Anisotropic and heterogeneous dynamics in stretched elastomer nanocomposites.

We use X-ray photon correlation spectroscopy (XPCS) to investigate the dynamics of a stretched elastomer by means of probe particles. The particles dispersed in the elastomer were carbon black or silica aggregates classically used for elastomer reinforcement but their volume fraction is very low (φ < 10-2). We show that their dynamics is slower in the direction of the tensile strain than in the perpendicular one. For hydroxylated silica which is poorly wetted by the elastomer, there is no anisotropy. Two-time correlation functions confirm anisotropic dynamics and suggest dynamical heterogeneity already expected from the q-1 behavior of the relaxation times. The height χ* of the peak of the dynamical susceptibility, determined by the normalized variance of the instantaneous correlation function, is larger in the direction parallel to the strain than in the perpendicular one. It also appears that its q dependence changes with the morphology of the probe particle. Therefore, the heterogeneous dynamic probed by the particles is not related only to that of the strained elastomer matrix. In fact, it results from modification of the dynamics of the polymer chains near the surface of the particles and within the aggregate porosity (bound polymer). It is concluded that XPCS is a powerful method for investigating the dynamics, at a given strain, of the bound polymer-particle units which are responsible, at large volume fractions, for the reinforcement.

Monte Carlo static and dynamic simulations of a three-dimensional Ising critical model.

The critical dynamics of 'model A" of Hohenberg and Halperin has been studied by the Monte Carlo method. Simulations have been carried out in the three-dimensional (3d) simple cubic Ising model for lattices of sizes L=16 to L=512. Using Wolff's cluster algorithm, the critical temperature is precisely found as ß_{c}=0.22165468(5). By Fourier transform of the lattice configurations, the critical scattering intensities I(q[over ⃗]) can be obtained. After circular averaging, the static simulations with L=256 and L=512 provide an estimate of the critical exponent γ/ν=2-η=1.9640(5). The |q[over ⃗]|-dependent distribution of I(q[over ⃗]) showed an exponential distribution, corresponding to a Gaussian distribution of the scattering amplitudes for a large q domain. The time-dependent intensities were then used for the study of the critical dynamics of 3d lattices at the critical point. To simulate results of an x-ray photon correlation spectroscopy experiment, the time-dependent correlation function of the intensities was studied for each |q[over ⃗]|-value. In the q region where I(q[over ⃗]) had an exponential distribution, the time correlations can be fit to a stretched exponential, where the exponent µ=γ/νz≃0.975 provides an estimate of the dynamic exponent z. This corresponds to z=2.0145, in agreement with the observed variations of the characteristic fluctuation time of the intensity: τ(q)∝q^{-z}, which gives z=2.015. These results agree with the ε expansion of field-theoretical methods (2.017). In this paper, the need to take account of the anomalous time behavior (µ<1) in the dynamics is exemplified. This dynamics reflects a nonlinear time behavior of model A, and its large time extension is discussed in detail.

Diffraction with a coherent X-ray beam: dynamics and imaging.

Methods for carrying out coherent X-ray scattering experiments are reviewed. The brilliance of the available synchrotron sources, the characteristics of the existing optics, the various ways of obtaining a beam of controlled coherence properties and the detectors used are summarized. Applications in the study of the dynamics of speckle patterns are described. In the case of soft condensed matter, the movement of inclusions like fillers in polymers or colloidal particles can be observed and these can reflect polymer or liquid-crystal fluctuations. In hard condensed-matter problems, like phase transitions, charge-density waves or phasons in quasicrystals, the study of speckle fluctuations provides new time-resolved methods. In the domain of lensless imaging, the coherent beam gives the modulus of the sample Fourier transform. If oversampling conditions are fulfilled, the phase can be obtained and the image in the direct space can be reconstructed. The forthcoming improvements of all these techniques are discussed.

Soft X-ray coherent scattering: instrument and methods at ESRF ID08.

An experimental setup has been developed to perform soft x-ray coherent scattering at beamline ID08 of the European Synchrotron Radiation Facility. An intense coherent beam was obtained by filtering the primary beam with the monochromator and a circular pinhole. A pinhole holder with motorized translations was installed inside the UHV chamber of the diffractometer. The scattered intensity was recorded in reflection geometry with a back-illuminated charge coupled device camera. As a demonstration we report experimental results of resonant magnetic scattering using coherent beam. The degree of coherence is evaluated, and it is shown that, while the vertical coherence is much higher than the horizontal one at the source, the situation is reversed at the diffractometer. The intensity of the coherent beam is also discussed.

ASAXS, SAXS and SANS investigations of vulcanized elastomers filled with carbon black.

Small-angle X-ray scattering (SAXS) performed down to small q values (q

Morphological investigation of chemically treated poly(ethylene terephthalate)-based activated carbons.

Complementary techniques, including low-temperature nitrogen adsorption and small-angle X-ray scattering (SAXS), are applied to detect the effects of surface functionalization on the morphology of activated carbon derived from poly(ethylene terephthalate) (PET). Scanning electron microscopy (SEM) is also employed as an auxiliary method to visualize the surface below the micron scale. The SEM images reveal a micron-sized ridgelike texture. Room temperature acid treatment makes the ridges become more pronounced, while treatment with boiling acid uncovers fiberlike structures of roughly 1 microm diameter. All samples display an apparent surface fractal dimension of Ds = 2.4 in the wave vector range 0.001-0.02 A(-1). Nitric acid at room temperature increases the surface oxygen content only by 3 at. %, while all the adsorption properties and structural parameters reported in this paper are virtually unaffected. Significant differences in the morphology at submicron scales appear only after boiling acid treatment. The resulting carbon remains highly microporous, but the loss of Brunauer-Emmett-Teller (BET) surface area from about 1150 to 304 m2/g is approximately 75%. In addition to the principal peak at around 8 A, fresh peaks appear in the polydisperse Horvath-Kawazoe (HK) pore size distribution owing to the burnoff of intervening walls. The average width of the slitlike pores calculated from the Dubinin-Radushkevich (DR) plot increases from 8.4 to 11 A. The minimum slit width where the applied probe molecules, that is, nitrogen and hexane, can enter increases from about 5 to about 5.4 A. The separation distance of the basic structural units is practically unchanged. When, however, this carbon is in contact with hexane, this distance expands from about 19 to 27 A. The swelling is consistent with the deformable nature of this sample also illustrated by the low-pressure hysteresis and the reduced helium density. Particular attention was paid to the surface areas derived from low-temperature nitrogen adsorption and X-ray measurements. Owing to the wide spatial range of the structures in these samples, estimates of the specific surface area of activated carbons can be substantially in error unless both upper and lower q ranges of the SAXS spectra are taken into account. Surface areas derived from the adsorption data either by the BET or the DR approaches were always below the values obtained by standard SAXS. As an example, the carbon sample functionalized at room temperature gave surface area values of 1114, 1293, and 1970 m2/g, respectively. The possibility that this difference is caused by inaccessible pores was excluded by contrast variation measurements with hexane.