Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows

Collapsed polymers in solution represent an oft-overlooked area of polymer physics, however recent studies of biopolymers in the bloodstream have suggested that the physics of polymer globules are not only relevant but could potentially lead to powerful new ways to manipulate single molecules using fluid flows. In the present article, we investigate the behavior of a collapsed polymer globule under the influence of linear combinations of shear and elongational flows. We generalize the theory of globule-stretch transitions that has been developed for the specific case of simple shear and elongational flows to account for behavior in arbitrary flow fields. In particular, we find that the behavior of a globule in flow is well represented by a two-state model wherein the critical parameters are the transition probabilities to go from a collapsed to a stretched state P_g-s and vice versa P_s-g. The collapsed globule to stretch transition is described using a nucleation protrusion mechanism, and the reverse transition is described using either a tumbling or a relaxation mechanism. The magnitudes of P_g-s and P _s-g govern the state in which the polymer resides; for P _g-s ≈ 0 and P_s-g ≈ 1 the polymer is always collapsed, for P_g-s ≈ 0 and P_s-g ≈ 0 the polymer is stuck in either the collapsed or stretched state, for P_g-s ≈ 1 and P_s-g ≈ 0 the polymer is always stretched, and for P_g-s ≈ 1 and P_s-g ≈ 1 the polymer undergoes tumbling behavior. These transition probabilities are functions of the flow geometry, and we demonstrate that our theory quantitatively predicts globular polymer conformation in the case of mixed two-dimensional flows, regardless of orientation and representation, by comparing theoretical results to Brownian dynamics simulations. Generalization of the theory to arbitrary three-dimensional flows is discussed as is the incorporation of this theory into rheological equations.