The effects of slit-like confinement on flow-induced polymer deformation

Abstract

This paper is broadly concerned with the dynamics of a polymer confined to a rectangular slit of width D and deformed by a planar elongational flow of strength γ̇. It is interested, more specifically, in the nature of the coil-stretch transition that such polymers undergo when the flow strength γ̇ is varied, and in the degree to which this transition is affected by the presence of restrictive boundaries. These issues are explored within the framework of a finitely extensible Rouse model that includes pre-averaged surface-mediated hydrodynamic interactions. Calculations of the chain's steady-state fractional extension x using this model suggest that different modes of relaxation (which are characterized by an integer p) exert different levels of control on the coil-stretch transition. In particular, the location of the transition (as identified from the graph of x versus the Weissenberg number Wi, a dimensionless parameter defined by the product of γ̇ and the time constant τ of a relaxation mode p) is found to vary with the choice of τ. In particular, when τ is used in the definition of Wi, the x vs. Wi data for different D lie on a single curve, but when τ is used instead (with τ > τ) the corresponding data lie on distinct curves. These findings are in close qualitative agreement with a number of experimental results on confinement effects on DNA stretching in electric fields. Similar D-dependent trends are seen in our calculated force vs. Wi data, but force vs. x data are essentially D-independent and lie on a single curve.

Fluctuation relations for flow-driven trapped colloids and implications for related polymeric systems

“…The results of the previous sections have immediate implications for our earlier study of polymer stretching under flow [21][22][23][24], which, as mentioned in the Introduction, was motivated by Schroeder et al's experimental and numerical investigations [17][18][19][20] of the work done when a flexible polymer in an initially unperturbed state is stretched under the action of an extensional flow of strength γ.…”

“…(As do the corresponding force-extension curves derived in Ref. [23] for the case of a flow-driven slit-confined polymer.) But these results also mean that W R in equation (21b) probably has to be identified with the B-K work, rather than with the thermodynamic work.…”

“…Our interest in this system actually goes beyond its purely heuristic value. Schroeder et al recently showed how one particular fluctuation theorem (the Jarzynski relation) could be used to determine the elasticity of single-stranded DNA from an examination of the molecule's work fluctuations in the presence of extensional flow [17][18][19][20], and we later showed how many of the experimental and simulation results from that study could be satisfactorily described by a path integral treatment of a finitely extensible Rouse chain [21][22][23][24]. But we have now come to realize that some of our earlier calculations were in error.…”