then filtered, washed with acetone, and then dried in an air oven at about 75 °C. The weight of polymer was recorded to calculate the productivity of the catalyst in terms of grams of polymer/grams of catalyst and grams of polymer/ millimole of Ti. The productivity was based on a 2 h period. Catalyst characterization was carried out by measuring parameters like slurry concentration for the solid content; compositional analysis for Ti, Mg, and Cl by UV-vis spectrophotometry and EDTA and argentometric titrations, respectively; oxidation states of Ti (quadrivalent, trivalent) by cerimetry; and the particle size distribution (PSD) for APS by a Malvern Mastersizer-E, a laser diffraction based particle size analyzer. The viscosity-based average molecular weight was calculated using Margolie’s equation. The reduced specific viscosity (RSV) was determined at 135 °C in decaline as solvent in an Ubbelohde viscometer with constant ) 0.01 by measuring
the flow times for solvent and subsequently a 0.02% solution of the polymer. Results and Discussion Titanium supported on MgCl2 (C-1) upon activation with AlRR′2 (an equal mixture of triisobutylaluminum and isoprenylaluminum) and hydrogen as the molecular weight regulator is being used for the generation of UHMWPE. There is enough literature precedence for the use of such catalysts with triethyl aluminum (TEAL) as an activator for the production of high density polyethylene (HDPE).12 Tailoring such catalyst to produce UHMWPE through process optimization in hydrocarbon media meeting rigid polymer specifications has been a challenge in the industrial arena. The necessary precatalyst C-1 has been prepared with 20% titanium loading on MgCl2 support and activated with AlRR′2, which yield catalysts with active titanium center. The catalyst batches with different Ti 3+ contents were synthesized by adjusting the AlRR′2 quantity and are C-2 (16% Ti3+), C-3 (21% Ti3+), C-4 (25% Ti3+), and C-5 (32% Ti3+). The process overview is given in Scheme 1. The role of aluminum alkyls in olefin polymerization is of paramount importance and consequently today we have a diverse range of such Lewis acids, each with a unique role to play in a polymerization. The crux of the earlier statements is that the correct aluminum alkyl has to be primarily identified for a polymerization process and then subsequently its amount with respect to the catalyst needs to be optimized to arrive at the desired productivity and polymer characteristics, namely, molecular weight, average particle size, bulk density, etc. The use of AlRR′2 as an activator yields the required polyethylene with ultrahigh molecular weight. For a particular ethylene pressure and catalyst system (C-3), we carried out the Al/Ti optimization experiments and we observed that the optimum value of Al/Ti is around 7-8 under the specified operating conditions, namely, 2 atm of ethylene pressure (PC2 2 atm). This exercise needs to be optimized when the conditions are changed. Thus, at an ethylene pressure above 5 atm we found the optimized Al/Ti ratio was around 4-5. By operating at a different Al/Ti value, besides yield, the other polymer properties like BD and average molecular weight also change, thus providing a lever to alter the polymer characteristics at the cost of yield. At 2 atm PC2, we have evaluated the polymerization with C-2 to C-5 and found that there is a close agreement between the polymer particle
Figure 1. Comparison of PSD of polymer with catalyst nature.
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Figure 2. (a) Effect of PC2 on polymer productivity. (b) Effect of Ti3+ content on molecular weight of the polymer obtained.
Figure 3. (a) H2 dosing bomb calibration. (b) Effect of H2 pressure on polymer RSV.
