Average gyration radius and their temperature-dependence of model macromolecular rings with different knot type

摘要

There are many examples of natural and synthetical polymers with the ring structure of their molecular architecture. In other words, the atoms in the main chain of the polymers form a closed ring in the space. For example, the formation of the cyclic chain for some deoxyribonucleic acids (DNA)~([1]) and cyclic polmers~([2]) have been known for a long time. In the view point of mathematics, the theoretical model of the macromolecular ring is connected to a branch of topology, i.e. the knot theory. There has been a great progress in the multi-discipline research es which are useful to understand the basic behaviour of the cyclic polymers.