Britovsek, GJP

Malinowski, R

McGuinness, DS

Nobbs, JD

Tomov, AK

Wadsley, AW

Young, CT

ACS Catalysis

English

The oligomerisation of ethylene produces
α-olefin distributions ranging from Schulz-Flory distributions
to alternating and selective oligomer distributions
which can be mathematically analysed and characterised
by recurrence relations

Spiral - Imperial College Digital Repository

Ethylene Oligomerisation Beyond Schulz-Flory Distributions  George J. P. Britovsek,*a Robert Malinowski,a David S. McGuinness,b James D. Nobbs,a Atanas K. Tomov,a Andrew W. Wadsleyc and Craig T. Young.a a) Department of Chemistry, Imperial College London, Exhibition Road, London, SW7 2AZ, UK b) School of Physical Sciences – Chemistry, University of Tasmania, Private Bag 75, Hobart 7001, Australia c) Stochastic Simulation, 85 Guthrie Street, Osborne Park, Perth 6017, Australia  Supporting Information PlaceholderABSTRACT: The oligomerisation of ethylene produces α-olefin distributions ranging from Schulz-Flory distri-butions to alternating and selective oligomer distribu-tions which can be mathematically analysed and charac-terised by recurrence relations.   The oligomerisation of ethylene is an important indus-trial process for the production of linear α-olefins (LAOs).1-3  More than 3 million tonnes of linear α-olefins are produced each year and used as intermediates for the production of detergents, lubricants and as co-monomers in polyethylene.  Several different LAO pro-cesses exist, for example the Shell Higher Olefin Pro-cess (SHOP),4 which generates a range of α-olefins from C4 (1-butene) to C20+ (see Chart 1).5  More selective oli-gomerisations are, for example the titanium-based IFP/Sabic Alphabutol® process for ethylene dimerisation to 1-butene,6-11 and the Sabic/Linde Alpha-SABLIN® process based on zirconium for C4-C10 α-olefins.2,9  A chromium-based ethylene trimerisation process to 1-hexene is operated by Chevron-Phillips and a chromi-um-based ethylene tetramerisation process to 1-octene was recently announced by Sasol.5,12-14   Chart 1.  Industrially applied oligomerisation systems. Following on from the groundbreaking treatise 80 years ago by Schulz and Flory,15,16 we present here a novel mathematical approach using recurrence relations to analyse olefin distributions, from the well-known simple Schulz-Flory distribution to more complicated alternating and selective oligomer distributions.  This approach provides a straightforward method to analyse and characterise LAO distributions, while demonstrating how selective trimerisations and tetramerisations can be understood as distributions beyond Schulz-Flory.    Simple α-Olefin Distributions Chain growth in ethylene oligomerisation can occur via different mechanisms.  Late transition metal oligo-merisation catalysts generally operate by a linear chain growth alkene insertion mechanism (Cossee mecha-nism).17  A metal hydride species [M–H] undergoes suc-cessive coordination and single insertions of ethylene with a given probability of propagation α to give longer metal alkyl species [M–Et], [M–Bu] etc. (Scheme 1).  Termination of chain growth occurs via competing β-H elimination with probability 1-α, resulting in a distribu-tion of linear α-olefins that follows an exponential decay function (a Schulz-Flory distribution).15,16  Scheme 1: Ethylene Oligomerisation via a Cossee mechanism  This distribution can be mathematically described as a first order linear homogeneous recurrence relation with constant coefficients.18  Each oligomer fraction is related to the previous fraction, Tn+1 = αTn, where Tn describes the molar amount of each oligomer n (n is the number of ethylene units in the oligomer, e.g. n = 1 is ethylene, n = 2 is 1-butene etc.) and α is the probability of chain prop-agation (sometimes referred to as K value).  The general solution to this relation takes the form Tn = crn, whereby in this case r = α and the constant c is the ratio of chain termination and propagation probabilities (1–α)α–1R (R = ΣTn, total moles of olefins produced in a given time).  