size distribution (PSD) and catalyst PSD (Figure 1). As we increase the % Ti3+, there is a reduction in catalyst PSD which in turn gets reflected in the APS of the polymer obtained with increased fines. The optimum value of Ti3+ content was found to be 20-25% under PC2 2 atm conditions (Figure 1). When we increased the pressure from 2 to 7.5 atm, we found there is not much difference in PSD of the polymer obtained among C-2 to C-5 catalyst systems, clearly revealing the importance of process conditions over polymer properties. Besides AlRR′2, we have also evaluated TEAL as the activator12 for selected catalyst batches for obtaining UHMWPE. At 2 atm PC2 employed, though molecular weight between 4 and 10 million g/mol could be achieved through H2 mediation, it was observed that BD was always around 0.25 g/cm3, and the fines generated were also on the higher side. Extensive process optimization studies need to be performed for better polymer characteristics. During the course of our investigation with a view to generate UHMWPE with the desired characteristics (BD, PSD/APS, RSV), we have carried out polymerizations with ethylene pressures ranging from 2 to 7.5 atm. With typical catalyst and process conditions, we could achieve productivity of ∼2.5 ( 0.5 kg of UHMWPE/g of catalyst at 7.5 atm ethylene pressure over 2 h (Figure 2a). Nonetheless, besides productivity, the other polymer characteristics could be fine-tuned by playing with the pressure. BD improved considerably at enhanced pressures, which is highly desirable. Changing the ethylene pressure was a convenient way to change the partial pressure of hydrogen during molecular weight control experiments, thus providing leverage for producing UHMWPE with desired average molecular weight. We have observed that the temperature at which the polymerization was performed had an effect on the average molecular
Table 1. Effect of H2 Pressure on Molecular Weight of UHMWPE at PC2 5 atma run PH2 (atm) productivity (g PE/g cat.) BD (g/cm3) APS (µ)b Mηc 1 2 3 4 5 6 7 8
3 2 1 0.5 2 2 0.17 0.34
1442 1282 1359 1195 1049 1344 1282 1303
0.36 0.36 0.35 0.35 0.33 0.36 0.36 0.36
94 94 97 108 97 100 103 98
4.0 4.4 4.3 5.3 4.6 4.4 5.1 4.2
a General conditions: PC2 5 atm, Al/Ti ) 5, 75 °C, 500 rpm; 0.34 g of C-4; PH2 in 100 mL bomb. b Analyzed by both Malvern PSA and traditional sieve shaker methods. c Viscosity-based average molecular weight (million g/mol) calculated using Margolie’s equation.
Table 2. Effect of H2 Pressure on Molecular Weight of UHMWPE at PC2 7.5 atma run PH2 (atm) productivity (g PE/g cat.) BD (g/cm3) APS (µ)b Mηc 9 10 11 12 13 14 15 16
0 3.0 1.0 0.65 0.60 0.55 0.34 0.08
3235 3468 3439 3453 3147 3246 3235 3351
0.41 0.40 0.41 0.40 0.41 0.41 0.42 0.41
124 115 120 121 116 118 114 125
8.3 2.1 3.1 4.2 4.3 4.2 4.5 4.2
a General conditions: PC2 7.5 atm, Al/Ti ) 5, 75 °C, 500 rpm; 0.34 g of C-4; PH2 in 100 mL bomb. b Analyzed by both Malvern PSA and traditional sieve shaker methods. c Viscosity-based average molecular weight (million g/mol) calculated using Margolie’s equation.
weight of UHMWPE, akin to what has been observed by other groups.13 Thus, keeping all other parameters constant and carrying out polymerizations at 70, 75, and 80 °C resulted in UHMWPE with progressive reduction in average molecular
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a
Table 3. Scale up Studies run
reactor size (L)
solvent vol (L)
catalyst concn (mmol Ti)
Al/Ti
productivity (g PE/g cat.)
Mηb
17 18 19 20
5 1 19 19
3 0.5 10 10
1.00 0.2 4.00 4.00
8 8 8 5
2760 3000 2250 1950
10.0 12.6 5.3 7.2
a General conditions: PC2 7.5 atm, PH2 0 atm, 75 °C, 500 rpm with C-4. b Viscosity-based average molecular weight (million g/mol) calculated using Margolie’s equation.
Figure 4. SEM images of the polymers produced from (a) C-2, (b) C-3, (c) C-4, and (d) C-5.
weight, though not on a major scale because of the small difference in temperature. It has to be realized that carrying out polymerization at much lower temperatures is not economical from the commercial angle, since the reaction rate drops down drastically for even a drop in temperature of about 10 °C. Under more or less similar operating conditions (within limits of experimental error) catalyst systems C-2, C-3, C-4, and C-5 containing 16, 21, 25, and 32% Ti3+ were screened for UHMWPE polymerization. The trend when ethylene pressure was 7.5 atm is shown in Figure 2b. We could see that the ethylene pressure predominates over the trivalent Ti content in the catalysts to alter the kinetics of the process. Hydrogen has been in regular use as a molecular weight regulator in ethylene and propylene polymerizations. It is convenient to use due to various practical reasons, since an extensive amount of data pertaining to its solubility in various solvents is available at different temperatures.14 Research groups have also determined the Henry’s constant for hydrogen and ethylene in hexane at different temperatures.15 We have also studied the solubility characteristics of ethylene, hydrogen, and their mixtures in solvents like varsol and hexane.16 Hydrogen is one such gas where its solubility increases with temperature, unlike the expected reverse trend. For UHMWPE systems, this can have far reaching implications since a proper combination
