Real space functions from experimental small angle scattering data

A model free evaluation of small angle scattering data of interacting particles results in real space curves that are often difficult to interpret. It is then easier to use a model for the inter and/or the intra particle effects. Such a procedure requires the selection of appropriate models. The selection of the correct model is facilitated by interpreting parts of the purely model free real space results of the scattering data. The corresponding functions for hard, charged, and attractive spheres are simulated as well as the curves of spheres in BCC crystalline order and of cylinders in hexagonal order. The simulated results are compared to experimental data obtained from concentrated emulsions. Estimations for particle diameter, type of interaction, next neighbour distance, and volume fraction can be deduced from most of the data.     

NMR analysis of interaction between styrene-divinylbenzene gel beads and small molecules

The interaction of small molecules such as cyclohexane, tetrahydrofuran, and acetonitrile with styrene-divinylbenzene copolymer gel beads were investigated by ¹³C-NMR spectroscopy. When the gel content was 0.1–0.3 g/mL, the ¹³C-NMR spectrum of the solvent displayed two peaks. A sharp peak at lower magnetic field was assigned to the free solvent, and a broad one to the solvent affected by the gel. This signal splitting is attributed to the upfield shift caused by aromatic rings of styrene units in the polymer chain. The nitrile carbon of acetonitrile showed the largest upfield shift. The mobility of small molecules in gel beads was also investigated using the nuclear magnetic relaxation method. In the case of good solvents for gel beads, the mobility was affected by the cross-linking density, whereas poor solvents exhibited little dependence of the cross-linking density. © 1995 John Wiley & Sons, Inc.     

Analysis of small angle neutron scattering data from strongly interacting polydisperse ionic micellar solutions

Small angle neutron scattering (SANS) intensity distributions from ionic micellar solutions without added salt generally show a prominent interaction peak at finite Q (magnitude of the wave vector transfer) related to a certain inter-micellar correlation distance. Analysis of this type of data requires, aside from the structural model of the micelle itself, a statistical mechanical theory for dealing with the inter-micellar correlations. We present a method for a consistent analysis of SANS data taking into account the surfactant chain packing, the aggregation number polydispersity, and the effective micellar charge. The micelle is modelled as a two-region spheroidal particle and the inter-micellar correlations calculated according to a generalized one-component macroion (GOCM) theory. GOCM uses an effective inter-micellar pair potential which is a finite concentration extension of the well-known Derjaguin-Landau-Verway-Overbeek (DLVO) double layer interaction potential. Two micellar solutions are treated as examples, namely that of sodium dodecyl sulfate (SDS) and sodium 1,2-bis(2-ethylhexyloxycarbonyl)ethanesulfonate (AOT). The effects of polydispersity are appreciable immediately above the critical micellar concentrations (CMC). Both the structural parameters of the micelle and the free energies of micellization and micellar growth can be extracted from SANS data.     

Molecular aspects of polymer network deformation - small angle neutron scattering and NMR studies

Poly(1,4-butadiene) networks obtained by a 4-functional random cross-linking reaction over a broad range of polymer concentration were studied by small angle neutron scattering(SANS), ²H NMR and Monte Carlo(MC) simulation in the isotropic and uniaxially deformed state. The defect structure of the networks has been characterized by MC simulation of the cross-linking reaction. The anisotropy of the radius of gyration in deformed networks determined from SANS has been analyzed by the theory of Ullman. It was found that the number of active cross-links per chain is in agreement with MC and that the chain deformation follows phantom behaviour. The local orientation as measured by ²H NMR is related to the global anisotropy of the network by a MC calculation of oriented chains. The ²H NMR line shape of the deformed network is analyzed in terms of two relaxation processes arising from interior parts of the chains and from segments at chain ends. The mobility of both decrease with strain. It was found that the orientation connected to the first process shows the classical strain dependence of rubber elasticity, whereas the second exhibits a weaker dependence on strain.     

