Small Angle X-Ray Scattering of Hematite Aggregates

Small angle X-ray scattering has been utilised to study the structure of hematite aggregates. The small angle X-ray scattering (SAXS) spectra obtained provided insight into structure of the hematite aggregates and the size of the primary particles. The structural analysis results obtained by SAXS are consistent with previous results obtained from static light scattering studies. Both techniques indicate that the mass fractal dimensions of hematite aggregates are markedly higher than those obtained for other particle systems.     

Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.     

Relationship between Floc Short Range Structure and Sediment Compaction

This paper studies the short and long‐range structure of silica aggregates using the small angle light scattering technique. Silica particles were made to aggregate by the addition of MgCl₂, with and without continuous shear. Two different short‐range structures were observed for different aggregation conditions. The small angle light scattering reveals two different floc structures at different length scales, a very compact floc at short length scale and a loose floc at large length scale. The sediments of these flocs were studied by allowing them to settle under gravity and consolidate at different centrifugal forces. The results show that the floc short‐range structure is important in governing the compaction behaviour of sediment.     

Off lattice simulations of cluster-cluster aggregation in dimensions 2–6

Cluster-cluster aggregation has been simulated in dimensions two to six using both linear and brownian cluster trajectories. Relatively efficient off lattice algorithms have allowed large clusters to be generated and values for the fractal dimensionalities of the aggregates have been obtained without finite concentration effects. The values for the fractal dimensionality are in good aggreement with lattice model simulations for euclidean dimensionalities 2–4. The effective dimensionality (D_β) obtained from the dependence of the radius of gyration on cluster size increases with increasing cluster size for all of our models (particularly for d ≥ 4). For clusters in the accessible size range (up to 10³-10⁴) D_β is slightly larger for cluster-cluster aggregation via linear trajectories than for brownian trajectories. For cluster-cluster aggregation via brownian trajectories, the limiting (large cluster size) fractal dimensionality is estimated to be 1.46 ± 0.04 for d=2,1.82 ± 0.10 for d = 3, 2.10 ± 0.15 for d = 4, 2.35 ± 0.15 for d = 4, 2.65 ± 0.25 for d = 6. For cluster- cluster aggregation via linear trajectories, the limiting fractal dimensionality is estimated to be 1.55 ± 0.04 for d = 2, 1.91 ± 0.10 for d = 3≥ 2.5 ± 0.06 for d = 5 and ≥2.64 ± 0.05 for d = 6.     

Monitoring the Dynamics of Concentrated Suspensions by Enhanced Backward Light Scattering

The shear-induced flocculation of kaolin-polymer flocs in a stirred tank is investigated at medium to high solids concentrations (ϕ=1−10% w/w). The evolution of the average floc size is monitored by the change in intensity of laser light scattered in the 180° direction. The measurements reflect the change in particle number concentration as flocculation proceeds. As flocculation begins, coagulation dominates and the floc size increases (total particle number decreases) and then levels off at a steady state value as fragmentation becomes significant and balances coagulation. At steady state, the measurements indicate the extent of flocculation. Increasing the shear rate increases the coagulation and fragmentation rates, resulting in smaller floc sizes at steady state. Increasing the flocculant concentration increases the steady state floc size by strengthening the bonds between primary particles to resist fragmentation. At constant shear rate and flocculant concentration, increasing the solids fraction decreases the steady state floc size indicating formation of weakly bonded flocs. Flocculant mixing was the most important factor for flocculation efficiency at high solids concentrations.     

Effect of pH and Protein Concentration on Rheological and Structural Behavior of Temperature-induced Bovine Serum Albumin Gels

The rheology of a temperature-induced protein bovine serum albumin gel is shown to strongly depend on the solution pH and protein concentration. Small-angle neutron scattering studies showed the presence of a fractal structure of the gels, resembling the aggregation of protein molecules and causing a three-dimensional network kind of arrangement. The fractal dimensions were observed to be constant and independent of the variation of pH and the protein concentration. The results of rheology and scattering experiments are correlated in terms of pH-dependent flexibility of flocs in the gels and hindrance to flow with concentration, while the structure of such flocs remains similar irrespective of the solution conditions.     

Fractal Character of Dynamic Light Scattering of Particles

Dynamic light scattering signals from particles, exhibit fractal characteristics. This feature can be used to determine the particle size. The use of the fractal dimension, as a quantitative method to analyze the properties of dynamic light scattering signals from submicron particles, is presented. The analysis is performed directly on the time‐resolved scattered intensity, and the Box Dimensions of light scattering signals of particles with diameters 100, 200, 500 and 1000 nm. The experimental results show that the fractal dimensions of light scattering signals correlate well with particle size. In the submicron size range, the smaller the particles, the larger their fractal dimensions. Compared with the PCS technique, only several hundreds of samples are required in the fractal method. Therefore, the data processing is easily accomplished. However, this method only provides the mean particle size, but not the particle size distribution.     

