Small-angle X-ray Scattering Profiles Research Articles

Fluctuations of lamellar structure prior to a lamellar-->gyroid transition in a nonionic surfactant system

Fluctuations of lamellar structure prior to a lamellar-->gyroid transition in a nonionic surfactant-water system has been investigated by means of small-angle x-ray scattering (SAXS) and differential scanning calorimeter measurements. For large DeltaT (DeltaT=T-T(LG), where T is the temperature and T(LG) the lamellar-->gyroid transition temperature) in the lamellar phase, the SAXS profiles can be described by a Caille correlation function for undulating lamellar structure. Approaching the temperature to the T(LG), an excess diffuse scattering grows at the lower Q (Q is the magnitude of scattering vector) side of the first lamellar peak. Highly oriented lamellar samples revealed that the excess diffuse scattering arises from in-plane density fluctuations. We attribute this diffuse scattering to the perforation fluctuation layer (PFL) structure and we show that the PFL is an equilibrium structure. At T(LG), the PFL transformed to the gyroid phase through a transient ordered structure having a rhombohedral symmetry.

Determination of specific surfaces of silica xerogets by SAXS

Small angle X-ray scattering (SAXS) with synchrotron radiation as X-ray source has been used to study the structure of silica xerogets prepared by sol-get process. Both the agreement of SAXS profiles with and the deviation from Porod’s law and Debye’s theory have been found, showing that there are differences between the structures of these xerogets. The specific surfaces of the samples whose SAXS profiles agreed with Porod’s law and Debye’s theory have been determined by analyzing SAXS data according to the methods of Porod and Debye, respectivety, and the results of both methods used were found to be similar. We have proposed the corresponding Porod and Debye analysis methods to determine the specific surfaces of samples whose SAXS profiles do not agree with Porod’s law and Debye’s theory, i.e. the negative or positive deviation. The results of both methods used here were also found to be close to each other. The specific surfaces fell between approximatety 80–150 m2/cm3 for the samples prepared under various conditions.

Effect of polydispersity on the evolution of density fluctuations to lamellar crystals in linear polyethylene

The effect of polydispersity on structure development in linear polyethylenes is studied by simultaneous real time small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS). Our measurements show that below 128 °C, changes in the SAXS and WAXS intensity profiles for a broad molecular-weight distribution sample occur simultaneously as previously reported for a narrow molecular-weight distribution sample. We demonstrate that variations in the SAXS profile can be correlated with the morphological changes associated with the evolution of single chain folded crystal lamellae to lamellar aggregates. At 128 °C and higher temperatures, changes in the SAXS intensity profile for the broad molecular weight distribution sample occur much earlier than the onset of lamellar crystal growth evidenced in the WAXS profile. For the period before crystal growth is manifest in the WAXS scattering, the SAXS intensity at low angles increases while the domain size remains constant. The low-angle intensity uptake in SAXS can be best described by the Guinier approximation. On the other hand, the temperature dependence of the variation in the average crystal thickness during isothermal crystal growth is a function of the relative rates of primary crystallization and thickening at a given temperature. We discuss the effect of a broad distribution in chain length on the various stages in the development of the morphology.

Precipitation in 18 wt% Ni maraging steel of grade 350

The evolution of precipitates in maraging steel of grade 350 was studied using the complementary techniques of small angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). These investigations revealed that ageing the steel at 703 K involved a rhombohedral distortion of the supersaturated b.c.c. martensite accompanied by the appearance of diffuse ω-like structures. This was followed by the appearance of well-defined ω particles containing chemical order. At the ageing temperature of 783 K, Ni 3(Ti, Mo) precipitates were the first to appear with a growth exponent of 1/3. The values of the Porod exponent obtained from the SAXS profiles indicated that the ω particles, formed below 723 K, had diffuse interfaces up to an ageing time of 48 h. On the other hand, Ni 3(Ti, Mo) precipitates, formed above 723 K, developed sharp interfaces in just about an hour. Also, the steel exhibited scaling in phase separation both at 703 and 783 K, but only during the early stages. Through this study it was established that, at temperatures of ageing less than 723 K, evolution of ω particles takes place through the collapse of the unstable b.c.c. lattice and, at temperatures above 723 K, precipitation of A 3B type of phases through the mechanism of clustering and ordering of atomic species. Sharp interfaces develop rather quickly when the mechanism of precipitation involves development and amplification of a concentration wave alone as in the nucleation of Ni 3(Ti, Mo) at 783 K than when an interplay of both the displacement and concentration waves is required as in the evolution of ω at 703 K. These results indicate towards the possibility of existence of two separate time–temperature–transformation (TTT) curves, one for the evolution of ω-phase and another for nucleation and growth of Ni 3(Ti, Mo).

