Chain shuttling polymerization makes use of two catalysts and a chain shuttling agent (CSA) to generate copolymers of alternating tacticity.  Catalyst 1 (Cat1) propagates a polyolefin of a desired tacticity.  Catalyst 2 (Cat2) generates another chain of a different tacticity.  The two chains are allowed to co-propagate in a single reactor in the same living polymer fashion as before.  To alternate the tacticity, a CSA will transfer the polymer chain from its respective catalyst.  The CSA can then bind to Cat2 and attach the chain to Cat2.  When the chain attaches to Cat2, the polymerization of that chain continues, except it now propagates with the tacticity dictated by Cat2, not Cat1.  The general result is that the chain will alternate between two different tacticities.  As the forward and reverse reactions occur, the polymer chain is “shuttled” back and forth between the two catalysts and a block copolymer is formed.
The shuttling of chains back and forth from catalysts via a CSA can be viewed as a competing chemical equilibrium.  Note that the forward and reverse reactions of CSA binding and leaving either Cat1 or Cat2 are possible.  This competition means that a chain can leave Cat1 via a CSA and the reattach to Cat1, polymerizing the same tacticity.  The rate at which the reattachment of Cat1 occurs can be controlled by altering the relative concentrations of Cat1, Cat2 and CSA.  For example, if one wanted to produce a polymer with the properties mainly resulting from the use of Cat1 and only wanted to influence its properties slightly by the presence of Cat2, a greater concentration of Cat1 would be used than for Cat2.  The rate of alternation between tacticity can be controlled by altering the concentration of CSA relative to Cat1 and Cat2; having a higher concentration of CSA means that the chains will shuttle back and forth more rapidly, creating shorter units of alternating tacticity.