Indirect Fourier Transformation Research Articles

Microemulsions supported by octyl monoglucoside and geraniol. 3. Microstructure & general pattern

This paper completes previous studies on the phase behaviour and microstructure of the quaternary microemulsion water – cyclohexane – n-octyl-β-D-glucoside (β-C8G1) – geraniol. The properties of this system are almost insensitive to temperature, while they can be tuned easily by adding an alcohol as co-surfactant. The addition of the alcohol changes the composition of the interfacial film, which, in turn, is the tuning parameter for the quaternary system. Studies of the phase behaviour together with SANS and NMR measurements allow drawing a quantitative picture of how the domain size ξ, the curvature H, and the interfacial tension σab depend on the composition of the interfacial film. The SANS data of both oil-in-water and water-in-oil droplet microemulsions recorded near the emulsification failure boundary were evaluated with the Generalised Indirect Fourier Transformation (GIFT), revealing a growth towards cylindrical structures when approaching the respective critical end point. We will show that the general behaviour of ternary and quaternary systems is equal if the appropriate tuning parameters are chosen. In addition, we will show that it is possible to apply the scaling description derived for temperature-dependent ternary systems to composition-dependent quaternary systems: plotting the reduced domain size, the reduced curvature and the reduced interfacial tension against the proper reduced tuning parameter, i.e., either the reduced temperature or the reduced interfacial composition, leads to one master curve for all systems.

Effect of polyols on membrane structures of liposomes: A study using small-angle X-ray scattering data and generalized indirect Fourier transformation

This study aimed to evaluate the membrane structure of distearoylphosphatidylcholine (DSPC) liposomes dispersed in water containing various types of polyols with low molecular weight such as glycerin (Gly), 1,3-butandiol (BG), and propylene glycol (PG). To clarify the detailed membrane structure, generalized indirect Fourier transformation (GIFT) analysis, which provides information about the bilayer spacing, bilayer thickness, number of lamellar layers, and membrane flexibility, was applied to small-angle X-ray scattering (SAXS) data of the present system. The GIFT results showed that the bilayer thickness of the DSPC liposomes followed the order Gly>>BG>PG. In addition, the membrane flexibility estimated by the Caille parameter was in the order Gly>>BG>PG; this result was supported by the gel-liquid crystal phase transition temperature (Tc) obtained by differential scanning calorimetry (DSC). These results, together with the Raman spectra, suggest that BG and PG incorporated into the bilayers of DSPC liposomes result in the formation of an interdigitated lamellar structure.

Experimental noise in small-angle scattering can be assessed using the Bayesian indirect Fourier transformation

Small-angle X-ray and neutron scattering are widely used to investigate soft matter and biophysical systems. The experimental errors are essential when assessing how well a hypothesized model fits the data. Likewise, they are important when weights are assigned to multiple data sets used to refine the same model. Therefore, it is problematic when experimental errors are over- or underestimated. A method is presented, using Bayesian indirect Fourier transformation for small-angle scattering data, to assess whether or not a given small-angle scattering data set has over- or underestimated experimental errors. The method is effective on both simulated and experimental data, and can be used to assess and rescale the errors accordingly. Even if the estimated experimental errors are appropriate, it is ambiguous whether or not a model fits sufficiently well, as the `true' reduced χ2 of the data is not necessarily unity. This is particularly relevant for approaches where overfitting is an inherent challenge, such as reweighting of a simulated molecular dynamics trajectory against small-angle scattering data or ab initio modelling. Using the outlined method, it is shown that one can determine what reduced χ2 to aim for when fitting a model against small-angle scattering data. The method is easily accessible via the web interface BayesApp.