Equilibrium short-range order in the isotropic phase of a poly(ester-imide) with a C22H44 alkane spacer

Small-angle X-ray scattering (SAXS) was performed on a sample of poly(4,4′- phthaloimidobenzoyldoeicosamethyleneoxycarbonyl) (PEIM-22) as a function of temperature. Wide-angle X-ray diffraction and differential scanning calorimetry were used to follow the isotropization of the crystalline PEIM-22. The crystals of PEIM-22 consist of biphasic layers up to the isotropization temperature. A series of SAXS peaks are observed for the crystals between θ = 0.3 and 3.5°. The width of these peaks indicates the formation of a smectic-like, crystalline layer structure of a coherently scattering domain size of only 3–4 repeating units. In the isotropic phase, a single, broader peak remained at a spacing of ≈2.6 nm, suggesting even at high temperature the existence of equilibrium, short-range, local order. The SAXS profiles were calculated based on a model of alternating layers of a linear, paracrystalline lattice. The results were discussed together with similar data on model compounds in the literature, and it is suggested that the short-range order in the isotropic phase is due to a nanometer-scale separation of the polar, aromatic phthaloimidobenzoyl from the flexible doeicosamethyleneoxycarbonyl. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 611–621, 2000

DETERMINATION OF AVERAGE PORE DIAMETER OF SiO2 XEROGELS BY SMALL ANGLE X-RA Y SCATTERING

Small angle X-ray scattering (SAXS) with synchrotron radiation as X-ray source h as been used to study the structure of SiO2 xerogels prepared by sol-gel pr ocess. All SAXS profiles in this paper deviate from Porod's law and show negativ e or positive deviation. In order to obtain the information of pore in SiO2 xerogels, we have proposed the corresponding methods to correct the negat ive and positive deviations from Porod's law. Then, the average pore diameter of SiO2 xerogels is determined with Debye's method and Guinier's method , separately, and the results are found to be close to each other. The average d iameters fall in the rangl 3-25nm for samples prepared under various conditions. The results of SAXS are also close to that determined by N2 adsorption met hod at 77K with ASAP2000.

Clustering in carboxylated polysulfone ionomers: A characterization by dynamic mechanical and small-angle X-ray scattering methods

The dynamic mechanical properties and morphology of carboxylated polysulfone ionomers were investigated by dynamic mechanical thermal analysis and small-angle X-ray scattering (SAXS) techniques. It was found that at 25 mol % of ions, ionomers show two glass transitions: one at about 200 °C (the matrix T g ) and the other at about 235 °C (the cluster T g ). It was also found that with increasing ion content up to about 37 mol %, the matrix T g shifted to higher temperatures and the size of tan δ peak decreased. The cluster T g did not change. From the results, it is suggested that even at high ion content, the ionomers contain a significant amount of unclustered material, but that the increase in the ion content does not increase the amount of clustered material. SAXS profiles showed the ionic peak, which represents the presence of multiplets in the cluster regions. In addition, the difference in the matrix and cluster T g 's of this ionomer system was found to be about 35°. Thus, it is postulated that ionic group aggregation is subject to steric hindrance owing to the bulkiness of benzene ring, and tension on polymer chains surrounding the multiplet owing to chain rigidity, which limit the size and stability of the multiplet significantly.

Supramolecular structure of the solid-state complexes of polyacrylamide and dodecylbenzenesulfonic acid

