Recent experiments on the return to equilibrium of solutions of entangled polymers stretched by extensional flows [Zhou and Schroeder, Phys. Rev. Lett. 120, 267801 (2018)] have highlighted the possible role of the tube model’s two-step mechanism in the process of chain relaxation. In this paper, motivated by these findings, we use a generalized Langevin equation (GLE) to study the time evolution, under linear mixed flow, of the linear dimensions of a single finitely extensible Rouse polymer in a solution of other polymers. Approximating the memory function of the GLE, which contains the details of the interactions of the Rouse polymer with its surroundings, by a power law defined by two parameters, we show that the decay of the chain’s fractional extension in the steady state can be expressed in terms of a linear combination of Mittag-Leffler and generalized Mittag-Leffler functions. For the special cases of elongational flow and steady shear flow, and after adjustment of the parameters in the memory function, our calculated decay curves provide satisfactory fits to the experimental decay curves from the work of Zhou and Schroeder and earlier work of Teixeira et al. [Macromolecules 40, 2461 (2007)]. The non-exponential character of the Mittag-Leffler functions and the consequent absence of characteristic decay constants suggest that melt relaxation may proceed by a sequence of steps with an essentially continuous, rather than discrete, spectrum of timescales.
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14 January 2021
Research Article|
January 13 2021
The relaxation dynamics of single flow-stretched polymers in semidilute to concentrated solutions
Special Collection:
Special Collection in Honor of Women in Chemical Physics and Physical Chemistry
Neha Tyagi
;
Neha Tyagi
Department of Inorganic and Physical Chemistry, Indian Institute of Science
, Bangalore 560012, India
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Binny J. Cherayil
Binny J. Cherayil
a)
Department of Inorganic and Physical Chemistry, Indian Institute of Science
, Bangalore 560012, India
a)Author to whom correspondence should be addressed: cherayil@iisc.ac.in
Search for other works by this author on:
a)Author to whom correspondence should be addressed: cherayil@iisc.ac.in
Note: This paper is part of the JCP Special Collection in Honor of Women in Chemical Physics and Physical Chemistry.
J. Chem. Phys. 154, 024907 (2021)
Article history
Received:
November 15 2020
Accepted:
December 18 2020
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Citation
Neha Tyagi, Binny J. Cherayil; The relaxation dynamics of single flow-stretched polymers in semidilute to concentrated solutions. J. Chem. Phys. 14 January 2021; 154 (2): 024907. https://doi.org/10.1063/5.0037513
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