of solvent, temperature, and hydrogen partial pressure can result in unique molecular weight control. With an objective of controlling the molecular weight of UHMWPE with hydrogen,17 we have calibrated the hydrogen dosing bomb hooked to the Buchi reactor. The bomb was pressurized at ambient temperature, 30 °C, with hydrogen at different pressures, and the volume of hydrogen was measured using a gas flow meter. The results are given in Figure 3a. This gave a method to measure the volume of hydrogen dosed based on the pressure employed in the bomb. The calibration results are quite linear, with an excellent regression constant of almost 1. During the course of our investigation for regulating the molecular weight of UHMWPE in polymerization, we realized that there is a threshold limit for hydrogen using the specified bomb under the employed conditions. This is essentially the threshold or saturated solubility of hydrogen in 3 L hexane at the specified operating conditions based on the partial pressures of hydrogen, ethylene, and hexane.18 We could not go down to lower hydrogen pressures than this due to the bomb limiting capacity. The size of the dosing bomb was approximately 100 mL at atmospheric pressure. The approach available to us was to hook up another bomb of smaller size, say 50 mL in capacity, or to reduce the hydrogen partial pressure by significantly
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increasing the ethylene pressure. We have used the second approach. Here also we could not go beyond 7.5 atm ethylene pressure due to system configurations. The results are depicted in Figure 3b. It can be observed how effectively the partial pressure of hydrogen is controlled at two different ethylene pressures, viz., 5 and 7.5 atm. Obviously, as expected the line at 5 atm ethylene pressure controls molecular weight regulation in a higher region than the 7.5 atm ethylene pressure, again verifying Henry’s law for the solubility of gases. We can observe from Figure 3b that achieving an average molecular weight of ∼4.5 million is statistically more favored at hydrogen pressures from 0.1 to 0.5 atm, since the partial pressure of hydrogen is not lowered down significantly at these lower hydrogen pressures. Molecular weight control with hydrogen pressure of 1, 2, and 3 atm reflects a linear response, with the molecular weight progressively dropping down since the partial pressure of hydrogen now becomes significant (Figure 3b). In case we wanted molecular weight control in a still higher region compared to 5 atm ethylene pressure, the approach would be to operate at lower ethylene pressures; this would lower the partial pressure of hydrogen, thus increasing the molecular weight. In doing so, we might realize that other vantage properties like productivity, BD and APS might get affected. In a nut shell, the overall game is optimization of all parameters such that we get all the desired properties.19 Thus, experiments at 5 atm ethylene pressure gave us good productivity, except that the bulk density was below 0.4 g/cm3 and APS was low. The results are shown in Table 1. Experiments at 7.5 atm ethylene pressure gave us most of the desired polymer properties. We found that it was an excellent recipe for making the 4.5 million molecular weight grade with enhanced productivity, desired BD, and PSD/APS (Table 2). UHMWPE produced using different catalyst batches with different Ti3+ contents (Figure 4) hardly showed any variation in morphology. The SEM images of several other batches mimic the same kind of images, confirming the consistent quality of the polymer obtained in different grades synthesized.7 After thorough examination of the 5 L scale laboratory experiments, we did scale up the same reaction to 19 L scale. The productivity and quality of the polymer in terms of other polymer characteristics were found to be comparable, but the molecular weight of the polymer obtained came down drastically (Table 3). This led us to do the reaction in smaller scale also and we indeed found that at 1 L scale the molecular weight was higher. The experiment with lesser aluminum alkyl, i.e. Al/Ti ratio of 5 in 19 L, gave polymer with comparable yield and increased molecular weight. It is worth noting that the aluminum alkyl, which is in excess, plays the role of a chain terminator, thereby reducing the molecular weight. The reaction in 1 L scale, having fewer aluminum alkyls available for chain termination, gave higher molecular weight polymer.11 Thus, controlling the effective alkyl aluminum concentration is an important parameter, especially while synthesizing polymers having ultrahigh molecular weight. Conclusion The production of UHMWPE having molecular weight of 4-6 million g/mol under specified operating conditions was established on a scale of 5 L. The polymer obtained had defined product characteristics, which is highly desirable from an industrial point of view. The study further emphasizes the importance of the proper concentration of catalyst and cocatalyst
