A numerical technique for studying topological effects on the thermal properties of knotted polymer rings

The topological effects on the thermal properties of several knot configurations are investigated using Monte Carlo simulations. In order to check whether the topology of the knots is preserved during the thermal fluctuations we propose a method that allows very fast calculations and can be easily applied to arbitrarily complex knots. As an application, the specific energy and heat capacity of the trefoil, the figure-eight and the 8₁ knots are calculated at different temperatures and for different lengths. Short-range repulsive interactions between the monomers are assumed. The knot configurations are generated on a three-dimensional cubic lattice and sampled by means of the Wang-Landau algorithm and of the pivot method. The results obtained show that the topological effects play a key role for short-length polymers. Three temperature regimes of the growth rate of the internal energy of the system are distinguished.