Non-continuum correlated intermolecular dynamical displacements in entangled biopolymer solutions.

Understanding correlated intermolecular motion is important in biology and of fundamental interest in polymer physics. We performed real space measurements of the correlated dynamical displacements of a pair of biopolymers in entangled F-actin solutions over mesoscopic and continuum length scales, and on time scales beyond the entanglement crossover but much shorter than the reptation time. A microscopic theory is constructed based on generalizing a recent force-level statistical mechanical approach for predicting the separation-dependent, non-hydrodynamic relative friction of a pair of colloids in polymer melts [1] and in dense suspensions [2]. In the mesoscopic time regime, individual biopolymers move by reptation, and the dynamically-emergent intermolecular correlation hole is proposed as the mechanism for inducing non-hydrodynamic collective Fickian motion. Non-continuum cross correlations are predicted to dominate for inter-polymer separations up to the rod length ($\sim$15 microns), beyond which a crossover to hydrodynamic behavior occurs. The theoretical results agree well with our measurements at different observation times and physical mesh values. [1] Yamamoto, Schweizer, J.Chem.Phys.139,064907(2013); [2] Dell, Tsang, Jian, Granick, Schweizer, Phys.Rev.E, in press, 2015