The solid-state complexes of a flexible polymer, polyacrylamide (PAA), and an amphiphilic surfactant, dodecylbenzenesulfonic acid (DBSA), have been investigated. Complexation between PAA and DBSA occurred via proton transfer from DBSA to the carbonyl group in PAA, giving rise to a “supramolecular comb-like polymer” with ionic bonding. The mesomorphic phase in the complexes was identified by the birefringent patterns under polarized optical microscopy. Wide angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) revealed that the complexes microphase separated into a lamellar morphology consisting of alternating polar and nonpolar layers with the long period of ca. 3 nm. As the composition x (the average number of DBSA molecules bound with a PAA repeating unit) ≥ 0.7, the SAXS profiles were characterized by a major scattering peak associated with the flat lamellar structure. Multiple scattering peaks were observed at lower degree of complexation (x ≤ 0.6), which were ascribed to the formation of undulated lamellae that organized into a macrolattice with the diffraction patterns observable by SAXS. Preliminary assignments of the lattice planes suggested that the lobes of the undulated lamellae organized into body centered cubic (bcc) or simple cubic (sc) types of unit cell. The glass transition temperature of the polar layers in PAA(DBSA) complexes increased with increasing degree of complexation owing to the stiffening of polymer chains. Complexation with DBSA also enhanced the thermal stability of PAA, where the thermal decomposition temperature can be raised by as much as 35 °C.

Structural characterization of lactate dehydrogenase dissociation under high pressure studied by synchrotron high-pressure small-angle X-ray scattering.

The effect of high pressure on lactate dehydrogenase (LDH) was studied using small-angle X-ray scattering (SAXS). The SAXS results are interpreted in terms of the dissociation and association of LDH within a compression and decompression cycle and its temperature dependence. LDH consists of four identical subunits. At 120 MPa and 25 degrees C, 50% of the LDH dissociates into subunits, while at 10 degrees C, this occurs at 78 MPa. The hysteresis in the dissociation and association under pressure was confirmed in terms of the radius of gyration and was seen to be more conspicuous at low temperature. Forward scattering, I(0)/C, which is proportional to molecular weight, showed that LDH dissociated into dimer (not monomer) subunits under pressure. The application of high pressure to dissociated dimers induced irreversible aggregation. This result is in sharp contrast with the result of fluorescence spectroscopy suggesting a dissociated monomer [King, L., and Weber, G. (1986) Biochemistry 25, 3637-3640]. As for structural change after reassociation, there was little structural difference between native and drifted LDH. The difference was smaller than the structure change by ligand binding. At 200 MPa, the presence of five scattering peaks in the medium-angle region indicates that the dissociated dimer does not have a molten globule-like structure but a core structure. We propose a model of the dissociated dimer, based on the SAXS profile, in which the volume is reduced without disrupting the core structure.

Rheological Behaviors and Microstructures of Aqueous Suspensions of Bimodal Core-Shell Structured Latex Particles.

Rheological behaviors and microstructures of aqueous suspensions of a bimodal core-shell type of carboxylated particles have been studied by varing a weight ratio of two particles. Diameters of these particles in the fully neutralized state were 176nm and 291nm, respectively. Steady shear flow was measured with a coni-cylinder rheometer, and the critical shear stress σc, defined as the stress at the transition point from Newtonian flow to shear thinning flow, was estimated. The distance ξ which is the center to center distance between neighboring particles in an ordered structure of the suspensions was estimated with the small angle X-ray scattering (SAXS) method. All suspensions tested exhibited psudoplatic flow and gave single diffraction peak in their SAXS profiles. This result suggests that an alloy structure made of the bimodal particles is formed in these suspensions. As a weight fraction of large particle increased, viscosity and a degree of shear-thinning of the suspension decreased, and also ξ decreased. The relationship between σc and ξis represented as σc=4kT/3πξ3. This indicates that σc is dominated by thermal motion of lattice of the ordered structure. These findings indicate that the shear-rate dependence of the viscosity of the suspension is attributed to dynamical competition between the thermal motion and the hydrodynamic motion under shear flow, and the mechanism is applied to not only uni-modal suspensions but also bimodal suspensions.

Characterization of a multilayer soft X-ray reflector fabricated by pulsed laser deposition

A Mo/Si multilayer (ML) has been fabricated as a reflector in the soft X-ray spectral region by pulsed laser deposition (PLD), using the second harmonic of Nd/YAG pulsed laser (5 ns, 532 nm light). The ML structure was characterized by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS) and photoelectron spectroscopy for chemical analysis (ESCA). The near-normal incidence reflectivity in the spectral range of 14–17 nm was measured using a soft X-ray reflectometer based on a laser-produced plasma. The structural parameters were evaluated by fitting to both the SAXS profile and the soft X-ray reflectance measurement with asymmetric interface profile, roughness and composition taken into account.

