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A general treatment of macrocyclization reactions occurring under thermodynamic control is presented. The fundamental quantities on which the treatment is based are the effective molarities of the cyclic oligomers and the equilibrium constant for the intermolecular model reaction between monofunctional reactants (K(inter)). Four typical cases have been considered, namely, addition and condensation of a monomer of the type A-B, addition of A-A, and addition of A-A + B-B. A critical comparison with the classical theory of Jacobson and Stockmayer is presented. It is shown that the phenomenon characterized by the critical monomer concentration (cut-off point) is a limiting phenomenon which would occur only for infinitely large values of K(inter). The treatment has been successfully applied to the DOS/DTC-induced cyclooligomerization of beta-propiolactone in CDCl3 solution that yields well-behaved ring-chain equilibrates closely adhering to the theoretical model. Best fit of the experimental product distributions to the general equations gave the equilibrium constant (K(inter)) of the intermolecular model reaction, as well as the effective molarities (EM(i)) for the cyclic oligomers from trimer to octamer. The EM(i) values decrease in proportion of the -2.5 power of the oligomerization degree, thus providing a strong indication that the oligomeric polylactones are essentially strainless. The extremely low value of K(inter) (2.5) is responsible for the absence of a cut-off point, which is usually present in ring-chain polymeric equilibrates.
Ercolani et al. (Sat,) studied this question.