NH +  CrCl3  +  AlEt3PhPNPPhPhPhRPhillipsSasolCrCl3ONiPR ROSHOPTi(OnBu)4  +  AlEt3AlphabutolM-H M-Et M-Bu M-Hex+ + + +α1-α(n = 1) (n = 2) (n = 3) This provides the standard Schulz-Flory formula: mol%(n) = Tn/R = (1–α)αn–1 (see Supporting Infor-mation for detailed derivations). Several oligomerisation catalysts based on early transi-tion metals, in particular chromium-based catalysts, are known to operate via a different chain growth mecha-nism involving the formation of metallacycles.  The ac-tive catalyst [M] generated from the pre-catalyst and the co-catalyst is in a lower oxidation state and undergoes oxidative addition upon coordination of ethylene.  Fur-ther additions and insertions of ethylene lead to expan-sion of the metallacycle, as illustrated in Scheme 2.  Elimination of the olefinic product occurs via β-H trans-fer to the chain end.  The Cossee and metallacyclic mechanisms can be experimentally differentiated by co-oligomerisation of equimolar mixtures of C2H4 and C2D4, as has been shown in a number of cases.19-22  Oli-gomer distributions from a simple metallacyclic mecha-nism follow a Schulz-Flory distribution, as shown in Figure 1 for bis(benzimidazole)pyridine chromium cata-lyst 1.  An α-olefin distribution with α = 0.84 was ob-tained, which can be determined by fitting the experi-mental data to the Schulz-Flory formula or from a plot of ln[mol%(n)] versus n (see inset Figure 1).21   Scheme 2: Ethylene oligomerisation via a metallacyclic mechanism   Figure 1.  Schulz-Flory α-olefin distribution as mol%(n) versus n (units of ethylene) obtained with cata-lyst 1 (1 µmol). Conditions: 4 bar ethylene pressure, 30 ˚C, co-catalyst MAO (8 mmol), toluene, 70 min.  Inset: ln[mol%(n)] versus n, α = e-0.1702 = 0.84.  Data used from 21. Alternating Distributions A remarkable chromium-based oligomerisation cata-lyst was discovered by Tomov et al. in 2006, which pro-duces an alternating distribution of α-olefins via a metallacyclic mechanism.23  The olefins obtained from an odd number of ethylene units (n = 1, 3, 5 etc.) are significantly less abundant than those from an even-number such as 1-butene, 1-octene, 1-dodecene etc., as shown for the bis(benzimidazole)methylamine (BIMA) chromium catalyst 2 in Figure 2. Figure 2.  Alternating α-olefin distribution as mol%(n) versus n (units of ethylene) obtained with chromium BIMA catalyst 2 (32 nmol).  Conditions: 4 bar ethylene pressure, 50 ˚C, co-catalyst MAO (7 mmol), toluene 200 mL, 1 hour.  Calculated: mol%(n) = 12.68(0.94)n + 13.57(–0.85)n (goodness of fit: R2 = 0.988).  Data used from 23.  An alternating distribution can be described as a se-cond order linear homogeneous recurrence relation with constant coefficients, Tn+2 = αTn+1 + βTn.  Each oligo-mer fraction is related to the previous fraction and the one before and the parameters α and β are in this case the probability of propagation via single ethylene coor-dination (α) and via double ethylene coordination (β).  The term 1–α–β represents the probability of termina-tion, as illustrated in Scheme 3. Scheme 3: Ethylene oligomerisation resulting in alter-nating distributions  The solution to this second order recurrence relation is more complicated and takes the general form Tn = c1r1n M+ + + +α1-α(n = 1) (n = 2) (n = 3)C2M C4M C6MM+ + + +α1−α−β(n = 1) (n = 2) (n = 3)C2M C4M C6M+ 2+ 2+ 2β+ 2 + c2r2n, whereby the terms c1,2 and r1,2 are related to α and β as shown in Table 1.  This relation can be ex-plained as an exponential decay function c1r1n with de-cay parameter r1, combined with an alternating function c2r2n with a negative and thereby alternating parameter r2, as is graphically illustrated in Figure S1 (see Support-ing Information).  Analysis of the oligomerisation results in Figure 2 is achieved by fitting the experimental data to the general formula Tn = c1r1n + c2r2n, which provides the equation mol%(n) = 12.68(0.94)n + 13.57(–0.85)n for this particular distribution.  