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Controlling the mechanical behavior of novel supramolecular materials is of the utmost importance and requires a fundamental understanding of the underlying physical processes. We present a multimethods approach to the dynamics of entangled transient polyisoprene networks. Small-angle neutron scattering (SANS) on randomly functionalized chains shows homogeneous supramolecular melts with Gaussian chain conformations. The H-bond lifetimes (dielectric α*-process) and the rheological response in terms of the loss modulus G″ differ by 2 orders of magnitude in time. Within the concept of a compact random walk (RW), where the random walker (urazole group acting as a sticker) undergoes multiple returns to its starting point and following the concept of theoretical proposed renormalized sticky bond lifetimes, we quantitatively solve this longstanding and unexplained large discrepancy: While the bond opening gives rise to the dielectric response, for rheological relaxation the association with a new partner is rele...

By neutron spin echo spectroscopy, we have studied the center of mass motion of short tracer chains on the molecular length scale within a highly entangled polymer matrix. The center of mass mean square displacements of the tracers independent of their molecular weight is subdiffusive at short times until it has reached the size of the tube d; then, a crossover to Fickian diffusion takes place. This observation cannot be understood within the tube model of reptation, but is rationalized as a result of important interchain couplings that lead to cooperative chain motion within the entanglement volume ∼d^{3}. Thus, the cooperative tracer chain motions are limited by the tube size d. If the center of mass displacement exceeds this size, uncorrelated Fickian diffusion takes over. Compared to the prediction of the Rouse model we observe a significantly reduced contribution of the tracer's internal modes to the spectra corroborating the finding of cooperative rather than Rouse dynamics within d^{3}.

The structure and the dynamics of supramolecular comblike polymers in the melt state is studied by a combination of linear rheology, dielectric spectroscopy, and small angle neutron scattering. The system consists of blends of 1,2-polybutyleneoxide (PBO) entangled backbones, randomly functionalized with thymine (thy) and barely entangled PBO graft chains—modified with 2,4-diamino-1,3,5-triazine (DAT) end groups. These bioinspired groups associate into a transiently branched comb architecture through heterocomplementary interaction involving the two different hydrogen bonding groups thy and DAT. In the present manuscript, we focus on the comparison of the macroscopic dynamics of the associating blends and permanent comb analogs. The viscoelastic and dielectric response of covalent and reversible combs are found to be comparable. The viscoelastic response of mixtures of thy-functionalized entangled backbones and DAT-end-modified barely entangled chains show a relaxation mechanism, which is mostly attributed to the association/breakage dynamics of the transient bonds with characteristic time ∼1 s at T=−25 °C. In the parallel dielectric investigation, the reversible branched structure is still evident from the comparison with the corresponding permanent combs and allows the distinction between fixed arms relaxation and the lifetime. A α∗ process of the thy-thy association is likewise detected. The time scale of the supramolecular association makes the thy-DAT pair an ideal candidate for the development of responsive materials that combine permanent and transient linkages for novel applications and self-healing properties

We present a detailed small-angle neutron scattering investigation of mixtures of poly(ethylene oxide) (PEO)/polyhedral oligomeric silsesquioxane (POSS) hybrids, a popular nanofiller, addressing the conformation of the model-grafted nanoparticles as well as their influence on the linear polymer matrix in which they are embedded. The nanofiller has a well-defined graft arm length and is monomolecular. Because of the identical chemical nature of the grafted arm and matrix chains, it can be considered as an ideal athermal mixture. We have introduced a random phase approximation approach with general application possibilities for other grafted nanofillers, combining the star-like and particle-like characteristics of the POSS nanofiller. The size of the nanofiller remained unaffected and Gaussian upon mixing with linear chains of various lengths, and no aggregation of the nanofiller was observed. This turns the POSS-based nanocomposite into an interesting model compound. The mixtures of PEO chains with the oct...

We present results from very long (on the order of several microseconds) atomistic molecular dynamics (MD) simulations for the density, microscopic structure, conformation, and local and segmental dynamics of pure, strictly monodisperse ring and linear poly(ethylene oxide) (PEO) melts, ranging in molar mass from ∼5300 to ∼20 000 g/mol. The MD results are compared with recent experimental data for the chain center-of-mass self-diffusion coefficient and the normalized single-chain dynamic structure factor obtained from small-angle neutron scattering, neutron spin echo, and pulse-field gradient NMR, and remarkable qualitative and quantitative agreement is observed, despite certain subtle disagreements in important details regarding mainly internal ring motion (loop dynamics). A detailed normal-mode analysis allowed us to check the degree of consistency of ring PEO melt dynamics with the ring Rouse model and indicated a strong reduction of the normalized mode amplitudes for the smaller mode numbers (compared ...

