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.