Dimensional characterization of cadmium selenide nanocrystals via indirect Fourier transform evaluation of small-angle X-ray scattering data

The correlation of single-particle imaging and absorption spectroscopy made the development of sizing curves possible and enabled rapid size determination of semiconductor nanocrystals based solely on optical properties. The increasing demand and production of such materials has resulted in a question of comparability between existing models and adequate volume-weighted size-determining measurement techniques. Small-angle X-ray scattering (SAXS) is a well-established method for obtaining nanostructural information from particle systems while operating sample quantities up to a commercial scale with a large amount of statistically based data. This work utilizes laboratory SAXS to characterize cadmium selenide nanocrystals with band edge energies between 1.97 and 3.08 eV. The evaluation of the scattering patterns is based on an indirect Fourier transformation (IFT), while dimensional parameters are derived from the model-free pair distance distribution functions (Dmode and Dg), as well as the modeled volume (Dv) and number (Dn)-weighted size-density distributions. We find that comparable data from Dn agree well with existing X-ray diffraction (XRD) and with transmission electron microscopy (TEM) results described in literature; this qualifies SAXS as an equivalent integral characterization method. Although based on an estimate, the radius of gyration yields equivalent accurate results. Additionally, corresponding volume-weighted data are shown that can be useful when transferring information to other techniques. Dmode parametrization represents the largest estimated size of the sample and implies that particles interact and deviate from the spherical morphology, whereas Dv demonstrates results not considering such effects. A full set of the parameters discussed quantifies the quality of a sample.

Analysis of small-angle scattering data using model fitting and Bayesian regularization

The structure of macromolecules can be studied by small-angle scattering (SAS), but as this is an ill-posed problem, prior knowledge about the sample must be included in the analysis. Regularization methods are used for this purpose, as already implemented in indirect Fourier transformation and bead-modeling-based analysis of SAS data, but not yet in the analysis of SAS data with analytical form factors. To fill this gap, a Bayesian regularization method was implemented, where the prior information was quantified as probability distributions for the model parameters and included via a functional S. The quantity Q = χ2 + αS was then minimized and the value of the regularization parameter α determined by probability maximization. The method was tested on small-angle X-ray scattering data from a sample of nanodiscs and a sample of micelles. The parameters refined with the Bayesian regularization method were closer to the prior values as compared with conventional χ2 minimization. Moreover, the errors on the refined parameters were generally smaller, owing to the inclusion of prior information. The Bayesian method stabilized the refined values of the fitted model upon addition of noise and can thus be used to retrieve information from data with low signal-to-noise ratio without risk of overfitting. Finally, the method provides a measure for the information content in data, N g, which represents the effective number of retrievable parameters, taking into account the imposed prior knowledge as well as the noise level in data.

Small Angle X-ray Scattering and Electron Spin Resonance Spectroscopy Study on Fragrance Infused Cationic Vesicles Modeling Scent-Releasing Fabric Softeners.

Industrially relevant systems for household and personal-care products often involve a large number of components. Such multiple component formulations are indispensable and effective for functionalization of the products, but may simultaneously provide more complex structural features compared to those in ideal systems comprising a smaller number of highly pure substances. Using cryogenic transmission electron microscopy (cryo-TEM), small angle X-ray scattering (SAXS), and electron spin resonance (ESR) spectroscopy, we have investigated effects of fragrance-incorporation into cationic vesicles on their bilayer structures and membrane-membrane interactions. Cationic vesicles were prepared from TEQ surfactant, whose major component was di(alkyl fatty ester) quaternary ammonium methosulfate, and fragrance components, l-menthol, linalool, and d-limonene, were infused into the vesicle membranes to model scent-releasing fabric softeners. The cryo-TEM images confirm formation of multilamellar vesicles (MLVs). Generalized indirect Fourier transformation (GIFT) analysis of the SAXS intensities based on the modified Caillé structure factor model reveals that incorporation of a more hydrophobic fragrance component leads to a more pronounced increase of the surface separation (water layer thickness). Furthermore, the fragrance-infused systems show longer-range order of the bilayer correlations and enhanced undulation fluctuation of the membranes than those in the TEQ alone system. The spin-label ESR results indicate different restricted molecular motions in the TEQ bilayers depending on the labeled position and their marked changes upon addition of the fragrance components, suggesting different mixing schemes and solubilization positions of the fragrance molecules in the TEQ bilayers. The present data have demonstrated how the infused fragrance molecules having different hydrophobicity and molecular architectures into the cationic vesicles affect the membrane structures and the intermembrane interactions, which may provide useful information for precisely controlling a fragrance-releasing property.

