Small-angle x-ray scattering from the surfaces of reversed-phase silicas: Power-law scattering exponents of magnitudes greater than four

Schmidt, Paul W.; Avnir, David; Lévy, David; Höhr, A.; Steiner, M.; Röll, A.

doi:10.1063/1.460006

Cited by 164 publications

(85 citation statements)

References 12 publications

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“…The non-homogeneity of these particles is determined by their interface conventionally defined here as a "diffusive surface". It is close to the concept introduced by Schmidt (Schmidt, 1995) of a diffusive interface between two homogeneous phases to explain the experimentally observed deviations of the scattering from the Porod law towards lower values of the power-law exponent (< 4) at large qvalues in reversed-phase silicas (Schmidt et al, 1991b). The same deviations were revealed for SANS from ethanol solutions of hydrolyzed TEOS (Avdeev et al, 2004).…”

Section: Introductionsupporting

confidence: 62%

Small-angle scattering from polydisperse particles with a diffusive surface

et al. 2014

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Small-angle scattering from polydisperse particles with a diffusive surfaceIn: Journal of Applied Crystallography (2014) Blackwell DOI: 10.1107/S1600576714001216Person to contact for this submission: Mikhail Avdeev (avd@nf.jinr.ru; phone: (+7-49621) 62-674; fax: (+7-49621) SynopsisSmall-angle scattering from polydisperse non-homogeneous particles with diffusive interface is considered for the case of small diffusivity. The deduced simplifications both in the analysis of polydispersity and inner structure (contrast variation) of the particles are used in the treatment of the small-angle neutron scattering data from liquid dispersions of detonation nanodiamonds. AbstractThe particles with a diffusive surface, which is characterized by a deviation from the Porod power-law asymptotic behavior in small-angle scattering towards the exponent below 4, are considered with respect to the polydispersity problem. The case of small diffusivity is emphasized, which allows one to describe the scattering length density distribution within the 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 the 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 2 of the experimental small-angle neutron scattering data from liquid dispersions of detonation nanodiamonds.The obtained scattering length density profile of the particles fits well a transition of the diamond states of carbon inside the crystallites to graphite-like states at the surface and makes it possible to combine the diffusive properties of the surface with the experimental shift of the mean scattering length density of the particles as compared to 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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Section: Introductionsupporting

confidence: 62%

Small-angle scattering from polydisperse particles with a diffusive surface

et al. 2014

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“…In this section I discuss the application of (16) and (17) in an investigation (Schmidt et at., 1991) of porous silicas in which hydrocarbon molecules had been attached to the pore surfaces. These silicas, which are often called reversed-phase silicas, have many important applications in chromatography.…”

Section: Power-law Scattering With Exponents Of Magnitude Greater Thamentioning

confidence: 99%

“…For points on the bound- ary surface, x = 0 and positive values of x specify points in the solid. The scattered intensity for this model is given by the equation (Schmidt et al, 1991) …”

Section: Power-law Scattering From Non-fractal Scatterersmentioning

confidence: 99%

“…This result is an extension of the fact that, as Ruland (1971) pointed out, when the density change at the surface of a scatterer is not sharp but instead is continuous, the scattered intensity decreases more rapidly than with q-4. We have considered (Schmidt et al, 1991) a porous solid in which the transition of the density A(x) at the surface of a porous solid with smooth pore surfaces is continuous and can be described by the power law…”

Section: Power-law Scattering From Non-fractal Scatterersmentioning

confidence: 99%

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Small-angle scattering studies of disordered, porous and fractal systems

Schmidt¹

1991

J Appl Crystallogr

578

390

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Small-angle X-ray and neutron scattering are important techniques for studying the structure of fractals and other disordered systems on a scale of lengths from about 10 to 2000 A. This review begins with a brief outline of some properties of fractals. The small-angle scattering from fractal systems is then discussed and the effect of polydispersity is considered. The intensity of small-angle scattering from fractals and other disordered systems is often proportional to a negative power of the quantity q = 4~,t-Isin(0/2), where 0 is the scattering angle and ,~ is the X-ray or neutron wavelength. From the magnitude of the exponent that describes this type of scattering, which is often called power-law scattering, much important information can be obtained. Some situations in which power-law scattering can be expected are described. To illustrate the scattering from fractals and disordered systems, several experimental investigations of mass-fractal silicas and porous solids are reviewed and some calculations of the small-angle scattering from model fractal systems are outlined.

