Small-Angle X-ray Scattering Size Parameters and Higher Moments of the Particle-Size Distribution Function in the Asymptotic Stage of Ostwald Ripening

1995 ◽  
Vol 28 (5) ◽  
pp. 553-560 ◽  
Author(s):  
J. Möller ◽  
R. Kranold ◽  
J. Schmelzer ◽  
U. Lembke
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Ostwald Ripening ◽  
Distribution Functions ◽  
Higher Moments ◽  
X Ray ◽  
Diffusion Limited ◽  
X Ray Scattering ◽  
Lsw Theory ◽  
Kinetics Of

Small-angle X-ray scattering (SAXS) is a powerful tool to study the kinetics of phase separation in materials. A simple procedure is presented that allows one to prove if the particle-size distribution established in a system in the late stages of phase separation corresponds to the predictions of the classical Lifshitz–Slyozov–Wagner (LSW) theory for the asymptotic stage of Ostwald ripening. The method is based on the correlations between certain SAXS size parameters and the higher moments of the LSW size distribution functions for diffusion-limited or reaction-limited ripening. It is suggested that the use of these size parameters, which can be obtained with high accuracy from the scattering curve, is frequently more advantageous than a direct comparison of the experimentally obtained size distributions with the asymptotic size-distribution functions predicted by the LSW theory. The method is applicable if the suppositions made in the LSW theory that the precipitated particles should be homogeneous spheres with volume fraction tending to zero are fulfilled. The method is applied to a photochromic glass; although the silver-halide precipitates contained in the glass develop according to the power law of diffusion-limited Ostwald ripening, their size distribution is shown not to correspond to the features of the LSW size distribution. Consequently, in this case the LSW theory cannot describe quantitatively the kinetics of ripening.

Tracking the Catalyst Layer Depth-Dependent Electrochemical Degradation of a Bimodal Pt/C Fuel Cell Catalyst: A Combined Operando Small- and Wide-Angle X-Ray Scattering Study

2021 ◽  
Author(s):  
Johanna Schröder ◽  
Rebecca K. Pittkowski ◽  
Isaac Martens ◽  
Raphaël Chattot ◽  
Jakub Drnec ◽  
...  
Keyword(s):  
Particle Size ◽  
Fuel Cell ◽  
Ostwald Ripening ◽  
Catalyst Layer ◽  
Wide Angle ◽  
Layer Depth ◽  
X Ray ◽  
Fuel Cell Catalyst ◽  
X Ray Scattering ◽  
Size Population

The combination of operando small- and wide-angle X-ray scattering (SAXS, WAXS) is here presented to provide insights into the changes in mean particle sizes and phase fractions in fuel cell catalyst layers during accelerated stress tests (ASTs). As fuel cell catalyst, a bimodal Pt/C catalyst was chosen that consists of two distinguishable particle size populations. The presence of the two different sizes should favor and uncover electrochemical Ostwald ripening as degradation mechanism, i.e., the growth of larger particles in the Pt/C catalyst at the expense of the smaller particles via the formation of ionic metal species. However, instead of electrochemical Ostwald ripening, the results point toward classical Ostwald ripening via the local diffusion of metal atoms on the support. Furthermore, the grazing incidence mode provides insights into the catalyst layer depth-dependent degradation. While the larger particles show the same particle size changes close to the electrolyte-catalyst interface and within the catalyst layer, the smaller Pt nanoparticles exhibit a slightly decreased size at the electrolyte-catalyst interface. During the AST, both size populations increase in size, independent of the depth. Their phase fraction, i.e., the ratio of smaller to larger size population, however, exhibits a depth-dependent behavior. While at the electrolyte-catalyst interface the phase fraction of the smaller size population decreases, it increases in the inner catalyst layer. The results of a depth-dependent degradation suggest that employing a depth-dependent catalyst design can be used for future improvement of catalyst stability.

Ostwald ripening of cobalt precipitates in silica aerogels? An ultra-small-angle X-ray scattering study

2005 ◽  
Vol 38 (1) ◽  
pp. 132-138 ◽  
Author(s):  
Artur Braun ◽  
Jan Ilavsky ◽  
Brian C. Dunn ◽  
Pete R. Jemian ◽  
Frank E. Huggins ◽  
...  
Keyword(s):  
Size Distribution ◽  
Small Angle ◽  
Ostwald Ripening ◽  
Supercritical Drying ◽  
Silica Aerogels ◽  
Radial Symmetry ◽  
Radius Of Gyration ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Monolithic silica aerogels with radial symmetry were synthesized by supercritical drying, doped to 2% and 10% with cobalt, and reduced with hydrogen. All samples were investigated with ultra-small-angle X-ray scattering. The non-doped aerogels have three populations of scatterers with radii of gyration of about 10, 40 and 60–70 Å. The doped aerogels show an additional structure with a radius of gyration ranging from 1050 to 3000 Å. This structure causes intensity oscillations, thus revealing a relatively narrow size distribution. Scattering curves of the 10%-doped aerogels fitted well to a Lifshitz–Slyozov–Wagner particle size distribution, thus revealing that Ostwald ripening might have occurred during aerogel preparation. The same range also shows differences depending on whether the samples were reduced, or in their as-prepared condition. Scattering curves obtained from the cylinder-axis region were different from the scattering curves obtained from the sample boundary, indicating a process-dependent skin effect.

scholarly journals A multi-step nucleation process determines the kinetics of prion-like domain phase separation

