Stretching tethered DNA chains in shear flow

– We discuss the stretching of tethered chains subject to a shear flow. Fluorescence microscopy measurements of the extension of sheared tethered DNA, “model polymers”, of various lengths are presented. The tethered chains approach full extension as the flow rate is increased, but very slowly. We show that a general theory to understand the large deformation of any sheared tethered chain must include both the correct nonlinear force-extension relation and chain fluctuations transverse to the flow direction, which themselves depend on the nonlinear elasticity of the chain. Direct comparison of derived scaling laws to simulations and experiments support our theory. Introduction. – Polymer molecules can be deformed and stretched when subject to a hydrodynamic flow. Recently, many groups have used double-stranded DNA molecules as a model system to directly observe polymer dynamics in flow. These single-molecule studies provide detailed information about chain configurations and have revealed a host of interesting phenomena including “molecular individualism” [1], shear-enhanced extension fluctuations [2] and chain tumbling [3]. The deformation of complex molecules tethered to surfaces is of particular interest because they occur in many practical applications ranging from colloidal stabilization [4] and lubrication [5], to biological systems where molecules can protrude from lipid bilayer membranes [6]. The deformation of a single tethered chain has been modeled by Brochard and coworkers [7] using blob models. At large shear rates the model considers that a molecule adopts a conformation containing a straight portion terminated by a blob, termed the Stem and Flower model. The nonlinear elasticity of the molecule is not explicitly accounted for in these calculations. Recent DNA experiments [2] show a much slower approach to full chain extension than predicted by the Stem and Flower model, and complex molecular dynamics. The dynamics of sheared polymers is nontrivial due to both a rotational and an extensional component to the flow. For free chains this leads to a tumbling motion [3]. Tethering the chain to a solid surface frustrates end-over-end tumbling and instead gives rise to cyclic dynamics [2]. Computer simulations suggest that the cyclic dynamics are driven by the tethering constraint and segment fluctuations perpendicular to the tethering surface which allow the chain to explore the linearly varying flow [2, 8]. These qualitatively different dynamics lead to very different steady-state mean extensions of the chain in the flow direction. These differences are most pronounced at large shear rates where a free chain approaches a mean extension (∗) E-mail: [email protected]