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The process is shown for a zirconium metallocene.

Water reacts with triethylaluminium to form a new catalyst, methylalumoxane (MAO)
The metallocene reacts with the MAO, and methyl groups replace chlorine on the metallocene. MAO then acts as a Lewis acid taking one of the methyl groups from the Zr to give
Mechanism of Metallocene Catalysis
The positive ion is stabilised by sharing electrons from a C-H bond.
In this form it catalyses polymerisation
The positively charged zirconium attracts ethene through the electrons of the double bond
To see the process in action click for an animation
The next ethene approaches from the other side where there is space
Movement of electrons continues as the electron pair of the double bond now form a new bond with zirconium, and the active site becomes vacant again for further reaction.
New bonds start to form as the double bond breaks. The arrows show the movement of electrons to give the transition state on the right.































This will continue until chain termination occurs