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Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show

The growing importance of microfluidic and nanofluidic devices to the study of biological processes has highlighted the need to better understand how confinement affects the behavior of polymers in flow. In this paper we explore one aspect of this question by calculating the steady-state extension of a long polymer chain in a narrow capillary tube in the presence of simple shear. The calculation is carried out within the framework of the Rouse-Zimm approach to chain dynamics, using a variant of a nonlinear elastic model to enforce finite extensibility of the chain, and assuming that the only effect of the confining surface is to modify the pre-averaged hydrodynamic interaction. The results, along with results from the corresponding calculations of finitely extensible versions of both the Rouse and Rouse-Zimm models, are compared with data from experiments on the flow-induced stretching of λ-phage DNA near a non-adsorbing glass surface [L. Fang, H. Hu, and R. G. Larson, J. Rheol. 49, 127 (2005)]. The comparison suggests that close to a surface hydrodynamic screening is significant, and causes the chains to become effectively free-draining.

The confinement of a polymer to volumes whose characteristic linear dimensions are comparable to or smaller than its bulk radius of gyration R(G,bulk) can produce significant changes in its static and dynamic properties, with important implications for the understanding of single-molecule processes in biology and chemistry. In this paper, we present calculations of the effects of a narrow rectangular slit of thickness d on the scaling behavior of the diffusivity D and relaxation time τr of a Gaussian chain of polymerization index N and persistence length l0. The calculations are based on the Rouse-Zimm model of chain dynamics, with the pre-averaged hydrodynamic interaction being obtained from the solutions to Stokes equations for an incompressible fluid in a parallel plate geometry in the limit of small d. They go beyond de Gennes' purely phenomenological analysis of the problem based on blobs, which has so far been the only analytical route to the determination of chain scaling behavior for this particular geometry. The present model predicts that D ∼ dN(-1)ln (N∕d(2)) and τr ∼ N(2)d(-1)[ln (N∕d(2))](-1) in the regime of moderate confinement, where l0 ≪ d < R(G,bulk). The corresponding results for the blob model have exactly the same power law behavior, but contain no logarithmic corrections; the difference suggests that segments within a blob may actually be partially draining and not non-draining as generally assumed.

The average time τr for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a "sink" term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of τr on N mirrors the behavior of the average time τc of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which τr ∼ N(2.2). A simulation study by Cheng and Makarov [J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N(2.2) behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react.