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

We present a tube model for the Brownian dynamics of associating polymers in extensional flow. In linear response, the model confirms the analytical predictions for the sticky diffusivity by Leibler-Rubinstein-Colby theory. Although a single-mode Doi-Edwards-Marcucci-Grizzuti approximation accurately describes the transient stretching of the polymers above a sticky Weissenberg number (product of the strain rate with the sticky-Rouse time), the preaveraged model fails to capture a remarkable development of a power law distribution of stretch in steady-state extensional flow: while the mean stretch is finite, the fluctuations in stretch may diverge. We present an analytical model that shows how strong stochastic forcing drives the long tail of the distribution, gives rise to rare events of reaching a threshold stretch, and constitutes a framework within which nucleation rates of flow-induced crystallization may be understood in systems of associating polymers under flow. The model also exemplifies a wide class of driven systems possessing strong, and scaling, fluctuations.

Automated summary

The tube model confirms analytical predictions for sticky diffusivity and shows a power law distribution of stretch in steady-state extensional flow. Strong stochastic forcing is found to be the driving factor behind the long tail of the distribution, leading to rare events of reaching a threshold stretch and offering insights into nucleation rates of flow-induced crystallization in systems of associating polymers under flow. The model also represents a wide class of driven systems with strong and scaling fluctuations.