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Organometallics 2009, 28, 244–248
Oligomerization of r-Olefins via Chromium Metallacycles David S. McGuinness* School of Chemistry, UniVersity of Tasmania, PriVate Bag 75, Hobart, Tasmania 7000, Australia ReceiVed August 27, 2008
Chromium complexes that oligomerize and polymerize olefins via a metallacycle mechanism represent possible models for the commercially important Phillips catalyst, which is still poorly understood mechanistically. Comparisons between the two might provide insight into the process, and as such the oligomerization of R-olefins (propene to 1-octene) with chromium(III)-bis(carbene)pyridine complexes in combination with MAO has been studied. Linear R-olefins are homo-oligomerized, as well as cooligomerized with ethylene, via a mechanism most likely involving metallacycles. Homo-oligomerization of R-olefins leads predominantly to head-to-tail dimers with vinylidene unsaturation, while a less favorable coupling leads to linear internal olefin dimers. With shorter chain monomers, trimerization and tetramerization become more significant, albeit still minor processes. The kinetics of 1-octene dimerization were studied and are found to be first-order in chromium but zero-order in 1-octene concentration. The results are interpreted in terms of the likely rate-determining step of the reaction, and comparisons are drawn between the behavior of this system and the heterogeneous Phillips catalyst. 1. Introduction The oligomerization and polymerization of ethylene via the metallacyclic mechanism (Scheme 1) has received much attention lately, primarily due to its implication in the selective trimerization and tetramerization of ethylene to 1-hexene and 1-octene, respectively.1-3 The key to the selectivity of these systems seems to lie in the energetically preferred tendency of M-C6 and M-C8 metallacycles to undergo product releasing β-hydrogen shift rather than further ethylene insertion. At the same time, a constrained geometry of the metallacycle prevents the β-hydrogen shift reaction at the M-C4 stage, and, as such, very low amounts of 1-butene are produced. While most of the recent interest in this mechanism stems from this selectivity effect, such a mechanism has long been proposed as one possibility for the polymerization of ethylene with the industrial chromium on silica Phillips catalyst, one of the most important yet mechanistically controversial catalyst systems known.4,5 It is certainly the case that chromium catalysts seem to have a certain predisposition to the metallacycle mechanism, as most trimerization and tetramerization catalysts are based upon this metal. Additionally, the possibility of an extended metallacycle mechanism, leading to higher oligomers and polymer, has recently been confirmed in a number of studies with homogeneous chromium catalysts.6-8 This work supports the possibility * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Dixon, J. T.; Green, M. J.; Hess, F. M.; Morgan, D. H. J. Organomet. Chem. 2004, 689, 3641. (2) Wass, D. F. Dalton Trans. 2007, 816. (3) Overett, M. J.; Blann, K.; Bollmann, A.; Dixon, J. T.; Haasbroek, D.; Killian, E.; Maumela, H.; McGuinness, D. S.; Morgan, D. H. J. Am. Chem. Soc. 2005, 127, 10723. (4) Groppo, E.; Lamberti, C.; Bordiga, S.; Spoto, G.; Zecchina, A. Chem. ReV. 2005, 105, 115. (5) Theopold, K. H. CHEMTECH 1997, 27, 26. (6) Tomov, A. K.; Chirinos, J. J.; Jones, D. J.; Long, R. J.; Gibson, V. C. J. Am. Chem. Soc. 2005, 127, 10166. (7) Tomov, A. K.; Chirinos, J. J.; Long, R. J.; Gibson, V. C.; Elsegood, M. R. J. J. Am. Chem. Soc. 2006, 128, 7704. (8) McGuinness, D. S.; Suttil, J. A.; Gardiner, M. G.; Davies, N. W. Organometallics 2008, 27, 4238.