The probabilities for single and double coordination are determined as α = 0.09 and β = 0.79 and the probability for termination is 1–α–β = 0.12.  Small deviations at the tail end of the distribution are most likely due to some precipitation of the higher olefins.  Table 1: Overview of oligomer distributions  Schulz-Flory Distribution Alternating  Distribution Relation type First order homo-geneous recur-rence relation with constant co-efficients Second order homo-geneous recurrence relation with constant coefficients Relation 𝑇!!! = 𝛼𝑇!  𝑇!!! = 𝛼𝑇!!! + 𝛽𝑇!  General solution 𝑇𝑛 =   𝑐𝑟! r = α, 𝑐 =    !!! !!  α = propagation probability  1–α = termina-tion probability  R = total moles of product produced during reaction time 𝑇𝑛 =    𝑐!𝑟!! + 𝑐!𝑟!! 𝑟!,! =   !  ±   !!!!!!  𝑐! =   !!!!! [!! !!!! !!!]!!(!!!!!)  𝑐! =   !!!!! [!! !!!! !!!]!!(!!!!!)  α/β = propagation probability by sin-gle/double coordina-tion 1–α–β = termination probability  R1 + R2 = total moles of product produced during reaction time Final equation: 𝑚𝑜𝑙% 𝑛 =    𝑐𝑟!/𝑅 =    (1 − 𝛼)𝛼!!!  𝑚𝑜𝑙%(𝑛) =    !!!!!!!!!!!!!!!!  The formation of alternating distributions relies on a mechanism that involves both single and double coordination of ethylene prior to insertion.  A related mechanism was first proposed by Lemos based on kinetic studies in Ziegler-Natta catalysis,24 has been implicated in other oligomerisation reactions.25  Both single ethylene coordination followed by insertion and double ethylene coordination with subsequent sequential insertion of two ethylene monomers, operate simultaneously.  This mechanism is related but mechanistically distinct from the “trigger mechanism” proposed by Ystenes,26 where the insertion of the first ethylene monomer is triggered by an incoming (but not completely coordinated) second monomer.  The first monomer will not insert as long as a second monomer is not interacting with the metal centre.  We have previously shown that the single and double coordination mechanism also operates in selective oligomerisation reactions such as the chromium-catalysed ethylene tetramerisation to 1-octene,27 and the relation between these systems will be discussed in the next section. Selective Oligomerisations Di-, tri- and tetramerisation of ethylene are examples of selective oligomerisation reactions, which can be regarded as further variations within the distributions landscape.  Dimerisation of ethylene via a Cossee mechanism can be easily understood and described as a Schulz-Flory distribution with a very high probability for chain termination (low α value).10  Selective tri- and tetramerisation reactions to 1-hexene and 1-octene, as observed with certain Cr/PNP catalysts, occur via a metallacyclic mechanism. For example, ethylene oligomerisation with chromium PNP catalyst 3 (PNP = Ph2PN(iPr)PPh2) shown in Figure 3, results in a very high selectivity for 1-octene (≈ 70 mol%), together with approximately 16 mol% 1-hexene, 3 mol% C10+ α-olefins and various coproducts of which methyl cyclopentane and methylene cyclopentane are the major components (≈ 4 mol% each).12,20  Coproducts in the C10-C14 fractions are a result of co-trimerisation and co-tetramerisation of ethylene with 1-hexene and 1-octene resulting in various isomers.27-30    Figure 3: Selective α-olefin distribution as mol%(n) versus n (units of ethylene) obtained with Cr/PNP/MAO catalyst 3 (10 µmol). Conditions: toluene, MAO (3 mmol), 30˚C, 30 bar, 30 min.  Inset: Expanded mol%(n) versus n for the C16-C32 fraction; α = 0.80 (R2 = 0.986).  Data used from 27.   The high selectivity to 1-octene is the result of a distribution generated according to Scheme 3 where the probabilities for propagation α and β, and consequently termination (1–α–β), are no longer constant for all metallacyclic intermediates.  The differences are most pronounced early on in the oligomerisation process.  Termination from a metallacyclopentane to give 1-butene is very unfavourable and therefore α+β ≈ 1, with β much larger than α as judged from large 1-octene/1-hexene ratios of 8/1 and 4.4/1 in Figures 2 and 3 respectively.  