A Monte Carlo simulation of a knotted linear chain system as an elementary network fragment

We present the results of the Monte Carlo simulations of the dynamics of the linear chain system. The chains were constructed on a simple cubic lattice. The simulations were carried out by means of the classical Metropolis sampling method with the excluded volume effect present. No other interactions were introduced into the system (athermal polymer case). The linear chains in the system were constructed in such a way that there were knots at certain positions. Also, some chains were threaded through the knots forming the topological constraints in the system. The system under consideration underwent a series of micromodifications during the simulation run. Then the trajectory was analysed and the dynamics of the system was described by means of the autocorrelation functions. The short-time dynamics enabled us to investigate whether or not the knotted constraints affect the local dynamics of the chains. Also the long-time dynamics of the system can be useful in the characterizations of the dynamical properties of the fragments of the networks.