Pulling knotted polymer rings and concatenated knotted polymer rings in order to understand the effects of entanglement on the mechanical properties of polymer materials

The topological structure of polymers is expected to produce relevant effects on the mechanical properties of polymer systems. However, to assess the contribution of topology by experiment is difficult, mainly due to technical obstacles in controlling the entanglement during the synthesis process, in particular the formation of knots and concatenations.

In this contribution presented are the results of numerical simulations focusing on the mechanical properties of topologically entangled polymer systems. First, the case of single knotted polymers pulled by an external force are discussed following [1]. With respect to [1], thanks to recent progress in computational techniques, much longer polymers are considered with up to 1000 monomers. Next, the stress-strain curves of a few concatenated knots with forces applied at different locations are shown. To check the validity of our simulations based on the Wang-Landau algorythm, two different methods are employed and their consistency is verified. The first method is an improved version of that explained in Ref. [1]. In the second method, starting from a simple Hamiltonian describing short-term interactions between the monomers, the contributions to the Boltzmann distribution due to the external forces applied to the system is treated as an observable whose expectation value is to be computed.

The final goal of this research is to understand the mechanical properties of more complex polymer materials characterized by an uniform distribution of knots or concatenated knots of a given topological type.