Ring-expanding polymerization by reversible ring fusion. A fascinating process driven by entropy

Grubbs et al. reported a successful method for synthesizing high-molecular weight cyclic polymers without the intermediacy of linear chains (Science 2002, 297, 2041). In spite of its practical significance, there are, however, important questions about this process that remain open. Here it is presented a theory of ring-expanding polymerization mediated by ring-ring equilibria, and driven by entropy only, that addresses the observed results. In particular the theory predicts the existence of a critical concentration (CC) below which only low-molecular weight cyclic oligomers are formed and above which the entire system is predicted to collapse into a single giant ring molecule, the process resembling an irreversible one. Dilution of the system below the CC is predicted to restore the mixture of low-molecular weight cyclic oligomers.