Inelastic x-ray measurements of polybutadiene are reported, performed over a wide temperature range covering both the glass and the liquid phase. At each temperature, the frequency position Omega and the width Gamma of the inelastic peaks of the spectra have been obtained for different values of the scattering vector Q. A linear behavior of Omega(Q) for Q<4 nm(- 1) has been revealed, allowing the determination of the unrelaxed sound velocity upsilon(infinity). Consistently with the results obtained in different glass-forming systems, the Q dependence of Gamma is well represented by a Q(2) law. For Q>5 nm(-1) the values of Gamma overtake those of Omega and the acousticlike excitations progressively loose their propagative nature. In the glass, upsilon(infinity)(T) compares well with previous Brillouin Light Scattering (BLS) determinations, while in the liquid the BLS sound velocity shows a steeper temperature dependence related to the structural relaxation. The temperature behavior of the nonergodicity factor has been derived both from upsilon(o) and upsilon(infinity) (in the liquid phase) and from the ratio between elastic and inelastic intensities of inelastic x-ray scattering spectra (in the whole investigated temperature range). Both temperature and Q behavior of this quantity might be consistently interpreted in the framework of the mode coupling theory.

Neutron spin echo measurements were performed on polymeric micelles consisting of deuterated polystyrene (d-PS)- polyisoprene (PI) diblock copolymers in dilute and concentrated solutions. The scattering length density of the core of the micelles matched to the solvent so that dynamics of polymer chains in the corona were measured. The observed intermediate scattering functions in the dilute solution were analyzed by the theory for tethered chains proposed by de Gennes. In the concentrated solutions, motional slowing down was observed, which may be caused not only by increase of the viscosity but also by decrease of the osmotic compressibility. (C) 1999 Elsevier Science Ltd. All rights reserved.

The static structure factor S(Q) and the coherent dynamic structure factor S(Q,t) are calculated from molecular dynamics simulations of polyisoprene melts and compared with neutron scattering results [R. Zorn, D. Richter, B. Farago, B. Frick, F. Kremer, U. Kirst, and L. J. Fetters, Physica B 180&181, 534 (1992)]. Both the shape and the absolute time scale of the calculated S(Q,t) are consistent with experimental results. The decay of S(Q,t) can be almost entirely attributed to intramolecular dynamics throughout the Q range studied (1.2 less than or equal to Q less than or equal to 3.0 Angstrom(- 1)), i.e., the full S(Q,t) can be approximated by considering only the self terms and the cross terms localized to within a few repeat units along the chain. It was found that the factor of 5 observed between the dynamics at the first two peaks of S(Q) is part of a general trend largely independent of whether S(Q) is at a minimum or a maximum. A comparison of S(Q,t) in the region of the first peak in S(Q) and the P2C-H bond vector orientation autocorrelation function F-C(t) suggests that the same molecular motions influence both the neutron spin echo and NMR T-1 relaxation experiments. [S1063-651X(98)12712-5].

Diblock copolymers in the melt exhibit order-disorder phase transitions (ODT), which are accompanied by strong concentration fluctuations. These transitions are generally described in terms of the random phase approximation (RPA) of Leibler and Fredrickson, which is able to explain small angle scattering results in the neighborhood of the ODT, in particular around the correlation peak at q*. The RPA theory has been extended to include dynamical phenomena, predicting the short time relaxation of the dynamic structure factor in polymeric multicomponent systems. We report small angle neutron scattering and neutron spin echo experiments on polyethylene- block-polyethylethylene (PE-PEE) and poly(ethylene-propylene)- block-polyethylethylene (PEP-PEE) copolymers with molecular weights of 16.500 and 68.000 g/mol, which explore the structure and dynamics of these block copolymers. Studying melts with different hydrogen/deuterium labeling it was possible to observe experimentally the different relaxation modes of such systems separately. In particular the collective relaxation behavior as well as the single chain motion were accessed. The experimental results were quantitatively compared with the RPA predictions, which were based solely on the dynamical properties of the corresponding homopolymers and the static structure factors. The collective dynamics exhibits an unanticipated fast relaxation mode. This mode is most visible at low wave numbers (q greater than or equal to q*) but extends to length scales considerably shorter than the radius of gyration. Furthermore, the dynamical RPA yields expressions for the mobilities of chain segments in the block copolymer melt. These combination rules are at variance with the experimental findings for the single chain dynamics, while they hold for the collective response. (C) 1999 American Institute of Physics. [S0021-9606(99)52120-X].

We investigated the single chain motions of monodisperse polyisobutylene chains in the melt by neutron spin echo spectroscopy. Thereby a wide range in momentum space over a large dynamic range was covered. Motional processes from the center of mass diffusion, the Rouse dynamics to the more local relaxation processes which limit the validity of the standard Rouse model, were elucidated. The observed dynamic structure factors were analyzed in terms of relevant theoretical approaches addressing the limiting factors of the Rouse model. We found that other than claimed in the literature effects of local chain stiffness-they were treated in terms of the all rotational states model and a bending force model-cannot account for the experimental observations. It appears that additional damping effects related to an internal viscosity of the chain have to be involved, in order to explain the experimental results. (C) 1999 American Institute of Physics. [S0021-9606(99)50537-0].

We have investigated the dynamics of polymers in bimodal polyethylene (PE) melts in the transition region from Rouse- to reptationlike behavior by varying the mass fraction Phi(t) of long tracer chains (N approximate to 3N(e) or 4N(e)) in a short-chain matrix (N approximate to N-e=entanglement segment number) over the full concentration range. At short times (ns) the dynamic structure factor for single-chain relaxation was investigated by neutron-spin-echo (NSE) spectroscopy. To obtain information about the long-time (ms) dynamics the tracer diffusion coefficient (D-NMR) was measured by pulsed-field- gradient (PFG)-NMR. We discuss our NSE data within a mode analysis which includes the relaxation rates W-p of the independent normal modes of the internal chain dynamics and the center-of-mass diffusion coefficient D-NSE as model parameters. Only modes exceeding the Phi(t)-dependent length of a single entanglement strand N-e(Phi(t)) are found to be strongly hindered by topological constraints. The D-NSE are Phi(t)- independent and systematically faster than the strong concentration-dependent D-NMR, suggesting an effective time- dependent diffusion coefficient. The Hess model, which we have generalized for polydisperse melts, provides a time-dependent diffusion coefficient. Taking chain-end effects into account we get an excellent description of the NSE data. The mobility of the chain ends is much higher than the mobility of the inner segments resulting in an entanglement segment number which increases with decreasing tracer concentration. The concentration dependence of N-e(Phi(t)), as obtained from the mode analysis and the Hess model, is in agreement with our calculation within a self-consistent modification of the model by Kavassalis and Noolandi for entanglement formation. (C) 1999 American Institute of Physics. [S0021-9606(99)50520-5].

