Small-angle scattering simulations for suspensions of nanocrystals

Suspensions of nanocrystals which possess large lattice spacings d(hkl) and only a small number of unit cells along the direction of the reciprocal lattice vector G(hkl) can feature broadened Bragg peaks in small-angle scattering (SAS) patterns. The scattering from molecules located at the interface between the nanocrystals and the dispersion medium which stabilize and functionalize the nanocrystals can interfere with the scattering of the nanocrystals and affect the shape and position of their Bragg peaks. This allows to study how these molecules arrange on the surface of the nanocyrstals. As an example we study suspensions of lecithin stabilized β-tripalmitin nanocrystals which adopt a platelet-like shape. Their SAS patterns exhibit a broadened 001 Bragg peak (cf. SAXS curves in the graphical abstract). With the x-ray and neutron powder pattern simulation analysis (XNPPSA) we have demonstrated that the SAXS and SANS patterns of dilute tripalmitin (3 wt%) suspensions can be simultaneously reproduced on an absolute scale [1,2]. Thereby, powder averaged SAS diffractograms are computed for an ensemble of nanocrystals which are embedded in a dispersion medium. The crystallographic structure of the nanocrystals (CIF-file) and their geometry are taken into account and the amphiphilic lecithin molecules which cover the nanocrystals are modelled with two shells (cf. model in the right inset). From the analysis of the fitted shell thicknesses and scattering length densities it turns out that the lecithin molecules arrange rather flatly and densely packed on the surface of the nanocyrstals. Moreover, the XNPPSA method allows a reliable determination of the thickness distribution of the nanocrystals with molecular resolution [1,2]. With rising tripalmitin concentration the platelets form self-assembled stack-like structures [1,3] and finally nematic liquid-crystalline domains. The XNPPSA allows to investigate the structure and amount of such stacks in the suspensions.

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A new time-of-flight small-angle scattering instrument at the Helmholtz-Zentrum Berlin: V16/VSANS

Journal of Applied Crystallography ◽

10.1107/s1600576713030227 ◽

2014 ◽

Vol 47 (1) ◽

pp. 237-244 ◽

Cited By ~ 20

Author(s):

Karsten Vogtt ◽

Miriam Siebenbürger ◽

Daniel Clemens ◽

Christian Rabe ◽

Peter Lindner ◽

...

Keyword(s):

Momentum Transfer ◽

Small Angle ◽

Soft Matter ◽

Scattering Length ◽

Time Of Flight ◽

Small Angle Scattering ◽

Neutron Guide ◽

Macromolecular Assemblies ◽

Angle Scattering ◽

The Individual

Small-angle scattering methods have become routine techniques for the structural characterization of macromolecules and macromolecular assemblies like polymers, (block) copolymers or micelles in the spatial range from a few to hundreds of nanometres. Neutrons are valuable scattering probes, because they offer freedom with respect to scattering length density contrast and isotopic labelling of samples. In order to gain maximum benefit from the allotted experiment time, the instrumental setup must be optimized in terms of statistics of scattered intensity, resolution and accessible range in momentum transferQ. The new small-angle neutron scattering instrument V16/VSANS at the Helmholtz-Zentrum in Berlin, Germany, augments neutron guide collimation and pinhole optics with time-of-flight data recording and flexible chopper configuration. Thus, the availableQrange and the respective instrumental resolution in the intermediate and high momentum transfer regions can be adjusted and balanced to the individual experimental requirements. This renders V16/VSANS a flexible and versatile instrument for soft-matter research.

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Contrast variation in small-angle scattering experiments on polydisperse and superparamagnetic systems: basic functions approach

Journal of Applied Crystallography ◽

10.1107/s0021889806049491 ◽

2007 ◽

Vol 40 (1) ◽

pp. 56-70 ◽

Cited By ~ 38

Author(s):

Mikhail V. Avdeev

Keyword(s):

Small Angle ◽

Magnetic Particles ◽

Scattering Length ◽

Small Angle Scattering ◽

Contrast Variation ◽

Match Point ◽

Scattering Intensity ◽

Scattering Length Density ◽

Angle Scattering ◽

Basic Functions

The development of the basic functions approach [Stuhrmann (1995).Modern Aspects of Small-Angle Scattering, edited by H. Brumberger, pp. 221–254. Dordrecht: Kluwer Academic Publishers] for the contrast variation technique in small-angle scattering from systems of polydisperse and superparamagnetic non-interacting particles is presented. For polydisperse systems the modified contrast is introduced as the difference between the effective mean scattering length density (corresponding to the minimum of the scattering intensity as the function of the scattering length density of the solvent) and the density of the solvent. Then, the general expression for the scattering intensity is written in the classical way through the modified basic functions. It is shown that the shape scattering from the particle volume can be reliably obtained. Modifications of classical expressions describing changes in integral parameters of the scattering (intensity at zero angle, radius of gyration, Porod integral) with the contrast are analyzed. In comparison with the monodisperse case, the residual scattering in the minimum of intensity as a function of contrast (effective match point) in polydisperse systems makes it possible to treat the Guinier region of scattering curves around the effective match point quite precisely from the statistical viewpoint. However, limitations of such treatment exist, which are emphasized in the paper. In addition, the effect of magnetic scattering in small-angle neutron scattering from superparamagnetic nanoparticles is considered in the context of the basic functions approach. Conceptually, modifications of the integral parameters of the scattering in this case are similar to those obtained for polydisperse multicomponent particles. Various cases are considered, including monodisperse non-homogeneous and homogeneous magnetic particles, and polydisperse non-homogeneous and homogeneous magnetic particles. The developed approach is verified for two models representing the main types of magnetic fluids – systems of polydisperse superparamagnetic particles located in liquid carriers.

