Multiple Size Scale Structures in Silica—Siloxane Composites Studied by Small-Angle Scattering (original) (raw)
Related papers
Structure of Fractal Colloidal Aggregates from Small Angle X-Ray Scattering
Le Journal de Physique Colloques, 1985
La s t r u c t u r e des a g r é g a t s de s i l i c e c o l l o i d a l e e s t é t u d i é e p a r d i f f u s i o n d e s rayons X aux p e t i t s a n g l e s . I l s app a r a i s s e n t r a m i f i é s e t peuvent ê t r e c o n s i d é r é s comme des o b j e t s f r a c t a l s de d i m e n s i o n n a l i t é D . D e s t obtenu à p a r t i r de l a pente du f a c t e u r d e s t r u c t u r e e n f o n c t i o n du v e c t e u r de d i f f u s i o n K dans l e régime KR >>1 >> Ka.
Journal of Non Crystalline Solids, 1994
A unified analysis method for small-angle scattering data is demonstrated by surveying complex systems that display multiple size-scale structures. Using this approach the relationship between micro-and nano-structures can be ascertained. The method uses a function that is general enough to adequately describe systems ranging from particulates with fractally rough interfaces to mass fractals such as polymer coils. Additionally multiple Guinier and power-law regimes can be treated. The unified method can distinguish Guinier regimes buried between two power-law regimes. Data from particulate filled systems, low crystallinity polymers and low density polymer foams are analyzed.
Journal of Non-Crystalline Solids, 1994
A unified analysis method for small-angle scattering data is demonstrated by surveying complex systems that display multiple size-scale structures. Using this approach the relationship between micro-and nano-structures can be ascertained. The method uses a function that is general enough to adequately describe systems ranging from particulates with fractally rough interfaces to mass fractals such as polymer coils. Additionally multiple Guinier and power-law regimes can be treated. The unified method can distinguish Guinier regimes buried between two power-law regimes. Data from particulate filled systems, low crystallinity polymers and low density polymer foams are analyzed.
The Journal of Chemical Physics, 1991
The small-angle x-ray scattering from fully and partially derivatized porous silicas has been studied. Power-law-scattering exponents of magnitude greater than 4 have been found in all cases. The magnitudes of the exponents increased with the alkyl chain length and with the degree of surface derivatization. In a preliminary model to explain these observations, a power-law-scattering exponent with magnitude greater than 4 is related to a "fuzzy" pore boundary, in which the density varies continuously at the pore boundary instead of changing discontinuously from a value of zero in the empty pore to the essentially constant density characteristic of the bulk silica, as is usually assumed in analyses of the small-angle scattering from porous silicas.
Particle size distributions from small-angle scattering using global scattering functions
Journal of Applied Crystallography, 2004
Control and quantification of particle size distribution is of importance in the application of nanoscale particles. For this reason, polydispersity in particle size has been the focus of many simulations of particle growth, especially for nanoparticles synthesized from aerosols such as fumed silica, titania and alumina. Single-source aerosols typically result in close to a log-normal distribution in size and micrograph evidence generally supports close to spherical particles, making such particles ideal candidates for considerations of polydispersity. Small-angle X-ray scattering (SAXS) is often used to measure particle size in terms of the radius of gyration,Rg, using Guinier's law, as well as particle surface area,S/V, from the Porod constantBand the scattering invariantQ. In this paper, the unified function is used to obtain these parameters and various moments of the particle size distribution are calculated. The particle size obtained from BET analysis of gas adsorption da...