Grazing-incidence transmission small angle X-ray scattering from thin films of block copolymers

Thin films of lamellar and cylindrical block copolymers are popular systems for low-cost nanolithography. To be useful as nanoscale templates, the lamellae or cylinders must be oriented perpendicular to the substrate. Domain orientations are usually characterized by microscopy measurements of the film surface, but these techniques cannot detect tilted, bent, or tortuous domains in the film interior. We report a simple method to quantify out-of-plane disorder in thin films of block copolymers based on a variant of grazing-incidence small angle X-ray scattering (GI-SAXS). A typical GI-SAXS experiment illuminates the center of a substrate-supported film at a grazing angle of incidence (near the film/substrate critical angle), and the strong reflected signal is interpreted with the distorted-wave Born approximation. In a new approach, the beam footprint is moved to the far edge of the sample, allowing the acquisition of a transmission pattern. The grazing-incidence transmission data are interpreted with the simple Born approximation, and out-of-plane defects are quantified through analysis of crystal truncation rods and partial Debye-Scherrer rings. Significantly, this study demonstrates that grazing-incidence transmission small angle X-ray scattering can detect and quantify the buried defect structure in thin films of block copolymers. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Block copolymer-homopolymer blends in the disordered state: Determination of the interaction parameter using small angle neutron scattering

The aim of this study was to determine the interaction parameter x_AB and its variation with temperature from the intensity scattered By pure block copolymer (A-B) and block copolymer-homopolymer (B) blends where A is polydeuteratedstyrene and B polybutadiene. SANS experiments on pure copolymers of low molecular weight have shown that the scattering curve exhibits a peak of intensity related to the correlation hole effect. χ_AB was determined by fitting the experimental curves using Leibler's theory and the law of variation of χ_AB versus temperature was established. In the case of copolymer-homopolymer blends, the scattering spectrum is modified because of a new and additional long range correlation effect (mixing effect) which dominates in the low q range and leads to strong forward scattering. We have not found any significant variation of χ with blend composition.     

Interaction strength between proteins and polyelectrolyte brushes: a small angle X-ray scattering study

We present an investigation of β-lactoglobulin adsorption onto spherical polyelectrolyte brushes (SPBs) by small angle X-ray scattering (SAXS). The SPB consists of a polystyrene core onto which long chains of poly(styrene sulfonate) are grafted. The amount and the distribution of proteins adsorbed in the brush layer at low ionic strength can be derived from SAXS. The analysis of the SAXS data reveals additionally that some of the protein molecules form aggregates of about six monomers in the adsorbed state. Furthermore, the position and the amount of slightly bound protein can be detected by the combination of the SAXS results and the SPB loading after extensive ultrafiltration. The total amount of adsorbed protein is compared to data derived from isothermal titration calorimetry. The comparison of both sets of data demonstrates that the protein molecules in the inner layers of the spherical polyelectrolyte brush are firmly bound. Proteins located in the outer layers are only weakly bound and can be washed out by prolonged ultrafiltration.     

A small angle neutron scattering study of the interface between solids and oil-continuous emulsions and oil-based microemulsions

