Statistical ring catenation under thermodynamic control: should the Jacobson-Stockmayer cyclization theory take into account catenane formation?

An extension of the Jacobson−Stockmayer theory is presented to include the reversible formation of [2]catenanes in a ring−chain system under thermodynamic control. The extended theory is based on the molar catenation constant, measuring the ease of catenation of two ring oligomers, whose expression was obtained in a previous work. Two scenarios have been considered: that of “thick” (hydrocarbon-like) chains and that of “thin” (DNA-like) chains. In the case of “thick” chains, the formation of catenanes can be neglected, unless in the unlikely case of a very large value of the equilibrium constant for linear propagation (K ≈ 108 mol−1 L, or larger). For K tending to infinity, the system becomes a chain-free system where only ring−catenane equilibria occur. Under this condition, there is a critical concentration below which only rings are present at equilibrium and above which the ring fraction remains constant, and the excess monomer is converted only into catenanes. In the case of “thin” chains, the formation of catenanes cannot be neglected even for values of K as low as 102 mol−1 L, thus justifying the use of the extended theory.