Scheme 1
of metallacycles being responsible for polyethylene production on heterogeneous chromium catalysts, although the mechanism still remains highly uncertain. In contrast to ethylene, very few studies have investigated the effect of higher R-olefins on the metallacyle mechanism. The formation and growth of metallacycles from R-olefins is expected to be slower than is the case for ethylene, while the rate of decomposition might be less affected. This should manifest in a different oligomer distribution (carbon number selectivity). The secondary incorporation of one molecule of R-olefin (1-hexene/1-octene) is well-known for trimerization and tetramerization catalysts; however, incorporation of more than one R-olefin unit is not observed with these systems.3,9,10 In addition, the codimerization of ethylene and 1-butene with titanium complexes is thought to occur via a metallacycle mechanism.11 To our knowledge, the only known system capable of homo-oligomerizing higher R-olefins via a metallacycle mechanism is the chromium-triazacyclohexane system of Ko¨hn and Wasserscheid.12,13 This catalyst selectively converts R-olefins to isomeric trimers, which are of interest as synthetic (9) Deckers, P. J. W.; Hessen, B.; Teuben, J. H. Organometallics 2002, 21, 5122. (10) Bowen, L. E.; Wass, D. F. Organometallics 2006, 25, 555. (11) You, Y.; Girolami, G. S. Organometallics 2008, 27, 3172. (12) Ko¨hn, R. D.; Haufe, M.; Kociok-Ko¨hn, G.; Grimm, S.; Wasserscheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 4337. (13) Wasserscheid, P.; Grimm, S.; Ko¨hn, R. D.; Haufe, M. AdV. Synth. Catal. 2001, 343, 814.
10.1021/om8008348 CCC: $40.75 2009 American Chemical Society Publication on Web 11/17/2008
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lubricants. The same catalyst converts ethylene to polyethylene (with some 1-hexene also formed), presumably also via a metallacycle mechanism. Such incorporation of R-olefins into metallacycles is relevant to ongoing debate around the mechanism of the Phillips catalyst, which is also known to incorporate R-olefins into the polymeric chain. Comparison of the products formed in each case might provide further insight into the mechanism of the Phillips catalyst. We recently reported8 that bis(carbene)pyridine complexes of chromium (1-3), previously14 established as highly active ethylene oligomerization catalysts (in combination with MAO), do so via an extended metallacycle mechanism. These systems were also found to incorporate the R-olefins formed in the process into higher oligomers, again via a metallacycle route. Herein, we report investigations into the oligomerization of R-olefins with these catalysts. Product selectivities and reaction kinetics have been studied to gain further insight into metallacycle formation, growth, and decomposition.
Figure 1. GC-FID trace of the C10+ olefins formed in the cooligomerization of ethylene/1-octene with 2/MAO (inset: plot of amount of vinylidene olefins (mmol) versus carbon number). *Vinylidene products resulting from the incorporation of R-olefins generated by ethylene homo-oligomerization. Scheme 2
2. Results and Discussion 2.1. Ethylene/1-Octene Co-oligomerization. Previously it was shown that R-olefins, formed as the primary products during ethylene oligomerization with 1-3, become incorporated into the reaction, leading to small amounts of vinylidenes and linear internal olefins.8 In an extension to this work, the oligomerization reaction with 2/MAO was carried out in 1-octene as the solvent [p(ethylene) ) 1 bar gauge]. Along with a distribution of linear R-olefins resulting from ethylene homo-oligomerization, a second major distribution of vinylidene olefins was also formed (Figure 1). The major product formed is 2-ethyl-1octene, which results from coupling of ethylene and 1-octene via metallacycle I, Scheme 2. Support for a metallacycle mechanism for R-olefin incorporation comes from co-oligomerization of CH2CH2, CD2CD2, and 1-octene, which produced only D0 and D4 isotopomers of 2-ethyl-1-octene, therefore ruling out a Cossee-Arlman linear growth mechanism.15,16 Progressively lower amounts of C12 and C14 vinylidenes result from further ethylene insertion into metallacycle I; however, it was noted that the amount of C16 vinylidene is well above that expected from a statistical distribution (Figure 1, inset). The major C16 product (90%) is 2-hexyl-1-decene. While this compound would be produced by three ethylene insertions into metallacycle I, the greatly increased amount suggests that it is also being produced by a second process. This second process is the oxidative coupling of two 1-octene units to afford metallacyle II (Scheme 2), representing metallacyclic dimerization of R-olefins (confirmed below). Although not clearly apparent in Figure 1, the amount of C18 formed is also elevated above that expected from a statistical distribution arising from (14) McGuinness, D. S.; Gibson, V. C.; Wass, D. F.; Steed, J. W. J. Am. Chem. Soc. 2003, 125, 12716. (15) Agapie, T.; Schofer, S. J.; Labinger, J. A.; Bercaw, J. E. J. Am. Chem. Soc. 2004, 126, 1304. (16) Agapie, T.; Labinger, J. A.; Bercaw, J. E. J. Am. Chem. Soc. 2007, 129, 14281.