We have made detailed comparison of the local and chain dynamics of a melt of 1,4-polybutadiene (PBD) as determined from experiment and molecular dynamics simulation at 353 K. The PBD was found to have a random microstructure consisting of 40% cis, 50% trans, and 10% 1,2-vinyl units with a number-average degree of polymerization (X-n) = 25.4. Local (conformational) dynamics were studied via measurements of the C-13 NMR spin- lattice relaxation time T-1 and the nuclear Overhauser enhancement (NOE) at a proton resonance of 300 MHz for 12 distinguishable nuclei. Chain dynamics were studied on time scales up to 22 ns via neutron spin-echo (NSE) spectroscopy with momentum transfers ranging from q = 0.05 to 0.30 Angstrom(-1). Molecular dynamics simulations of a 100 carbon (X-n = 25) PBD random copolymer of 50% trans and 50% cis units employing a quantum chemistry-based united atom potential function were performed at 353 K. The T-1 and NOE values obtained from simulation, as well as the center of mass diffusion coefficient and dynamic structure factor, were found to be in qualitative agreement with experiment. However, comparison of T1 and NOE values for the various distinguishable resonances revealed that the local dynamics of the simulated chains were systematically too fast, whereas comparison with the center of mass diffusion coefficient revealed a similar trend in the chain dynamics. To improve agreement with experiment, (1) the chain length was increased to match the experimental M-z, (2) vinyl units groups were included in the chain microstructure, and (3) rotational energy barriers were increased by 0.4 kcal/mol in order to reduce the rate of conformational transitions. With these changes, dynamic properties from simulation were found to differ 20-30% or less from experiment, comparable to the agreement seen in previous simulations of polyethylene using a quantum chemistry-based united atom potential.

We present results of molecular dynamics simulations of an undercooled polymer melt, performed to study the validity of mode-coupling theory (MCT) for realistic polymer melts in general. The mean square displacements of the chain segments are computed to study the diffusion constant of the Rouse-like motion. It is shown that this diffusion constant follows a power law behavior as a function of the temperature, as predicted by the MCT. In addition, we studied the incoherent part of the intermediate scattering function and show that these functions obey the second scaling law of the MCT. We also calculated the relaxation times of the alpha-relaxation and found that they follow the same power law (gamma = 2.9) as the diffusion constant. Using gamma, and the relationships given by MCT, we obtain values for a (0.27) and b (0.46) and use these exponents to describe the beta-relaxation regime. We find that the long time part of the beta-relaxation can be described accurately by the Von Schweidler relaxation over a wide range of wave numbers. In the short time regime of the beta- relaxation, no critical decay is observed. [S1063- 651X(99)08111-8].

A model solution system of 1,4-polybutadiene in oligomeric butadiene of high vinyl content is studied to show how polymer friction dynamics depend explicitly on the solvent dynamics and are approximately determined by the overall glass transition temperatures of the solutions as a function of concentration (i.e., weight fraction phi) and temperature T. Among the most striking findings are the invariance of the overall molecular relaxation time with phi from phi = 1.0 to 0.3 at a special temperature To Below To, the solutions possess longer reptation times than that of the pure PBD melt. Moreover, through oscillatory shear measurements of linear viscoelasticity, the scaling of the tube dilation with phi is found rheologically as a proportional to phi(-2/3), which agrees with the previous neutron spin echo studies. Since viscoelastic properties of the entangled solutions reveal dynamics associated with the polymeric component, a general methodology is established here based on the present model system for characterization of component dynamics in miscible polymer blends.

In this paper we show that the concentration dependence of the plateau shear elastic modulus and of the viscosity can be understood if two lengths, the correlation length of concentration fluctuations and the tube diameter, are considered. To interpret the temperature variation of the viscosity and of the self-diffusion coefficient with the solvent quality, one has to take into account the local viscosity to which monomers are sensitive. This concentration dependent local viscosity, deduced from neutron spin-echo measurements, is independent of the polymer molecular weights, solvent viscosities and Theta temperatures. The local viscosity decreases to reach the solvent viscosity value at high temperature, that is, under good solvent conditions. The role of the macroscopic concentration on a local scale, seems to indicate that, in semidilute Theta solutions, the polymers are transparent to each other, as far as dynamic properties are concerned.

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism! does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints.

In 1997 the instrumental basis for neutron spin echo (NE) investigations of polymer dynamics was considerably enlarged as new and improved spectrometers became available. The scientific highlights include NSE studies on the segmental motion of polymers with various chain architectures in the liquid as well as in the solid state and a direct comparison of NSE findings with the results of molecular dynamics simulations.

We have investigated the dynamic structure factor for single- chain relaxation in a polyethylene melt by means of molecular dynamics simulations and neutron spin echo spectroscopy. After accounting for a 20% difference in the chain self-diffusion coefficient between simulation and experiment we find a perfect quantitative agreement of the intermediate dynamic structure factor over the whole range of momentum transfer studied. Based on this quantitative agreement one can test the experimental results for deviations from standard Rouse behavior reported so far for only computer simulations of polymer melt dynamics.

We present neutron spin-echo and dielectric results on the local dynamics of polyisobutylene. The dielectric spectra reveal the existence of a so far unknown secondary relaxation process being distinctly different to previous theoretical predictions. Neutron spectra have been taken over a large range in momentum transfer Q and temperature. At the Q value of the first structure factor maximum the dynamic pair correlation function is selective for interchain motions. There the neutron spectra display the same temperature dependence and shape as the classical rheological data taken in the terminal zone and do not follow the temperature laws based on spectroscopic results. A quantitative evaluation combining the information content of the dielectric and neutron results reveals a small stepwidth of 0.5-0.9 Angstrom involved in the secondary process. The alpha process is diffusive and follows the Gaussian approximation resulting in a sublinear time development of associated mean squared displacements.

The dynamic structure factor S(q, t) of polyethylene (PEB-2) was measured by neutron spin echo in the Fourier time range of t = 0.3-175 nsec and for momentum transfers q between 0.05 and 0.145 Angstrom(-1) to test the validity of competing phenomenological theories of relaxation in polymer melts. Previous spin-echo experiments limited to t < 25 nsec were equally well described by a variety of models. This ambiguity has now been lifted, and the experiment clearly favors the reptation model, showing that the dominant relaxation mechanism in entangled linear polymers is via reptation.

