Particle size distributions from small-angle scattering using global scattering functions

2004 ◽  
Vol 37 (4) ◽  
pp. 523-535 ◽  
Author(s):  
G. Beaucage ◽  
H. K. Kammler ◽  
S. E. Pratsinis
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Small Angle ◽  
Particle Surface ◽  
Spherical Particles ◽  
Radius Of Gyration ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Bet Analysis

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 data directly agrees with the moment calculated fromS/V. Scattering results are also compared with TEM particle-counting results. The potential of scattering to distinguish between polydisperse single particles and polydisperse particles in aggregates is presented. A generalized index of polydispersity for symmetric particles, PDI =BRg4/(1.62G), whereGis the Guinier prefactor, is introduced and compared with other approaches to describe particle size distributions in SAXS, specifically the maximum-entropy method.

scholarly journals Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 2. Interparticle forces and the quasi-stationary equilibrium hypothesis

1984 ◽  
Vol 143 ◽  
pp. 387-411 ◽  
Author(s):  
I. A. Valioulis ◽  
E. J. List ◽  
H. J. Pearson
Keyword(s):  
Monte Carlo Simulation ◽  
Particle Size ◽  
Monte Carlo ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Dimensional Analysis ◽  
Spherical Particles ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Coagulation Rate

Hunt (1982) and Friedlander (1960a, b) used dimensional analysis to derive expressions for the steady-state particle-size distribution in aerosols and hydrosols. Their results were supported by the Monte Carlo simulation of a non-interacting coagulating population of suspended spherical particles developed by Pearson, Valioulis & List (1984). Here the realism of the Monte Carlo simulation is improved by accounting for the modification to the coagulation rate caused by van der Waals', electrostatic and hydrodynamic forces acting between particles. The results indicate that the major hypothesis underlying the dimensional reasoning, that is, collisions between particles of similar size are most important in determining the shape of the particle size distribution, is valid only for shear-induced coagulation. It is shown that dimensional analysis cannot, in general, be used to predict equilibrium particle-size distributions, mainly because of the strong dependence of the interparticle force on the absolute and relative size of the interacting particles.

Determination of Particle Size Distribution in a Dispersion Hardened Nickel Alloy Using Small Angle X-Ray Scattering

1968 ◽  
Vol 12 ◽  
pp. 87-96
Author(s):  
R. W. Gould ◽  
S. R. Bates
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Small Angle ◽  
Spherical Particles ◽  
Scattering Data ◽  
Size Distributions ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

AbstractIt has been recently shown that particle size distributions can be determined from small angle x-ray scattering data. Size distributions have previously been measured in aluminum-zinc and aluminum-silver alloys containing spherical Guinier-Preston zones. Inorder to obtain the size distribution it is only necessary to calculate the Guinier radius and the Porod radius.Dispersion hardened nickel alloys containing small spherical particles of thoria appear to be amenable to this type of analysis. A nickel-20% chromium-2% ThO2 alloy was selected for this study. The particle size distribution obtained by small angle x-ray scattering is compared with the transmission electron microscopy results found in the literature.

Determination of Particle Size Distribution of Nano-TiO2 Coating Film by AFM and Image Analysis

2010 ◽  
Vol 177 ◽  
pp. 22-24
Author(s):  
Zheng Min Li ◽  
Zhi Wei Chen ◽  
Min Tan ◽  
Ke Jing Xu ◽  
Bing Jiang
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Coating Film ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Nano Tio2 ◽  
Tio2 Particles ◽  
Atom Force Microscope

Nano-TiO2 coating film is one of the efficient photocatalysts. The particle size distribution of TiO2 has important influence on photocatalytic activity. A new method to determine the particle size distribution of TiO2 nano-film coated on ceramic was developed, by which the images of film acquired by Atom force microscope (AFM) were processed, and TiO2 particles contacted with others were separated and detected. The particle size distributions of two TiO2 nano-films were determined.