Journal of Colloid and Interface Science, 2000
The early stages of formation of Stöber silica particles have been investigated in situ during the hydrolysis and condensation of tetraethylorthosilicate under base-ammonia conditions in different alcoholic solvents. Time-resolved ultra-small-angle X-ray scattering by the entities produced in the solutions is used for structural characterization and monitoring of the growth kinetics of the particles. Our primary focus is to assess the polydispersity of the formed colloidal particles and its evolution as a function of time. We first applied a maximum entropy analysis of the scattering data to determine the size distribution and the time evolution of the size distribution of the colloidal particles. Second, we extended the cumulant method to analyze our earlier small-angle X-ray scattering data (H. Boukari, J. S. Lin, and M. T. Harris, J. Colloid Interface Sci. 194, 311, 1997; Chem. Mater. 9, 2376, 1997) and search for the presence of a distribution of fractal particles. The maximum entropy analysis indicates that there is a continuous nucleation of particles during the synthesis, and that this takes place within a relatively narrow size distribution. The cumulant analysis shows that, except at later times, the data are not adequate to confirm conclusively the presence of a distribution of fractal dimension at any time during the experiment. We discuss the impact of these results on growth kinetic models proposed for this system. C 2000 Academic Press
Small-angle scattering and scale-dependent heterogeneity
Journal of Applied Crystallography, 2016
Although small-angle scattering is often discussed qualitatively in terms of material heterogeneity, when it comes to quantitative data analysis this notion becomes somehow hidden behind the concept of correlation function. In the present contribution, a quantitative measure of heterogeneity is defined, it is shown how it can be calculated from scattering data, and its structural significance for the purpose of material characterization is discussed. Conceptually, the procedure consists of using a finite probe volume to define a local average density at any point of the material; the heterogeneity is then quantitatively defined as the fluctuations of the local average density when the probe volume is moved systematically through the sample. Experimentally, it is shown that the so-defined heterogeneity can be estimated by projecting the small-angle scattering intensity onto the form factor of the chosen probe volume. Choosing probe volumes of various sizes and shapes enables one to c...
Fractal scaling of small angle neutron scattering data
Power-law variations of small-angle neutron-scattering intensities from nonionic micellar solutions of isooctylphenoxy polyethoxy ethanol ͑Triton X-100͒ in D 2 O for a range of concentrations ͑1-4 wt %͒ and temperatures ͑295-335 K͒ are interpreted in terms of simple models of fractal aggregates. The results show a large increase in dimensionality from ϳ1 at ambient temperature to ϳ2.3 near the cloud points. The variation of fractal dimension with temperature is almost the same for the three concentrations studied. Thus one arrives at a picture of micellar aggregates becoming more and more tenuous as cloud points are approached. ͓S1063-651X͑96͒08305-5͔ PACS number͑s͒: 82.70Ϫy, 05.40ϩj, 64.70.Ϫp, 61.10.Eq An exhaustive set of small-angle neutron-scattering ͑SANS͒ experiments from Triton X-100 ͑isooctylphenoxy polyethoxy ethanol, Aldrich͒ solutions in D 2 O covering a wide range of concentrations ͑1-15 wt %͒ and temperatures ͑295-335 K͒ was reported by us recently ͓1͔. These solutions show the well-known clouding phenomena ͓2͔ with a lower consolute point in the phase diagram at c ϳ6 wt % and temperature T c ϳ335 K. The clouding temperatures for 1, 2, 4, 8, 12, and 15 wt % solutions, the systems for which SANS measurements were made, are 336.5, 336, 335, 335.5, 337, and 338 K, respectively. The measurements were made at the Intense Pulsed Neutron Source at Argonne National Laboratory, Argonne, Illinois, U.S.A., by using the smallangle diffractometer ͑SAD͒ ͓3͔.
Physical review. B, Condensed matter, 1994
Fractal aggregates are built on a computer using off-lattice cluster-cluster aggregation models. The aggregates are made of spherical particles of different sizes distributed according to a Gaussianlike distribution characterised by a mean a0 and a standard deviation σ. The wave vector dependent scattered intensity I(q) is computed in order to study the influence of the particle polydispersity on the crossover between the fractal regime and the Porod regime. It is shown that, given a0, the location qc of the crossover decreases as σ increases. The dependence of qc on σ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.