Statistical Ring Catenation under Thermodynamic Control: Should the Jacobson–Stockmayer Cyclization Theory Take into Account Catenane Formation?

Abstract

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 ≈ 10 8 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 10 2 mol −1 L, thus justifying the use of the extended theory.

Kinetic Investigation on the Cationic Polymerization of o-Phthalaldehyde: Understanding Ring-Expansion Polymerization

“…Ercolani and Di Stefano have produced noteworthy efforts in extending the JS theory to describe systems of cyclic polymers without the intermediacy of linear polymers, 28 and systems that have the ability to thermodynamically form catenanes. 29 In both cases, the efforts focus on understanding what occurs beyond the cyclic critical concentration as defined by the JS theory. In the cyclic-only case, the authors use entropic calculations to argue that above the critical concentration, the equilibrium favors the formation of a single cyclic polymer chain via ring fusion.…”

Simple and General Approach for Reversible Condensation Polymerization with Cyclization

“…Recently, several models were discussed to estimate the impact of concatenation on the weight distributions of linear, cyclic, and concatenated molecules in equilibrium polymers. , The results of these works indicate that concatenation may be ignored for flexible polymers, while semiflexible rings may form predominantly catenated states that enhance the observed molecular weights. Therefore, we expect that our analysis should apply well for flexible chain systems, since these are not disturbed largely by concatenation.…”

Soft silicone elastomers with no chemical cross-linking and unprecedented softness and stability

“…Both plateaus suggest a 3-dimensional network of the elastomer, which is usually expected for a covalently cross-linked elastomer only (e.g., the reference elastomer Elastomer-V25). Since covalent crosslinks in the elastomer were not detected by Goff et al [22] and concatenated rings may form through intramolecular reactions [29], topological linkages between concatenated rings are believed to act similar to covalent crosslinks by creating a 3-dimensional network (as shown in Figure 1a).…”