scholarly journals Factors influencing particle size distributions in finely ground forage

1994 ◽  
Vol 74 (2) ◽  
pp. 383-385 ◽  
Author(s):  
R. Soofi-Siawash ◽  
G. W. Mathison
Keyword(s):  
Particle Size ◽  
Moisture Content ◽  
Particle Size Distribution ◽  
Key Words ◽  
Size Distribution ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Routine Procedure ◽  
Factors Influencing

Two studies were conducted to assess the possibility of using particle size distribution following grinding as a routine procedure of forage evaluation. It was concluded that although differences in particle size distribution could be detected when different feeds were ground, it would be difficult to standardize the technique since particle size distributions were influenced by type of mill used for grinding, particle size of forage before grinding, and moisture content of the forage. Key words: Forages, grinding, particle size, moisture, mill

Influence of particle-size distribution homogeneity on shearing of soils subjected to internal erosion

2020 ◽  
Vol 57 (11) ◽  
pp. 1684-1694
Author(s):  
Shijin Li ◽  
Adrian R. Russell ◽  
David Muir Wood
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Soil Sample ◽  
Size Distribution ◽  
Fine Particles ◽  
Internal Erosion ◽  
Triaxial Tests ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Homogeneous Particle

Internal erosion (suffusion) is caused by water seeping through the matrix of coarse soil and progressively transporting out fine particles. The mechanical strength and stress–strain behavior of soils within water-retaining structures may be affected by internal erosion. Some researchers have set out to conduct triaxial erosion tests to study the mechanical consequences of erosion. Prior to conducting a triaxial test they subject a soil sample, which has an initially homogeneous particle-size distribution and density throughout, to erosion by causing water to enter one end of a sample and wash fine particles out the other. The erosion and movement of particles causes heterogeneous particle-size distributions to develop along the sample length. In this paper, a new soil sample formation procedure is presented that results in homogeneous particle-size distributions along the length of an eroded sample. Triaxial tests are conducted on homogeneous samples formed using the new procedure as well as heterogeneous samples created by the more commonly used approach. Results show that samples with homogeneous post-erosion particle-size distributions exhibit slightly higher peak deviator stresses than those that were heterogeneous. The results highlight the importance of ensuring homogeneity of post-erosion particle-size distributions when assessing the mechanical consequences of erosion. Forming samples using the new procedure enables the sample’s response to triaxial loading to be interpreted against a measure of its initially homogenous state.

Effect of particle size distribution of UiO-67 nano/microcrystals on the adsorption of organic dyes from aqueous solution

CrystEngComm ◽  
2018 ◽  
Vol 20 (38) ◽  
pp. 5672-5676 ◽  
Author(s):  
Run-Zhi Zhang ◽  
Yong-qing Huang ◽  
Wei Zhang ◽  
Ji-Min Yang
Keyword(s):  
Aqueous Solution ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Solvothermal Method ◽  
Organic Dyes ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Effect Of Particle Size

UiO-67 nano/microcrystals with different particle size distributions (PSDs) were successfully obtained by a simple solvothermal method.

Combustion Synthesis of β-SiAlON Using 3D Ball Milling

2017 ◽  
Vol 898 ◽  
pp. 1717-1723 ◽  
Author(s):  
Xue Mei Yi ◽  
Shota Suzuki ◽  
Xiong Zhang Liu ◽  
Ran Guo ◽  
Tomohiro Akiyama
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Combustion Synthesis ◽  
Ball Mill ◽  
Raw Materials ◽  
Raw Material ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Material Particle

Combustion synthesis (CS) of β-SiAlON was conducted using a 3D ball mill, with a focus on the effect of the 2D/3D ball mill premixing conditions on the CS raw material particle size as well as on the yield and grain shape of the final products. The results showed that the particle size distribution of the raw materials was significantly affected by the premixing conditions. Various particle sizes and particle size distributions could easily be obtained by using a 3D mill instead of a 2D mill due to the complex biaxial rotation movement of 3D milling. The particle size was more sensitive to the rotation ratio (vertical spin/horizontal spin, Vv/Vh) than the rotation rate when using 3D milling. Finally, β-SiAlON with less than 5 mass% unreacted Si was obtained using premix milling conditions of 135×200 [vertical spin (rpm) × horizontal spin (rpm)]. The grain shapes of the final products were clearly influenced by the particle size distribution of the raw mixtures.

