Comparison of Individual Chain Dynamics of a Short-Chain Polyethylene Dense Liquid with Equivalent Free-Draining Dilute Solution Using An Atomistic and Mesoscopic Level Approach

Observing the motion of individual molecules in polymeric liquids and comparing macroscopic properties from different levels of description allows for the development of more accurate rheological and topological models of the dynamics of these materials. In this study, the motions of single chains in the dense liquid (C₇₈H₁₅₈) and equivalent free-draining dilute solution of bead-rod chains are investigated and also various properties of both systems are examined. The mean-squared, end-to-end vector of the dense liquid increases as Weissenberg (Wei) number increases and obtains maximum value at high Wei. It shows similar behavior and especially attains maximum value at the same value of Wei in dilute solution. We proposed that rotation or tumbling of single chains plays an important role and explains maximum at high Wei in these two different systems. The probability distribution of magnitude of end-to-end vector in both systems has Gaussian behavior at low Wei; however, it is non-Gaussian at high Wei in both liquids, with a decidedly bimodal character in the dense liquid.  The probability distribution of magnitude of end-to-end vector in the dense liquid displays two peaks which are associated with rotation and stretching of the individual chains while a very wide distribution with a single long-extension peak is exhibited by the dilute solution. Based on time trajectories of individual chains for magnitude of end-to-end vector and the individual chain orientation angles, the quasi-periodic rotation or tumbling motion of the individual chains in each liquid is different. In dilute solution, chains retract and almost collapse to tightly coiled configurations during the tumbling cycle. On the other hand, they rotate in hairpin configurations in the dense liquid.  We observed that the characteristic timescales, calculated from auto- and cross-correlations between components of end-to-end vector, have qualitatively similar behavior in both liquids and decreased as functions of Wei.  The characteristic frequencies of molecular rotation of the dense liquid changed from Wei^-0.75 to Wei^-0.66 after Wei = 2 in the dense liquid. This is caused by a decrease in elastic response of system due to relaxation of the rotational correlation. Similarly, characteristic frequencies reveal similar behavior (Wei^-0.68 and Wei^-0.66) in dilute solution. Other properties, such as probability distribution of representative chain configuration classes, positive and negative chain orientations, and so on, are also compared to explore similarities and differences between these two systems.