TY - JOUR
T1 - Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows
AU - Sing, Charles E.
AU - Alexander-Katz, Alfredo
N1 - Funding Information:
This research was supported in part by the National Science Foundation through TeraGrid resources under Grant No. TG-DMR090139. We also thank the National Defense Science and Engineering Fellowship and NSF CAREER Award No. 1054671 for financial support.
PY - 2011/7/7
Y1 - 2011/7/7
N2 - 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 Pg-s and vice versa Ps-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 Pg-s and P s-g govern the state in which the polymer resides; for P g-s ≈ 0 and Ps-g ≈ 1 the polymer is always collapsed, for Pg-s ≈ 0 and Ps-g ≈ 0 the polymer is stuck in either the collapsed or stretched state, for Pg-s ≈ 1 and Ps-g ≈ 0 the polymer is always stretched, and for Pg-s ≈ 1 and Ps-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.
AB - 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 Pg-s and vice versa Ps-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 Pg-s and P s-g govern the state in which the polymer resides; for P g-s ≈ 0 and Ps-g ≈ 1 the polymer is always collapsed, for Pg-s ≈ 0 and Ps-g ≈ 0 the polymer is stuck in either the collapsed or stretched state, for Pg-s ≈ 1 and Ps-g ≈ 0 the polymer is always stretched, and for Pg-s ≈ 1 and Ps-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.
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U2 - 10.1063/1.3606392
DO - 10.1063/1.3606392
M3 - Article
C2 - 21744916
AN - SCOPUS:79960276249
SN - 0021-9606
VL - 135
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 1
M1 - 014902
ER -