ethylene insertions into metallacycle I. Initially it was thought that this must arise from ethylene insertion into metallacycle II; however, such a route cannot generate the structure of the main C18 oligomer (2-hexyl-1-dodecene). Instead, 1-octene insertion into metallacycle I must be responsible, as shown in Scheme 2.17 This product therefore represents cotrimerization with incorporation of two R-olefins and demonstrates that higher R-olefins are capable of inserting into the Cr-C4 metallacycle of the active species formed from catalyst 2. As a result of these observations, it was decided to investigate the homo-oligomerization of R-olefins with catalysts 1-3. 2.2. r-Olefin Oligomerization. The results of oligomerization of R-olefins catalyzed by 1-3/MAO are shown in Table 1. The combination of complex 2 and 1-octene was trialed first (entry 1), which led to a turnover number in 1-octene of 1120 after 3 h. There is no real increase in productivity after 24 h, indicating that the catalyst has deactivated after 3 h. The major (17) Co-oligomerization of C2H4, C2D4, and 1-octene yielded only D0 and D4 isotopomers of the main C18 product (2-hexyl-1-dodecene), again indicating a metallacycle mechanism for its formation.
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McGuinness
Table 1. r-Olefin Oligomerization with Complexes 1-3/MAOa
Scheme 3
linear vinylidene internal catalyst TON dimer dimer trimer entry R-olefin ([Cr] mM) TON 3 h 24 h (wt %) (wt %) (wt %) 1 2 3 4 5 6 7
1-octene 1-octene 1-octene 1-octene 1-pentene 1-butene propene
2(0.33) 1(0.33) 3(0.33) 3(0.067) 3(0.33) 3(0.33) 3(0.33)
1120 190 2420 4920 3085 1800
1170 412 3480 8600 6370
91 86 75 74 62 68 50d
9 12 16 15 22 16 7
trace 2 7 9 11b 12c 20e
a Conditions: toluene (20 mL), R-olefin (10 mL), 500 equiv of MAO, 20 °C. b 1 wt % tetramer also formed. c 2 wt % tetramer also formed. d 4-Methyl-2-pentene and 4-methyl-1-pentene amounting to 19 wt % also formed; see text. e 4 wt % tetramer also formed.
product formed is the head-to-tail vinylidene dimer 2-hexyl-1decene (91%), followed by linear internal olefin dimers (9%). The linear dimers (at least three double bond isomers were partially resolvable by GC-MS) would result from decomposition of metallacycle III (reaction 1) with the position of the double bond being dependent upon the site of β-hydrogen transfer (endocyclic or exocyclic). Given that three isomers are detected, cis/trans isomers must be also be present, although the exact identity of these linear internal olefins was not investigated further. Trace products of formula C24H48 were also detected, corresponding to 1-octene trimers. This again indicates that R-olefins are capable of inserting into the Cr-C4 metallacycles formed from 2, albeit unfavorable as compared to metallacycle decomposition.
Catalyst 1 led to much lower conversion of 1-octene (entry 2), although the product distribution was similar to that obtained with 2. In contrast, 3 was the most active catalyst for 1-octene conversion (entry 3), as it was for ethylene oligomerization.14 In this case, increased amounts of linear internal olefin dimers resulted, and the amount of trimers increased to 7%.18 Additionally, at least three other minor dimers resulted (2 wt % in total). Not all of these minor dimers were identified; however, hydrogenation of the sample produced 7,8-dimethyltetradecane, indicating one of these compounds is the vinylidene resulting from decomposition of metallacycle IV (reaction 2).