We present a united atom force field for simulations of 1,4- polybutadiene based on ab initio quantum chemistry calculations on model molecules. The geometries and energies of conformers and rotational energy barriers in model alkenes and dienes have been determined from high-level quantum chemistry calculations. A rotational isomeric state (RIS) model for 1,4-polybutadiene based on the conformer geometries and energies of the model molecules has been derived. The characteristic ratio and its temperature dependence for cis-1,4-polybutadiene and trans-1,4- polybutadiene, and the characteristic ratio of a random copolymer of cis and trans units, as predicted by tile RIS model, are in good agreement with experimental values, thereby supporting the accuracy of the quantum chemistry calculations. Torsional potentials fur the united atom force field have been parametrized to reproduce the quantum chemistry conformer energies and rotational energy barriers for rotations about the C(sp(2))-C(sp(2)), C(sp(2))-C(sp(3)), and C(sp(3))-C(sp(3)) dihedrals for the model compounds. The CH2-CH2 united atom nonbonded potential has been taken from previous work on polyethylene melts, while the CH-CH united atom nonbonded potential has been parametrized so as to reproduce the energies of chose conformers of the model molecules involving conformation-dependent second-order interactions. Finally, NPT molecular dynamics simulations have been performed on a melt of 1,4-poly(cis(0.5)-r-trans(0.5)butadiene). and the CH2-CH nonbonded potential has been adjusted so that the experimental melt density of the polymer as a function of temperature is accurately reproduced.

The local dynamics of 1,4 polybutadiene below and above the merging of the alpha- and beta-relaxations have been investigated by means of Neutron Spin Echo. At temperatures below the merging, the dynamic structure factor can be described by considering localized motions on a length scale of 1.5 Angstrom for the beta-process with the barrier distribution obtained from dielectric spectroscopy. Above the merging of the alpha- and beta-relaxations, the experimental data have been successfully described by assuming that both processes are statistically independent.

Dynamical properties of vulcanized polymer networks are addressed via a Rouse-type model that incorporates the effect of permanent random cross-links. The incoherent intermediate scattering function is computed in the sol and gel phases, and at the vulcanization transition between them. At any nonzero cross-link density within the sol phase Kohlrausch relaxation is found. The critical point is signaled by divergence of the longest time scale, and at this point the scattering function decays algebraically, whereas within the gel phase it acquires a time-persistent part identified with the gel fraction. [S0031-9007(97)04323-8].

This paper deals with mixtures of homopolymers and copolymers in solvents under the zero average contrast condition. This condition is chosen in order to decouple the correlations due to polymer composition fluctuations from those due to polymer concentration fluctuations. This makes the measurement of these correlations much easier using techniques based on static light scattering, photoncorrelation spectroscopy, small angle neutron scattering, neutron spin echo or X-ray scattering. In the first part of the paper, a simple theoretical framework is developed to present the guidelines for the interpretation of the scattering data. In the second part, some experimental examples are discussed using the scattering techniques mentioned above. Data obtained from various systems involving alike (deuterated and ordinary) homopolymers and diblock copolymers as well as unalike species are considered. An example of mixtures of polyelectrolytes in aqueous solutions is also discussed within the framework of the zero average contrast condition. (C) 1997 Elsevier Science Ltd.

Experimental heat capacity, dielectric, and shear spectroscopy data are reported on the alpha beta splitting region of poly(n- octyl methacrylate). New facets of a major difference between the high-temperature alpha relaxation at frequencies above the alpha beta splitting region and the ordinary alpha relaxation below are obtained: An alpha cooperativity onset in the splitting region and dominance of Rouse-Zimm-like modes R for the alpha relaxation. The alpha and alpha relaxations are not related by temperature-time superposition.

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. (C) 1997 John Wiley & Sons, Inc.

Neutron spin echo (NSE) spectroscopy, an advanced high- resolution quasi-elastic neutron scattering technique, provides the unique opportunity to investigate long-range relaxation processes of macromolecules simultaneously in space and time on nano-scales. In particular, information on the single-chain behavior is not restricted to dilute solutions, but may also be obtained from concentrated solutions and melts, if labelling by proton deuterium exchange is used. Thus, this method facilitates a direct microscopic study of molecular models developed to explain the macroscopic dynamic properties of polymers, e.g. transport and viscoelastic phenomena. This article gives a short outline of the method and reviews the relevant experimental results obtained from polymer melts and networks and from dilute and semi-dilute solutions of chain molecules with different architectures since the first successful NSE work on polymers was published in 1978. The experimental observations are compared with the predictions of the related microscopic models and other theoretical approaches, which are briefly introduced and adapted accordingly.

We report results of a molecular dynamics simulation of an ''isotope'' mixture of polymer chains, which are represented by a standard bead-spring model, and whose two species differ only by their monomer masses. Detailed analysis of the Rouse modes shows that for sufficiently short (non-entangled) chains this system can be well described by the Rouse model. Each species is described by its individual monomeric friction coefficient, whose dependence on both mass ratio as well as mixing ratio is studied. The main effect of mixing is an acceleration of the slower chains and a slowdown of the faster ones, while both species remain dynamically different. Some microscopic insight into the mechanism is obtained by studying the short-time behavior of the monomeric velocity autocorrelation function. Studies in the slightly entangled regime (chain length up to N = 150, where the typical entanglement chain length is N-e approximate to 35) seem to further corroborate the hypothesis that the ''tube diameter'' of the reptation model is a quantity which results mainly from the static configurations, i.e., is an equilibrium thermal average. The usefulness of recently suggested analysis methods in this regime is briefly discussed. (C) 1997 American Institute of Physics. [S0021-9606(97)52141- 6].

This short review presents quasielastic neutron scattering and dielectric experiments on the alpha and beta(slow) relaxation in polybutadiene. Exploiting the momentum transfer dependent dynamic structure factor, spatial information about the underlying molecular motions is obtained. While the beta(slow) process reveals itself as a local jump with average jump distances of about 1.5 Angstrom, the alpha relaxation is diffusive and occurs statistically independently from the beta(slow) process. With this result a consistent interpretation of dielectric spectra on the same polymer is achieved.

One of the basic problems in the dynamics of polymers concerns the importance of geometrical or topological interactions which are directly related to the large scale molecular structures. In the famous reptation model these constraints are pictured in terms of a tube of localization following the average chain profile and confining the chain motion to the curve-linear tube. Recently studying the dynamic structure factor of a single labeled chain in a polymer melt by means of neutron spin echo spectroscopy (NSE) led to a direct observation of these tube constraints. Here I shall summarize these neutron spin echo experiments. I shall address the NSE technique, present results on the entropy driven segmental chain dynamics, discuss the dynamics of single chains in the melt where the chain length is increased through the transition to ''reptation'' dynamics and display NSE measurements on long chain systems which revealed the molecular existence of the entanglement distance. Their magnitudes agree very well with tube diameters derived from dynamical mechanical measurements on the basis of the reptation model proving thereby the basic assumption of this Nobel Price winning concept.