Nanoparticle size distribution quantification: results of a small-angle X-ray scattering inter-laboratory comparison.

This paper presents the first worldwide inter-laboratory comparison of small-angle X-ray scattering (SAXS) for nanoparticle sizing. The measurands in this comparison are the mean particle radius, the width of the size distribution and the particle concentration. The investigated sample consists of dispersed silver nanoparticles, surrounded by a stabilizing polymeric shell of poly(acrylic acid). The silver cores dominate the X-ray scattering pattern, leading to the determination of their radius size distribution using (i) the generalized indirect Fourier transformation method, (ii) classical model fitting using SASfit and (iii) a Monte Carlo fitting approach using McSAS. The application of these three methods to the collected data sets from the various laboratories produces consistent mean number- and volume-weighted core radii of Rn = 2.76 (6) nm and Rv = 3.20 (4) nm, respectively. The corresponding widths of the lognormal radius distribution of the particles were σn = 0.65 (1) nm and σv = 0.71 (1) nm. The particle concentration determined using this method was 3.0 (4) g l-1 or 4.2 (7) × 10-6 mol l-1. These results are affected slightly by the choice of data evaluation procedure, but not by the instruments: the participating laboratories at synchrotron SAXS beamlines, commercial and in-house-designed instruments were all able to provide highly consistent data. This demonstrates that SAXS is a suitable method for revealing particle size distributions in the sub-20 nm region (at minimum), out of reach for most other analytical methods.

The Distribution of Nanoclay Particles at the Interface and Their Influence on the Microstructure Development and Rheological Properties of Reactively Processed Biodegradable Polylactide/Poly(butylene succinate) Blend Nanocomposites.

The present work investigates the distribution of nanoclay particles at the interface and their influence on the microstructure development and non-linear rheological properties of reactively processed biodegradable polylactide/poly(butylene succinate) blend nanocomposites. Two types of organoclays, one is more hydrophilic (Cloisite®30B (C30B)) and another one is more hydrophobic (BetsopaTM (BET)), were used at different concentrations. Surface and transmission electron microscopies were respectively used to study the blend morphology evolution and for probing the dispersion and distribution of nanoclay platelets within the blend matrix and at the interface. The results suggested that both organoclays tended to localize at the interface between the blend’s two phases and encapsulate the dispersed poly(butylene succinate) phase, thereby suppressing coalescence. Using small angle X-ray scattering the probability of finding neighboring nanoclay particles in the blend matrix was calculated using the Generalized Indirect Fourier Transformation technique. Fourier Transform-rheology was utilized for quantifying nonlinear rheological responses and for correlating the extent of dispersion as well as the blend morphological evolution, for different organoclay loadings. The rheological responses were in good agreement with the X-ray scattering and electron microscopic results. It was revealed that C30B nanoparticles were more efficient in stabilizing the morphologies by evenly distributing at the interface. Nonlinear coefficient from FT-rheology was found to be more pronounced in case of blends filled with C30B, indicating better dispersion of C30B compare with BET which was in agreement with the SAXS results.

