Fingerprinting Brownian Motions of Polymers under Flow

Zhiqiang Shen, Jan-Michael Y. Carrillo, Bobby G. Sumpter, and Yangyang Wang

Phys. Rev. Lett. 129, 057801 – Published 28 July 2022

Abstract

We present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.

Received 7 March 2022
Accepted 8 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.057801

Physics Subject Headings (PhySH)

Brownian motion Rheology

Polymer melts

Molecular dynamics

Polymers & Soft Matter

Authors & Affiliations

Zhiqiang Shen , Jan-Michael Y. Carrillo , Bobby G. Sumpter , and Yangyang Wang ^*

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*wangy@ornl.gov

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Issue

Vol. 129, Iss. 5 — 29 July 2022

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Images

Figure 1
(a) Illustration of the two reference frames for decomposing polymer self-dynamics under flow. (b) Two-dimensional color maps of the spherical harmonic expansion coefficients ${\tilde{F}}_{0, 0}^{cm} (Q, t)$ and ${\tilde{F}}_{2, 0}^{cm} (Q, t)$ of the c.m. self-intermediate scattering function ${\tilde{F}}_{cm} (Q, t)$ in the flow frame. The wave number $Q$ is scaled by the radius of gyration $R_{g, 0}$ in the equilibrium state. (c) Coefficients ${\hat{F}}_{0, 0}^{mon} (Q, t)$ and ${\hat{F}}_{2, 0}^{mon} (Q, t)$ of the monomer self-intermediate scattering function ${\hat{F}}_{mon} (Q, t)$ in the c.m. frame. The dashed lines indicate cuts of the 2D maps at fixed correlation times. The results given here are based on NEMD simulations of the $N = 300$ system under steady extensional flow of ${Wi}_{R} = \dot{ϵ} τ_{R} = 3$ , with $τ_{R}$ being the Rouse time.
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Figure 2
Center-of-mass motions of the $N = 20$ and $N = 300$ melts in the flow frame. (a) c.m. mean-squared displacements ${\tilde{g}}_{cm} (t)$ relative to the flow field. (b) Relative change of diffusivity ${\tilde{D}}_{cm} / {\tilde{D}}_{cm, 0}$ with the Weissenberg number Wi. ${\tilde{D}}_{cm, 0}$ is the diffusivity without flow. $Wi \equiv \dot{ϵ} τ_{chain}$ , with $τ_{chain}$ being the chain relaxation time. The dashed line is a guide for the eye. The dash-dotted line indicates the prediction of the Rouse model. (c) Spherical harmonic expansion coefficients ${\tilde{F}}_{0, 0}^{cm} (Q, t)$ and ${\tilde{F}}_{2, 0}^{cm} (Q, t)$ of the c.m. self-intermediate scattering function ${\tilde{F}}_{cm} (Q, t)$ of the $N = 20$ system at different correlation times $t$ and Rouse-Weissenberg numbers ${Wi}_{R}$ . The results of the same ${Wi}_{R}$ are represented by the same symbol. Furthermore, the data of the same normalized correlation time ${Wi}_{R} t$ are shown in the same color. The dashed lines show anisotropic Gaussian fits of the expansion coefficients according to Eq. (5) with no adjustable parameters. (d) Results for the $N = 300$ melts.
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Figure 3
Monomer motions in the c.m. frame. (a) Two-dimensional color maps of the isotropic expansion coefficient ${\hat{F}}_{0, 0}^{mon} (Q, t)$ of the self-intermediate scattering function ${\hat{F}}_{mon} (Q, t)$ at equilibrium, ${Wi}_{R} = 0.3$ , and ${Wi}_{R} = 30$ . The dashed lines are contour lines of ${\hat{F}}_{0, 0}^{mon} (Q^{*}, t) = e^{- 1}$ . (b) Characteristic wave number $Q^{*} R_{g, 0}$ at various Rouse-Weissenberg numbers for the $N = 20$ and $N = 300$ melts. (c) Rate dependence of the characteristic length scale in the long-time limit $ξ_{L}$ . (d) Dependence of $ξ_{L}$ on the steady-state tensile stress $σ$ .
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Figure 4
(a) Isotropic component ${\hat{G}}_{0, 0}^{mon} (r, t)$ of the c.m. frame self-correlation function ${\hat{G}}_{mon} (r, t)$ of the $N = 300$ melt at equilibrium. (b) ${\hat{G}}_{0, 0}^{mon} (r, t)$ at ${Wi}_{R} = 10$ . The solid lines show approximations of the long tails of ${\hat{G}}_{0, 0}^{mon} (r, t)$ by an exponent function $\exp (- r / λ)$ . (c) Change of characteristic length $λ$ under steady extensional flow for the $N = 20$ melt. (d) Results for the $N = 300$ melt.
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