We report neutron spin echo experiments on the momentum (Q) and time (t)-dependent dynamic structure factor S(Q, t) from the glass-forming polymers polyisobutylene (PIB) and polybutadiene (PB). Performing measurements in a Q-range encompassing the first and second structure factor peaks, we are able to separate inter and intrachain relaxations and to assign the secondary Johari-Goldstein beta-relaxation to an intrachain relaxation. While for PB this process exhibits average motional amplitudes of about 1.5 Angstrom, the underlying jump distances for PIE are much smaller (0.6 Angstrom). The structural alpha- relaxation is characterized as an interchain process displaying anomalous diffusion. Its temperature dependence thereby agrees with that of the viscous flow. The data bear evidence that a polymer segment undergoes primary and secondary relaxation in a statistically independent way. (C) 1998 Elsevier Science B.V. All rights reserved.

The single chain dynamics of bimodal saturated polybutadiene melts is addressed by neutron spin echo spectroscopy. A mode analysis of the structure factor provides an access to different relaxation modes (different spatial extension) separately. For the generalized Rouse model formulated by Hess an extension from monomodal to bimodal melts is presented.

The microscopic dynamics of several monomeric and polymeric glass-forming materials has been investigated by time-resolved fluorescence measurements of doped malachite green molecules in a wide temperature region. For monomers, 1-prapanol, propylene glycol, and glycerol, and a polymer without side chains, polybutadiene, the temperature dependence of nonradiative decay time of doped malachite green molecules behaves in a similar way through the glass-transition region. Besides a kink around the calorimetric glass-transition temperature T-g, another crossover at a critical temperature T-c about 30-50 K above T-g has been clearly observed. This experimental finding is in agreement with the prediction of the mode-coupling theory that a dynamical transition exists well above T-g. On the other hand, for the complex polymers with side chains, poly(vinyl acetate), poly(methyl acrylate), and poly(ethyl methacrylate), the crossover at T-g is less pronounced than those for the monomers and the polymer without side chains. Moreover, although we could not distinguish any singularities above T-g for these complex polymers, we observed another kink below T-g, which may be attributed to the side-chain motions.

Using neutron spin echo and dielectric spectroscopy we have studied the molecular motions of 1-4 polybutadiene in the alpha-beta relaxation regime. At the first peak of the static structure factor the relaxation times follow the temperature dependence of the viscosity, while near the second peak the Arrhenius law of the beta relaxation is observed. Considering localized motions on a length scale of 1.5 Angstrom with the barrier distribution from dielectric spectroscopy the dynamic structure factor in the beta relaxation regime can be described quantitatively.

Here we report results obtained by neutron spin echo on semidilute theta solutions of polystyrene in deuterated cyclohexane. It is shown that the pertinent length for the diffusion coefficient is not the correlation length xi(theta) of concentration fluctuations but rather the distance between binary contacts. At length scales smaller than this distance, the dynamics is linked to the local viscosity, which is found to be surprisingly concentration and temperature dependent.

The local dynamics of 1,4 polybutadiene below and above the merging of the alpha and beta relaxations have been investigated by combining neutron spin echo (NSE) and dielectric spectroscopy. The study of the dynamic structure factor measured by NSE over a wide momentum transfer range allows us to characterize the alpha relaxation as an interchain process while the beta relaxation originates from mainly intrachain motions. At temperatures below the merging, the dynamic structure factor can be described by a superposition of elemental processes for the beta relaxation as obtained from dielectric spectroscopy. The elemental motions behind this process can be related to rotational jumps of the chain building blocks around their center of mass. Furthermore, we have been able to consistently describe the dynamic structure factor above the merging of the alpha and beta relaxations by assuming that both processes are statistically independent. In the framework of this scenario a procedure for analyzing the dielectric response in the alpha-beta merging region has been developed. Its application to the dielectric data allows us to describe the dielectric response in this region on the basis of the low temperature behavior of the alpha and beta processes and without considering any particular change in the relaxation mechanism of these processes. The temperature dependence found for the relaxation time of the alpha process follows now the viscosity, a masked feature in the experimental data due to the merging process. In this way, we have been able to consistently describe the relaxation of both, the polarization and the density fluctuations, by using the same scenario, i.e., independent alpha and beta processes, and considering the same functional forms and temperature dependences of the characteristic times of the two processes.

This article reviews the understanding of static and dynamic scattering properties of multicomponent polymer systems in solution achieved during the past decade. We shall describe particularly ternary polymer systems which include polyelectrolyte solutions (polyion/counter-ions/water), mixture of homopolymers (A and B)/solvent and the case of diblock copolymer (A-B, linear or cyclic) solutions. The purpose of this paper is not an extensive survey of theoretical and experimental results obtained on the scattering behavior of these systems but rather an updating of recent results. For polyelectrolyte systems we shall focus, by means of scattering techniques, on the conformation of the polyelectrolyte chain and on the structure of the system induced by the dominant electrostatic interactions in solution involving polyions, counter-ions and solvent. As for the mixture of homopolymers in solution and diblock copolymer/solvent systems, we shall mainly discuss their dynamic behavior and show that using linear response theory and the Random Phase Approximation (RPA), two relaxation modes describe the autocorrelation functions as revealed using dynamic light scattering (DLS) or/and Neutron Spin Echo (NSE) techniques: the first mode characterizes the concentration fluctuations and the second one the composition fluctuations. We shall discuss the scattering properties of these systems on the basis of recent developments with emphasis on possible coiling of the polyelectrolyte chain at low charge density and also how important parameters such as the mobility of the chain (diffusion process) and the interaction parameter (compatibility), which control the dynamics and the thermodynamics in homopolymer mixtures and diblock copolymer systems, could be deduced from scattering experiments.

The main transition of amorphous polymers is analyzed with respect to a fine structure by means of new experimental dynamic shear, dielectric, and heat capacity data for the following polymers: poly(n-alkyl methacrylate)s with alkyl = methyl, ethyl, propyl, butyl, and hexyl, polystyrene, poly(vinyl acetate), a series of weakly vulcanized natural rubbers, a series of butyl rubbers with different carbon black content, polyisobutylene, and bromobutyl rubber. The components of the fine structure are assumed to be a proper glass transition at short times, followed by a confined flow zone, and, at large times, a hindering zone caused by entanglements at large times. Two lengths are assumed to correspond to the first and third components, respectively, the characteristic length to the proper glass transition and the entanglement spacing to the hindering zone. The confined flow will be described by a dispersion law (general scaling) across the main transition. The characteristic length of the glass transition for the poly(n-alkyl methacrylate)s-only of order 1 nm as determined by calorimetry-is confirmed by backscaling from the entanglement spacing by means of a Rouse dispersion law for shear. The fate of the Rouse modes below the alpha beta splitting of the glass transition is discussed for the other amorphous polymers. Finally, a speculative molecular picture of the different modes in the main transition is described. The new element is a low-viscosity longitudinal motion of individual chain parts in the confined flow zone. A simple rheological model for the confined flow is also presented.

