Curvilinear Dynamics of Topologically Constrained Polymers

The current physical picture for topologically constrained polymer dynamics is that the motion of a chain is constrained to a curvilinear path dictated by the surrounding topology – with diffusion along this path proceeding via (unconstrained) Rouse dynamics. In this talk, we present results on a micromechanical version of an early model system for topologically constrained polymers – a two-dimensional Rouse chain in the presence of point-like obstacles – where the curvilinear path and unconstrained Rouse motion are defined exactly. In linear response, we find that the obstacles introduce an entropic barrier to curvilinear motion (on length scales comparable to the obstacle spacing), manifested as an increased timescale for curvilinear relaxation. While in linear-response one can interpret this topological “friction” as a shift-factor, non-Rouse physics emerges in both the transient and steady state response to weakly non-linear microrheological deformation. For example, upon dragging a chain-end at a constant velocity, we find an initial and prolonged elastic response that is in marked contrast to Rouse physics. We discuss the origin and possible consequences of these curvilinear topological effects.