In Situ Structural Changes of Biological Macromolecules with BioSAXS

Biological small angle X-ray scattering (BioSAXS) is a nowadays well-established technique to study low resolution structural changes within biological macromolecules in their native environment. In addition, SAXS is a powerful tool for structural characterization and the quantitative analysis of flexible system as a highly complementary method to the high resolution methods of X-ray crystallography and NMR. In general, BioSAXS allows studying three dimensional low resolution structures in different chemical environments under defined conditions (e.g., temperature, pH, dielectric properties, etc.) using not only ab initio methods but also rigid body modeling. Furthermore, the shape (form factor) and interaction potential (structure factor) of the active quaternary protein structure can be assessed using the pair distance distribution function (PDDF) with the use of the generalized indirect Fourier transformation (GIFT). Especially in situ measurements of biological macromolecules have gained a lot of attention in the last decades due to the related structural changes and correlated bioactivity (i.e., native and denatured state).As model substance, Lysozyme was analyzed in terms of its quaternary structural changes upon in situ heat treatment and changes in the dielectric constant of the chemical environment. The validation of the form and structure factor components of the analyzed system allows determining the influence of the changed environmental conditions on the protein structure. The changed chemical environment causes an elongation of the previously globular protein structure. In aqueous environment, Lysozyme is stabilized via electrostatic stabilization. In ethanolic solution, the stabilization mechanism is changed, resulting in a change of structure (e.g., elongation).

Scattering and Spectroscopic Study on the Hydration and Phase Behavior of Aqueous Alcohol Ethoxylate and Methyl Ester Ethoxylate: Effects of Terminal Groups in Hydrophilic Chains.

Using dielectric relaxation spectroscopy (DRS), small-angle X-ray scattering (SAXS), dynamic light scattering (DLS), and viscometry, we have investigated the hydration behavior, static structures, Brownian dynamics, and mechanical properties of aqueous solutions of alcohol ethoxylate (C12E15) and methyl ester ethoxylate (C12MEE), hereafter abbreviated as AE and MEE, respectively, in which we especially focus on the effects of the endcaps of these nonionic surfactants. We find that AE and MEE exhibit fairly different phase behaviors in water: AE produces liquid crystalline phases at w (surfactant weight fraction) > 0.35, whereas MEE retains a liquid phase in an extremely wide concentration range (w < 0.7) at ambient temperature. The structure factor deduced from SAXS intensities using a generalized indirect Fourier transformation technique and the effective hydration number evaluated from the negative excess bulk water relaxation amplitude revealed by DRS unambiguously demonstrate that hydration water molecules, exhibiting about 4-times-slower collective reorientational dynamics than that of bulk water, contribute to the excluded volume of the micelles. The blocked terminal hydrogen-bond donor/acceptor site of MEE leads to smaller hydration number of MEE than compared to that of AE, and consequently the lower excluded volume of the MEE micelles. The effective micellar volume fraction, ϕ(eff), should be defined by incorporating such different hydration effects. Importantly, voluminosity, defined as the micellar volume fraction per unit mass, is clearly a decreasing function of w, demonstrating progressive dehydration at a higher w. The collective diffusion constants determined by DLS for the AE and MEE micelles show a monotonous increase up to ϕ(eff) ≈ 0.5, as expected for the hard spheres. Low-shear-rate viscosities follow a Krieger-Dougherty model in the identical micellar packing fraction range. All static, dynamic, and mechanical properties of these micellar solutions can be explained in a consistent and quantitative manner only when the excluded volume of hydration water molecules is properly taken into account.

Structural features and surfactant properties of core–shell type micellar aggregates formed by gemini piperidinium surfactants

Abstract Aqueous micellar solution of piperidinium gemini surfactants was investigated by small angle X-ray scattering (SAXS) and the real space structural information of the micelles was deduced by indirect Fourier transformation (IFT) method. The maximum dimension of the micelles and their shape were determined by evaluating the pair distance distribution function (PDDF) and the electron density profile of the aqueous surfactant solution. These gemini surfactants formed core–shell type micelles in the aqueous solution above their cmc values having ellipsoidal structure. The dilute aqueous solutions of these surfactants were further investigated to determine their surfactant properties by surface tension and conductivity method. The self-aggregation and thermodynamic properties as well as the shape, size and internal structure of the micelles formed by these surfactants were found to be dependent on the methylene spacer units and hydrophobic alkyl chain length of the gemini surfactants.

