Dynamics of a single polymer chain: Ergodicity and conformation of a rotating chain

The dynamics of an isolated polymer chain has irreversible aspects that lead to the decorrelation of configurational properties over time. For simple mechanical models with time reversible equations of motion, the irreversibility is a consequence of the chaotic nature of the dynamics which, for a many body system, is expected to result in ergodic mixing. Here we study a fixed bond length N-mer interaction-site chain with fixed total energy and angular momentum. For N >= 4 the equations of motion for such a chain are nonintegrable and chaotic dynamics is expected. We directly assess the ergodicity of short repulsive Lennard-Jones chains by comparing phase space and time averages for structural and energetic properties. The phase space averages are determined from the exact microcanonical partition function while the time averages are obtained from molecular dynamics (MD) simulations. For N=4 and 5 we find that our exact phase space averages agree with the MD time averages, as expected for an ergodic system. The N=3 system is integrable and thus displays regular dynamics for which time averages are found to depend on initial conditions. In all cases, the total angular momentum is found to have a large effect on both the average chain conformation and the partitioning of the total energy between potential, vibrational, and rotational contributions. Compared to a nonrotating chain, a small to moderate angular momentum slightly speeds up the internal chain dynamics, while a large angular momentum dramatically slows the internal dynamics.