We review some of our latest contributions in the field of neutron scattering of polymers with linear and non-linear architecture. On the one hand, the reviewed Small Angle Neutron Scattering investigations cover dilute mixtures of dendritic polymers and linear polymers that were investigated during relaxation after a fast step strain or in situ during a strain ramping. The focus was on the otherwise not accessible long time dynamics of the inner branches. The parameters of the model are those of the tube model and include the evolution of liberated chain ends, the size and time dependence of the confining tube diameter and branch-point related dynamics. The case of deformed tube diameters could be obtained from a permanently-linked network state as the limiting case of a deformed melt. On the other hand, recently, cyclic polymers as a special class of branched architectures showed to be of high significance to detect similar features directly from equilibrium measurements by means of quasi-elastic Neutron Spin Echo spectroscopy. We show that by means of polymer rings as a probe different aspects of the tube concept can be distinguished in a unique way.

We present a small angle neutron scattering (SANS) investigation of a blend composed of a dendritic polymer and a linear matrix with comparable viscosity in start-up of an elongational flow at T-g + 50. The two-generation dendritic polymer is diluted to 10% by weight in a matrix of a long well-entangled linear chains. Both components consist of mainly 1,4-cis-polyisoprene but differ in isotopic composition. The resulting scattering contrast is sufficiently high to permit time-resolved measurements of the system structure factor during the start-up phase and to follow the retraction processes involving the inner sections of the branched polymer in the nonlinear deformation response. The outer branches and the linear matrix, on the contrary, are in the linear deformation regime. The linear matrix dominates the rheological signature of the blend and the influence of the branched component can barely be detected. However, the neutron scattering intensity is predominantly that of the (branched) minority component so that its dynamics is clearly evident. In the present paper, we use the neutron scattering data to validate the branch point withdrawal process, which could not be unambiguously discerned from rheological measurements in this blend. The maximal tube stretch that the inner branches experience, before the relaxed outer arm material is incorporated into the tube is determined. The in situ scattering experiments demonstrate for the first time the leveling-off of the strain as the result of branch point withdrawal and chain retraction directly on the molecular level. We conclude that branch point motion in the mixture of architecturally complex polymers occurs earlier than would be expected in a purely branched system, presumably due to the different topological, environment that the linear matrix,presents to the hierarchically deep-buried tube sections.

A new dual network elastomer is developed that consists of polybutadiene crosslinked with both permanent and transient bonds. The transient network is formed by the association of urazole groups that are randomly attached to the polymer backbone. Subsequent orthogonal covalent crosslinking through hydrosilylation in the melt state leads to a dual network with variable permanent and transient crosslinking density. Small angle neutron scattering (SANS) investigations show a homogeneous distribution of the transient bonds in both the functionalized polymers and the dual network products. The enhanced mechanical properties of the dual networks compared to conventional polybutadiene elastomers are characterized by stress–strain measurements. The increased toughness can be explained by a protective mechanism where the weaker supramolecular bonds act as sacrificial bonds that dissipate energy.

We present a structural and dynamic study on the simplest supramolecular hetero-association, recently investigated by the authors to prepare architectural homogeneous structures in the melt state, based on the bio-inspired hydrogen-bonding of thymine/diaminotriazine (thy&ndash, DAT) base-pairs. In the combination with an amorphous low Tg poly(butylene oxide) (PBO), no micellar structures are formed, which is expected for nonpolar polymers because of noncompatibility with the highly polar supramolecular groups. Instead, a clear polymer-like transient architecture is retrieved. This makes the heterocomplementary thy&ndash, DAT association an ideal candidate for further exploitation of the hydrogen-bonding ability in the bulk for self-healing purposes, damage management in rubbers or even the development of easily processable branched polymers with built-in plasticizer. In the present work, we investigate the temperature range from Tg + 20 &deg, C to Tg + 150 &deg, C of an oligomeric PBO using small-angle X-ray scattering (SAXS) and linear rheology on the pure thy and pure DAT monofunctionals and on an equimolar mixture of thy/DAT oligomers. The linear rheology performed at low temperature is found to correspond to fully closed-state dimeric configurations. At intermediate temperatures, SAXS probes the equilibrium between open and closed states of the thy&ndash, DAT mixtures. The temperature-dependent association constant in the full range between open and closed H-bonds and an enhancement of the monomeric friction coefficient due to the groups is obtained. The thy&ndash, DAT association in the melt is more stable than the DAT&ndash, DAT, whereas the thy&ndash, thy association seems to involve additional long-lived interactions.

