Non-Equilibrium Dynamics of Ring-Linear Polymer Solution Blends: Concentration and Molecular Weight Effects

The non-equilibrium dynamics of polymer solutions are relevant to many coating, spinning, and printing flows used in polymer processing. The broad parameter space of polymer solutions provides great functional versatility in designing viscoelastic flow behavior and material properties. However, this also causes challenges in quantitatively predicting the polymer conformations, which are intrinsically linked to continuum properties. We develop an understanding of the effect of polymer concentration, chain architecture, and applied strain rate on polymer dynamics using Brownian dynamics simulations with hydrodynamic interactions (HI) and topological constraints. We consider blends of ring and linear polymers in planar extensional flow at concentrations from nominally dilute (0.1c*) to semidilute (3c*). We control polydispersity via the mass fraction and molecular weight ratio of ring versus linear polymers. When the maximum stretch in the flow direction is the same for ring and linear chains (L_L/L_R= 1, M_L/M_R= 0.5), the dynamics match the expected coil-stretch transition found previously for dilute and semidilute polymer solutions. When the linear polymer molecular weight is matched to that of the rings (L_L/L_R= 2, M_L/M_R= 1), we find a distinct departure in the ring dynamics, including ring extension overshoots in startup flow and large conformational fluctuations at steady state. The steady state conformational fluctuations further increase with size disparity up to L_L/L_R= 4, M_L/M_R= 2. We find that the overshoots in ring extension are caused by intermolecular hooks between ring and linear polymers, and the steady state fluctuations are caused by intermolecular HI between the highly stretched linear chains and weakly stretched rings. We show that these conformational fluctuations are related to transient local deviations from planar extensional flow on the length scale of the smaller component. Fluctuations grow with concentration and mass fraction of linear polymers due to the increased perturbation of the solvent velocity.