The remaining experiments were conducted using complex 3. Entry 4 reveals that relatively high turnover numbers can be achieved with a prolonged run time (24 h) and low catalyst loading, although the system was not optimized further as we (18) As pointed out by a referee, the increase in the amount of trimers formed with complex 3 (the most sterically encumbered complex) is somewhat counterintuitive. Complex 3 is inherently more active than 1 and 2, both in ethylene and in R-olefin oligomerization. We are unsure of the reason for this, but it may be related more to electronic factors than to sterics (as increased bulk might be expected to slow catalysis, if anything). The greater incidence of trimerization might simply result from the higher rate of alkene insertion with 3. At the same time, however, the sterics of the R-olefin do seem to play a role, as shorter chain monomers do lead to increases in the trimer and tetramer fractions (Table 1).
were primarily interested in product selectivities. Oligomerization of 1-pentene (entry 5) proceeds at approximately twice the rate of 1-octene oligomerization (as judged by the turnover number), and the product selectivity is shifted somewhat. In particular, 1% tetramer was formed in this run. With 1-butene (entry 6),19 the dimer selectivity shifts again, but there is no clear trend in selectivity within the dimer fraction for different monomers. In this run, 2% tetramer was formed, and there does seem to be a gradual increase in trimers and tetramers with shorter chain monomers. A significant decrease in the selectivity toward the main vinylidene dimer (2-methyl-1-pentene) was found when propene was tested (entry 7). This is partly due to increased trimer and tetramer formation (20% and 4%, respectively). However, a significant change in selectivity within the dimer fraction is also observed, which is now made up of 25% 4-methyl-2-pentene and 4-methyl-1-pentene. These represent double bond isomers of the main dimer, 2-methyl-1-pentene (66% of the C6 fraction), and would originate from β-hydrogen transfer from three different sites of metallacycle V (Scheme 3). The corresponding isomers are not observed in runs with longer chain monomers (although may be accounted for by minor unidentified products), and the reason for this selectivity change is unclear. 2.3. Kinetics of 1-Octene Dimerization. Theoretical studies of ethylene trimerization catalysts generally suggest that metallacyclopentane formation is fast, while metallacycle growth is the rate-determining step.20-22 Therefore, the kinetics of product formation are controlled by insertion of ethylene into the M-C4 metallacycle. With the present system in combination with R-olefins, insertion into the metallacyclopentane is not favored, providing an opportunity to investigate the kinetics of metallacycle formation and decomposition. As such, the rates of formation of the major 1-octene dimerization products (2hexyl-1-decene and internal hexadecenes) have been measured for complex 3/MAO. Rate plots for these dimers at two chromium concentrations are shown in Figure 2. These measurements were limited to around 1 h such that catalyst degradation did not affect the results. This corresponds to approximately one-half-life, and as such a halving of the 1-octene concentration over the run. At a given chromium concentration, the rates of formation of both vinylidene and internal olefin dimers are constant, showing that the reaction is zero-order in 1-octene. This is somewhat surprising given that two molecules of 1-octene are involved in the reaction. In contrast, dimerization is first-order in chromium, and the rate equation can be expressed as r ) k[Cr], where the rate constant (19) The productivities reported for the gaseous monomers (1-butene, propene) are not comparable to those for the liquid monomers (1-octene, 1-pentene), due to differences in purity. The liquid monomers were distilled from sodium-benzophenone and can be considered rigorously anhydrous and oxygen free. 1-Butene and propene, on the other hand, were used as received (Aldrich 99%). (20) Tobisch, S.; Ziegler, T. Organometallics 2003, 22, 5392. (21) Blok, A. N. J.; Budzelaar, P. H. M.; Gal, A. W. Organometallics 2003, 22, 2564. (22) Janse van Rensburg, W.; Grove, C.; Steynberg, J. P.; Stark, K. B.; Huyser, J. J.; Steynberg, P. J. Organometallics 2004, 23, 1207.
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9.5 mM), 1-octene dimerization was quenched with dilute hydrochloric acid 30 s into a run. Hydrolysis of chromium metallacycles would be expected to generate the corresponding paraffins, while hydrolysis of a bis-olefin complex would simply release the olefins. Despite the presence of the expected 1-octene dimers, there were no traces of paraffin, suggesting that there is no appreciable concentration of metallacycles present. While negative evidence such as this is by no means conclusive, it does lean toward a rate-determining oxidative coupling and a bis-olefin catalyst resting state.
