Single Polymer Dynamics in A Random Flow Yonggang Liu,* 1 Victor Steinberg 2 Summary: The dynamics and conformations of a single fluorescently stained T4 DNA molecule are studied in a random flow of elastic turbulence created by the same unlabeled molecules. The explored polymer concentration covers the dilute and semi-dilute unentangled regimes, according to the measurement of the longest relaxation time by extension relaxation of single polymer chains. The criterion of the coil-stretch transition was found to be close to the theoretically predicted value. Using measured polymer stretching statistics and its known elastic properties, the elastic stress in elastic turbulence is obtained over a broad range of Weissenberg number and polymer concentration. The existing theory of elastic turbulence is disproved by the measurements of the elastic stress and the degree of polymer stretching. The role of increasing shear rate on polymer extension and angular statistics in a random flow is also studied and compared with theory and numerical simulations. Keywords: conformational analysis; fluorescence; imaging; rheology; single polymer chain Introduction Dynamics and conformations of single polymer molecules in flow is considered to be the key ingredient in hydrodynamics of dilute polymer solutions and have remained an outstanding problem in poly- mer physics for several decades. [1] It is also directly related to the occurrence of drag reduction in turbulent flows, in which the addition of small quantity of high molecular weight polymers to a turbulent pipe flow drastically decrease the drag. [2] The dynam- ics of single polymer chains in a turbulent flow was widely discussed [3] but complete understanding and in particular its experi- mental verification are still lacking. Pioneering by the seminal studies of Chu and collaborators, the dynamics and statis- tics of single polymer chains in stationary elongation, [4] shear, [5] and mixed [6] flows were extensively studied experimentally. A good agreement with theory [7] and numeri- cal simulation [8–10] was found. In contrast, it is difficult to study single polymer dynamics in a general 3D random flow, due to the difficulty to create a random flow in a microscopic-size volume. A general way to create chaotic or turbulent flow is to work at high velocities, V, and in a large-size vessel, L, to reach large Reynolds numbers, Re  VL/n, where n is the kinematic viscosity. Large Re flow cannot be achieved in a hundred micron cell for single molecule experiment. The recently discovered elastic turbulence, a random flow at low Re, [11] opens the door to study the dynamics and conformation of single polymer molecules in a random flow. Long polymer chains added to a fluid make it elastic and can store non-linear elastic energy when they were stretched in a flow. An elastic instability shows up when the elastic energy over- comes the dissipation due to polymer relaxation. The ratio of the elastic term to the relaxation term is defined by the Wissenberg number, Wi  lV/L, where l is the longest polymer relaxation time. In flows of dilute polymer solutions with 1 State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China E-mail: yonggang@ciac.ac.cn 2 Department of Physics of Complex Systems, Weiz- mann Institute of Science, Rehovot 76100 Israel Macromol. Symp. 2014, 337, 34–43 DOI: 10.1002/masy.201450304 34 | ß 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Changchun Institute of Applied Chemistry, Chinese Academy Of Sciences