Single-polymer dynamics of starch-like branched ring polymers in steady shear flow.

The stretching dynamics and dynamical behaviors of individual branched ring polymer (BRP), a coarse-grained model for some types of the starch, in steady shear flow are studied by using a hybrid mesoscale simulation approach that combines multiparticle collision dynamics with standard molecular dynamics. By analyzing the stretched configuration of BRPs, we find the polymer size increases nonmonotonically with increasing branch length. Meanwhile, the decrease of the alignment angle of the stretched configuration of BRPs follows a universal power law during the first downward phase as the shear rate increases. Constructing the three-dimensional surface of the polymer's ring backbone and tracing the temporal fluctuations of the surface's normal vector along the simulation trajectory, the tumbling and tank-treading motion are clearly reflected by periodic and non-periodic changes of the normal vector. Interestingly, these temporal changes are much more regular than that of the gyration tensor. Thus, a novel cross-correlation function, which is the correlation between fluctuations of the normal vector along the flow direction and the velocity-gradient direction, is proposed to analyze the tumbling motion that usually coexists with the tank-treading motion. This function can naturally address the fails of traditional method that analyzing the tumbling motion by determining the correlation of temporal fluctuations of the gyration tensor G. By analyzing the dynamical behaviors of BRPs, diverse dependences of the tumbling frequency ω and tank-treading frequency ω on the shear rate γ̇ are observed at a wide range of shear rates and polymer sizes. Furthermore, our simulations also reveal that the tank-treading motion is more stable than the tumbling motion for small-branch-size BRPs but the tumbling motion is more stable than the tank-treading motion for large-branch-size BRPs.