Phase Transition between Microemulsion and Lamellar Phases in a C12E5/Water/n-octane Amphiphilic System

A ternary amphiphilic system consisting of water, n-octane and C12E5 has been studied by small angle X-ray scattering (SAXS) to elucidate the mechanism of phase transition between lamellar and microemulsion phases. SAXS profiles in the region between lamellar and microemulsion phases show two distinct peaks, which indicate that different structures coexist. These structures change continuously as transition goes on, which is in good agreement with the lever rule in phase diagram. The transition behavior has been explained as a result of the change of curvatures of the interfacial film as a function of temperature and subsequent change of bending elastic energy. A boundary of the coexistence region is determined by the double tangent construction for the free energies of the microemulsion and lamellar phases.

Small-Angle X-ray Scattering Study of the Interfacial Characteristics Between δ' Phase and Matrix in Al–2.70 mass% Li Alloy

Small-angle X-ray scattering (SAXS) has been used to study the δ′ precipitation in an Al-2.70 mass% Li alloy aged at 463 K for 8 and 30 h. It is shown that the SAXS profile does not agree with Porod's law and has a negative slope. This suggests that the dispersive interfacial layer exists between the δ′ phase and the matrix. It is positive evidence that spinodal decomposition takes place during the precipitation process of the δ′ phase. The thicknesses of the interfacial layers are found to be 4.75 and 6.63 nm for the samples aged at 463 K for 8 and 30 h, respectively.

Nanoscale Supramolecular Structures in the Gels of Poly(Diallyldimethylammonium Chloride) Interacting with Sodium Dodecyl Sulfate

A highly ordered supramolecular structure is formed in the polyelectrolyte−surfactant complex between the anionic surfactant sodium dodecyl sulfate (SDS) and the cationic network of poly(diallyldimethylammonium chloride) (PDADMACl). From small-angle X-ray scattering (SAXS), the complexes between PDADMACl and SDS were shown to exhibit a hexagonal type of microstructure which is different from that of pure SDS. A d spacing of 3.7 nm corresponding to the interdistance between SDS aggregates in the gel network was obtained. The intensity of the diffraction peaks and the degree of order increased with increasing initial SDS concentration and charge content of the PDADMACl gels. The diffraction peaks were broadened when the concentration of SDS in the external solution phase was higher than its critical micelle concentration (cmc). The SAXS profiles were unexpectedly independent of the degree of cross-linking of the PDADMACl gels in the range of 0.5−2%.

Gelation mechanism of methylhydroxypropylcellulose in aqueous solution

The reversible gelation behavior of methylhydroxypropylcellulose aqueous solutions was observed on heating and cooling by means of differential scanning calorimetry (DSC) and time-resolved small angle X-ray scattering (SAXS). DSC results indicate that the gelation proceeds in two steps and the structuring or destructuring of water along polysaccharide chains was responsible for the observed thermal behavior. An extent of inhomogeneity evaluated from the SAXS profile was found to increase from 4–5 nm in sol to a few tens nm upon gelation. It was speculated that gelation takes place by the fringed micelle formation with a large size distribution and by the subsequent phase separation.

Small-angle X-ray scattering study of nanopore evolution of macroporous silica gel by solvent exchange

Small-angle X-ray scattering (SAXS) together with nitrogen adsorption, have been employed to analyse the pore-structure evolution behaviour, on the nanometre scale, by varying solvent-exchange treatment for silica gels having bicontinuous interconnected macropores. For the gels prepared in the system containing poly(acrylic acid), the difference in SAXS profile between gels immersed in ethanol and 1 mol dm–3 nitric acid was small in the wet state, but was considerably enlarged on drying. The dried gel immersed in ethanol exhibited a mass fractal feature, while that immersed in 1 mol dm–3 nitric acid was non-fractal up to several nanometres. The evolution behaviour during heat-treatment also differed, leading to a smaller size and lower volumes of the pores in the former gel. These variations in pore structures are explained by the occurrence of swelling in ethanol, and microscopic phase separation in 1 mol dm–3 nitric acid solution. However, for gels prepared in the system containing poly(ethylene oxide), the difference in profiles of similarly treated dried gels was not so evident, possibly because the progress of microscopic phase separation was restricted by the adsorbed organic polymer on silanols of the gel matrix. On the other hand, a significant increase in the average pore size, as well as the pore volume, was observed by solvent exchange in basic conditions, irrespective of the kind of polymer or catalyst used for gel preparation. This effect is interpreted as a coarsening process through a dissolution and reprecipitation mechanism. The time evolution of the Porod slope, as well as its dependence on the solution pH in the wet state, were monitored by in situ SAXS measurements. The steep increase of the Porod slope accompanied by the extension of the power-law region in the wet state indicated reorganization within the silica gel structures.