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Structure and order in lamellar phases determined by small-angle scattering

Journal of Applied Crystallography ◽

10.1107/s0021889804012956 ◽

2004 ◽

Vol 37 (5) ◽

pp. 703-710 ◽

Cited By ~ 53

Author(s):

Thomas Frühwirth ◽

Gerhard Fritz ◽

Norbert Freiberger ◽

Otto Glatter

Keyword(s):

Form Factor ◽

Small Angle ◽

Structure Factor ◽

Scattering Length ◽

Small Angle Scattering ◽

Scattering Data ◽

X Rays ◽

Model Free ◽

Angle Scattering

Multilamellar phases can be identified and characterized by small-angle scattering of X-rays (SAXS) or neutrons (SANS). Equidistant peaks are the typical signature and their spacing allows the fast determination of the repeat distance,i.e.the mean distance between the midplane of neighbouring bilayers. The scattering function can be described as the product of a structure factor and a form factor. The structure factor is related to the ordering of the bilayers and is responsible for the typical equidistant peaks, but it also contains information about the bilayer flexibility and the number of coherently scattering bilayers. The form factor depends on the thickness and the internal structure (scattering length density distribution) of a single bilayer. The recently developed generalized indirect Fourier transformation (GIFT) method is extended to such systems. This method allows the simultaneous determination of the structure factor and the form factor of the system, including the correction of instrumental broadening effects. A few-parameter model is used for the structure factor, while the determination of the form factor is completely model-free. The method has been tested successfully with simulated scattering data and by application to experimental data sets.

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SCryPTA: A web-based platform for analyzing Small-Angle Scattering curves of lyotropic liquid crystals

10.1101/791848 ◽

2019 ◽

Author(s):

Raphael Dias de Castro ◽

Bruna Renata Casadei ◽

Barbara Vasconcelos Santana ◽

Mayra Lotierzo ◽

Natália F. de Oliveira ◽

...

Keyword(s):

Liquid Crystals ◽

Small Angle ◽

Hexagonal Phase ◽

Small Angle Scattering ◽

Lyotropic Liquid Crystals ◽

Crystal Phase ◽

Scattering Data ◽

Crystallographic Structure ◽

Physical Parameters ◽

Angle Scattering

ABSTRACTSmall angle X-ray scattering (SAXS) is a powerful technique for the characterization of systems with highly ordered structures, such as liquid crystals and self-assembly systems. In the field of nanotechnology and nanomedicine, SAXS can be used to characterize the crystallographic properties of the crystal phase of lyotropic systems and nanoparticles with internal crystal phase, such as cubosomes, hexosomes and multi-lamellar vesicles. In this work, we introduce a new web platform named SCryPTA: Small Angle Scattering Crystallographic Peak Treatment and Analysis, capable of reading SAXS data and providing a comprehensive visualization of the scattering curve along with the calculation of important physical parameters, such as the lattice parameter of the crystal structure, the lipidic bilayer width, among others. Cubic, hexagonal and multilamellar scattering data had their crystallographic structure characterized in SCryPTA. So far, four different cubic structures, (Pn3m (Q224), Fd3m (Q227), Im3m (Q229), Ia3d (Q230)), the hexagonal phase and also multi-lamellar vesicle systems are described in the platform. We believe that SCryPTA may help researchers from several fields, since it has a user-friendly interface. The platform is available at: www.if.usp.br/scrypta.

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Small-angle scattering from polydisperse particles with a diffusive surface

Journal of Applied Crystallography ◽

10.1107/s1600576714001216 ◽

2014 ◽

Vol 47 (2) ◽

pp. 642-653 ◽

Cited By ~ 18

Author(s):

Olexandr V. Tomchuk ◽

Leonid A. Bulavin ◽

Viktor L. Aksenov ◽

Vasil M. Garamus ◽

Oleksandr I. Ivankov ◽

...

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Power Law ◽

Small Angle ◽

Scattering Length ◽

Small Angle Scattering ◽

Scattering Data ◽

Scattering Length Density ◽

Angle Scattering

Particles with a diffusive surface, characterized by a deviation from the Porod power-law asymptotic behavior in small-angle scattering towards an exponent below −4, are considered with respect to the polydispersity problem. The case of low diffusivity is emphasized, which allows the description of the scattering length density distribution within spherically isotropic particles in terms of a continuous profile. This significantly simplifies the analysis of the particle-size distribution function, as well as the change in the scattering invariants under contrast variation. The effect of the solvent scattering contribution on the apparent exponent value in power-law-type scattering and related restrictions in the analysis of the scattering curves are discussed. The principal features and possibilities of the developed approach are illustrated in the treatment of experimental small-angle neutron scattering data from liquid dispersions of detonation nanodiamond. The obtained scattering length density profile of the particles fits well with a transition of the diamond states of carbon inside the crystallites to graphite-like states at the surface, and it is possible to combine the diffusive properties of the surface with the experimental shift of the mean scattering length density of the particles compared with that of pure diamond. The moments of the particle-size distribution are derived and analyzed in terms of the lognormal approximation.

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