We have measured the small angle neutron scattering (SANS) from slurries of powder in contact with surfactant solutions and emulsions to determine the fluid/solid interfacial structure. The slurry solids consisted either of graphite or pyrites particles; and the fluids were hexadecane containing the robust commercial polyisobutylenesuccinamide (PIBSA) surfactant, or a high internal phase emulsion of aqueous ammonium nitrate in hexadecane stabilised by PIBSA. To resolve the interfacial structure for both systems, combinations of deuterated and protonated materials were used.At low concentration in hexadecane, PIBSA forms a complete monolayer on graphite with a footprint per molecule of 103 Å² and a layer thickness of 19 Å. At higher concentrations, the complete monolayer of footprint is 61 Å² and 30 Å thick indicating compression of the PIBSA chain coil structure. Geometric exclusion effects caused by the stacking of the graphite particles also results in an excess of oil for ca. 160 Å above the surfactant monolayer.For pyrites in contact with surfactant in hexadecane, the oxidised surface layer, while smooth at the oil interface, is diffuse and/or rough at the interface with the bulk sulphide below. There is again a complete monolayer of surfactant adsorbed at the oxide surface, in a relatively compressed state with a footprint of 70 Å², more tightly bound than on graphite. The excess of oil phase above the adsorbed surfactant monolayer is observed for samples with larger pyrites particle sizes but not for a sample with smaller particles. This suggests that the oil excess does arise from purely geometric solid particle packing, but that the local particle surface curvatures are significantly higher than the overall particle size would suggest.The scattering from the pyrites/emulsion interface was modelled by a 30 Å thick monolayer of surfactant coating an oxide surface with a molecular footprint of 123 Å². For the larger particle size samples, there is a 30 Å thick layer of oil above the pyrites particle surface before a bulk emulsion/pyrites mixture is reached.These results extend previous reflectometry experiments on the silicon/emulsion interface, indicating that for stable emulsions the structures are qualitatively similar for three dissimilar solid surfaces. They show that useful results on surfactant structure and emulsion layering at the solid/emulsion and other solid/fluid interfaces can be simply obtained by SANS on powder samples variously contrasted by deuteration. SANS can be applied to a much greater range of solid interfaces than reflectometry since large neutron-transparent single crystals are not required, although the variety of faces in a powdered material degrades the quality of the information.     

Some aspects of data analysis of multi‐angle dynamic light scattering

In dynamic light scattering the signal to noise ratio may become very low because of short measurement times or low intensities. Then the analysis of the data becomes a central point and it is worthwhile to accept some numerical efforts and an increased calculation time caused by more sophisticated data analysis. In the following three aspects of an improved data analysis are discussed for multi‐angle dynamic light scattering. In the first part of this paper, the influence of the correlation of the errors of the autocorrelation time function is considered. With decreasing measurement time the errors of the autocorrelation time function increase. The more the errors increase, however, the more important the error model becomes. On the other hand, with increasing number of photons the correlations of the errors of the autocorrelation time function become important: The non‐diagonal elements of the covariance matrix of the data errors increase and may become of the order of the diagonal elements. In the second part the sensitivity of the nonlinear simultaneous multi‐angle regularization to aberrations in the experimental set‐up is investigated. Therefore, for a given bimodal radii distribution and different scattering angles data were simulated taking into account the finite aperture of the detector as well as the laser light backscattered at the back of the cuvette. This improved model is compared with the classical model, which neglects these aberrations in the experimental setup. Finally, the advantage of the simultaneous regularization method over averaging over single‐angle results is demonstrated. Estimating of the radii distribution from all multi‐angle data at once leads to a higher solution compared to averaging over the single‐angle results.     

Structure of star-burst dendrimers: a comparison between small angle x-ray scattering and computer simulation results

We investigated the generation dependent shape and internal structure of star-burst dendrimers under good solvent conditions using small angle x-ray scattering and molecular modeling. Measurements have been performed on poly(amidoamine) dendrimers with generations ranging from g=0 up to g=8 at low concentrations in methanol. We described the static form factor P(q) by a model taking into account the compact, globular shape as well as the loose, polymeric character of dendrimers. Monomer distributions within dendrimers are of special interest for potential applications and have been characterized by the pair correlation function gamma(r), as well as by the monomer and end-group density profile, rho(r) and rho(e)(r), respectively. Monomer density profiles and gamma(r) can be derived from P(q) by modeling and via a model independent approach using the inverse Fourier transformation algorithm first introduced by Glatter. Experimental results are compared with computer simulations performed for single dendrimers of various generations using the cooperative motion algorithm. The simulation gives direct access to gamma(r) and rho(r), allows an independent determination of P(q), and yields in addition to the scattering experiment information about the distribution of the end groups. Excellent qualitative agreement between experiment and simulation has been found.     