3. Summary and Conclusions
Figure 2. Kinetic plot for the formation of 2-hexyl-1-decene (vinylidene) and linear internal olefins (LIO) in 1-octene dimerization with 3/MAO. Conditions: toluene (20 mL), 1-octene (10 mL), 500 equiv of MAO, 20 °C. Scheme 4
This work has shown that chromium complexes of bis(carbene)pyridine ligands catalyze the oligomerization of R-olefins when activated with MAO, leading predominantly to head-totail dimers with vinylidene unsaturation. The results strongly indicate a metallacycle mechanism is operative, in common with ethylene oligomerization. Although not investigated in this work, it is possible to speculate as to what form the active species might take. The fact that MAO is the activator of choice suggests that a formally cationic complex is responsible.25 This is supported by the fact that activation with AlR3/Ph3C-B(C6F5)4 is also effective, albeit less so than that with MAO.14 A CrIfCrIII cycle is one possibility, starting at complex 4. Such a redox couple has been suggested for chromium trimerization and tetramerization catalysts that incorporate neutral ancillary ligands.15,26,27
k for vinylidene formation is 0.16 s-1 and that for internal olefins is 0.042 s-1.23 There are two possible mechanistic explanations for such a rate equation (Scheme 4). The first is that formation of a bisolefin complex VI is fast, followed by a rate-determining oxidative coupling to form the metallacycle (as such, VI would represent the catalyst resting state, k2 < k1, k3). Applying the steady state approximation to VI, the rate equation would be r ) k2[VI]. The second possibility is that metallacycle formation is fast, followed by a rate-determining β-hydrogen shift and product release, in which case the catalyst resting state would be the metallacycles II-IV (k3 < k1, k2). In this case, the steady state approximation would yield the rate equation r ) k3[II-IV]. It is difficult to differentiate between these two possibilities. On the one hand, β-hydride transfer in metallacyclopentanes is predicted to be slow20,21,24 (and is so for selective trimerization catalysts), suggesting this may be the rate-determining step. On the other hand, 1-butene formation is very rapid when 1-3 are employed in ethylene oligomerization, showing that, with the present systems at least, metallacyclopentane decomposition is facile. To investigate this further, quick-kill experiments were conducted in which attempts were made to hydrolyze any metallacycles present. At very high catalyst loadings ([Cr] ≈
While the reaction of 1-3/MAO with ethylene produces longer chain oligomers and some polymer, the change to R-olefins leads to a dramatic shift in selectivity to dimers. Selectivity is controlled by the rates of chain propagation (insertion) versus chain termination (metallacycle decomposition) and reveals that the relative rate of chain termination is increased when R-olefins are present. This is most likely because further insertion into a disubstituted metallacyclopentane is more difficult on steric grounds. However, termination is also accelerated in the co-oligomerization of ethylene and R-olefins, showing that incorporation of even one R-olefin into the metallacycle favors decomposition. Several parallels can be drawn between this system and the heterogeneous Phillips catalyst. First, it has likewise been reported that the presence of R-olefin promotes chain termination in ethylene polymerization with the Phillips catalyst.28 Second, R-olefin incorporation in this case leads predominantly to terminal vinylidene unsaturation in the polymer (with rare internal unsaturation). Thus, the preference for termination via vinylidene formation matches that found in this work. Additionally, the Phillips catalyst will catalyze the homopolymerization of R-olefins, and as in this
(23) As different internal olefin isomers are not fully resolvable by GC, the rate constant measured represents the sum of the rate constants for each individual isomer. As each originates from a common metallacycle (III), the measured rate constant reflects the rate of decomposition of this metallacycle. (24) de Bruin, T. J. M.; Magna, L.; Raybaud, P.; Toulhoat, H. Organometallics 2003, 22, 3404.
(25) Chen, E. Y.-X.; Marks, T. J. Chem. ReV. 2000, 100, 1391. (26) Ko¨hn, R. D.; Smith, D.; Mahon, M. F.; Prinz, M.; Mihan, S.; Kociok-Ko¨hn, G. J. Organomet. Chem. 2003, 683, 200. (27) Rucklidge, A. J.; McGuinness, D. S.; Tooze, R. P.; Slawin, A. M. Z.; Pelletier, J. D. A.; Hanton, M. J.; Webb, P. B. Organometallics 2007, 26, 2782. (28) McDaniel, M. P. AdV. Catal. 1985, 33, 47.
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work the reaction is zero-order in olefin.29 All of these observations can also be explained on the basis of a CosseeArlman linear chain growth mechanism, but they do at least show that the behavior of the Phillips catalyst closely matches that of a catalyst with an established metallacycle mechanism.