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.

We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes, and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts η0,linear to their ring counterparts η0,ring at isofrictional conditions is discussed as a function of the number of entanglements Z. In the unentangled regime η0,linear/η0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation η0,linear/η0,ring = 2. In the entanglement regime, the Z-dependence of ring viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1 < Z < 20, η0,linear/η0,ring Z1.2±0.3, is weaker than the scaling prediction (η0,linear/η0,ring Z1.6±0.3) and the simulations (η0,linear/η0,ring Z2.0±0.3). Nevertheless, the present collection of state-of-the-art experimental data unambiguously demonstrates that rings exhibit a universal trend clearly departing from that of their linear counterparts, and hence it represents a major step toward resolving a 30-year-old problem.

In this work we present a combined analysis of small-angle neutron scattering, linear rheology and pulsed field gradient nuclear magnetic resonance spectroscopy experiments on the supramolecular association and chain structure of well-defined telechelically modified poly(ethylene glycol) (PEG) in the bulk. Oligomeric PEG was functionalized with directed heterocomplementary hydrogen-bonding end-groups, thymine (Thy) and diaminotriazine (DAT). The polarity of the backbone polymer is comparable to the end groups and avoids clustering of the groups basing on energetic arguments. Their linear association behavior in the ideal melt state was investigated on the microscopic/molecular level as a function of temperature. By means of a selective labeling scheme, which should ideally lead to the formation of alternating hydrogeneous-deuterated building block sequences if the hydrogen bonding reaction is exclusively heterocomplementary, we showed that the Thy–DAT association is dominant and a Thy–Thy homoassociation ...

We revisit the nonuniversal aspect of polymer dynamics by considering both new and existing data on the zero-shear viscosity and linear viscoelastic response of various polymers, each with a wide range of molecular weights. Analysis of the zero-shear viscosity data in terms of the packing length p, whose role in entanglements has been discussed previously by Fetters and co-workers, reveals a behavior that is irreconcilable with our current understanding based on the tube model. Specifically, we find that the transition regime between Rouse and pure reptation dynamics, currently understood as the regime where contour length fluctuations are active, systematically shrinks as the packing length of the polymer increases. Further, we find that the slope of the loss moduli in the high-frequency wing of the terminal peak of well-entangled systems also decreases from the common −0.25 to −0.125 with increasing p. This is contrary to the single expected value of −0.25 from tube models which include contour length f...

Considering topology among all polymer architectures polymer rings are unique, as they are the simplest closed structures without ends. In this review we present recent experimental advances addressing the structure and dynamics of rings. We focus mainly on neutron scattering results that reveal experimental insight on a molecular scale. We first briefly reflect on the progress in ring chemistry that made the experimental access possible. Structural investigations characterizing rings as compact objects in the melts are put into theoretical context. In contrast to the plateau regime common for all other high molecular weight polymer systems, the dynamic modulus of pure ring systems is characterized by a power law decay, while the viscosity displays a much weaker molecular weight dependence as a corresponding linear melt. The dynamics of ring melts is uniquely addressed by neutron spin-echo spectroscopy. The sub-diffusive center of mass motion at short times agrees well with simulation as well as theoretical concepts. In the internal dynamics the basic length scale of the ring molecule, the loop size, manifests itself clearly. The experiments reveal strong evidence for loop motions and call for further theoretical work describing them. Finally, small fractions of ring molecules in linear melts turn out to be very sensitive probes in order to scrutinize the dynamics of the host with the potential to reveal fundamental aspects of the dynamics of branched polymer systems.

We present a neutron scattering analysis of the structure and dynamics of PEO polymer rings with a molecular weight 2.5 times higher than the entanglement mass. The melt structure was found to be more compact than a Gaussian model would suggest. With increasing time the center of mass (c.o.m.) diffusion undergoes a transition from sub-diffusive to diffusive behavior. The transition time agrees well with the decorrelation time predicted by a mode coupling approach. As a novel feature well pronounced non-Gaussian behavior of the c.o.m. diffusion was found that shows surprising analogies to the cage effect known from glassy systems. Finally, the longest wavelength Rouse modes are suppressed possibly as a consequence of an onset of lattice animal features as hypothesized in theoretical approaches.