Shear induced deformation of polystyrene coils in dilute solution from small angle neutron scattering

The deformation of the overall conformation of polystyrene,M _w =280000 g/ mole in dilute solution in a constant shear gradient has been investigated by small angle neutron scattering (SANS). The experiments were performed with a new Couette-type apparatus, consisting of two concentric quartz cylinders in which the outer one rotates and the solution is confined in the gap between both cylinders. The observation of the elastic coherent small angle scatterring intensity at a shear gradient ofG=400 s^?1 has revealed a distinct anisotropy of the scattering pattern on the two dimensional detector, as estimated from equilibrium chain dynamics. After extrapolation to zero angle and zero concentration two different values for the overall size of the single macromolecule parallel and perpendicular to the flow-direction are deduced.     

Informing the improvement of forest products durability using small angle neutron scattering

A better understanding of how wood nanostructure swells with moisture is needed to accelerate the development of forest products with enhanced moisture durability. Despite its suitability to study nanostructures, small angle neutron scattering (SANS) remains an underutilized tool in forest products research. Nanoscale moisture-induced structural changes in intact and partially cut wood cell walls were investigated using SANS and a custom-built relative humidity (RH) chamber. SANS from intact wood sections cut from each primary wood orientation showed that although wood scattered anisotropically across 1.3–600 nm length scales, measurement of elementary fibril spacing and low-q surface scattering were independent of orientation. Water sorption caused spacing between elementary fibrils to increase with RH, and this swelling accounted for over half the transverse swelling in S2 secondary wood cell walls. Elementary fibril spacing in longitudinally cut wood cells, which were designed to mimic cells near wood-adhesive bondlines, was greater than the spacing in intact cells above 90 % RH. This suggested that some cell wall hoop constraint from the S1 and S3 cell wall layers on the S2 layer was released by cutting the cells. Furthermore, increased spacing between elementary fibrils may also create diffusion channels that are hypothesized to be responsible for the onset of fungal decay in wood. Protocols were established to use SANS in future research to study adhesives and protection treatments to improve moisture durability in forest products.     

Osmotic virial coefficients for model protein and colloidal solutions: importance of ensemble constraints in the analysis of light scattering data

Protein-protein interactions in solution may be quantified by the osmotic second virial coefficient (OSVC), which can be measured by various experimental techniques including light scattering. Analysis of Rayleigh light scattering measurements from such experiments requires identification of a scattering volume and the thermodynamic constraints imposed on that volume, i.e., the statistical mechanical ensemble in which light scattering occurs. Depending on the set of constraints imposed on the scattering volume, one can obtain either an apparent OSVC, A(2,app), or the true thermodynamic OSVC, B(22)(osm), that is rigorously defined in solution theory [M. A. Blanco, E. Sahin, Y. Li, and C. J. Roberts, J. Chem. Phys. 134, 225103 (2011)]. However, it is unclear to what extent A(2,app) and B(22)(osm) differ, which may have implications on the physical interpretation of OSVC measurements from light scattering experiments. In this paper, we use the multicomponent hard-sphere model and a well-known equation of state to directly compare A(2,app) and B(22)(osm). Our results from the hard-sphere equation of state indicate that A(2,app) underestimates B(22)(osm), but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A(2,app) and B(22)(osm) may be quantitatively significant, but may also be obscured in experimental application by statistical uncertainty or non-steric interactions. Consequently, the two OSVCs that arise in the analysis of light scattering measurements do formally differ, but in a manner that may not be detectable in actual application.     

