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Power Law Stretching of Associating Polymers in Steady-State Extensional Flow.

Charley Schaefer1, Tom C B McLeish1

  • 1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom.

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We developed a polymer dynamics model for extensional flow, revealing power-law stretch distributions and large fluctuations in associating polymers. This framework aids understanding flow-induced crystallization nucleation rates.

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Area of Science:

  • Polymer Physics
  • Soft Matter Physics
  • Rheology

Background:

  • Associating polymers exhibit complex dynamics under flow.
  • Existing models like Doi-Edwards-Marrucci-Grizzuti approximations capture some behaviors but fail to describe steady-state phenomena.
  • Understanding polymer stretching and fluctuations is crucial for predicting material properties and phenomena like flow-induced crystallization.

Purpose of the Study:

  • To present a tube model for Brownian dynamics of associating polymers in extensional flow.
  • To investigate the steady-state behavior of polymer stretch distribution and fluctuations.
  • To provide a framework for understanding nucleation rates in flow-induced crystallization.

Main Methods:

  • Development of a tube model for polymer Brownian dynamics.
  • Analysis of linear response and comparison with Leibler-Rubinstein-Colby theory.
  • Investigation of transient and steady-state stretching using a single-mode approximation and an analytical model.
  • Examination of stochastic forcing effects on stretch distribution.

Main Results:

  • The model confirms analytical predictions for sticky diffusivity in linear response.
  • A single-mode approximation accurately describes transient stretching but fails for steady-state.
  • A power-law distribution of stretch with potentially diverging fluctuations emerges in steady-state extensional flow.
  • Strong stochastic forcing drives the long tail of the distribution and rare threshold-crossing events.

Conclusions:

  • The developed analytical model captures the emergence of power-law stretch distributions and large fluctuations in associating polymers under extensional flow.
  • This model provides a framework for understanding nucleation rates of flow-induced crystallization.
  • The findings exemplify a broader class of driven systems with strong, scaling fluctuations.