We present a small angle neutron scattering (SANS) study of the association of heterocomplementary telechelic polypropylene glycol (PPG) polymers, bearing either diaminotriazine (DAT) or thymine (Thy) stickers as end-groups, both in the melt and in dilute solution. The SANS data are critically examined for the architecture and morphology as well as relative extent of linear assembly in the apolar solvent toluene. A random phase approximation (RPA) approach, adapted for a supramolecularly assembled multiblock copolymer is presented, which allows to extract the interaction parameters between the constituents and the medium. From the proposed approach, which describes very well heterocomplementary hydrogen-bonding telechelic polymers in both diluted toluene solution and in the melt, we conclude that linear association prevails.

Supramolecular groups in polymeric systems lead to responsive materials which are ideally suited for applications in dynamic environments. The key to their advanced properties such as shape-memory or self-healing is the reversibility of secondary interactions which can be triggered by external stimuli such as temperature, light, or pH-value. Controlling the (mechanical) behavior of such systems requires a precise understanding of intrinsic properties. We present a multimethod study of transient polyisoprene networks that were functionalized with different amounts of hydrogen bonding urazole groups. This work aims at understanding rich rheological features on the basis of their microscopic origin. First, the thermorheological simple behavior is validated experimentally. Subsequently, we characterize the underlying microscopic processes by broadband dielectric spectroscopy (α-process and α∗-process), differential scanning calorimetry (glass transition behavior), and Fourier-transform infrared spectroscopy (thermodynamics of group association/dissociation). Based on these results, the influence of the supramolecular groups on the rheological response is analyzed. The observed features such as the onset of elastomeric properties in the flow regime, a drastic increase in the chain relaxation time with an increasing amount of functional groups, and the occurrence of a second rheological relaxation process, which is the most prominent effect, are discussed and related to their physical origin.

The combination of dielectric and mechanical spectroscopies is very powerful. However, it is not quite clear in your paper how the time scales of your supramolecular combs compare from these two spectroscopies. Maybe you can make a plot of the temperature dependence of the time scales for arm retraction and for terminal relaxation that are obtained by these two methods? That would really help the reader understand not only how they compare but what temperature ranges can be studied for these two vital time scales....

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 (NSE) spectroscopy and a labeling scheme unique to neutron scattering the motion of a labeled branch point of a three-arm polyethylene star has been observed on a molecular level. The measured dynamic structure factor shows a clear transition to a plateau, signifying the stronger confinement of the star center in comparison to a corresponding center labeled linear chain. A shortening of one star arm to about only one entanglement length leads to the same topological confinement as for the symmetric star within the accessible time range of NSE. This reflects a stronger effect of such a small branch than expected and is consistent with rheological measurements on the same system.

We present a systematic investigation of well-characterized, experimentally pure polystyrene (PS) rings with molar mass of 161 000 g/mol in dilute solutions. We measure the ring form factor at θ - and good-solvent conditions as well as in a polymeric solvent (linear PS of roughly comparable molar mass) by means of small-angle neutron scattering (SANS). Additional dynamic light scattering (DLS) measurements support the SANS data and help elucidate the role of solvent quality and solution preparation. The results indicate the increase of ring dimensions as the solvent quality improves. Furthermore, the experimental form factors in both θ -solvent and linear matrix behave as ideal rings and are fully superimposable. The nearly Gaussian conformations of rings in a melt of linear chains provide evidence of threading of linear chains through rings. The latter result has implications for the dynamics of ring-linear polymer mixtures.

