Synthesis of Cyclic Polymers via Ring Closure

Cyclic polymers have intrigued scientists for many years and their diffusion process may have important implications for polymer physics. In this contribution, we focus on the ring-closure method for synthesis of linear polymers made by "living" radical polymerization. In the first part, the probability of two chain ends being in a capture volume to undergo ring closure will be described using the well-known Gaussian chain end-to-end distance. The probability for knot or catenane structures will also be discussed. We then describe the thermodynamic Jacobson-Stockmayer theory for monocyclic ring closure, and an empirical equation based on kinetics. Finally, we give examples of ring closure for many different polymer systems, including the formation of many complex cyclic topologies.