Simulations of stress relaxation in a model polymer melt of freely-jointed chains with N = 300 bonds are performed with the use of a nonequilibrium molecular dynamics algorithm. After a deformation is applied in a short loading period, special attention is paid to the decay of bond orientation, P-2(t;1), and the relation of this quantity to the stress sigma(t) computed by the atomic virial stress formula. It is found that the ratio P-2(t;1)sigma(t) has a low value in the early glassy period and then undergoes a transition to a higher value that remains substantially constant. An explanation on the atomic level for the behavior of this ratio, which bears a close relation to the stress-optical coefficient is given. Various modes of coarse-graining the model melt are considered by subdivision of each chain into segments, each with NR bonds. A second, molecular, calculation of the stress is made for the coarse-grained melt by use of the entropic spring stress formula and denoted by sigma(e)(t;N-R). At early times sigma(t) > sigma(e)(t;N-R) for all N-R. At later times, the value of N-R for which sigma(t) = sigma(e)(t;N-R) increases from N-R = 5 to N-R = 50. In these simulations, no value of N-R is found for which sigma = sigma(e) for an extended period. Conceptual difficulties, suggested by these simulations, with the use of Rouse dynamics for the calculation of the plateau onset and plateau modulus are discussed.

The initial decay rate Omega((k) over bar) of the dynamical scattering factor of a single regular star polymer is investigated with the chain conformational renormalization group method up to first order in epsilon. The reduced relaxation rate Omega((k) over bar)/k(3) is expressed as the ratio of the mobility to the static structure factor, and we have analyzed the two contributions separately. At the Gaussian fixed point we have found a qualitatively different result to that of the standard calculation in three dimensions, and the difference comes from the effect of the epsilon-expansion on the mobility. The renormalization group result at the self- avoiding fixed point describes qualitatively well the behavior of Omega((k) over bar)/k(3) observed in neutron scattering experiments for 12-arm-stars in a good solvent.

Using the neutron spin echo spectroscopy, the internal segmental diffusion of chain molecules in polymer melts and concentrated solutions was studied. These investigations show that beyond a characteristic length d(t) and after a cross over time tau(e)(d(t)) the segmental diffusion of the single chains is strongly impeded and deviates from the Rouse dynamics. d(t) is polymer specific and depends on the temperature as well as on the polymer concentration. Within the framework of the reptation concept, where d(t) is identified with the mean distance between intermolecular entanglements or with the tube diameter, the microscopically determined d(t)-values agree quite well with those derived from related macroscopic measurements of the plateau modulus. A similar good agreement is also found with respect to the segmental friction coefficients obtained either from the Rouse regime of the NSE spectra or from theological data of corresponding short chain systems, where entanglements are not yet effective.

Polymer brushes forming the outer shells of micellar aggregates of A-B diblock copolymers in a selective solvent allow for the observation of collective relaxational motions via neutron spin-echo spectroscopy. New neutron spin-echo investigations on planar FEB-brushes on the surface of crystalline PE-cores of platelet-like aggregates are reported. The data are discussed in comparison to a continuum model of the brush assuming a parabolic density profile, semidilute solution scaling relations for the elastic properties and friction coefficient. For the planar brush a full 3D solution of the model is accessible. The observed scattering from an isotropic sample is compatible with the continuum model with an added static fluctuation contribution.

A statistical dynamical theory of the crossover from unentangled Rouse dynamics to entangled behavior is constructed for chain polymer solutions and melts. Both time and spatial crossovers in long chain fluids, and the degree of polymerization crossover for short polymers, are treated. The analysis is based on a microscopic theory of the perturbative dynamical corrections to Rouse theory arising from chain connectivity and intermolecular excluded volume forces. The dependence of crossover properties such as the plateau shear modulus and entanglement time and length scale on solution density, solvent quality, and chain statistical segment length are derived by combining the dynamical theory with equilibrium liquid state integral equation methods. Scaling relations are obtained which appear to be in general accord with most experiments on both solutions and melts. The physical origin of the predicted scaling behaviors is the fractional power law temporal decay of the entanglement friction memory function on intermediate time scales, and power law reduced density dependence of the equilibrium force correlations. The theory is also applied to compute the dependence of the chain normal mode relaxation times on polymer density and chain length. Favorable qualitative comparisons with recent neutron spin echo experiments are made. (C) 1995 American Institute of Physics.

We present calculations of the single-chain dynamic structure factor for a polymer melt composed of linear molecules of the same chemical identity but of two different chain lengths. The fluid is treated within a dynamical mean-held approach, in which each molecule is represented as a freely jointed chain moving among stochastic obstacles. The obstacles are of two types, each representing the obstruction of local conformational changes by one of the species present. The obstacle dynamics are determined self-consistently by equating the relaxation rate of an obstacle of a given type to the smallest conformational relaxation rate of the species that it represents. Calculation of the dynamic structure factor is mapped onto the solution of a random walk with dynamical disorder, in which a walker moves on a one-dimensional lattice with hopping rates that randomly fluctuate among three states. The relevant random walk problem is solved within the effective medium approximation, and the results are employed to examine the dependence of the dynamic structure factor on time, wave vector, chain lengths, and fluid composition. (C) 1995 American Institute of Physics.

In this work, we present calculations of the dynamic structure factor for monodisperse melts of linear polymers. Our calculations are based on a model in which a freely jointed chain encounters fluctuating obstacles whose relaxation is self-consistently determined from that of the chain conformation. The calculation of the structure factor is related to the solution of a one-dimensional random walk with dynamical disorder, which is treated within the dynamical effective medium approximation. This model has been applied previously to the calculation of the self-diffusion coefficient and the mean-squared displacement of a chain segment. We present calculations of the structure factor over a wide range of wave vectors, times, and entanglement molecular weights. Our predictions are compared with calculations from the theories of Ronca and of de Gennes, and with the experimental results for polyethylene-butylene-2 obtained by Richter et al. from neutron spin echo measurements. Our calculations show semiquantitative agreement with the experimentally determined structure factors for the time range accessible to these experiments.

Using neutron spin echo spectroscopy, the dynamics of high molecular weight poly(dimethylsiloxane) in the melt (T = 473 K) was investigated. In order to decide whether the lateral constraints are uniform or nonuniform with respect to the contour of a test chain, chains were labeled either completely or partially by a corresponding proton-deuterium exchange. It was found that the central and the terminal chain sequences experience the same amount of lateral confinement, which in the framework of the reptation or tube model - can be characterized by a tube diameter d(t) of about 70 angstrom. Nearly the same d(t) value is obtained from the plateau modulus of rheological measurements, too. Thus, these experiments show unambiguously that the lateral constraints, responsible for the reptational chain dynamics, are quite homogeneous, even in the case of extremely large tube dimensions.