In this work, an investigation of the hydrogen-bonding mechanism in a transiently branched comb-like polymer system in the melt is reported. The system under investigation consists of a polybutylene oxide (PBO)-based backbone, randomly functionalized with thymine (thy) groups, in combination with shorter PBO graft chains, end-functionalized with diaminotriazine (DAT) groups. The functional groups are able to associate through hydrogen bonding. The heterocomplementary association of these groups leads to the formation of a transiently branched comb-like polymer system. Since recently virtually exclusive heterocomplementary association could be observed in the supramolecular association of telechelically modified oligomeric PEG chains, here we aim to extend the supramolecular assembly mechanism toward branched structures. The present work combines small angle neutron scattering (SANS) experiments on a selectively labeled system with macroscopic dynamics measured in linear rheology response. The association of thy- and DAT-modified components was studied as a function of temperature and composition. The scattering function reveals the formation of a block copolymer and can be exclusively attributed to heterocomplementary association of the hydrogen-bonding groups. Scattering functions of nonfunctionalized blends are also reported as references and evidence the change in the microstructure induced by the heterocomplementary association. All scattering profiles were described by means of the random phase approximation (RPA) formalism from which the average aggregation number, i.e., comb arm functionality and the equilibrium association constant could be determined directly in the melt state as a function of temperature. On the other hand, rheological measurements were performed in the melt state to study the influence of the reversible bonds on the macroscopic dynamics of the polymer system. The rheology data are in good agreement with the SANS results and confirm the transient comb-like branched architecture. The supramolecular association exhibits characteristic bonding times of the groups in the order of 1 s at −25 °C and therefore makes the thy–DAT pair an ideal candidate for the development of responsive materials that combine permanent and transient linkages for novel applications and self-healing properties.

We have studied the motion of polyhedral oligomeric silsesquioxane (POSS) nanoparticles modified with poly(ethylene glycol) (PEG) arms immersed in PEG matrices of different molecular weight. Employing neutron spin echo spectroscopy in combination with pulsed field gradient (PFG) NMR we found the following. (i) For entangled matrices the center of mass mean square displacement (MSD) of the PEG-POSS particles is subdiffusive following a ${t}^{0.56}$ power law. (ii) The diffusion coefficient as well as the crossover to Fickian diffusion is independent of the matrix molecular weight and takes place as soon as the center of mass has moved a distance corresponding to the particle radius---this holds also for unentangled hosts. (iii) For the entangled matrices Rubinstein's scaling theory is validated; however, the numbers indicate that beyond Rouse friction the entanglement constraints appear to strongly increase the effective friction even on the nanoparticle length scale imposing a caveat on the interpretation of microrheological experiments. (iv) The oligomer decorated PEG-POSS particles exhibit the dynamics of a Gaussian star with an internal viscosity that rises with an increase of the host molecular weight.

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.

In entangled polymer melts, contour length fluctuations are supposed to lift the chain confinement starting from the chain ends. Using neutron spin echo spectroscopy on polyethylene chains of intermediate length, where only the center part is labeled, allows us to separate the contribution of contour length fluctuations to the dynamic structure factor and thereby explicitly prove the effect on a molecular level. While a corresponding fully labeled chain shows the relaxation by contour length fluctuations additional to the primary relaxation, the data of the center-labeled chain, where the visibility of the fluctuations is switched off, is in excellent agreement with results for a nearly infinite long chain, where contour length fluctuations are known to be negligible.

We present a static and quasi-elastic neutron scattering study on both the structure and dynamics of a ring polymer in a ring and linear polymer melt, respectively. In the first case, the ring structure proved to be significantly more compact compared to the linear chain with the same molecular weight. In the mixture, the ring molecules swell as was confirmed by small angle neutron scattering ( SANS) in accordance with both theory and simulation work. The dynamical behavior of both systems, which for the first time has been explored by neutron spin echo spectroscopy (NSE), shows a surprisingly fast center of mass diffusion as compared to the linear polymer. These results agree qualitatively with the presented atomistic MD simulations. The fast diffusion turned out to be an explicit violation of the Rouse model.

Neutron scattering accesses the space time evolution of molecular motion on atomistic length and time scales covering all dynamical processes from local relaxations to overall chain diffusion. Using the dynamics of a chain in the melt as an example, we review results obtained by the various high resolution neutron scattering techniques and outline future opportunities.

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.

The interaction between low frequency localized modes and sound waves in glasses is treated in terms of the simplest possible model, namely a single elastic dipole proportional to the displacement of the localized mode. The approximation makes it possible to calculate the contribution of the localized mode to the inelastic coherent neutron or X-ray scattering with relatively small momentum transfer. The connection to the classical second moment sum rule is discussed.

