Charged diblock copolymer rings linked together and fluctuating in an ion solution that screens the long range Coulomb interactions are considered.
The thermodynamic properties of the circular polymer catenanes of L.Tubiana et al, PRL 129 (2022), 227801, are discussed. It is found that these catenanes have a few phase transitions. Two of them have been identified and correspond to the different scales which are relevant for the circular catenane: that of the single rings and that of the catenane as a whole.
Finally, the results of the simulations of simple chainmails composed of a maximum of forty rings will be presented.