Abstract
Hydrodynamic interactions can dramatically influence the dynamics of fully flexible, ring-shaped polymers in ways unknown for any other polymer architecture or topology. Tumbling under shear is a common dynamic pattern of motion for all polymer architectures. Here we show the existence of a shear-induced inflation phase exclusive to ring polymers, the onset of which depends on the ring’s contour length. This is accompanied by a strong suppression of tumbling, which resumes at even higher shear rates. The ring swells in the vorticity direction, and the horseshoe regions on the stretched and swollen ring are effectively locked in place relative to its center-of-mass. Furthermore, knots tied onto such rings can serve as additional ‘stabilisation anchors'. Under strong shear, the knotted section remains well-localised while tank-treading from one horseshoe region to the other in sudden bursts. We find knotted polymers of high contour length behave very similarly to unknotted rings of the same contour length.
Highlights
Hydrodynamic interactions can dramatically influence the dynamics of fully flexible, ringshaped polymers in ways unknown for any other polymer architecture or topology
Through a coupling between hydrodynamic interactions (HI) and topology unique to the ring architecture, circular polymers under shear have been shown to swell in the vorticity direction, a phenomenon that is absent for linear chains and it disappears for circular polymers when HI is switched off[22,51,52]
We present the emergence of an inflationary phase for longer ring polymers under simple, pure shear and fully developed hydrodynamics caused by a backflow from the horseshoe regions
Summary
Hydrodynamic interactions can dramatically influence the dynamics of fully flexible, ringshaped polymers in ways unknown for any other polymer architecture or topology. The conformations of single molecules and the ensuing effective interactions[7,8,9], the self-organisation of concentrated ring polymer solutions and melts[10,11,12,13,14], the viscosity and stress relaxation under shear[5,15,16,17] as well as the possibility of emergence of novel, topologically glassy states for ring polymer melts[18,19] are a few characteristic examples of the variety of properties unique to cyclic polymers. We present the emergence of an inflationary phase for longer ring polymers under simple, pure shear and fully developed hydrodynamics caused by a backflow from the horseshoe regions. In this phase, the ring undergoes full unfolding in all directions and transforms itself to an almost rigid, stretched, non-
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