Semidilute polymer solutions can be considered as transient networks of lifetime, tau(g) and of average meshsize xi. xi depends on the polymer concentration, c, and the solvent conditions. If the segmental diffusion of such systems is studied on timescales t << tau(g), using the neutron spin echo technique, different relaxation modes and continuous transitions between them are identified by varying the magnitude of the scattering vector, q. Under good solvent conditions, a crossover from single chain Zimm dynamics, as valid in dilute solutions on the entire intramolecular length scale, to the collective many chain diffusion is found at q xi(c) approximate to 1. The corresponding relaxation rates, Omega(q), vary from Omega(q) similar to q(3) to Omega(q) similar to q(2). In Theta-solvents, the many chain regime was not accessible. However, due to the existence of self- entanglements, which introduce an additional length scale xi(i)(c) < xi(c), the crossover from disentangled (Omega(q) similar to q(3)) to entangled single chain relaxation (Omega(q) similar to q) becomes visible.

Brillouin-light-scattering measurements have been performed on both bulk and thin supported polybutadiene (PB) films, in the frequency range 1-300 GHz. The results obtained on the relaxation behavior of PB have been interpreted in the framework of the mode-coupling theory and compared with neutron spin-echo data relative to the same system. For temperatures higher than the critical temperature T(c), a quantitative agreement of the mean relaxation time with the viscosity time scale has been found, together with the validity of a time- temperature scaling law. For temperatures approaching the glass transition, a departure of relaxation time from the viscosity time scale has been observed. This phenomenon has been attributed to a decoupling between structural and secondary relaxation processes.

A molecular simulation of many-arm star polymers in solvents of varying quality is presented. The number of arms f in each star covered the range 3 less-than-or-equal-to f less-than-or-equal- to 80 with N = 50 and 100 monomers per arm. The resulting equilibrium structures are compared to scaling predictions based on the blob model and to experimental results. The monomer density rho(r) from the center was found to fall off as a power law, r(-a), for both a good and THETA solvent in agreement with the scaling predictions. The free ends were found to be excluded from a region near the center of the star and the distribution of center-to-end distances R was found to be well approximated by a Gaussian for many-arm stars (f greater than or similar to 20) for all solvents. For small f, there were some deviations from a Gaussian form, particularly for small R. For both a good and THETA solvent, the relaxation time for the shape fluctuations depended imperceptibly on the number of arms f.

A-B block copolymers in a selective solvent-good for the B- species and bad for the A-species-form micellar aggregates with a compact A-core with a corona (brush) of B <> reaching into the solvent. Whereas polystyrene(PS)-polyisoprene(PI) in decane forms spherical micelles with a PS core of about 10 nm radius, polyethylene(PE)-polyethylenepropylene(PEP) forms micellar platelets, the shape of which is goverend by the habitus of PE crystallites forming the core. These planar aggregates have large (several hundred nanometers) lateral extension and a core thickness in the range of 10 nm. Both systems are model systems for polymer brushes, either on a spherical surface or planar. Neutron spin-echo experiments allow for the investigation of the dynamics of the brushes which reflects their viscoelastic properties. Results of neutron small-angle and spin-echo investigations are reported. The brush dynamics is explained using a model based on an idea of de Gennes describing the brush properties in terms of scaling relations for osmotic pressure and viscosity of a semi- dilute solution with inhomogeneous density.

Employing neutron spin-echo spectroscopy we have studied the dynamic structure factors for the relaxation of a single. chain;in polymer melts. We have varied the molecular weights through the transition region from unrestricted Rouse dynamics to entanglement controlled behavior. Investigating the dependence of the dynamic structure factor on the momentum transfer and, it is possible to access the different relaxation modes separately. We found that, depending on their spatial extension in relation to the entanglement distance, larger scale relaxations are successively slowed down compared to Rouse relaxation. A comparison with macroscopic diffusion and viscosity data yields excellent internal consistency. Furthermore, we solve explicitly the generalized Rouse model by Hess(12) and compare its. predictions to our data. Fitting only two parameters, all the Q and molecular weight dependent structure factors can be well reproduced.

Using the bond fluctuation model for flexible polymer chains in a dense melt the intermediate coherent scattering function for chains containing N = 200 monomers is calculated and interpreted in terms of a recent theory of des Cloizeaux. The theory yields an explicit description for the crossover from the Rouse model to the regime where reptation prevails, for the limit N --> infinity. While the Monte Carlo data are qualitatively compatible with this description, an accurate estimation of the tube diameter is prevented due to the onset of a diffusive decay of the scattering function, not included in the theory. For a full quantitative analysis of the Monte Carlo data (as well as of experiments on chains with not extremely large molecular weight) an extension of the theory for finite N would be required.

This paper discusses the dynamic-scattering properties of an (A-B)r ring diblock-copolymer chain in semi-dilute solutions. The expressions of the frequencies describing the dynamic behaviour of such systems are given in both models: the Zimm model, where the hydrodynamic effects are important and the Rouse model, where these effects are neglected. The results show sensitive differences with respect to the corresponding linear diblock copolymer (A-B)l. This is mainly due to the effect of connectivity of the chain extremities A and B, leading to different conformations for both types of diblock- copolymer chains. Although the description we discuss in this paper is valid for any cyclic diblock-copolymer chain (i.e. at any composition), explicit equations are given for the symmetrical case (50/50 composition) where the effects are more pronounced. Experimental investigations using neutron spin echo (NSE) are particularly useful in order to test these theoretical predictions.

The rheological properties of star-shaped polyisoprenes having a wide range of arm numbers and arm molecular weights are reported. In contrast to linear polymers, stars have a broad relaxation spectrum and a viscosity that increases exponentially with arm molecular weight. A comparison of eight pairs of samples having 3 and 4 arms and identical arm molecular weights showed that the viscosity of 3-arm stars is approximately 20% lower. For higher degrees of functionality, 4 less-than-or-equal-to f less-than-or-equal-to 33, the effect of functionality saturates and the viscosity is determined by arm molecular weight only. The nonlinear properties of one sample were studied using step-strain tests and found to be essentially identical to those of linear polymers. The predictions of a molecular theory for star polymers based on an extension of the reptation model are reviewed and shown to be in good agreement with the experimental data.

Polystyrene(PS)-polyisoprene(PI) diblock copolymers dissolved in n-decane aggregate into spherical micelles with a PS core and a corona of tethered PI chains. The PI corona may be considered as a brush on the surface of a sphere or as the outer part of a many-armed polymer star. The thermal density fluctuations of the PI corona have been observed by neutron spin-echo spectroscopy. The peculiar multi-decay time relaxation behavior can be described remarkably well by a model based on an idea of de Gennes for treating the corona as a semidilute polymer solution with varying concentration profile.

