Finding the Tube with Isoconfigurational Averaging

In an entangled polymer melt or solution, the uncrossability of chains effectively restricts a given chain to move within a confining tube. In this work, we find the tube for a simulated melt of topologically equilibrated rings by averaging chain trajectories over a short time interval, combined with "isoconfigurational" averaging over initial velocities for the same starting configuration. This method allows us to nondestructively image the tube and determine its shape, confining potential, and statistical properties. Using this approach, we investigated the effects of a free surface; we find that tube segments within a few tube diameters of the surface have increased tube diameters by about 25%, and strongly tend to lie parallel to the surface.