The methyl halides belong to the simplest organic molecules that contain CH3 groups. The lattice dynamics of these molecules were modeled recently based on the exact crystallographic structure and transferable pair potential parameters. Experiments were done using the NEAT spectrometer at BENSC, HMI, Germany and the BSJ spectrometer at FZJ, Germany to obtain values for the individual activation energy. The experimental values for the activation energies were used to refine the Fourier parameters of the individual rotational potential. Experimentally determined activation energies for all molecules, but the methyl fluoride, agree with single particle model predictions.

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.

We present neutron spin echo experiments that address the much debated topic of dynamic phenomena in polymer melts that are induced by interacting with a confining surface. We find an anchored surface layer that internally is highly mobile and not glassy as heavily promoted in the literature. The polymer dynamics in confinement is, rather, determined by two phases, one fully equal to the bulk polymer and another that is partly anchored at the surface. By strong topological interaction, this phase confines further chains with no direct contact to the surface. These form the often invoked interphase, where the full chain relaxation is impeded through the interaction with the anchored chains., The support of the DFG Priority Program SPP1369 Polymer-Solid Contacts: Interfaces and Interphases is gratefully acknowledged. A. A. and J. C. acknowledge financial support from Projects No. MAT2007-63681 and No. IT-436-07 (G.V.). The research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.

Incoherent neutron-spin-echo spectroscopy (NSE) has been employed to directly determine the time-dependent mean-squared segment displacement 〈 x ( t ) 2 〉 of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. The predicted transition of the time dependence of 〈 x ( t ) 2 〉 from 〈 x 2 〉∝ t 1/2 to ∝ t 1/4 is clearly corroborated by the incoherent NSE results.

The close comparison of linear rheology data of some long-chain polymer melts with the reptation model indicates the existence of additional degrees of freedom limiting the topological chain confinement. As one candidate contour length fluctuations (CLF) were proposed and indeed account for the observed power law in the dynamic loss modulus G ″( ω ). In order to study these mechanisms on a microscopic scale we have performed neutron spin echo investigations of the single-chain dynamic structure factor from polyethylene (PE) melts over a large range of chain lengths. A systematic loosening of the confinement with decreasing chain length is found and can be described quantitatively by the effect of CLF on the confining tube establishing this mechanism on a molecular level in space and time.

The position and strength of the boson peak in silica glass vary considerably with temperature $T$. Such variations cannot be explained solely with changes in the Debye energy. New Brillouin scattering measurements are presented which allow determining the $T$-dependence of unrelaxed acoustic velocities. Using a velocity based on the bulk modulus, scaling exponents are found which agree with the soft-potential model. The unrelaxed bulk modulus thus appears to be a good measure for the structural evolution of silica with $T$ and to set the energy scale for the soft potentials., Accepted for publication in Physical Review Letters

The dynamics of linear polymer chains in the melt depends strongly on the chain length: for short, unentangled chains, the dynamics is determined by a balance of viscous and entropic forces; for long chains, topological constraints are dominant. In this chapter, the experimental exploration of chain dynamics is introduced and discussed in detail. The focus is on neutron spin-echo (NSE) spectroscopy, which is one of the most powerful tools to explore the different dynamic regimes in polymer melts on a microscopic scale. It allows direct observation of the transition from a regime of free relaxation at short times, which can be described in terms of the Rouse model, to constrained motion at longer times. The constrained motion is caused by the entanglements that emerge in long-chain polymer systems. The tube concept models these topological confinements by assuming the chain to be confined in a virtual tube formed by adjacent chains. This concept of chains reptating in a tube is strongly supported by experiments in the limit of long chains. However, there is also strong experimental evidence that the tube model starts to fail if the polymer chains become shorter. In this regime of intermediate chain length, neither the Rouse model nor the pure reptation concept are applicable. A close comparison of linear rheology data with the predictions of the reptation model indicates the existence of additional degrees of freedom that release the topological confinement. Fluctuating chain ends that destroy the tube confinement starting from both ends were proposed as one candidate. This process, called contour length fluctuations (CLF), indeed accounts for the observed behavior of the mechanical relaxation function. In this chapter, we present a systematic study of this mechanism on a microscopic scale.

