The mathematics of ethylene oligomerisation and polymerisation

Linear α-olefins or LAOs are produced by the catalytic oligomerisation of ethylene on a multimillion ton scale annually. A range of LAOs is typically obtained with varying chain lengths which follow a distribution. Depending on the catalyst, various types of distributions have been identified, such as Schulz–Flory, Poisson, alternating and selective oligomerisations such as ethylene trimerisation to 1-hexene and tetramerisation to 1-octene. A comprehensive mathematical analysis for all oligomer distributions is presented, showing the relations between the various distributions and with ethylene polymerisation, as well as providing mechanistic insight into the underlying chemical processes. Linear α-olefins or LAOs are produced by the catalytic oligomerisation of ethylene on a multimillion ton scale annually. A range of LAOs is typically obtained with varying chain lengths which follow a distribution. Depending on the catalyst, various types of distributions have been identified, such as Schulz–Flory, Poisson, alternating and selective oligomerisations such as ethylene trimerisation to 1-hexene and tetramerisation to 1-octene. A comprehensive mathematical analysis for all oligomer distributions is presented, showing the relations between the various distributions and with ethylene polymerisation, as well as providing mechanistic insight into the underlying chemical processes

Mechanistic study of ethylene tri- and tetramerisation with Cr/PNP catalysts: effects of additional donors

The mechanism of ethylene trimerisation and tetramerisation with chromium–diphosphinoamine (Cr–PNP) catalysts has been studied by experimental and theoretical (DFT) methods. The effects of a pendant ether donor (ortho-methoxyaryl ligand substitution) and of anion coordination to the active species have been studied. In the former case, coordination of the ether donor to chromium favours 1-hexene by suppressing formation of the bisIJethylene) chromacyclopentane intermediate which is postulated to be the major route to 1-octene. The effect of anion coordination is similar and as the coordination strength increases, displacement of the anion by a second ethylene ligand becomes more difficult, again favouring trimerisation over tetramerisation. Hence, the experimentally observed effects of pendant donor coordination and changes in anion coordination strength can be rationalised

From alternating to selective distributions in chromium-catalysed ethylene oligomerisation with asymmetric BIMA ligands

The oligomerisation of ethylene with chromium-based catalysts containing asymmetric BIMA (bis(benzimidazole)methylamine) ligands produces linear alpha olefins (LAOs) that follow an alternating distribution. The catalytic activity and the degree of alternation is affected by the different ligands; in particular variations at the backbone of the ligand affect the nature of the distribution. For certain catalysts a deviation from regular alternating behaviour is observed, whereby increased amounts of 1-hexene and 1-octene (up to 29 mol%) are obtained compared to the amount expected from the distribution analysis based on C₁₀–C₃₄ LAOs. This behaviour towards more selective oligomerisation to 1-hexene and 1-octene can be explained by varying probabilities of single and double ethylene insertion. The deviations will depend on the size of the metallacycle and are most pronounced early on during the metallacycle growth

Biaryl group 4 metal complexes as non-metallocene catalysts for polyethylene with long chain branching

A series of biaryl Group 4 complexes with a bidentate and a tridentate pincer ligand have been synthesized and characterized. The complexes have been applied as metallocene analogues for the controlled polymerization of ethylene and the copolymerization of ethylene and 1‐hexene, with a particular focus on the control of the degree of long chain branching in these polymers

Alternating alpha-olefin distributions via single and double insertions in chromium-catalyzed ethylene oligomerization.

The catalytic oligomerization of ethylene with chromium-based complexes containing bis(benzimidazolemethyl)amine (BIMA) ligands results in alternating distributions of linear α-olefins (LAOs). Extremely high activities are obtained (>100 000 g mmol–1 h–1 bar–1) with N-alkyl-substituted BIMA ligands, whereas bulky groups on the central nitrogen or alternative central donors result in much lower activities. Variations in the ligand backbone, as well as methylation of the benzimidazole units, lead to reduction in activity. The alternating LAO distributions have been mathematically analyzed using second-order recurrence relations. The shape of the distributions is affected by ethylene pressure (1–4 bar) and by the cocatalyst to some degree. On the basis of the results and analysis presented herein, we propose that the alternating behavior originates from the ability of these chromium BIMA catalysts to undergo single as well as double ethylene insertion reactions. A minor second distribution (<5 wt %) of 2-ethyl-1-alkenes is obtained under certain conditions, resulting from incorporation of 1-butene. DFT studies (M06L) and experimental observations regarding the reaction between AlMe3 and the N-methyl BIMA ligand 2 have shown that deprotonation of the benzimidazole N–H units can occur, which suggests a change in coordination of the BIMA ligand under oligomerization conditions