Caught in the Tube

Abstract

Using neutron spin echo spectroscopy, we show that the segmental dynamics of polymer rings immersed in linear chains is completely controlled by the host. This transforms rings into ideal probes for studying the entanglement dynamics of the embedding matrix. As a consequence of the unique ring topology, in long chain matrices the entanglement spacing is directly revealed, unaffected by local reptation of the host molecules beyond this distance. In shorter entangled matrices, where in the time frame of the experiment secondary effects such as contour length fluctuations or constraint release could play a role, the ring motion reveals that the contour length fluctuation is weaker than assumed in state-of-the-art rheology and that the constraint release is negligible. We expect that rings, as topological probes, will also grant direct access to molecular aspects of polymer motion which have been inaccessible until now within chains adhering to more complex architectures. [7]. Furthermore, in the fields of material science and engineering, blends of different polymer architectures including rings are employed aiming to produce polymer materials with emerging properties [8,9]. Recently, simulation science in particular led to new insights into ring dynamics on a coarse grained level [10,11]. In chemistry, novel procedures have enabled the production of appreciable amounts of pure, well-defined rings [12][13][14][15][16] that in turn permit detailed physical investigations of their structure and dynamics.One of the important and fundamental goals of this broad approach is the understanding of entangled polymer dynamics far beyond the state-of-the-art standpoint. For cyclic polymers, reptation as well as the related relaxation through contour length fluctuations (CLFs) and constraint release (CR) are fully suppressed, requiring qualitatively different relaxation behavior in ring melts. The center of mass (c.m.) motion in such melts was found to be subdiffusive, characterized by a t 3=4 power law [17] which was understood in terms of the lattice animal theory [18] as well as in a recent approach of the diffusion of centrality [19]. Very recently the internal dynamics was also successfully addressed experimentally [17]: Rings relax via a combination of free internal loop-motion and loop migration. As a result, the mean-square displacement for internal segment motion follows a weak t 0.3 power law, a finding also supported by simulation [20].The unique ring topology also severely affects the ring structure and dynamics when blended with linear chains. Simulations showed that other than in the ring melts the ring conformation is close to Gaussian and no compaction is visible, at least in the range of ring concentrations below overlap [21]. On the other hand, rheological investigations display a very strong influence of small amounts of linear chains on the rheological response of a ring melt [22]. Threading linear chains through the rings crucially influences the long-range diffusion of rings [23,24], e.g., single-molecul...

Glass transition of polymers in bulk, confined geometries, and near interfaces

“…Further advancements on our comprehension of polymer dynamics came from the investigation of more complicated topologies, such as stars, combs, H-shaped polymers, and rings [22]. For example, the real diameter of the 'tube' of a polymer, a value obtained as the mean square displacement over which chains can relax before encountering an obstacle, has only been recently measured.…”

“…where C FKR is a temperature-invariant constant. equation (22) implies that the temperature dependence of τ and T g ther are identical. This FKR relation is at the base of the current view on the phenomenology of vitrification (T g ther ) coupled to an increase in τ upon cooling (T g dyn ).…”