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Erik W. Martin ◽  
Tyler S. Harmon ◽  
Jesse B. Hopkins ◽  
Srinivas Chakravarthy ◽  
J. Jeremías Incicco ◽  
...  
Keyword(s):  
Phase Separation ◽  
Size Distribution ◽  
Mixing Time ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
Assembly Kinetics ◽  
Domain Phase ◽  
Kinetics Of ◽  
Liquid Liquid Phase Separation

AbstractCompartmentalization by liquid-liquid phase separation (LLPS) has emerged as a ubiquitous mechanism underlying the organization of biomolecules in space and time. Here, we combine rapid-mixing time-resolved small-angle X-ray scattering (SAXS) approaches to characterize the assembly kinetics of a prototypical prion-like domain with equilibrium techniques that characterize its phase boundaries and the size distribution of clusters prior to phase separation. We find two kinetic regimes on the micro- to millisecond timescale that are distinguished by the size distribution of clusters. At the nanoscale, small complexes are formed with low affinity. After initial unfavorable complex assembly, additional monomers are added with higher affinity. At the mesoscale, assembly resembles classical homogeneous nucleation. Careful multi-pronged characterization is required for the understanding of condensate assembly mechanisms and will promote understanding of how the kinetics of biological phase separation is encoded in biomolecules.

Tracking the Catalyst Layer Depth-Dependent Electrochemical Degradation of a Bimodal Pt/C Fuel Cell Catalyst: A Combined Operando Small- and Wide-Angle X-Ray Scattering Study

2021 ◽  
Author(s):  
Johanna Schröder ◽  
Rebecca K. Pittkowski ◽  
Isaac Martens ◽  
Raphaël Chattot ◽  
Jakub Drnec ◽  
...  
Keyword(s):  
Particle Size ◽  
Fuel Cell ◽  
Ostwald Ripening ◽  
Catalyst Layer ◽  
Wide Angle ◽  
Layer Depth ◽  
X Ray ◽  
Fuel Cell Catalyst ◽  
X Ray Scattering ◽  
Size Population

The combination of operando small- and wide-angle X-ray scattering (SAXS, WAXS) is here presented to provide insights into the changes in mean particle sizes and phase fractions in fuel cell catalyst layers during accelerated stress tests (ASTs). As fuel cell catalyst, a bimodal Pt/C catalyst was chosen that consists of two distinguishable particle size populations. The presence of the two different sizes should favor and uncover electrochemical Ostwald ripening as degradation mechanism, i.e., the growth of larger particles in the Pt/C catalyst at the expense of the smaller particles via the formation of ionic metal species. However, instead of electrochemical Ostwald ripening, the results point toward classical Ostwald ripening via the local diffusion of metal atoms on the support. Furthermore, the grazing incidence mode provides insights into the catalyst layer depth-dependent degradation. While the larger particles show the same particle size changes close to the electrolyte-catalyst interface and within the catalyst layer, the smaller Pt nanoparticles exhibit a slightly decreased size at the electrolyte-catalyst interface. During the AST, both size populations increase in size, independent of the depth. Their phase fraction, i.e., the ratio of smaller to larger size population, however, exhibits a depth-dependent behavior. While at the electrolyte-catalyst interface the phase fraction of the smaller size population decreases, it increases in the inner catalyst layer. The results of a depth-dependent degradation suggest that employing a depth-dependent catalyst design can be used for future improvement of catalyst stability.

An improved small-angle X-ray scattering analysis of δ′ precipitation in an Al–Li alloy for growth kinetic studies

1999 ◽  
Vol 32 (3) ◽  
pp. 426-435 ◽  
Author(s):  
Cheng-Si Tsao ◽  
Tsang-Lang Lin
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Hard Sphere ◽  
Volume Fraction ◽  
The Other ◽  
Improved Method ◽  
Saxs Data ◽  
X Ray ◽  
X Ray Scattering ◽  
Two Parameters

An improved method for small-angle X-ray scattering (SAXS) data analysis is developed to reconstruct the free-form particle size distribution of δ′ precipitation in an Al–Li alloy. This improved method consists of four iterative steps; the interparticle interference is also included. The indirect transform method (ITM) plus a hard-sphere (HS) model which considers the depleted zones are used in the analysis of δ′ precipitation in an Al–Li alloy. Two parameters, namely the hard-sphere volume fraction, ηHS, and the ratio of hard-sphere radius to the particle radius,RHS/R, which determine the structure factor of the interparticle effect, are iteratively calculated using the monodisperse assumption and Gaussian size distribution. These two parameters are finally used in reconstructing the particle size distribution by the ITM + HS method. This method is tested by analysing simulated SAXS data and shows a better agreement than found in similar studies. This improved method is applied to analyse a set of experimental SAXS intensities from δ′ (Al3Li particles) precipitation in an Al–9.7 at.% Li alloy. The monodisperse results are compared with the polydisperse ITM + HS results. The current ITM + HS method fits the SAXS data better than the other methods. The variations of average radii with aging time were found to follow the kinetic power law. The SAXS results are used to investigate the theoretical kinetic model of the volume-fraction effect on late-stage coarsening (Ostwald ripening). By comparing both experimentally obtained asymptotic size distributions of δ′ particles as well as coarsening rate constants with those predicted by the various kinetic models, the modified Lifshitz–Slyozov–Wagner (MLSW) theory is found to be in better agreement with the experimental results than the other theories.

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