Coupling between different modes in local chain dynamics: A modal correlation analysis

A correlation analysis is proposed for studying the coupling between low- and high-frequency rotational motions in polymers. Molecular dynamics simulations are used to generate trajectories of a polyethylene-like polymer chain. Contributions to the observed trajectories from characteristic modes of various frequencies are identified by extensive use of filtering techniques. Correlations between modes are represented in terms of a modal correlation function. The latter is expressed as the sum of two contributions, reflecting the degrees of coupling and incoherence, respectively, between various modes. The term modal is used throughout to prevent confusion with the widely studied time-correlation functions in the literature. The analysis of the kinetic-energy trajectories of backbone atoms indicates that after an initial relaxation taking place within picoseconds, the kinetic-energy fluctuations are adequately described by a few lowest-frequency modes of the total spectrum. Strong mode-mode coupling, both coherent and incoherent, is observed among the modes in the range ν < 20 cm^-1, whereas the correlations among modes with frequencies 20 < ν/cm^-1 < 30 are mainly expressed by incoherent motions increasing with the separation between atoms along the chain contour. The flow of kinetic energy between backbone atoms is found to take place mostly through modes of comparable frequencies. However, communication between modes of distinct frequencies does also exist, which is particularly pronounced during bond rotational jumps from one isomeric state to another and gives rise to localization of the motion in space.