Termination from the subsequent metallacycloheptane and -cyclononane intermediates is much more favourable, such that >95 mol% of the total oligomeric product has been generated at this point in the oligomerisation sequence.  The probability of double coordination (β) is high for the metallacyclopentane intermediate, but rapidly decreases for larger metallacycles.  From the inset in Figure 3 it can be seen that the tail end of the α-olefin distribution (approximately 3 mol%) from C16-C32 (n = 8-16) can be described by a Schulz-Flory distribution with α = 0.80 (and consequently β = 0).  The differences between the individual metallacycles become negligible for larger metallacycles, and their termination probabilities converge to a constant value of 1–α–β = 0.2.  The varying propagation and termination probabilities for the different metallacycles are believed to be a result of the different stabilities of the various metallacycles in these particular PNP chromium catalysts.  Our recent computational studies on the related PNP* chromium catalyst system (where (PNP* = Me2PN(Me)PMe2) provided a barrier of +20.8 kcal/mol for termination from a metallacyclopentane intermediate to give 1-butene, which decreases to +13.9 and +11 kcal/mol for the metallacycloheptane and -cyclononane intermediates, respectively.27  In addition, the formation of a metallacyclopentane complex with two coordinated ethylene units is a downhill process by –9.2 kcal/mol, whereas a doubly coordinated metallacycloheptane is uphill by +8.5 kcal/mol.  The difference may be attributable to steric reasons.  Selective oligomerisation reactions such as ethylene tetramerisation and trimerisation to 1-hexene with related PNP chromium catalysts, can be described as distributions generated according to Scheme 3 where the probabilities for propagation and termination vary during the oligomerisation process.  These distributions can be mathematically described as a recurrence relation with variable coefficients, but such relations are not easily solved.   In conclusion, α-olefin distributions generated from metal-catalysed ethylene oligomerisation can be mathematically described by recurrence relations.  A Schulz-Flory distribution, generated by a Cossee or a metallacyclic mechanism, is a first order homogeneous recurrence relation with constant coefficients and is the simplest olefin distribution.  Alternating α-olefin distributions, generated by a metallacyclic mechanism via single and double ethylene coordination, are described by second order homogeneous recurrence relations with constant coefficients.  Selective oligomerisations such as ethylene trimerisation and tetramerisation to 1-hexene or 1-octene are oligomer distributions that follow recurrence relations with variable coefficients.  The analysis of oligomer distributions shown here for the three selected catalysts 1-3 can also be applied to other distributions and other monomers.  Further explorations of the fascinating oligomer distributions landscape are underway, as well as mathematical developments to analyse and model their underlying mechanisms. Acknowledgement. Financial support from INEOS Technologies is kindly acknowledged.  We thank the Australian Research Council for financial support through grant FT100100609 to D.S.M and the University of Tasmania for Visiting Scholars funding to G.J.P.B.  Supporting Information Available: Mathematical derivations and solutions for the recurrence relations. References (1) Forestière, A.; Olivier-Bourbigou, H.; Saussine, L. Oil Gas Sci. Technol. 2009, 64, 649. (2) Olivier-Bourbigou, H.; Forestière, A.; Saussine, L.; Magna, L.; Favre, F.; Hugues, F. Oil Gas Eur. Mag. 2010, 36, 97. (3) Belov, G. P.; Matkovsky, P. E. Pet. Chem. 2010, 50, 283. (4) Keim, W. Angew. Chem. 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Ethylene Oligomerisation Beyond Schulz-Flory Distributions

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Ethylene Oligomerisation Beyond Schulz-Flory Distributions

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