**Dynamics of individual chains in linear polyethylene liquids under shear**

J.M. Kim, B.J. Edwards, B. Khomami, and D.J. Keffer (University of Tennessee, USA)

Many previous studies have investigated the dynamics of polymer chains under shear. In this work, we examine the dynamics of individual polymer chains in linear polyethylene liquids under shear using nonequilibrium molecular dynamics (NEMD) simulation and Brownian dynamics (BD) simulation. As expected, the probability distribution function of the end-to-end vectorâ€™s magnitude follows Gaussian behavior at low shear rate, but as the shear rate increases to intermediate values, individual polymer chains continue to be stretched on average, but also begin to rotate with the local fluid kinematics. Therefore, the end-to-end vector distribution begins to exhibit non-Gaussian behavior. Indeed, we observe a bimodal probability distribution function at intermediate and high values of the shear rate. The first peak of the distribution at low magnitudes of the end-to-end vector is associated with the rotational motion of the chains, and the peak at higher values of the end-to-end vector corresponds to the degree of chain elongation. We also calculate time auto- and cross-correlation functions of each component of the end-to-end vector with respect to itself and the other components, and extract multiple timescales of the chain dynamics, associated with various physical mechanisms, including the rotational motion of the chains. These time scales vary strongly with shear rate.

We compare NEMD simulation data with BD simulation results by mapping atomistic configurations to a bead-rod model. Each mapped atomistic chain is classified as Stretched, Dumbbell, Half Dumbbell, Kink, Fold, or Coil according to its configuration and compared with BD results--see the schematic below. We also calculate the time that each chain spends in the four quadrants of its coordinate system, and found that an individual chain spends more of its time with a positive orientation with respect to the direction of flow as the shear rate increases. For example, the chains spend 66% of their time witht a positive orientation at the highest shear rate examined, compared to 50% of the time at equililbrium.

*Configuration classes of linear polymer chains*