Combination of 47Ti and 48Ti for the determination of highly polydisperse TiO2 particle size distributions by spICP-MS

2019 ◽  
Vol 34 (7) ◽  
pp. 1380-1386 ◽  
Author(s):  
Guillaume Bucher ◽  
François Auger
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Tio2 Particle ◽  
Size Distributions ◽  
Particle Size Distributions

Particle size distribution (PSD) of a highly polydisperse TiO2 sample determined by spICP-MS.

Comparison of functions for evaluating the effect of Fe and Al oxides on the particle size distribution of kaolin and quartz

Clay Minerals ◽  
1997 ◽  
Vol 32 (1) ◽  
pp. 3-11 ◽  
Author(s):  
M. Arias ◽  
E. Lopez ◽  
M. T. Barral
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Probability Density ◽  
Size Distribution ◽  
Probability Density Functions ◽  
Density Functions ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Soil Particles ◽  
Quartz Substrates

AbstractAlthough it is generally agreed that Fe and Al can act to bind soil particles, their relative efficiencies as aggregants are still disputed. In this work, the aggregating efficiencies of both aged and non-aged Fe and Al oxides precipitated on kaolin or quartz substrates were characterized by comparing their effects on particle size distributions (PSD). To facilitate comparison of PSD data, these were parameterized by fitting them with five different probability density functions (the normal, lognormal, Jaky, fractal and Rosin-Rammler functions). The best fits were given by the Rosin-Rammler function (R2 = 0.997), whose α parameter was used to compare the aggregating efficiency of Fe and Al oxides: in order of decreasing efficiency, non-aged Al > non-aged Fe ≈ aged Fe > aged Al-precipitates.

scholarly journals Particle size distributions from laboratory-scale biomass fires using fast response instruments

2010 ◽  
Vol 10 (16) ◽  
pp. 8065-8076 ◽  
Author(s):  
S. Hosseini ◽  
Q. Li ◽  
D. Cocker ◽  
D. Weise ◽  
A. Miller ◽  
...  
Keyword(s):  
United States ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Geometric Mean ◽  
The United States ◽  
Biomass Combustion ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Mean Diameter

Abstract. Particle size distribution from biomass combustion is an important parameter as it affects air quality, climate modelling and health effects. To date, particle size distributions reported from prior studies vary not only due to difference in fuels but also difference in experimental conditions. This study aims to report characteristics of particle size distributions in well controlled repeatable lab scale biomass fires for southwestern United States fuels with focus on chaparral. The combustion laboratory at the United States Department of Agriculture-Forest Service's Fire Science Laboratory (USDA-FSL), Missoula, MT provided a repeatable combustion and dilution environment ideal for measurements. For a variety of fuels tested the major mode of particle size distribution was in the range of 29 to 52 nm, which is attributable to dilution of the fresh smoke. Comparing mass size distribution from FMPS and APS measurement 51–68% of particle mass was attributable to the particles ranging from 0.5 to 10 μm for PM10. Geometric mean diameter rapidly increased during flaming and gradually decreased during mixed and smoldering phase combustion. Most fuels produced a unimodal distribution during flaming phase and strong biomodal distribution during smoldering phase. The mode of combustion (flaming, mixed and smoldering) could be better distinguished using the slopes in MCE (Modified Combustion Efficiency) vs. geometric mean diameter than only using MCE values.

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