Measurements of swelling pressure, neutron spin-echo scattering, and dynamic light scattering were made in an end- linked poly(dimethylsiloxane) (PDMS) gel swollen to equilibrium in a good solvent (toluene) and also in the equivalent solution. The macroscopic osmotic modulus is depressed in the gel. Neutron spin echo observations at intermediate and high values of the scattering vector Q reveal that the mobility of the monomers is unaffected by cross-linking. Elastic neutron scattering at small Q detects non-uniformities in the polymer concentration distribution, which are absent from the solution. These non-uniformities play a major role in the dynamic response of the system at lower Q, and and appear to be the cause of the observed reduction in osmotic pressure.

The static and dynamic structure factors for star polymers in THETA solutions are derived for semiflexible models and the partially stretched (PS) arm model. The PS model for the static structure factor is found to be in fairly good agreement with SANS experiments with exclusion of the high-k region, where only a qualitative agreement is obtained. The nonpreaveraged first cumulant for the PS model reproduces fairly well the peculiar effects found by neutron spin-echo experiments even though those experiments were carried out in good solvents. The effects of preaveraging and screening of the hydrodynamic interaction are considered. Results for the full dynamic structure factor are presented only in the preaveraging approximation.

A nonperturbative approximation and a fortuitous cancellation of errors lead to an accurate, simple approximation for the dynamic single-chain structure factor-or coherent intermediate scattering function-of a Rouse polymer fluid in the short to intermediate time and wave vector region. With this approximation the breakdown at small wave vector of the wave vector to the fourth scaling of the ''Rouse frequency'' is illustrated, and compared to recent neutron spin-echo measurements on polydimethylsiloxane. Experimental study of this breakdown might provide information about the relation between static structure and dynamic behavior in polymer melts.

Conventional resolution inelastic neutron scattering spectroscopy allows us to explore the behaviour of condensed matter essentially on the time scale of thermal atomic vibrations. By the application of the Neutron Spin Echo trick, which enables us to get around the Liouville theorem limitation of conventional methods, the resolution can be improved very substantially. This opened up the field for the study of a large variety of slow motion phenomena (critical slowing down, relaxation effects, disordered dynamics, soft matter), i.e. the investigation of processes on a mesoscopic time scale between microscopic collision times and macroscopic dynamics.

We present dynamic light scattering data which show that aqueous gelatin gels display a power-law relaxation to a nonergodic background. In the pregel sol this power law is terminated by a stretched exponential which restores ergodicity and which has a q dependent characteristic time proportional to the viscosity. The power-law exponent is q dependent and related to a characteristic length in the gel. Except for the q dependences these behaviors are similar to the alpha and beta relaxation behavior in glasses. It is proposed that the different q dependences of the gels and glasses is a result of different characteristic length scales.

By neutron spin echo spectroscopy we have investigated the dynamic structure factors for single chain relaxation in polymer melts varying the molecular weight through the transition from unrestricted Rouse motion to entanglement controlled behavior. From an analysis of the structure factors with respect to the different relaxation modes we found that, depending on their spatial extension in relation to the entanglement length, large-scale relaxations are successively suppressed with increasing molecular weight. A comparison with macroscopic diffusion and viscosity data yields excellent internal consistency.

The plateau zone in the dynamic modulus of large chain polymer melts characterizes most strikingly their viscoelasticity reflecting the rubber-like properties of entangled chains. In this paper we shall summarize neutron spin-echo experiments which unravel the underlying microscopic large scale chain motions. NSE thereby facilitates a space-time analysis of the density fluctuations in a labeled chain among equals. The experiments show the microscopic existence of an intermediate dynamic length scale, related to the rubbery plateau. Scaling models of entanglement formation are scrutinized by systematically varying the two length scales considered to be important. Diluting with oligomers changes the contour length density. A temperature variation changes the Kuhn length. The NSE results favour binary contact models and exclude packing models. Finally, the build-up of entanglements at the crossover from Rouse to entanglement behavior is addressed by varying the chain length.

Neutron scattering experiments have been performed to explore the dynamics of polymers near the glass transition. The experimental data show three distinct types of relaxations: (1) Susceptibility spectra exhibit a contribution in addition to phonons around a temperature independent frequency. (2) Neutron-spin-echo (NSE) experiments show a slow relaxation of the stretched exponential type. Above 220 K, the characteristic time of this process strictly follows the Vogel-Fulcher dependence of viscosity data indicating the direct connection between microscopic and macroscopic relaxation. (3) Below 220 K, the temperature dependence of the relaxation observed by NSE changes to an Arrhenius form while the viscosity still follows the Vogel-Fulcher law. Analysis of the Q dependence from IN13 backscattering data reveals a change of mechanism at the crossover. The experimental findings will be discussed emphasizing the comparison with the mode coupling theory. Aspects of agreement as well as deviations will be pointed out in the discussion.

The static scattering function for a regular star-branched polymer is calculated in the full excluded-volume limit with renormalization group techniques, and a closed-form expression for the scattering intensity I(k) is given. The influence of the excluded-volume interaction between monomers becomes more noticeable as the functionality f of the star increases, qualitative differences appearing between I(k) and the Gaussian limit I0(k). A simplified formula for I(k) is provided, which can be used for the treatment of experimental data. The scattering of one labeled arm of the star is also investigated and the radius of gyration of the arm is calculated, giving a quantitative expression for the stretching of the branches.

Concentration fluctuations in swollen gels are controlled by a collective diffusion coefficient D(c). Two experimental observations are described in which a swollen gel is mechanically deformed from its equilibrium configuration. In the first, the anisotropy of D(c) in a uniaxially deswollen polyacrylamide-water gel is investigated using dynamic light scattering. No anisotropy is detected. In the second, D(c) is measured by the neutron spin echo technique in a stretched poly (dimethylsiloxane) gel swollen in toluene. The measured anisotropy is small and at the limit of the experimental error.

Combined measurements are described involving elastic and quasi-elastic neutron scattering, quasi-elastic light scattering, nuclear magnetic resonance, and swelling pressure on an end-linked poly-(dimethylsiloxane) (PDMS) gel swollen to equilibrium in a good solvent (toluene) and the equivalent solution. The factors affecting the collective diffusion coefficient are considered. The swelling pressure measurements show that the osmotic modulus is appreciably depressed in the gel. The neutron spin-echo measurements reveal no difference in the dynamic response at intermediate and high values of the scattering vector Q. Elastic neutron scattering at small Q detects nonuniformities in the network structure, which are absent from the solution. These nonuniformities play a major role in the dynamic response of the system at lower Q and appear to be the cause of the observed reduction in osmotic pressure. The NMR measurements show a small increase of the solvent mobility in the gel, which is consistent with the appearance of structural nonuniformities in the system.

