Origin of Tank-Treading and Breathing Dynamics of Star Polymers in Shear Flow

Abstract

We investigate tank-treading and breathing dynamics of individual star molecules under shear flow and their relation with the macromolecule architecture. Tank-treading consists of the rotation of the arms of the star around a molecule’s center, whereas breathing consists in expansions and contractions of the whole molecule at a certain characteristic frequency. We derive scaling arguments for the trends of the frequency and decorrelation rates of both rotation and breathing modes versus the shear rate γ̇, which are supported by extensive Brownian hydrodynamics simulations. We find that breathing occurs if γ̇ is made faster than the equilibrium decorrelation rate Γ0 of two perpendicular eigenvectors of the gyration tensor. Γ0 increases with the star functionality, F, as Γ0 ≈ F 0.5, which contrasts with the rotational and arm-length relaxation rates (F –0.6 and F –0.15 respectively). For γ̇ > Γ0, the star becomes ellipsoidal and elongates in the flow direction and this determines the onset of the non-Newtonian regime. Remarkably, γ̇/Γ0 provides universal trends for the shape, dynamics, and rheology of the star polymer.