Interpreting SAXS data recorded on cellulose rich pulps

A simulation method was developed for modelling SAXS data recorded on cellulose rich pulps. The modelling method is independent of the establishment of separate form factors and structure factors and was used to model SAXS data recorded on dense samples. An advantage of the modelling method is that it made it possible to connect experimental SAXS data to apparent average sizes of particles and cavities at different sample solid contents. Experimental SAXS data could be modelled as a superposition of a limited number of simulated intensity components and gave results in qualitative agreement with CP/MAS 13C-NMR data recorded on the same samples. For the water swollen samples, results obtained by the SAXS modelling method and results obtained from CP/MAS 13C-NMR measurements, agreed on the ranking of particle sizes in the different samples. The SAXS modelling method is dependent on simulations of autocorrelation functions and the time needed for simulations could be reduced by rescaling of simulated correlation functions due to their independence of the choice of step size in real space. In this way an autocorrelation function simulated for a specific sample could be used to generate SAXS intensity profiles corresponding to all length scales for that sample and used for efficient modelling of the experimental data recorded on that sample. Graphical abstract

Interpreting SAXS Data Recorded On Cellulose Rich Pulps

A simulation method was developed for modelling SAXS data recorded on cellulose rich pulps. The modelling method is independent of the establishments of separate form factors and structure factors and was used to model SAXS data recorded on dense samples. An advantage of the modelling method was that it made it possible to connect experimental SAXS data to apparent average sizes of particles and cavities at different sample solid contents. Experimental SAXS data could be modelled as a superposition of a limited number of simulated intensity components and gave results in qualitative agreement with CP/MAS 13C-NMR data recorded on the same samples. For the water swollen samples, results obtained by the SAXS modelling method and results obtained from CP/MAS 13C-NMR measurements, agreed on the ranking of particle sizes in the different samples. The SAXS modelling method is dependent on simulations of autocorrelation functions. The time needed for simulations could be reduced by rescaling of simulated correlation functions, due to their independence of the choice of step size in real space. This way an autocorrelation function simulated for a specific sample could be used to generate SAXS intensity profiles corresponding to all length scales for that sample and used for efficient modelling of the experimental data recorded on that sample.

Ab initio determination of the shape of membrane proteins in a nanodisc

New software, called Marbles, is introduced that employs SAXS intensities to predict the shape of membrane proteins embedded into membrane nanodiscs. To gain computational speed and efficient convergence, the strategy is based on a hybrid approach that allows one to account for the contribution of the nanodisc to the SAXS intensity through a semi-analytical model, while the embedded membrane protein is treated as a set of beads, similarly to as in well known ab initio methods. The reliability and flexibility of this approach is proved by benchmarking the code, implemented in C++ with a Python interface, on a toy model and two proteins with very different geometry and size.

Ab-initio determination of the shape of membrane proteins in a nanodisc

We introduce a new software, called Marbles, that employs SAXS intensities to predict the shape of membrane proteins embedded into membrane nanodiscs. To gain computational speed and efficient convergence, the strategy is based on a hybrid approach that allows one to account for the nanodisc contribution to the SAXS intensity through a semi-analytical model, while the embedded membrane protein is treated as set of beads, similarly to well known ab-initio methods. The code, implemented in C++ with a Python user interface, provides a good performance and includes the possibility to systematically treat unstructured domains. We prove the reliability and flexibility of our approach by benchmarking the code on a toy model and two proteins of very different geometry and size.

Structural studies on fluid Hg and fluid Se at high temperatures and high pressures by means of X-ray diffraction and small angle X-ray scattering

X-ray diffraction (XRD) and small angle X-ray scattering (SAXS) measurements for fluid Hg and fluid Se up to the supercritical region have been carried out using synchrotron radiation at SPring-8. We obtained the structure factor, $S\left(Q\right)$, including a small angle region, and the pair distribution function, $g\left(r\right)$, for both fluids from the liquid to the dense vapor region. Change of the local structure and medium-range correlations at the metal-insulator transition in fluid Hg were revealed. On the other, the average coordination number of two was preserved at the semiconductor-metal transition in fluid Se. From a SAXS experiment of fluid Se in 2012, SAXS spectra near the semiconductor-metal transition region show the Ornstein–Zernike profile and the SAXS intensity is reduced with increasing pressure. These results indicate difficulties of separating fluctuations intrinsic to the semiconductor-metal transition from those arising from the liquid-vapor critical point in fluid Se, although fluctuations intrinsic to the electronic transitions are largely expected in both fluids.

Determination of the melting temperature of spherical nanoparticles in dilute solution as a function of their radius by exclusively using the small-angle X-ray scattering technique

In this investigation the dependence on radius of the melting temperature of dilute sets of spherical nanocrystals with wide radius distributions was determined by a novel procedure exclusively using the results of small-angle X-ray scattering (SAXS) measurements. This procedure is based on the sensitivity of the SAXS function to small and rather sharp variations in the size and electron density of nanocrystals at their melting temperature. The input for this procedure is a set of experimental SAXS intensity functions at selected q values for varying sample temperatures. In practice, the sample is heated from a minimum temperature, lower than the melting temperature of the smallest nanocrystals, up to a temperature higher than the melting temperature of the largest nanocrystals. The SAXS intensity is recorded in situ at different temperatures during the heating process. This novel procedure was applied to three samples composed of dilute sets of spherical Bi nanocrystals with wide radius distributions embedded in a sodium borate glass. The function relating the melting temperature of Bi nanocrystals with their radius – determined by using the procedure proposed here – agrees very well with the results reported in previous experimental studies using different methods. The results reported here also evidence the predicted size-dependent contraction of Bi nanocrystals induced by the large surface-to-volume ratio of small nanocrystals and an additional size-independent compressive stress caused by the solid glass matrix in which liquid Bi nanodroplets are initially formed. This last effect is a consequence of the increase in the volume of Bi nanoparticles upon crystallization and also of differences in the thermal expansion coefficients of the crystalline phase of Bi and the glass matrix. This additional stress leads to a depression of about 10 K in the melting temperature of the Bi nanocrystals confined in the glass. The procedure described here also allowed the determination of the specific masses and thermal expansion coefficients of Bi nanoparticles in both liquid and crystalline phases.

Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements

A new model is proposed for the measurement errors incurred in typical small-angle X-ray scattering (SAXS) experiments, which takes into account the setup geometry and physics of the measurement process. The model accurately captures the experimentally determined errors from a large range of synchrotron and in-house anode-based measurements. Its most general formulation gives for the variance of the buffer-subtracted SAXS intensity σ2(q) = [I(q) + const.]/(kq), where I(q) is the scattering intensity as a function of the momentum transfer q; k and const. are fitting parameters that are characteristic of the experimental setup. The model gives a concrete procedure for calculating realistic measurement errors for simulated SAXS profiles. In addition, the results provide guidelines for optimizing SAXS measurements, which are in line with established procedures for SAXS experiments, and enable a quantitative evaluation of measurement errors.