We report neutron spin echo measurements of the dynamic correlation function of cross-linked polydimethylsiloxane disolved in toluene. The experiments were performed on semi- dilute solutions. The main result is that at the frequencies probed by the spectrometer, there is no difference between the dynamics of cross-linked and uncrosslinked polymers. The dynamics is Zimm like and includes hydrodynamic interactions. Using a reduced time variable, it is possible to plot all the experimental data for both concentrations we studied on the same mastercurve. Moreover, previous results by Csiba et al. on uncross-linked PDMS are also located on the same curve. This shows that cross-linking has no dramatic effect on the local dynamics of the linear chains,

Using neutron spin echo spectroscopy, we have studied the melt dynamics of polyisoprene (PI), saturated polybutadiene (PEB-2), and poly(ethylene-propylene) alternating copolymer (PEP). The experiments on all three polymers show that beyond a characteristic length d and after a crossover time tau(e) the relaxational density fluctuations within a given chain are strongly impeded. The presence of an intermediate dynamic length scale in the chain dynamics establishes the microscopic existence of a well-defined entanglement distance confirming thereby one of the essential assumptions of the reptation concept. The microscopically determined lengths agree well with those obtained from the plateau moduli if interpreted in terms of the reptation theory. The detailed line shape of the dynamic structure factor supports the concept of local reptation.

Neutron spin echo spectroscopy allows the observation of long range internal relaxation mechanisms of macromolecules, simultaneously in space and time. Thereby, it facilitates a microscopic study of the molecular origins of the macroscopic viscoelastic properties of polymer materials. The molecular understanding of polymer dynamics bases on concepts of entropic forces and topological and hydrodynamic interactions. I shall briefly outline the different concepts and then discuss experimental results on these different aspects of polymer motion on a molecular scale.

Studying the dynamic structure factor of polybutadiene in the first valley of S(Q) we decoupling of microscopic and macroscopic time scales about 40 K above T(g). At higher temperatures the time scale set by the viscosity scales with the microscopic scale, while at lower T strong decoupling effects occur. We present evidence that the decoupled low- temperature relaxation is distinctly different from the high- frequency "beta-process." The decoupling temperature coincides with the critical temperature of the mode coupling theory.

The temperature dependence of the dynamics of polymer chains in the melt is studied in a Monte Carlo simulation of the bond fluctuation model. Temperature enters via a bond angle potential determining the stiffness of the chains. The model is simulated at a melt volume fraction of PHI = 0.5 and for chains of lengths N = 20, 50, 100, and 200. For the short chains we are determining the temperature range over which a random coil description of these semiflexible chains is possible, i.e. the temperature region for which the chains show the behavior of random coils in the melt. We then examine to what extent the Rouse model is able to describe the dynamics of these chains. We will look especially at the Rouse scaling for the dynamic structure factor. For the longest chains it has been shown that our model in the athermal limit can be described by the reptation picture of DeGennes and Doi and Edwards and the density dependence of the tube diameter has been established. Here we now measure the temperature dependence of this dynamic length scale by analyzing the dynamic structure factor. It is shown to decrease slightly with decreasing temperature in accord with recent findings of neutron spin echo experiments.

We have used neutron spin echo and dielectric spectroscopy to investigate the relaxational properties of polyisoprene. NSE data reveal a relaxation similar to what was found previously in polybutadiene. The comparison to the dielectric relaxation and rheological data exhibits that all time scales shift with the same temperature dependent factor.

Equilibrium and dynamical properties were obtained by light scattering methods for solutions of multiarm polyisoprene star polymers in a good solvent, cyclohexane, over a wide concentration range. Results for 8-arm and 18-arm stars were compared with the behavior of linear polymers in the dilute and semidilute regimes and were analyzed in terms of recent theories based on the Daoud-Cotton model. In dilute solutions the temporal fluctuations on distance scales smaller than the overall dimensions were found to be markedly slower for stars than for linear chains of the same size. Evidence for star- star repulsion and liquidlike ordering near the overlap concentration was also obtained. Such differences between linear polymers and stars vanish in the semidilute region, however, with the osmotic pressure derivative and mutual diffusion coefficient becoming power law functions of the polymer concentration alone. The scaling law prefactors depend on the arm number but less strongly than predicted by theory.

Relaxation times of concentration fluctuations in semi-dilute solutions of polydimethylsiloxane, have been measured at several values of the reciprocal wave vector q, with the neutron spin echo spectrometer of the Laboratoire Leon Brillouin. The experiment has been carried out successively on a solute of identical chains, and on a solute divided in equal parts between labelled and non labelled chains at zero average contrast. We report observations of the dispersion relation associated with the Brownian motion of the polymer chains, in the vicinity of the inverse mesh size 1/xi. For values of q which are greater than 1/xi, the two experiments give identical results but when q decreases below 1/xi, the dispersion curves associated with each experiment are different. A bifurcation occurs at 1/xi and two distinct transport processes become observable, which are related to cooperative diffusion and to inter-diffusion respectively. The observed coefficents are compared with predictions of the effective medium and the dilute solution theories.

In this short review we discuss experimental results on molecular motion in polymer melts, obtained by neutron spin echo spectroscopy (NSE). We show that in the short-time regime the assumption of entropic restoring forces (Rouse model) describes perfectly well the space and time dependence of self- and pair-correlation functions of one chain molecule. For longer times or stronger geometrical constraints we observe systematic deviations from the Rouse model revealing the presence of a well-defined intermediate dynamical length scale beyond which density fluctuations within a given chain are strongly reduced. Its value is found to be in excellent agreement with the entanglement distance obtained from rheological measurements. Measurements of the temperature dependence of the enlargement distance, the radius of gyration and the plateau modulus give first insight into the molecular origin of entanglement constraints. The data favour packing models and contradict the topological approach.

Neutron spin-echo spectroscopy allows the observation of the long-range internal relaxation mechanism of macromolecules simultaneously in space and time. Thereby, it facilitates a microscopic study of molecular models applied for the explanation of macroscopic viscoelastic properties of polymer materials. After an outline of the method, experimental results on chain relaxation in polymer melts are discussed. It is shown that in the short-time regime, the Rouse model describes perfectly well the space and time dependence of the self- and the pair-correlation function. For longer times distinct deviations from the Rouse model towards slower relaxation are observed. These deviations exhibit a systematic dependence on the momentum transfer, Q, and thus show that beyond a certain length scale the relaxation of density fluctuations within a given chain is strongly reduced. This intermediate dynamic length scale shows direct evidence of the existence of a well-defined entanglement distance in polymer melts, confirming thereby the essential assumption of a reptation concept. Its value is found to be in excellent agreement with the entanglement distance obtained from the rheological measurement.