ANALYSIS OF ORIENTATION AUTOCORRELATION AND CROSS-CORRELATION FUNCTIONS FOR POLYETHYLENE IN THE INCLUSION COMPLEX WITH PERHYDROTRIPHENYLENE

The first and second orientation autocorrelation functions have been c omputed and analyzed for polyethylene in the inclusion complex with pe rhydrotriphenylene at 223,300, and 373 K. Two coordinate systems have been used-an internal coordinate system defined by the polyethylene ch ain and an external coordinate system defined by the channel. The orie ntation autocorrelation functions are denoted by M1,int(t), M2,int(t), M1,ext(t), and M2,ext(t). Cross-correlation functions have also been computed. The trajectories that provide the raw data are those reporte d by Zhan and Mattice (Macromolecules 1992, 25, 4078) for n-tetraconta ne in a channel formed by 90 molecules of perhydrotriphenylene. The re sults show the dynamics of the internal and external motions occur on different time scales which can be conveniently separated. The rigid-b ody rotation about the chain axis dominates the overall chain motion. The short-term memory of the direction of this rotation produces as li ght overshoot to the decay of M1,ext(t) and M2,ext(t) at 223 and 300 K . This feature can be rationalized by a simple model for the rigid-bod y rotation. The internal motions are of higher frequency. They are dom inated by the librational motions of internal C-C bonds, on a picoseco nd time scale, within the trans rotational isomeric state.