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“…The N 2 -gas adsorption method has been widely used to measure the specific surface area (SSA) and characterize the open porosity of airdried soil particles, especially the mesoporosity (pore width between 2-50 nm) and microporosity (pore width not exceeding 2 nm) (Mayer et al, 2004;Pronk et al, 2011). The small-angle X-ray scattering (SAXS) technique (Guinier and Fournet, 1955) has been used more generally for the internal and external structural characterization of porous solid materials on a length scale of typically 1 nm to 100 nm as in the case of silica gel (Schmidt, 1991;Schmidt et al, 1991) and clay minerals (Pernyeszi and Dékány, 2003). It has been shown that SAXS technique is suitable for studying fractal dimensions, (D) of powders with porous or irregular surface (Höhr et al, 1988;Schmidt, 1991) where D values are provided from a power law of the measured scattered intensity I(q) as a function of the scattering angle 2θ.…”

Section: Introductionmentioning

confidence: 99%

Effect of metal oxide on surface area and pore size of water-dispersible colloids from three German silt loam topsoils

et al. 2014

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Abstract:The surface area and pore structure of easily dispersed soil particles < 2 µm in size (water-dispersible colloids, WDCs) are important for carbon sequestration and transport in soil. Two processes are essential for the terrestrial carbon cycling. In this work, we determine the effects of dithionite-citrate-bicarbonate (DCB) extractable metal oxides, and oxalate extractable metal oxides on the specific surface area (SSA) and pore structure of WDCs from silt loam topsoils of three TERENO test sites with a similar clay content (20%) in Germany (arable (Selhausen), grassland (Rollesbroich) and forest (Wuestebach) soils). The N 2 gasadsorption (−196°C), small-angle X-ray scattering (SAXS), dynamic light scattering (DLS) and microelectrophoretic (ME) methods were used and compared. Results show that 1) the SSA of the WDCs from Selhausen, Rollesbroich, and Wuestebach decreased more after DCB treatment (27%, 35%, and 44%) than after oxalate treatment (5%, 14%, and 22%). DCB removed metal oxide nanoparticles from WDCs were found to have diameters (d p ) ranging from 4 nm to 8 nm and the surface loading ratios on the surface of aluminosilicate residues in WDCs were estimated to be 11% to 22% for three soils where the highest value was found in the acidic forest soil. 2) Pore sizes in the mesopore range (2 nm to 50 nm) were analyzed in the WDC fractions. The results were discussed in terms of accessible open pores for the pristine WDCs and WDC samples from which metal oxide nanoparticles and organic carbon (OC) had been removed. The lower average pore radius (R p ) measured by the N 2 gasadsorption method based on the total volume (V t ) to SSA ratio variations in WDCs without metal oxides compared to WDC with metal oxides indicated a contraction of the porous structure of WDCs due to the presence of metal oxide nanoparticles. The pore size distribution (PSD) analysis showed a sensitive contribution of metal oxide nanoparticles in the low range of pore sizes (< 25 nm) of WDCs. In SAXS measurements, higher surface fractal dimensions (D s ) were observed in WDCs before the metal oxides removal, which supports a roughness increase of the interfaces in the presence of nanoparticles. The colloidal characterization of WDCs by the DLS and ME methods shows, at a µm scale, the role of positively charged metal oxide nanoparticles in forming WDCs with a more compact structure by decreasing the particle size (d z ) and the negative zeta potential (ζ).3) The comparison of R p , k, d z and d p results between different soils also indicates the dependence on the clay mineralogy of WDCs so that the heterocoagulation between kaolinite and illite (clay minerals of different aspect ratios) increases the size of soil mesopores (Rollesbroich). In conclusion, the results of this study clearly show that the combination of the N 2 gas-adsorption, SAXS, DLS and ME methods allows the characterization of soil porosity in the nanometer range where metal oxide nanoparticles contribute to a more compact structure of WDC.

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Small-angle x-ray scattering from the surfaces of reversed-phase silicas: Power-law scattering exponents of magnitudes greater than four

Cited by 164 publications

References 12 publications

Small-angle scattering from polydisperse particles with a diffusive surface

Small-angle scattering from polydisperse particles with a diffusive surface

Small-angle scattering studies of disordered, porous and fractal systems

Effect of metal oxide on surface area and pore size of water-dispersible colloids from three German silt loam topsoils

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