Single polymer dynamics under large amplitude oscillatory extension

Yuecheng Zhou and Charles M. Schroeder

Phys. Rev. Fluids 1, 053301 – Published 20 September 2016

Abstract

Understanding the conformational dynamics of polymers in time-dependent flows is of key importance for controlling materials properties during processing. Despite this importance, however, it has been challenging to study polymer dynamics in controlled time-dependent or oscillatory extensional flows. In this work, we study the dynamics of single polymers in large-amplitude oscillatory extension (LAOE) using a combination of experiments and Brownian dynamics (BD) simulations. Two-dimensional LAOE flow is generated using a feedback-controlled stagnation point device known as the Stokes trap, thereby generating an oscillatory planar extensional flow with alternating principal axes of extension and compression. Our results show that polymers experience periodic cycles of compression, reorientation, and extension in LAOE, and dynamics are generally governed by a dimensionless flow strength (Weissenberg number $Wi)$ and dimensionless frequency (Deborah number $De)$ . Single molecule experiments are compared to BD simulations with and without intramolecular hydrodynamic interactions (HI) and excluded volume (EV) interactions, and good agreement is obtained across a range of parameters. Moreover, transient bulk stress in LAOE is determined from simulations using the Kramers relation, which reveals interesting and unique rheological signatures for this time-dependent flow. We further construct a series of single polymer stretch-flow rate curves (defined as single molecule Lissajous curves) as a function of $Wi$ and $De$ , and we observe qualitatively different dynamic signatures (butterfly, bow tie, arch, and line shapes) across the two-dimensional Pipkin space defined by $Wi$ and $De$ . Finally, polymer dynamics spanning from the linear to nonlinear response regimes are interpreted in the context of accumulated fluid strain in LAOE.

Received 29 March 2016

DOI:https://doi.org/10.1103/PhysRevFluids.1.053301

Physics Subject Headings (PhySH)

Microfluidics Polymer conformation changes Rheology Viscoelasticity

Single molecule techniques

Fluid DynamicsPhysics of Living SystemsCondensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

Yuecheng Zhou¹ and Charles M. Schroeder^1,2,3,*

¹Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
³Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

^*cms@illinois.edu

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Issue

Vol. 1, Iss. 5 — September 2016

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Images

Figure 1
Single polymer dynamics in large-amplitude oscillatory extension (LAOE). (a) Sinusoidal strain rate input for single polymer LAOE in orthogonal directions. Inset: optical micrograph of PDMS-based microfluidic cross-slot device showing four inlet ports $(p 1 − p 4)$ . Scale bar: 2 mm. (b) Schematics of time-dependent sinusoidal oscillatory extensional flow inside the cross-slot device.
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Figure 2
Single polymer dynamics in LAOE from experiments and simulations. (a) Experimental trajectories of maximum projected polymer fractional extension $l / L$ over the $x − y$ plane for an ensemble of $> 30$ individual molecules (black) overplotted with single polymer trajectories (gray) at ${Wi}_{0} = 6.5$ and $De = 0.45$ . (b) Maximum projected polymer fractional extension $l / L$ from free-draining BD simulations at ${Wi}_{0} = 6.5$ and $De = 0.45$ for an ensemble average over 250 molecules (black) overplotted with single polymer trajectories (gray). Also shown is the ensemble average fractional extension $l / L$ from BD simulations with HI and EV (dashed blue line). (c) Probability distribution of four experimentally observed molecular configurations (folded, kinked, dumbbell, and half-dumbbell) in LAOE at ${Wi}_{0} = 6.5$ and $De = 0.45$ . (d) Power spectral density of polymer extension $l$ from experiments and simulations at ${Wi}_{0} = 6.5$ and $De = 0.45$ .
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Figure 3
Single polymer LAOE at ${Wi}_{0} = 6.5$ and $De = 0.45$ . (a) A series of single polymer snapshots is used to characterize polymer motion during one sinusoidal strain rate input cycle. The time between each snapshot is 1 s. (b) Experimental single polymer Lissajous plot showing the average projected fractional extension $l / L$ as a function of ${Wi}_{y} (t)$ at ${Wi}_{0} = 6.5$ and $De = 0.45$ . The color scale denotes the rate of change of the strain rate input function $d {Wi}_{y} / d t$ . (c) Experimental strain rate input function with period $T = 10$ s.
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Figure 4
Single polymer Lissajous curves from experiments, BD simulations with hydrodynamic interactions (HI) and excluded volume (EV) interactions, and free-draining (FD) BD simulations at (a) $De = 0.1$ and ${Wi}_{0} = 5$ , (b) $De = 0.25$ and ${Wi}_{0} = 5$ , and (c) $De = 0.45$ and ${Wi}_{0} = 6.5$ . Polymer contribution to the total stress along the $y y$ direction calculated from Kramers expression at (d) $De = 0.1$ and ${Wi}_{0} = 5$ , (e) $De = 0.25$ and ${Wi}_{0} = 5$ , and (f) $De = 0.45$ and ${Wi}_{0} = 6.5$ . Polymer contribution to the total stress along the $x x$ direction calculated from Kramers expression at (g) $De = 0.1$ and ${Wi}_{0} = 5$ , (h) $De = 0.25$ and ${Wi}_{0} = 5$ , and (i) $De = 0.45$ and ${Wi}_{0} = 6.5$ .
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Figure 5
Single polymer Lissajous curves showing subplots of average transient fractional extension $l / L$ as a function of the transient flow strength ${Wi}_{y} (t)$ . Individual Lissajous curves are plotted over the two-dimensional Pipkin space as functions of the maximum flow strength ${Wi}_{0}$ and probing frequency $De$ . Results are shown from free-draining BD simulations. The gray region represents line shapes, the blue region represents arch shapes, the orange region represents bow-tie shapes, and the red region represents butterfly shapes.
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Figure 6
Quantitative analysis of accumulated fluid strain during the early (compression), intermediate (extension), and late (retraction) stages of a half cycle in LAOE. (a) Fraction of fluid strain accumulated during the early stage of a half sinusoidal cycle $ε_{1} / ε_{T / 2}$ . Here, the strain during the early stage $ε_{1}$ is plotted relative to the total strain during a half cycle $ε_{T / 2}$ . (b) Fraction of fluid strain accumulated during the intermediate stage of a half sinusoidal cycle $ε_{2} / ε_{T / 2}$ . (c) Fraction of fluid strain accumulated during the late stage of a half sinusoidal cycle $ε_{3} / ε_{T / 2}$ .
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