4. Experimental Section 4.1. General Comments. All manipulations were carried out using standard Schlenk techniques or in a nitrogen glovebox, using solvents purified by passage through an Innovative Technologies solvent purification system (purification over activated alumina, copper catalyst, and/or molecular sieves). Ethylene was purified by passage through activated 3 Å molecular sieves followed by alumina. 1-Octene and 1-pentene were distilled from sodium/ benzophenone, while 1-butene and propene were purchased from Aldrich and used as received. Methylaluminoxane (MAO) in toluene was supplied by Albemarle. 1H NMR spectra were recorded on a Varian Mercury Plus NMR spectrometer operating at 300 MHz, with spectra referenced against residual solvent peaks. 4.2. 1-Octene/Ethylene Co-oligomerization. Catalyst 2 (10 µmol) was suspended in 37 mL of 1-octene and treated with 1000 equiv of MAO. Ethylene was immediately added to a pressure of 1 bar gauge. The solution was held at 25 °C with vigorous stirring for 30 min, after which it was quenched with 10% HCl and an internal standard (nonane, 1.00 mL) was added. The organic fraction was analyzed by GC-FID, while no solid polymer was formed. 1H NMR analysis of the reaction solution showed a composition of 6 mol % internal olefins (5.30-5.40 ppm), 77 mol % R-olefins (4.84-5.00 ppm), and 17 mol % vinylidene olefins (4.68-4.78 ppm). After removal of the volatiles under vacuum (leaving the C10+ oligomers), the composition was 4 mol % internal, 12 mol % R, and 84 mol % vinylidene. A total of 8.4 g of oligomers was formed in the run, with the following carbon-number weight percentages: C4 (12.2%); C6 (13.2%); C10 (44.4%); C12 (12.2%); C14 (4.0%); C16 (10.4%); C18 (2.5%); C20 (0.8%); C22 (0.3%). 4.3. 1-Octene/C2H4/C2D4 Co-oligomerization. The co-oligomerization reaction was repeated with a mixture of 1:1 C2H4:C2D4. (29) Weiss, K.; Krauss, H.-L. J. Catal. 1984, 88, 424.
McGuinness GC-MS analysis revealed only D0 and D4 isotopomers of 2-ethyl1-octene and 2-hexyl-1-dodecene. 4.4. r-Olefin Oligomerization. The general procedure is illustrated here by the dimerization of 1-octene with catalyst 2 (Table 1, entry 1). Ten micromoles of 2 was suspended in 10 mL of 1-octene, 0.250 g of n-tridecane (internal standard), and toluene such that the final volume was 30 mL (in cases where gaseous olefins (1-butene, propene) were used, the toluene suspension was saturated with the olefin by continued bubbling). MAO solution (500 equiv) was added, and the temperature was held at 20 °C through the use of a water bath. Aliquots were taken at desired intervals, quenched with 10% HCl, and analyzed by GC-FID. Removal of volatiles under vacuum left only 2-hexyl-1-decene and linear internal hexadecenes. 1H NMR (toluene-d8): 0.88 (t, 6H, CH3); 1.25 (m, br, 16H, CH2); 1.43 (q, br, 4H, CH2CH3); 2.01 (2t, 4H, CH2C(R)dCH2); 4.81 (s, 2H, CdCH2, 83 mol %); 5.42 (m, br, 2H, HC(R)dC(R)H, 17 mol %). 4.5. Oligomer Analysis. Oligomers were identified by GC-MS analysis of both olefinic and hydrogenated samples. Hydrogenation was carried out over PtO2 at 80 °C under 12 bar of hydrogen (generally overnight). A combination of characteristic electron ionization spectra together with Kovats’ retention indices was used, together with NMR analysis where required. Further details of oligomer identification are given in the Supporting Information of ref 8.
Acknowledgment. We thank Albemarle Asia Pacific for donating MAO solution and Tony Caselli of Plastral Pty Ltd. for facilitating this. Noel Davies is thanked for acquisition of GC-MS data and analysis. The Australian Research Council is thanked for financial support and a QEII Fellowship to D.S.M. Supporting Information Available: Details of ethylene/1-octene co-oligomer distribution analysis and procedure for 1-octene dimerization kinetic experiments. This material is available free of charge via the Internet at http://pubs.acs.org. OM8008348