A close inspection of neutron spectra of glass formers in the frequency region above the boson peak does not show the constant eigenvalue density expected for a random dynamical matrix, but a slow decrease towards higher eigenvalues. In 1,4-polybutadiene and selenium, the slope becomes steeper with increasing temperature in the undercooled liquid, suggesting an influence of the vibrational entropy. One can describe the behaviour quantitatively in terms of a balance between level repulsion (from the randomness of the dynamical matrix) and vibrational entropy. On the basis of this evidence, the boson peak must be a crossover from such a balance at higher frequencies to a mixture of sound waves and additional excitations at low frequency., Letter, 4 pages, 4 figures, 24 references

We present a neutron scattering investigation on a miscible blend of two polymers with greatly different glass-transition temperatures Tg. Under such conditions, the nearly frozen high-Tg component imposes a random environment on the mobile chain. The results demand the consideration of a distribution of heterogeneous mobilities in the material and demonstrate that the larger scale dynamics of the fast component is not determined by the average local environment alone. This distribution of mobilities can be mapped quantitatively on the spectrum of local relaxation rates measured at high momentum transfers.

The three isomeric dimethylxanthines and trimethylxanthine are studied by neutron spectroscopy up to energy transfers of 100 meV at energy resolutions ranging from 0.7 microeV to some meV. The loss of elastic intensity with increasing temperature can be modeled by quasielastic methyl rotation. The number of inequivalent methyl groups is in agreement with those of the room temperature crystal structures. Activation energies are obtained. In the case of theophylline, a doublet tunneling band is observed at 15.1 and 17.5 microeV. In theobromine, a single tunneling band at 0.3 microeV is found. Orientational disorder in caffeine leads to a 2.7 microeV broad distribution of tunneling bands around the elastic line. At the same time, broad low energy phonon spectra characterize an orientational glassy state with weak methyl rotational potentials. Librational energies of the dimethylxanthines are clearly seen in the phonon densities of states. Rotational potentials can be derived which explain consistently all observables. While their symmetry in general is threefold, theophylline shows a close to sixfold potential reflecting a mirror symmetry.

The dynamics of binary polymer blends of few labeled long chains in successively shorter matrix chains has been investigated by neutron spin echo (NSE) spectroscopy. For the first time the effect of constraint release on the chain relaxation has been directly observed on a microscopic scale. Decreasing the matrix chain length reduces the topological confinement until unconfined Rouse motion is observed, when the matrix chains are too short to confine the long chain in a tube. Whereas an analytical description of the effect is not yet available, a new simulation based on the slip-link model shows perfect agreement with the NSE data over the full range of matrix molecular weights.

We derive an energy landscape interpretation of dielectric relaxation times in undercooled liquids, comparing it to the traditional Debye and Gemant-DiMarzio-Bishop pictures. The interaction between different local structural rearrangements in the energy landscape explains qualitatively the recently observed splitting of the flow process into an initial and a final stage. The initial mechanical relaxation stage is attributed to hopping processes, the final thermal or structural relaxation stage to the decay of the local double-well potentials. The energy landscape concept provides an explanation for the equality of thermal and dielectric relaxation times. The equality itself is once more demonstrated on the basis of literature data for salol., Comment: 7 pages, 3 figures, 41 references, Workshop Disordered Systems, Molveno 2006, submitted to Philosophical Magazine

The dynamics of polymers in nanoconfinement was studied by using neutron spectroscopy. A number of pronounced effects on different time and length scales for the polymers confined in nanopores of anodic aluminium oxide were observed. Local segmental dynamics was found to be dependent on the type of the interaction between the solid pore wall and polymer: attractive interactions lead to the formation of a surface layer with the dynamics slowed down as compared to the dynamics of pure polymer; neutral/repulsive interaction do not change the local dynamics. Attractive interactions cause anchoring of polymer segments on the surface creating an interphase between the polymer in close vicinity to the solid surface and pure polymer. In addition, at strong confinement conditions the dilution of the entanglement network is observed. mesh sizes were even found to lead to a non-monotonic behaviour of the chain relaxation with confinement size (10). The strong confinement effect (so-called corset effect) was concluded from NMR relaxometry studies performed on poly(ethylene oxide) confined in solid methacrylate matrix. A reduction of the effective tube diameter of the Doi-Edwards reptation model in confined polymer by about one order of magnitude as compared to the bulk has been reported (11). These results have been suggested to be the consequence of a number of combined effects: polymer-surface interaction, the mutual uncrossability of polymer chains (entanglements) and confinement geometry. In this paper we present a review of recent microscopic investigations of the dynamics of different polymer melts embedded in nanopores of anodic aluminium oxide (AAO) or Alumina nanopores by means of neutron scattering.