Small-angle x-ray scattering investigation of temperature influences on microstructures of an ionomer

Ionomer morphology has received extensive studies due to its interesting characteristics in the molecular aggregation of ionic groups. The strong scattering peak in the small-angle X-ray scattering (SAXS) profile has been accounted for by several models. From the multiphase relaxation point of view, Eisenberg et al. proposed that the ionic multiplets were the basic unit of aggregation. The ionic aggregates were surrounded by a spherical region of polymer backbones of restricted mobility. Some overlap of the restricted regions of the ionic phases could be characterized by a high-temperature relaxation relative to the one for the surrounding matrix. The electron density inhomogeneity in a length scale comparable to the average distance between two adjacent multiplets leads to an ionic peak in the SAXS profile. The SAXS profiles of ionomers at different temperatures depended on the counterions and the method of sample preparation. In this paper the authors report SAXS measurements of an ionomer which has undergone different thermal treatment. Extra care was taken in correcting the thermal expansion which was responsible for the primary change in the SAXS profile at different temperatures. The authors used an approach developed by Fischer and Gehrke et al. The modified Porod law and the inversemore » Fourier transform were used to evaluate the microstructure parameters.« less

Small-angle X-ray scattering study of lamellar microdomains in a block copolymer

Lamellar microdomains formed in the solvent-cast films of a poly[styrene-block-(ethylene-alt-propylene)] (SEP) diblock polymer were studied by small-angle X-ray scattering (SAXS). The SAXS profiles, displaying a series of peculiar scattering maxima which cannot be ascribed to the higher-order diffraction maxima from a regular lamellar spacing, were analyzed based on a model of the one-dimensional paracrystal with a preferential orientation. The results suggest that these maxima are due to higher-order scattering maxima from single lamellar microdomains. The maxima suggest that the relative standard deviation for the distribution of the polystyrene lamellar size is much smaller than that of the lamellar spacing, giving rise to a situation in which the oscillation of the particle factor with scattering vector h persists up to high h values while that of the lattice factor damps to unity at low h values. The SAXS result was interpreted as being due to a bending distortion of the polystyrene lamella with a smaller thickness and a narrower thickness distribution than those of the poly(ethylene-alt-propylene) lamella. A study by transmission electron microscopy tends to support this result.

On the morphology of oriented nylon-12

The morphology of drawn and annealed sheets of nylon-12 was investigated by transmission electron microscopy of stained sections, and the results compared with equivalent small-angle X-ray scattering (SAXS) patterns. A three-component structure was observed, consisting of crystalline (C) and amorphous (A) regions in the microfibrils and an interfibrillar component whose density was deduced to be intermediate between that of the C and A regions. The crystallite width was given satisfactorily by a Guinier analysis of the SAXS profile.

An Apparatus for High Speed Measurements of Small-Angle X-Ray Scattering Profiles with a Linear Position Sensitive Detector

An apparatus for high speed measurements of small-angle X-ray scattering (SAXS) is described. This apparatus utilizes a 12 kW rotating anode X-ray generator, a linear position sensitive proportional counter (multicathode delay line PSPC), and a two-parameter multichannel pulse height analyzer (MCA) with 12 kwords (16 bits/word) memory area available for SAXS intensity data as a function of position (scattering angles) and time slice. The two-parameter MCA is constructed within a microcomputer system, by utilizing its R/W memory for data storage, and the memory incrementing and real-time CRT display is implemented by using two direct memory access (DMA) controllers. The cycle time of the access is about 10 μs. The measuring time for SAXS profiles with this apparatus can be shortened approximately by three orders of magnitude in comparison with the measuring time with SAXS apparatuses utilizing a conventional step-scanning goniometer and a conventional X-ray tube, thus permitting time-resolved analyses of SAXS profiles. Some applications of the apparatus to dynamic SAXS measurements are presented for polymeric systems, the preliminary results of which seem to indicate the possibility of obtaining a new class of data on dynamics in structural transformation, deformation, formation and annihilation in the scale of a few tens to several hundred Angstroms.