The local dynamics of 1,4 polybutadiene below and above the merging of the ␣ and ␤ relaxations have been investigated by combining neutron spin echo ͑NSE͒ and dielectric spectroscopy. The study of the dynamic structure factor measured by NSE over a wide momentum transfer range allows us to characterize the ␣ relaxation as an interchain process while the ␤ 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 ␤ 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 ␣ and ␤ relaxations by assuming that both processes are statistically independent. In the framework of this scenario a procedure for analyzing the dielectric response in the ␣-␤ 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 ␣ and ␤ processes and without considering any particular change in the relaxation mechanism of these processes. The temperature dependence found for the relaxation time of the ␣ 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 ␣ and ␤ processes, and considering the same functional forms and temperature dependences of the characteristic times of the two processes. ͓S1063-651X͑96͒07209-1͔

We have studied the aggregation behavior of polyethylene−poly(ethylenepropylene) (PE−PEP) diblock copolymers dissolved in decane. For this purpose PE−PEP diblock copolymers of various molecular weights, compositions, and degrees of deuteration were synthesized via an anionic route. The structure and morphology of the aggregates was studied by small angle neutron scattering varying both the contrast as well as the polymer labeling. We found a hierarchy of structures:  The PE component crystallizes in lamellar sheets (thickness 40−80 Å) surrounded on both sides by a PEP brush which exhibits a close to parabolic density profile. Different aggregates form macroaggregates of needlelike shape with the PE lamellar planes in the long direction. This macroaggregation is well described by a paracrystalline structure factor. The structural parameters depending on composition and molecular weights can be well understood in terms of a free energy of formation based on a scaling model. A quantitative evaluation of the different contributions to the free energy reveals an important role of defect structures resulting from the ethylene side branches in the polyethylene component. Finally, we show in a semiquantitative approach that the van der Waals energy between the brushes is large enough to facilitate macroaggregation.

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. [S0031-9007(98)05363-0] PACS numbers: 61.25.HqThe dynamics of polymer chains in a dense melt could be supposed to pose a theoretical problem requiring a very complex and mathematically involved description. We have to describe a liquid of intertwined threads where each of them has on average excluded volume interactions with p N other threads, where N is the degree of polymerization of the chains. According to all experimental evidence so far, e.g., Refs. [1-3], however, it seems that all these complex topological interactions can be completely neglected as long as the degree of polymerization of the chains is below some critical value, the so-called entanglement molecular weight N e . For chains longer than N e the entanglements have to be taken into account [4-7] but for shorter chains the simple Rouse theory [8] is supposed to describe the chain dynamics. Computer simulations of abstract [9,10] as well as atomistic [11] polymer models, on the other hand, show systematic deviations from the Rouse behavior, which can be traced to the interactions between the chains in the melt.We will show in this paper the first detailed quantitative comparison between a molecular dynamics (MD) simulation of the melt dynamics of an atomistic polymer model and a neutron spin echo (NSE) determination of the single-chain dynamics in the same polymer melt. By establishing the quantitative agreement between simulation and experiment for the internal dynamics of the chains we can then draw conclusions about the validity or shortcom-ings of the Rouse model from the combined information of simulation and experiment.Simulations and experiments were performed on a dense polyethylene melt of n-C 100 H 202 at 509 K. Experimentally we had already obtained information on the dynamic behavior of longer chain polyethylene (PE) samples at the same temperature from neutron scattering studies [1,2], and we had validated a united atom (UA) model (CH 2 groups treated as one superatom) [12] as well as an explicit atom (EA) model [13] by simulations of shorter chain alkanes. The C 100 chains are slightly shorter than the entanglement length of PE at this temperature (N e 136 [2]) and long enough to show Gaussian chain statistics in their conformations [14], thereby making them the ideal test system for a description by the Rouse model. After equilibration for 3 ns we performed a NVT (constant number of particles, volume, and temperature) mole...

The ability of colloidal particles to form equilibrium cluster phases under conditions where the particles interact via a potential consisting of a soft long-range repulsion and a shortrange attraction is well documented. 1,2 In this class of systems, the short-range attraction drives cluster formation, whereas the increasing long-range repulsion due to the accumulating charge of the clusters limits their size. After an initial report 3 that demonstrated the existence of such clusters in systems as diverse as concentrated lysozyme solutions at low ionic strength and weakly charged colloids in a low dielectric constant solvent with added nonadsorbing polymers (to induce a short-range attraction via a depletion mechanism), cluster phases have been demonstrated to exist in a large range of colloidal systems. 4À8In particular, the finding that equilibrium clusters may form in protein solutions under appropriate solution conditions has attracted considerable attention due to its potential biological significance in areas such as protein crystallization or protein condensation diseases. 9À16The initial evidence of the existence of clusters in concentrated lysozyme solutions at low ionic strength has been obtained from the rather peculiar small-angle X-ray (SAXS) and small-angle neutron scattering (SANS) pattern obtained for these systems, 3,17 where an analysis of the dependence of the scattering intensity as a function of the magnitude of the scattering vector q clearly reveals the existence of two peaks in the static structure factor S(q). Surprisingly, both the low as well as the high-q peak were found to be almost independent of the volume fraction φ at sufficiently high values of φ. This was subsequently interpreted as the signature of the presence of equilibrium clusters, where the low-q peak was attributed to a clusterÀcluster interaction peak and thus denoted q c , while the high-q peak was thought to reflect the monomerÀ monomer correlations within the cluster and thus denoted q m .This interpretation was subsequently challenged by Shukla et al., 18 who also conducted SANS and SAXS experiments with lysozyme solutions at low ionic strength. On the basis of the fact that they saw a clear shift of the cluster peak position at lower protein volume fractions, they questioned the existence of equilibrium clusters in lysozyme solutions. However, it has already been pointed out that for comparable experimental conditions, the claim of Shukla et al. relied in fact on scattering data that showed no significant differences to the earlier data on which the cluster model had been based.19,20 SAXSABSTRACT: We present a detailed experimental and numerical study of the structural and dynamical properties of salt-free lysozyme solutions. In particular, by combining small-angle X-ray scattering (SAXS) data with neutron spin echo (NSE) and rheology experiments, we are able to identify that an arrest transition takes place at intermediate densities, driven by the slowing down of the cluster motion. Using an effective pair pote...

Thickness fluctuations have long been predicted in biological membranes but never directly observed experimentally. Here, we utilize neutron spin echo spectroscopy to experimentally reveal such fluctuations in a pure, fully saturated, phosphocholine lipid bilayer system. These fluctuations appear as an excess in the dynamics of undulation fluctuations. Like the bending rigidity, the thickness fluctuations change dramatically as the lipid transition temperature is crossed, appearing to be completely suppressed below the transition. Above the transition, the relaxation rate is on the order of 100 ns and is independent of temperature. The amplitude of the thickness fluctuations is 3:7 # A AE 0:7 # A, which agrees well with theoretical calculations and molecular dynamics simulations. The dependence of the fluctuations on lipid tail lengths is also investigated and determined to be minimal in the range of 14 to 18 carbon tails.