We report a direct determination of the time dependent mean-squared segment displacement of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. This has been achieved by a neutron spin-echo (NSE) measurement of the segmental self-correlation function as conveyed by the spin-incoherent scattering from two fully protonated polymer melts, polyethylene and polyethylene propylene. Within the scenario of de Gennes reptation model a transition of the time dependence of segmental mean-squared displacements from proportional, variant t(1/2) to proportional, variant t(1/4) is expected and clearly corroborated by the incoherent NSE results.

As will be made very conspicuous by the computer simulations shown in Sect. 4.2, glass structure is not unique but cooling-rate dependent. This gives a theoretical explanation for the long-established finding that the glass properties are cooling-rate dependent, too.

It is known since a decade that polyethylene shows a characteristic deviation from the Rouse dynamics, i.e. pronounced entanglement effects, now observable in neutron spin-echo (NSE) spectroscopy as a plateau at high Fourier times t . Earlier spin-echo data were limited to t =20–40 ns and could only determine entanglement distances but not decide between competing models. The now available time range up to 200 ns and more at the IN15 (ILL) NSE spectrometer allowed to distinguish the various models and to decide in favour of de Gennes’ Reptation model. In this model the restriction of motion originates from a trapping of the chains in a virtual tube. We present a series of new NSE-data from PE-melts at 509 K with different molecular weights between M w =12 000 g / mol and M w =190 000 g / mol extending to 170 ns that allow for the first time a systematic investigation of the reptation dynamics of PE-melts over a wide range of molecular weights.

Quasielastic neutron scattering experiments were carried out using the multichopper time-of-flight spectrometer V3 at the Hahn-Meitner Institut, Germany and the backscattering spectrometer at Forschungszentrum Julich, Germany. Activation energies for CH(3)X, X=F, Cl, Br, and I, were obtained. In combination with results from previous inelastic neutron scattering experiments the data were taken to describe the dynamics of the halides in terms of two different models, the single particle model and the coupling model. Coupled motions of methyl groups seem to explain the dynamics of the methyl fluoride and chloride; however, the coupling vanishes with the increase of the mass of the halide atom in CH(3)Br and CH(3)I.

The x-ray diffraction studies of the title complex were carried out at room temperature and 14 K for H/D (in hydrogen bridge) isotopomers. At 82 K a phase transition takes place leading to a doubling of unit cells and alternation of the hydrogen bond lengths linking tetramethylpyrazine (TMP) and chloranilic acid molecules. A marked H/D isotope effect on these lengths was found at room temperature. The elongation is much smaller at 14 K. The infrared isotopic ratio for O-H(D)...N bands equals to 1.33. The four tunnel splittings of methyl librational ground states of the protonated complex required by the structure are determined at a temperature T=4.2 K up to pressures P=4.7 kbars by high resolution neutron spectroscopy. The tunnel mode at 20.6 microeV at ambient pressure shifts smoothly to 12.2 microeV at P=3.4 kbars. This is attributed to an increase of the strength of the rotational potential proportional to r(-5.6). The three other tunnel peaks show no or weak shifts only. The increasing interaction with diminishing intermolecular distances is assumed to be compensated by a charge transfer between the constituents of deltae/e approximately 0.02 kbar(-1). The phase transition observed between 3.4 and 4.7 kbars leads to increased symmetry with only two more intense tunneling bands. In the isotopomer with deuterated hydrogen bonds and P=1 bar all tunnel intensities become equal in consistency with the low temperature crystal structure. The effect of charge transfer is confirmed by a weakening of rotational potentials for those methyl groups whose tunnel splittings were independent of pressure. Density functional theory calculations for the model TMP.(HF)2 complex and fully ionized molecule TMP+ point out that the intramolecular rotational potential of methyl groups is weaker in the charged species. They do not allow for the unequivocal conclusions about the role of the intermolecular charge transfer effect on the torsional frequencies.

Literature dielectric data of glycerol, propylene carbonate and ortho-terphenyl (OTP) show that the measured dielectric relaxation is a decade faster than the Debye expectation, but still a decade slower than the breakdown of the shear modulus. From a comparison of time scales, the dielectric relaxation seems to be due to a process which relaxes not only the molecular orientation, but the entropy, the short-range order and the density as well. On the basis of this finding, we propose an alternative to the Gemant-DiMarzio-Bishop extension of the Debye picture., Comment: 7 pages, 4 figures, 68 references; 3. version extended following referee advice