Abstract

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.

Highlights

  • Linear alpha olefins (LAOs, or 1-alkenes) find extensive use as co-monomers in olefin polymerisation and as intermediates to detergents, lubricants, and plasticisers [1,2,3]

  • A variety of different distributions—including Schulz–Flory, alternating, selective-LAO, and Poisson distributions—of linear hydrocarbon products can be obtained from ethylene oligomerisation and polymerisation processes

  • Oligomerisation processes are steady-state in nature, and can be mathematically described using recurrence relations

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Summary

Introduction

Linear alpha olefins (LAOs, or 1-alkenes) find extensive use as co-monomers in olefin polymerisation and as intermediates to detergents, lubricants, and plasticisers [1,2,3]. Following on from the ground-breaking work 80 years ago by Schulz and Flory [18, 19], novel mathematical approaches for analysing product distributions from ethylene oligomerisation and polymerisation processes are presented in this paper. These approaches provide straightforward, applicable methods for characterising key mechanistic features of underlying catalytic processes, and demonstrate how Schulz–Flory, alternating, selective-LAO, and Poisson distributions may be considered as parts of a connected product distribution landscape

First‐Order Oligomerisation Processes
Derivation of the Schulz–Flory Equation via Recurrence Relations
Application of the Fitting Procedure to Experiment
Derivations of Further Experimentally‐Relevant Metrics
Second‐Order Oligomerisation Processes
Derivation of the Alternating Equation via Recurrence
Connecting First‐Order and Second‐Order Oligomerisation Processes
Degree of Alternation
Implications for Second‐Order Fitting with “Gently”
Steady‐State Oligomerisation with Nonconstant Propagation Probabilities
First‐Order Recurrence Relations with Nonconstant Propagation Probabilities
Connecting Schulz–Flory Distributions and Poisson Distributions
First Principles
Derivation of Poisson’s Equation for First‐Order Living Polymerisation
Non‐Steady‐State Living Polymerisation with Catalysed Chain Growth
Numerical Simulations
The Fitting Process
Model Outputs
Conclusions and Summary
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