Nonionic amphiphile nanoarchitectonics: self-assembly into micelles and lyotropic liquid crystals

Amphiphiles, molecules that possess both hydrophilic and hydrophobic moieties, are architecturally simple molecules that can spontaneously self-assemble into complex hierarchical structures from lower to higher dimensions either in the bulk phase or at an interface. Recent developments in multifunctional nanostructure design using the advanced concept of nanoarchitectonics utilize this simple process of assembly. Amphiphilic self-assemblies involving lipids or proteins mimic the structure of biological systems, thus highlighting the necessity of a fundamental physical understanding of amphiphilic self-assembly towards a realization of the complex mechanisms operating in nature. Herein, we describe self-assembled microstructures of biocompatible and biodegradable tetraglycerol lauryl ether (C12G4) nonionic surfactant in an aqueous solvent system. Temperature-composition analyses of equilibrium phases identified by using small-angle x-ray scattering (SAXS) provide strong evidence of various spontaneously self-assembled mesostructures, such as normal micelles (Wm), hexagonal liquid crystal (H1), and reverse micelles (Om). In contrast to conventional poly(oxyethylene) nonionic surfactants, C12G4 did not exhibit the clouding phenomenon at higher temperatures (phase separation was not observed up to 100 °C), demonstrating the greater thermal stability of the self-assembled mesophases. Generalized indirect Fourier transformation (GIFT) evaluation of the SAXS data confirmed the formation of core–shell–type spherical micelles with a maximum dimension ca. 8.7 nm. The shape and size of the C12G4 micelles remained apparently unchanged over a wide range of concentrations (up to 20%), but intermicellar interactions increased and could be described by the Percus–Yevick (PY) theory (after Carnahan and Starling), which provides a very accurate analytical expression for the osmotic pressure of a monodisperse hard sphere.

Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures

The new two-dimensional indirect Fourier transformation converts small-angle scattering patterns obtained by means of area detectors into two-dimensional real-space functions. These functions contain identical information to the scattering patterns, but many parameters related to the microstructure can be obtained directly from them. The size and shape of the microstructures are mainly reflected in the contours of the real-space functions. Their height can be used to get information on the internal architecture of the microstructures. The principles are demonstrated on nanostructured silica biotemplated by spruce wood.

Structure of Micelles Calcium Didodecyl Sulfate: A SAXS Study

This paper reports the structure of micelles of Calcium Didodecyl Sulfate (CDS), Ca(DS)2 , as studied using Small Angle X-ray Scattering (SAXS). CDS is a dianionic surfactant consisting of two DS- tails attached to Ca++ divalent ion. There is considerable interest in understanding the structure (especially the outer shell of counter-ions) of micelles of CDS as unlike conventional surfactants (e.g. CTAB, SDS) where counter-ion is monovalent, CDS has a divalent counter-ion. SAXS is an ideal technique for obtaining information about the outer shell of the Ca(DS)2 micelle, as the constituents (S, Ca, O etc.) of the shell are strong X-ray scatterers. The SAXS measurements have been made on salt-free aqueous solutions of calcium didodecyl sulfate for surfactant concentrations of 0.5, 1.0, 2.5, and 20 weight % (or 8.8, 17.7, 44.92 and 438.01 mM/dm3 ) respectively. Single step indirect Fourier transformation method has been utilized to generate particle distance distribution function. It is found that micelles are prolate ellipsoidal in shape. The size parameters of the ellipsoidal micelles have been determined. Other relevant parameters like mean aggregation number and effective fractional charge has been determined by fitting an ellipsoidal shaped core-shell model to the Fourier transformed scattering data. It is seen that increase in surfactant concentration results in lowering of aggregation number, increase of shell thickness and lowering of total charge and probably lowering of water association.

Two-dimensional indirect Fourier transformation for evaluation of small-angle scattering data of oriented samples

An extension of the indirect Fourier transformation method for two-dimensional small-angle scattering patterns is presented. This allows for a model-free investigation of real-space functions of oriented structures. The real-space function is built from two-dimensional basis functions. The Fourier transformed basis functions are approximated to the scattering pattern. The solution to this problem in reciprocal space can be used to compute the corresponding real-space functions. These real-space functions contain information on size, shape, internal structure and orientation of the structures studied. Information on structures that are oriented in different distinct directions can be partly separated. The applicability of the technique is demonstrated on simulated data of oriented cuboids and on two experimental data sets based on the nanostructure of spruce normal wood.

