Some nontrivial thermodynamic properties of polymer catenanes and chainmails

First, the case of a 4-plat consisting in two linked polymer rings is presented. A recent analytical model of this system [1] shows that it has remarkable properties. In particular, when the loops are very long and the density of monomers becomes homogeneous, the local interactions between the monomers due to the topological constraints disappear similarly to what happens for the excluded volume interactions in the case of very dense polymer systems. In this situation, the two linked rings turn out to have a complex energy landscape, with a plethora of solutions minimizing the energy that correspond to conformations with particular symmetries. Here we will present the results of numerical simulations in the case in which the rings are in a solution. While it is difficult to reproduce the analytic results, it is shown by using a contact map method [3] and by close inspection of randomly taken samples that the conformations of the system are roughly self-similar.

Such conformations are stable and persist in a wide range of temperatures.

Next, the thermodynamic properties of the circular polymer catenanes of [2] are discussed. It is found that these catenanes exhibit 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 discussed.