Several aspects of cyclization reactions in step-growth polymerizations are
considered. The Jacobson-Stockmayer ring-chain equilibrium theory provides
the basis for understanding these systems, but there are circumstances whe
re some modifications to the theory are needed. In particular, for ring exp
ansion polymerizations, i.e. those for which there is never a significant f
raction of open chains, the statistics are a bit different from those appro
priate for ring-chain equilibrium. Also, if the reactions are irreversible
the occurrence of rings is significantly different from the reversible case
. Rings are more prevalent in irreversible reactions. The implications of t
hese observations for the processing of polymers are briefly considered. (C
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