A SAXS Study of Aggregation in the Synergistic TBP–HDBP Solvent Extraction System

The macroscopic phase behaviors of a solvent system containing two extractants, tri-n-butyl phosphate (TBP) and di-n-butyl phosphoric acid (HDBP) in n-dodecane, were investigated through use of liquid-liquid extraction and small-angle X-ray scattering (SAXS) experiments. Five organic solutions, each containing a total extractant concentration (TBP + HDBP) of 1 M in varying molar ratios (0, 0.25, 0.5, 0.75, and 1.0 [TBP]:[TBP + HDBP]), were contacted with 0.2 M HNO3 aqueous solutions without and with dysprosium(III) at a concentration of 10(-4) M. An enhancement of the extraction of Dy(3+)--due to effects of synergism arising from the binary combination of extractants--was observed. SAXS data were collected for all solution compositions from 0 to 1 mol-fraction end ratios of TBP after contact with the acidic aqueous solutions both in the absence and presence of Dy as well as for the organic phases before aqueous contact. In the precontacted solutions, no notable changes in the SAXS data were observed upon combining the extractants so that the scattering intensity (I) measured at zero angle (Q = 0 Å(-1))--parameter I(0)--the experimental radius of gyration (R(g)), and the maximum linear extent (MLE) of the extractant aggregates were arithmetic averages of the two end members, 1 M HDBP, on the one hand, and 1 M TBP, on the other. In contrast, after contact with the aqueous phases with and without Dy(3+), a significant reorganization occurs with larger aggregates apparent in the extractant mixtures and smaller in the two end member solutions. In particular, the maximum values of the metrical parameters (I(0), R(g), and MLE) correlate with the apparent optimal synergistic extraction mole ratio of 0.25. The SAXS data were further analyzed using the recently developed generalized indirect Fourier transformation (GIFT) method to provide pair-distance distribution functions with real-space information on aggregate morphology. Before aqueous contact, the organic phases show a systematically varying response from globular-like reverse micelles in the case of 1 M TBP to rod-shaped architectures in the case of 1 M HDBP. After aqueous contact, the aggregate morphologies of the mixed extractant systems are not simple linear combinations of those for the two end members. Rather, they have larger and more elongated structures, showing sharp discontinuities in the metrics of the aggregate entities that are coincident with the synergistic extraction mixture for Dy(3+). The results in this initial study suggest a supramolecular, micellization aspect to synergism that remains underexplored and warrants further investigation, especially as it concerns the contemporary relevance to decades-old process chemistry and practices for high throughput separations systems.

Structure of Nonionic Reverse Micelles in Octylbenzene

We report structure and rheology (flow property) of diglycerol monomyristate (designated as C14G2) reverse micelles in an aromatic solvent octylbenzene. Structural characterization has been made using small-angle x-ray scattering (SAXS), while flow property is studied using rheometry. SAXS data have been evaluated by the generalized indirect Fourier transformation (GIFT) method and geometrical model fittings. We found that, under ambient conditions of temperature and pressure, C14G2 spontaneously self-organize into ellipsoidal prolate-type micelles with maximum core diameter of about 6.5 nm in octylbenzene. Shape and size of the micelles remain essentially unchanged over wide concentrations (3–20%). On the other hand, micellar size decreases with increase in temperature, which is anticipated to be due to an increase in the critical packing parameter (CPP). Since surfactant becomes lipophilic upon heating, micellar curvature becomes more negative at higher temperatures. Steady-shear rheological experiments showed that the present reverse micelles behave as a Newtonian fluids; measured viscosity is independent of the applied shear. Zero-shear viscosity tends to increase with weight fraction of the surfactant, which is assumed to be caused due to an increase in number density of micelles.