and other process conditions for achieving the desired polymer characteristics. Acknowledgment We thank Mr. Viral Kumar Patel for his technical and analytical assistance throughout the course of the work. Sincere thanks are due to Dr. R. Char and his team for the pilot plant studies. We also sincerely thank Dr. Ajit Mathur and Dr. Rakh V. Jasra for their continuous encouragement to carry out this work. Supporting Information Available: The detailed procedure for estimating total titanium content and different oxidation states present in the catalyst systems is given in detail. This material is available free of charge via the Internet at http:// pubs.acs.org. Literature Cited (1) Kurtz, S. M. UHMWPE Handbook, 1st ed.; Elsevier: New York, 2004. (2) For more information visit www.dsm.com/en_US/html/dep/ stamylanuh.htm. (3) (a) Kurtz, S. M.; Muratoglu, O. K.; Evans, M.; Edidin, A. A. Advances in the processing, sterilization, and crosslinking of ultra-high molecular weight polyethylene for total joint arthroplasty. Biomaterials 1999, 20, 1659. (b) Rose, R. M.; Cimino, W. R. Exploratory investigations on the structure dependence of the wear resistance of polyethylene. Wear 1982, 77, 89. (c) Weightman, B.; Light, D. A comparison of RCH 1000 and HiFax 1900 ultra-high molecular weight polyethylenes. Biomaterials 1985, 6, 177. (d) Nakayama, K.; Furumiya, A.; Okamot, T.; Yag, K.; Kaito, A.; Choe, C. R.; Wu, L.; Zhang, G.; Xiu, L.; Liu, D.; Masuda, T.; Nakajima, A. Structure and mechanical properties of ultra-high molecular weight polyethylene deformed near melting temperature. Pure Appl. Chem. 1991, 63, 1793. (4) Patent search results related to UHMWPE: (a) Siegfried, L.; Birnkraut, H. W.; Moser, H. Process for the polymerization of alpha olefins. US Patent 3,910,870, 1975. (b) Heinrich, A.; Bohm, L.; Scholz, H. A. Process for the preparation of ethylene (co)polymers. US Patent 5,292,837 1994. (c) Ehlers, J.; Walter, J. Process for the preparation of ultrahigh molecular polyethylene having high bulk density. US Patent 5,587,440, 1996. (d) Bilda, D.; Boehm, L. Process for the preparation of a polymerization and copolymerization of ethylene to give ultra high molecular weight ethylene polymers. US Patent 6,114,271, 2000. (e) Payer, W.; Ehlers, J. Method for the production of olefin polymers and selected catalysts. US Patent 7,157,532, 2007. (f) Ehlers, J.; Haftka, S.; Wang, L. Method for producing a polymer. US Patent 7,141,636, 2006. (5) (a) Honma, S.; Tominari, K.; Kurisu, M. Injection molding polyolefin composition. US Patent 5,019,627, 1991. (b) Liu, J. C. Olefin polymerization with pyridine moiety-containing single-site catalysts. US Patent 6,767,975, 2004. (6) For synthesis of the catalyst recipes MgOEt2 + TiCl4, see: Berthold, J.; Diedrich, B.; Franke, R.; Hartlapp, J.; Schafer, W.; Strobel, W. Process for the preparation of a polyolefin, and a catalyst for this process. US Patent 4,447,587, 1984; Process for the preparation of a polyolefin, and a catalyst for this process. US Patent 4,448,944, 1984. (7) Da Silva, J. C.; De Figueiredo, M. O. Spherical ultra high molecular weight polyethylene. US Patent 5,807,950, 1998. (8) (a) Martin, J. I.; Secora, S. J. Benham, E. A.; McDaniel, M. P.; Hsieh, E.; Johnson, T. W. Olefin polymerization process and products thereof. US Patent 6,034,186, 2000. (b) Martin, J. I.; Bergmeister, J. J.; Hsieh, E.; McDaniel, M. P.; Benham, E. A.; Secora, S. J. Olefin polymerization process and products thereof. US Patent 6,657,034, 2003. (9) Liu, J. C.; Mack, M. P.; Lee, C. C. Preparation of ultra high molecular weight polyethylene. US Patent 6,265,504, 2001. (10) Novel catalysts reported in the scholarly literature demonstrated to produce ultrahigh molecular weight polyethylenes:(a) Tamm, M.; Randoll, S.; Herdtweck, E.; Kleigrewe, N.; Kehr, G.; Erker, G.; Rieger, B. Imidazolin2-iminato titanium complexes: Synthesis, structure and use in ethylene polymerization catalysis. Dalton Trans. 2006, 459. (b) Starzewski, K. A. O.; Xin, B. S.; Steinhauser, N.; Schweer, J.; Benet-Buchholz, J. Donor-acceptor metallocene catalysts for the production of UHMW-PE: Pushing the selectivity for chain growth to its limits. Angew. Chem. 2006, 118, 1831. (c) Karam, A.; Casas, E.; Catarı´, E.; Pekerar, S.; Albornoz, A.; Me´ndez, B.
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ReceiVed for reView December 29, 2008 ReVised manuscript receiVed February 25, 2009 Accepted March 17, 2009 IE802000N