Theoretical study of the influence of small angle scattering on diffraction enhanced imaging

Small angle scattering plays an important role in diffraction enhanced imaging (DEI). The DEI equation proposed by Chapman is accepted and widely used by many applications in medical, biological and material researches. However, in this framework the contribution of the small angle scattering determined by the crystal analyzer is neglected and the extinction contrast caused by the rejection of the small angle scattering by the analyzer is not explicitly expressed. In this contribution we introduce two additional terms in the DEI equation that describe the additional background introduced by the small angle scattering collected by the analyzer crystal and the extinction contrast associated to the rejection of the small angle scattering by the analyzer crystal, respectively. Four kinds of images of the DEI method were considered by using these revised equations and results were presented and discussed.     

The structure of water in the hydration shell of cations from x-ray Raman and small angle x-ray scattering measurements

X-ray Raman scattering (XRS) spectroscopy and small angle x-ray scattering (SAXS) are used to study water in aqueous solutions of NaCl, MgCl(2), and AlCl(3) with the particular aim to provide information about the structure of the hydration shells of the cations. The XRS spectra show that Na(+) weakens the hydrogen bonds of water molecules in its vicinity, similar to the effect of increased temperature and pressure. Mg(2+) and Al(3+), on the other hand, cause the formation of short and strong hydrogen bonds between the surrounding water molecules. The SAXS data show that Mg(2+) and Al(3+) form tightly bound hydration shells that give a large density contrast in the scattering data. From the form factors extracted from the SAXS data, we found that Mg(2+) and Al(3+) have, respectively, an equivalent of one and one and a half stable hydration shells that appear as a density contrast. In addition, we estimated that the density of water in the hydration shells of Mg(2+) and Al(3+) is, respectively, ～61% and ～71% higher than in bulk water.     

Simulated unfolded-state ensemble and the experimental NMR structures of villin headpiece yield similar wide-angle solution X-ray scattering profiles

With the advent of powerful synchrotron sources, solution X-ray scattering is being increasingly used to get basic information about the structure of polypeptides. The solution scattering technique essentially provides one-dimensional data, which are then interpreted in terms of a three-dimensional structure through model building. Here we calculate wide-angle solution scattering patterns for an ensemble of simulated unfolded structures of villin headpiece, which differ from the native structure by rmsd = 8.8 +/- 1.0 A and have only negligible amounts of native secondary structure. We show that the wide-angle solution scattering pattern of such an ensemble shares significant similarity with the one based on the experimental NMR structures of the molecule. Our results suggest that solution scattering in the wide-angle limit, by itself, provides very little information about the secondary structure content of a polypeptide or its side-chain packing.     

甲基蓝与血红蛋白相互作用的共振瑞利散射光谱研究及小分子的影响

在弱酸性条件下,甲基蓝(MB)可以通过静电和疏水作用聚集到血红蛋白(Hb)上并形成离子缔合物,不仅使得吸收光谱发生变化,而且使得共振瑞利散射增强。据此发展了一种测定Hb的RRS便捷方法,其线性范围和检出限分别为0.2~20μg/mL和0.012μg/mL。与RRS法相比,分光光度法的线性范围和检出限分别为8~60μg/mL和0.688μg/mL(344 nm),5~60μg/mL和0.398μg/mL(408 nm)。此RRS法可用于尿样中Hb的痕量检测。实验考察了体系的吸收、散射光谱性质和最佳聚合条件,并在最佳条件下研究了分析参数及作用机理。并初步讨论了有机小分子对体系的影响,结果表明分子间氢键是主要作用力不容忽视。     

Fractal behaviour of carbon black and smectite dispersions by small angle neutron scattering

From dielectric spectroscopy on mechanically sheared dispersions of carbon black in mineral oil it was known that the distribution of relaxation times was invariant irrespective of the applied shear rate. From this observation fractal behaviour was suspected and a small angle neutron scattering experiment was set up for confirmation. Indeed, by this experiment a fractal dimension has been found of d=2.19, a value which is perfectly comparable tod=2.0 found by dielectric spectroscopy.The dielectric behaviour of the smectite dispersion is different from the carbon black and small angle neutron scattering confirms this. Ad-value of 2.8 has been found, pointing to a more compact object than could be expected from a fractal.