Bayesian reconstruction ofP(r) directly from two-dimensional detector imagesviaa Markov chain Monte Carlo method

The interatomic distance distribution, P(r), is a valuable tool for evaluating the structure of a molecule in solution and represents the maximum structural information that can be derived from solution scattering data without further assumptions. Most current instrumentation for scattering experiments (typically CCD detectors) generates a finely pixelated two-dimensional image. In contin-uation of the standard practice with earlier one-dimensional detectors, these images are typically reduced to a one-dimensional profile of scattering inten-sities, I(q), by circular averaging of the two-dimensional image. Indirect Fourier transformation methods are then used to reconstruct P(r) from I(q). Substantial advantages in data analysis, however, could be achieved by directly estimating the P(r) curve from the two-dimensional images. This article describes a Bayesian framework, using a Markov chain Monte Carlo method, for estimating the parameters of the indirect transform, and thus P(r), directly from the two-dimensional images. Using simulated detector images, it is demonstrated that this method yields P(r) curves nearly identical to the reference P(r). Furthermore, an approach for evaluating spatially correlated errors (such as those that arise from a detector point spread function) is evaluated. Accounting for these errors further improves the precision of the P(r) estimation. Experimental scattering data, where no ground truth reference P(r) is available, are used to demonstrate that this method yields a scattering and detector model that more closely reflects the two-dimensional data, as judged by smaller residuals in cross-validation, than P(r) obtained by indirect transformation of a one-dimensional profile. Finally, the method allows concurrent estimation of the beam center and Dmax, the longest interatomic distance in P(r), as part of the Bayesian Markov chain Monte Carlo method, reducing experimental effort and providing a well defined protocol for these parameters while also allowing estimation of the covariance among all parameters. This method provides parameter estimates of greater precision from the experimental data. The observed improvement in precision for the traditionally problematic Dmax is particularly noticeable.

Generalized Indirect Fourier Transformation as a Valuable Tool for the Structural Characterization of Aqueous Nanocrystalline Cellulose Suspensions by Small Angle X-ray Scattering

Small angle X-ray scattering (SAXS) is employed to characterize the inner structure and shape of aqueous nanocrystalline cellulose suspensions using the generalized indirect Fourier transformation (GIFT). The use of the GIFT approach provides a single fitting procedure for the determination of intra- and interparticle interactions due to a simultaneous treatment of the form factor P(q) and the structure factor S(q). Moreover, GIFT allows for the determination of particle charges and polydispersity indices. As test material, aqueous nanocrystalline cellulose suspensions (aNCS) prepared by the H2SO4 route have been investigated and characterized (SAXS, dynamic light scattering, zeta potential).

Nonionic Reverse Micelles near the Critical Point

We report shape, size, and internal cross-sectional structure of diglycerol monomyristate (C₁₄G₂) reverse micelles in n-hexadecane near the critical point using small-angle X-ray scattering (SAXS). Pair-distance distribution function, p(r), which gives structural information in real-space, was obtained by indirect Fourier transformation (IFT) method. The p(r) showed a clear picture of rodlike micelles at higher temperatures well above the critical point (micellar solution phase separates into two immiscible liquids at ~ 48°C). At a fixed surfactant concentration (5% C₁₄G₂), decrease in temperature increases the micellar size monotonously and surprisingly shape of the p(r) curve at 50°C; close to the critical point, mimics the shape of the two dimensional disk-like micelles indicating the onset of critical fluctuations (attractive interactions among rodlike micelles forming a weak network). A similar behavior has been observed with normal micelles in aqueous system near the critical point. When the system is heated to 60°C, shape of the p(r) curve regains rodlike structure. At fixed temperature of 60°C, increase in C₁₄G₂ concentration induced one dimensional micellar growth. Maximum length of micelles increases from ca. 23.5 to 46.0 nm upon increasing concentration from 1 to 12% keeping cross section diameter apparently unchanged at ca. 4.0 nm.