Dynamics of DNA in the Flow-Gradient Plane of Steady Shear Flow: Observations and Simulations Charles M. Schroeder, † Rodrigo E. Teixeira, † Eric S. G. Shaqfeh,* ,‡ and Steven Chu § Department of Chemical Engineering, Stanford University, Stanford, California 94305; Departments of Chemical and Mechanical Engineering, Stanford University, Stanford, California 94305; and Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305 Received September 16, 2004; Revised Manuscript Received November 15, 2004 ABSTRACT: The dynamical behavior of DNA in steady shear flow has been elucidated using a combination of Brownian dynamics (BD) simulation and single molecule visualization using fluorescence microscopy. Observations of DNA motion in the flow-gradient plane of shear flow using a novel flow apparatus allow for measurement of the gradient-direction polymer thickness (δ 2), a microscopic conformational property that has direct influence on macroscopic polymer solution properties. To complement experimental results for λ-phage DNA (22 µm in length) and 84 µm DNA, we present BD simulation results for DNA in terms of both free-draining bead-spring models and models including both intramolecular hydrodynamic interactions (HI) and excluded volume (EV) interactions. Good agreement between experiments and BD simulations is obtained for ensemble averaged measurements of polymer extension, δ 2, and orientation angle over a wide range of flow strengths. Macroscopic solution properties, including the polymer contribution to the shear viscosity (η p ) and first normal stress coefficient (Ψ 1 p ), are calculated in BD simulations. Power law scalings of η p and Ψ 1 p from the single molecule experiment and BD simulation agree well with bulk rheological characterization of dilute polymer solutions. Histograms of polymer extension demonstrate good agreement between experiment and BD simulation, though histograms of δ 2 from BD simulation slightly differ from experimental results. Cross- correlations of polymer extension and δ2 display rich dynamical polymer behavior, which we discuss on a physical basis. Finally, the power spectral density of polymer extension and δ2 is presented for DNA for both single molecule experiment and BD simulation. 1. Introduction The dynamical behavior of flexible polymer molecules in simple shear flow is replete with interesting and complex physics. 1-3 Fluid flow past any solid boundary gives rise to shear flow. 4 The ubiquitous nature of this flow type engenders a great deal of practical interest. Dilute solutions of flexible polymers in shear flow exhibit flow-dependent viscosities and enhanced normal stresses. 1 These macroscopically observed quantities arise from microscopic, flow-induced conformational changes in polymer chains. Flow type directly influences the nature of the con- formational response of a polymer. 5,6 In general, a two- dimensional, planar flow may be created from a linear superposition of varying amounts of purely extensional and purely rotational flow. 4 Extension dominated flows such as those produced in injection molding applications or near the stagnation point in cross-slot devices are very effective in stretching flexible polymer mol- ecules. 1,3,7 Fluid flows with dominant amounts of rota- tion tend not to perturb polymer conformations far from the coiled state. 3,6 Simple shear flow consists of equal amounts of rotation and extension giving rise to intrigu- ing, albeit complicated, polymer physics. It is now known that in simple shear flow flexible polymers never reach a steady-state molecular extension; 8 rather, in- dividual polymer chains continually undergo tumbling motion with large fluctuations in polymer extension. 8,9 Results from earlier computational studies of Liu 10 and Doyle et al. 11 support this experimental observation. A primary goal of polymer rheology is to establish a direct link between microscopic quantities such as polymer conformation and macroscopic experimental quantities such as solution viscosity. Traditional experi- ments involving optical techniques such as birefringence and light and neutron scattering have sought polymer microstructural information in shear flow. 12-17 Light scattered by flowing macromolecules may be used to infer conformational information through the radius of gyration tensor. 15 Many experiments employing light scattering techniques indicated that polymers did not substantially stretch in shear. 15,17 Although the flow strengths probed were generally low due to technical issues, experimentally determined polymer conforma- tion changes were considerably smaller than predicted by Rouse and Zimm models for polymer dynamics or by Brownian dynamics simulations of nonlinear bead- spring chains. 17 Single molecule techniques using fluorescence mi- croscopy have allowed for the direct observation of DNA chains in flowing solution 7,8,18-20 The first single mol- ecule study of fluorescent DNA in simple shear flow showed that polymers may indeed substantially stretch in shear flow. 8 Furthermore, observation of DNA dy- namics in steady shear revealed large fluctuations in polymer extension, suggestive of end-over-end polymer tumbling. Observations from the experimental study of Smith et al. 8 showed that although DNA molecules constantly exhibit large (atemporal) fluctuations in molecular extension, the average polymer extension † Department of Chemical Engineering. ‡ Departments of Chemical and Mechanical Engineering. § Departments of Physics and Applied Physics. * To whom correspondence should be addressed. E-mail: eric@ chemeng.stanford.edu. 1967 Macromolecules 2005, 38, 1967-1978 10.1021/ma0480796 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/10/2005