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 DEMG 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 pre-averaged 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 drive 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 understood in systems of associating polymers under flow. The model also exemplifies a wide class of driven systems possessing strong, and scaling, fluctuations.
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