Sizing Polydisperse Dispersions by Focused Beam Reflectance and Small Angle Static Light Scattering

In this work, two different methods for particle characterization, namely focused beam reflectance and small angle static light scattering, are quantitatively compared. The results are presented in the form of moment ratios of the particle size distribution, i.e., the number weighted diameter, D_1/0, and the volume weighted diameter, D_4/3, for a broad range of particle size distributions ranging from 20 to 400 μm. Various aqueous dispersions including narrow, broad, and bimodal particle size distributions of spherical shaped ceramic beads were used in the comparison. It was found that the moment ratios obtained by focused beam reflectance measurements and small angle static light scattering correlate well, in the case of spherical particles. Furthermore, it was found that the D_1/0 values obtained by focused beam reflectance measurements are more sensitive to the presence of a small fraction of fine particles in a bimodal distribution than those obtained by small angle static light scattering.     

Limits to gelation in colloidal aggregation

We show that the dynamics of large fractal colloid aggregates are well described by a combination of translational and rotational diffusion and internal elastic fluctuations, allowing both the aggregate size and internal elasticity to be determined by dynamic light scattering. The comparison of results obtained in microgravity and on Earth demonstrates that cluster growth is limited by gravity-induced restructuring. In the absence of gravity, thermal fluctuations ultimately inhibit fractal growth and set the fundamental limitation to the lowest volume fraction which will gel.     

Instantaneous in-flame measurement of soot volume fraction, primary particle diameter, and aggregate radius of gyration via auto-compensating laser-induced incandescence and two-angle elastic light scattering

A new combination of soot diagnostics employing two-angle elastic light scattering and laser-induced incandescence is described that is capable of producing non-intrusive, instantaneous, and simultaneous, in situ measurements of soot volume fraction, primary particle size, and aggregate radius of gyration within flames. Controlled tests of the new apparatus on a well-characterized laminar flame show good agreement with existing measurements in the literature. From a detailed and comprehensive Monte Carlo uncertainty analysis of the results, it was found that the uncertainty in all three measured parameters is dominated by knowledge of soot properties and aggregation behavior. The soot volume fraction uncertainty is dominated by uncertainty in the soot refractive index light absorption function; the primary particle diameter uncertainty is dominated by uncertainty in the fractal prefactor; while the uncertainty in the aggregate radius of gyration is dominated by the uncertainty in the width of the distribution of aggregate sizes.     

气溶胶凝聚粒子散射特性的数值计算

利用Cluster-cluster aggregation (CCA)模型,模拟了由相同数目球形原始微粒凝聚而成的四种随机取向气溶胶凝聚粒子．根据物质的电结构,将气溶胶凝聚粒子离散为一系列偶极子,结合离散偶极子近似方法,在获得每一个偶极子的电偶极矩之后,数值计算了气溶胶凝聚粒子散射强度的角分布,并分析了散射强度随入射光入射角度和气溶胶凝聚粒子尺寸参数变化的规律．结果显示：当散射角较小时,气溶胶凝聚粒子取向和入射光的入射角度对散射强度影响不大,当散射角增大时,散射强度则明显依赖于气溶胶凝聚粒子取向和入射光的入射角度;对于不同尺寸参数的气溶胶凝聚粒子,在同一角度入射情况下,随尺寸参数的增加,气溶胶凝聚粒子的散射主要集中于前向散射．     

Kinetic stability of hematite nanoparticles: the effect of particle sizes

Nanoparticles are ubiquitous in environment and are potentially important in many environmental processes such as sorption, coprecipitation, redox reactions, and dissolution. To investigate particle size effects on nanoparticle aggregation and stability, this study tested aggregation behavior of 12(±2), 32(±3), and 65(±3) nm (hydrated radius) hematite particles under environmental relevant pH and ionic strength conditions. The results showed that at the same ionic strength and pH conditions, different particle sizes show different tendency to aggregate. At the same ionic strength, aggregation rates are higher for smaller particles. The critical coagulation concentration also depends on particle size, and decreases as particle size decreases. As the particle size decreases, fast aggregation shifted to lower pH. This may be related to a dependence of PZC on particle size originating from change of structure and surface energy characteristics as particle size decreases. Under the same conditions, aggregation occurs faster as particle concentration increases. Even though the nanoparticles of different sizes show different response to the same pH and ionic strength, DLVO theory can be used to qualitatively understand hematite nanoparticle aggregation behavior.     

Modification of a SAXS camera to study structures on multiple scales

A compact small-angle X-ray scattering (SAXS) camera was modified in order to cover a significantly wider size range than that typically covered by conventional lab-based devices. A new housing with a larger sample-to-detector distance (230 → 1300 mm) was developed and a new focusing Göbel mirror was installed to provide a narrower beam width needed to detect scattering intensities very close to the primary beam. A new photon-counting detector was applied to probe the intensity at small scattering vectors while an imaging plate detector serves to simultaneously collect data at large scattering angles up to 90°. The relevant features of the camera are shown and discussed based on raytracing simulations and SAXS measurements, respectively. The minimum scattering vector could be decreased by a factor of 10 to a value of 0.008 nm^?1 corresponding to structures up to 780 nm in size. Structural analyses of selected particle systems demonstrate ability of the modified camera to probe various structural parameters on multiple scales, e.g., crystallite size, primary particle size, aggregate size, and fractal dimensions. The modified camera system is promising for structural studies of particle formation and growth/aggregation mechanisms since it provides information on multiple scales ranging from angstroms to several hundred nanometers.     

