Parameter inversion of a polydisperse system in small-angle scattering

An accurate and efficient method for model- and form-free inversion of a polydisperse small-angle scattering system is presented. It supports an arbitrary number of model parameters and both 1D and 2D intensity observations.

A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.

Structural Characterization Study of a Lipid Nanocapsule Formulation Intended for Drug Delivery Applications Using Small-Angle Scattering Techniques

Lipid nanocapsules (LNCs) are increasingly being used for various drug delivery applications due to their versatile nature and ability to carry a wide variety of therapeutic drug molecules. In the present investigation, small-angle X-ray (SAXS) and neutron scattering (SANS) techniques were used to elucidate the structure of LNCs. Overall, size measurements obtained from SAXS and SANS techniques were complemented with dynamic light scattering, zeta potential, and cryogenic transmission electron microscopy measurements. The structural aspects of LNCs can be affected by drug loading and the properties of the drug. Here, the impact of drug loading on the overall structure was evaluated using DF003 as a model drug molecule. LNCs with varying compositions were prepared using a phase inversion method. Combined analysis of SAXS and SANS measurements indicated the presence of a core–shell structure in the LNCs. Further, the drug loading did not alter the overall core–shell structure of the LNCs. SANS data revealed that the core size remained unchanged with a radius of 20.0 ± 0.9 nm for unloaded LNCs and 20.2 ± 0.6 nm for drug-loaded LNCs. Furthermore, interestingly, the shell becomes thicker in an order of ∼1 nm in presence of the drug compared to the shell thickness of unloaded LNCs as demonstrated by SAXS data. This can be correlated with the strong association of hydrophilic DF003 with Kolliphor HS 15, a polyethylene glycol-based surfactant that predominantly makes up the shell, resulting in a drug-rich hydrated shell.

The very small angle neutron scattering instrument at the National Institute of Standards and Technology

A description and the performance of the very small angle neutron scattering diffractometer at the National Institute of Standards and Technology are presented.

A description and the performance of the very small angle neutron scattering diffractometer at the National Institute of Standards and Technology are presented. The measurement range of the instrument extends over three decades of momentum transfer q from 2 × 10⁻⁴ to 0.7 Å⁻¹. The entire scattering angle range from 8 × 10⁻⁵ to π/6 rad (30°) can be measured simultaneously using three separate detector carriages on rails holding nine 2D detector arrays. Versatile choices of collimation options and neutron wavelength selection allow the q resolution and beam intensity to be optimized for the needs of the experiment. High q resolution is achieved using multiple converging-beam collimation with circular pinholes combined with refractive lenses and prisms. Relaxed vertical resolution with much higher beam intensity can be achieved with narrow slit collimation and a broad wavelength range chosen by truncating the moderator source distribution below 4 Å with a Be crystalline filter and above 8 Å with a supermirror deflector. Polarized beam measurements with full polarization analysis are also provided by a high-performance supermirror polarizer and spin flipper, capable of producing flipping ratios of over 100, along with a high-efficiency ³He polarization analyzer.

Comparative study of flocculation and adsorption behaviour of water treatment proteins from Moringa peregrina and Moringa oleifera seeds

Trees of Moringa oleifera are the most widely exploited species of Moringa and proteins extracted from its seeds have been identified as the most efficient natural coagulant for water purification. Largely for climatic reasons, other Moringa species are more accessible in some regions and this paper presents a comparative study of the adsorption to different materials of the proteins extracted from seeds of Moringa peregrina and Moringa oleifera to explore their use as flocculating agents in regions where each is more readily accessible. Results showed that Moringa peregrina seed proteins had higher adsorption to alumina compared to silica, in contrast to opposite behavior for Moringa oleifera. Both species provide cationic proteins that can act as effective coagulants for the various impurities with different surface potential. Despite the considerable similarity of the amino acid composition, the seed proteins have significantly different adsorption and this presents the opportunity to improve processes by choosing the optimal species or combination of species depending on the type of impurity or possible development of separation processes.

Charged Polystyrene Nanoparticles Near a SiO2/Water Interface

Quartz crystal microbalance with dissipation (QCM-D) monitoring is used to investigate the adsorption processes at liquid-solid interfaces and applied increasingly to characterize viscoelastic properties of complex liquids. Here, we contribute new insights into the latter field by using QCM-D to investigate the structure near the interface and the high-frequency viscoelastic properties of charge-stabilized polystyrene particles (radius 37 nm) dispersed in water. The study reveals changes with increasing ionic strength and particle concentration. Replacing water with a dispersion is usually expected to give rise to a decrease in frequency, f. Increases in both f and dissipation, D, were observed on exchanging pure water for particle dispersions at a low ionic strength. The QCM-D data are well-represented by a viscoelastic model, with viscosity increasing from 1.0 to 1.3 mPa s as the particle volume fraction changes from 0.005 to 0.07. This increase, higher than that predicted for noninteracting dispersions, can be explained by the charge repulsion between the particles giving rise to a higher effective volume fraction. It is concluded that the polystyrene particles did not adhere to the solid surface but rather were separated by a layer of pure dispersion medium. The QCM-D response was successfully represented using a viscoelastic Kelvin-Voigt model, from which it was concluded that the thickness of the dispersion medium layer was of the order of the particle-particle bulk separation, in the range of 50-250 nm, and observed to decrease with both particle concentration and addition of salt. Similar anomalous frequency and dissipation responses have been seen previously for systems containing weakly adherent colloidal particles and bacteria and understood in terms of coupled resonators. We demonstrate that surface attachment is not required for such phenomena to occur, but that a viscoelastic liquid separated from the oscillating surface by a thin Newtonian layer gives rise to similar responses.

Learning about SANS instruments and data reduction from round robin measurements on samples of polystyrene latex

Measurements of a well-characterized `standard' sample can verify the performance of an instrument. Typically, small-angle neutron scattering instruments are used to investigate a wide range of samples and may often be used in a number of configurations. Appropriate `standard' samples are useful to test different aspects of the performance of hardware as well as that of the data reduction and analysis software. Measurements on a number of instruments with different intrinsic characteristics and designs in a round robin can not only better characterize the performance for a wider range of conditions but also, perhaps more importantly, reveal the limits of the current state of the art of small-angle scattering. The exercise, followed by detailed analysis, tests the limits of current understanding as well as uncovering often forgotten assumptions, simplifications and approximations that underpin the current practice of the technique. This paper describes measurements of polystyrene latex, radius 720 Å, with a number of instruments. Scattering from monodisperse, uniform spherical particles is simple to calculate and displays sharp minima. Such data test the calibrations of intensity, wavelength and resolution as well as the detector response. Smoothing due to resolution, multiple scattering and polydispersity has been determined. Sources of uncertainty are often related to systematic deviations and calibrations rather than random counting errors. The study has prompted development of software to treat modest multiple scattering and to better model the instrument resolution. These measurements also allow checks of data reduction algorithms and have identified how they can be improved. The reproducibility and the reliability of instruments and the accuracy of parameters derived from the data are described.