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A key ingredient within theories focusing on the rheology of entangled polymers is the way how the topological constraints of an entangled chain are lifted by unconstrained segments, i.e., how the constraining tube is dilated. This important question has been addressed by directly measuring the tube diameter $d$ at the scale of the tube by neutron spin echo spectroscopy. The tube diameter $d$ and plateau modulus ${G}_{N}^{0}$ of highly entangled polyethylene oxide (PEO) chains of volume fraction $c$ that are diluted by low molecular PEO show a concentration dependence $d\ensuremath{\propto}{c}^{a/2}$ and ${G}_{N}^{0}\ensuremath{\propto}{c}^{1+a}$ with an exponent $a$ close to $4/3$. This result allows the clear discrimination between different theoretical models that predict $4/3$ or other values between 1 and 2 and provides an important ingredient to tube model theories.

The chain and association dynamics of supramolecular polymer ensembles decisively determines their properties. Using neutron spin echo (NSE) spectroscopy we present molecular insight into the space and time evolution of this dynamics. Studying a well characterized ensemble of linearly associating telechelic poly(ethylene glycol) melts carrying triple H-bonding end groups, we show that H-bond breaking significantly impacts the mode spectrum of the associates. The breaking affects the mode contributions and not the relaxation times as was assumed previously. NSE spectra directly reveal the so far intangible H-bond lifetimes in the supramolecular melt and demonstrate that for both the microscopic and the macroscopic dynamics of the supramolecular ensemble the instantaneous average of the ${M}_{w}$ distribution governs the system response at least as long as the Rouse picture applies.

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.

We present neutron scattering data on the structure and dynamics of melts from polyethylene oxide rings with molecular weights up to ten times the entanglement mass of the linear counterpart. The data reveal a very compact conformation displaying a structure approaching a mass fractal, as hypothesized by recent simulation work. The dynamics is characterized by a fast Rouse relaxation of subunits (loops) and a slower dynamics displaying a lattice animal-like loop displacement. The loop size is an intrinsic property of the ring architecture and is independent of molecular weight. This is the first experimental observation of the space-time evolution of segmental motion in ring polymers illustrating the dynamic consequences of their topology that is unique among all polymeric systems of any other known architecture.

We present a one-to-one comparison of polymer segmental fluctuations as measured by small angle neutron scattering in a network under deformation with those obtained by neutron spin echo spectroscopy. This allows an independent proof of the strain dependence of the chain entanglement length. The experimentally observed nonaffine square-root dependence of the tube channel on strain is in excellent agreement with theoretical predictions and permits us to exclude an often invoked nondeformed as well as affinely deformed tube.

The process of retraction in entangled linear chains after a fast nonlinear stretch was detected from time-resolved but quenched small angle neutron scattering (SANS) experiments on long, well-entangled polyisoprene chains. The statically obtained SANS data cover the relevant time regime for retraction, and they provide a direct, microscopic verification of this nonlinear process as predicted by the tube model. Clear, quantitative agreement is found with recent theories of contour length fluctuations and convective constraint release, using parameters obtained mainly from linear rheology. The theory captures the full range of scattering vectors once the crossover to fluctuations on length scales below the tube diameter is accounted for.

The effect of topological constraints on the microscopic deformation of network chains in a statistically cross-linked rubber under uniaxial deformation is addressed by small-angle neutron scattering (SANS) on labeled paths in a network. The observed SANS patterns exhibit a pronounced transition from elliptical to lozengic shapes. Within a tube approach for the constraining potential the scattering function is calculated in the 2D detector plane. Excellent agreement between the statistical mechanical model and the experimental results is obtained.

We present a study on the temperature dependence of the microscopic entanglement distance, the chain dimension, and the plateau modulus of poly(ethylene propylene) alternating copolymer. The results provide insight into the microscopic origin of entanglement constraints and favor packing and scaling models over the topological approach. Furthermore, these results are at variance with one of the basic relations of the Doi-Edwards theory of viscoelasticity which unites the elastic response of a polymer melt with the entanglement distance.