Formation of fractal structures by aggregation of anisometric iron (III) hydroxide particles

Coagulation of anisometric iron (III) hydroxide sols has been studied by dynamic light scattering, TEM and ultra-small-angle X-ray scattering. The anisometry of rod-like individual colloidal particles can be characterised with a mean aspect ratio of 10. It was established for the first time, that the aggregates formed by coagulation of anisometric particles show definite fractal structure with a mass fractal dimension of 1.95 ± 0.05.     

Monte Carlo studies of two measures of polymer chain size as a function of temperature

Monte Carlo simulations of single polymer chains with both excluded volume and nearest-neighbor interaction energies are discussed. Two measures of chain size are obtained in the simulation, the radius of gyration of the polymer chain and the inverse radius of the polymer chain. Both of these are reported as a function of temperature, or interaction energy, and chain length,N. The possibility of estimating the fractal dimensions of these measures from the Monte Carlo data is discussed in the context of two different interpolation functions for the temperature dependence of the fractal dimensions. The approach to the fractal dimension as a function of chain length,N, is studied. It is suggested that the approach to fractal dimension of the measures of chain size of polymers is slow, perhaps a fractional power itself.     

Brownian dynamics simulation of linear chain growth

Growth of linear chains is simulated by the technique of Brownian dynamics. The influence of the initial volume fraction of particles on the rate of the process and the structure of the chains is studied. Results show that aggregation is swift at the beginning of the process and very slow at the end. This is due to the decrease of the number of flocs in solution and the decrease in the efficiency of collisions when the degree of aggregation increases. The polydispersity of the system increases during aggregation and reaches a maximum value when the reaction is 96% complete. This increase is greater at higher concentrations. Results indicate that for lower concentrations aggregate growth is principally by reactive collision between aggregates of similar molecular weight, while for higher concentrations there is a relatively high fraction of reactive collisions between aggregates with very different molecular weights. The concentration effect on the structure of the chains is studied, evaluating the fractal dimensions of the chains. When the concentration increases there is a transition from very open structures (fractal dimension 1.76) to very tangled structures, where chains are collapsed (fractal dimension 3).     

应用低相干动态光散射法测量悬浮液中的颗粒粒径分布

利用低相干动态光散射法测量不同浓度悬浮液中的颗粒粒径分布。由低相干光源和迈克尔逊干涉仪,结合传统的动态光散射技术组成低相干动态光散射装置,通过检测单次背散射光的能谱分布,利用CONTIN算法得到不同浓度悬浮液中颗粒的粒径分布。结果表明,对于1%～10%体积浓度范围内的单分散悬浮液羊品测量得到的颗粒粒径精确度在4%以内。     

Messung kohärenter Streulängen durch Kleinwinkelstreuung von Neutronen im Schwerkraft-Refraktometer

Using the small angle scattering of neutrons by a “Christiansen-Filter”, a mixture of a grained powder with a liquid, it has been possible to determine the scattering amplitude of powders and liquids with an error within ± 1% or lower. By measurements with Tungsten-powder and mixtures of the liquids C₂Cl₄ and C₆H₅Cl and with mixtures of heavy and light water we got the scattering amplitudes of the bound atoms: Deuteruma=(6.70 ± 0.05) f and Tungstena=(4.77 ± 0.05) f.     

小粒子动态光散射信号的计算机模拟及分析

用计算机模拟了小粒子（０．００１μｍ～１μｍ）的动态光散射信号，并对其进行了分析，同时运用分形几何学（ＦｒａｃｔａｌＧｅｏｍｅｔｒｙ）的理论和概念，对信号的时间复杂性进行了分数维（ＦｒａｃｔａｌＤｉｍｅｎｓｉｏｎ）的计算，得出了它与粒子尺寸之间的关系。     

Fractal dimension of long electrical discharges

The fractal dimension of 500 mm long electrical discharges is presented by analyzing a set of photographic images. Three popular fractal dimension estimation techniques, box counting, sandbox and correlation function methods were used to estimate the fractal dimension of the discharge channels. To remove the apparent thickness due to varying magnitudes of current in the discharge channels, edge detection algorithms were utilized. The estimated fractal dimensions for box counting, sandbox and correlation function for long laboratory sparks were 1.20 ± 0.06, 1.66 ± 0.05 and 1.52 ± 0.12 respectively. Within statistical uncertainties, the estimated fractal dimensions of positive and negative polarities agreed very well.