Comparative Test of Methods to Determine Particle Size and Particle Size Distribution in the Submicron Range

Among the most important characteristic properties of disperse systems such as latices, pigments, ceramic materials or drug formulations are the particle size and the particle size distribution. To measure these quantities, several methods and measuring instruments based on different physical principles are available. These include turbidimetry, dynamic and static light scattering, electron microscopy with image analysis, ultra- and disc centrifugation, light diffraction and the electrical sensing zone method. All these measuring techniques are doubtless necessary because of the large product variety and the broad particle size range. However, some problems arise if different techniques are used and the results are compared uncritically without considering to the application range and the resolution of the methods. An extensive comparative test was therefore carried out using seven latices in the submicron range with defined monomodal, bimodal and hexamodal particle size distributions. The most important methods of determining average particle size values and particle size distributions were tested and compared. Of the methods to determine only average particle sizes, turbidimetry is the most efficient, followed by dynamic light scattering with cumulants evaluation. Static light scattering only yields accurate results for small particles with narrow particle size distributions. Of the methods to determine particle size distributions, ultracentrifugation and, somewhat less, disc centrifugation and electron microscopy with image analysis are the most efficient. Dynamic light scattering only yields reliable results in the case of small particles with narrow distribution curves. Light diffraction and the electrical sensing zone method are less suitable for the submicron range.     

The Use of Small Angle Light Scattering to Study Structure of Flocs

In this paper, a new approach using small angle light scattering to study the structure of large micron sized flocs is described. The flocs were made up from uniformly sized, approximately spherical hematite particles, induced to aggregate using 250 mM KCl to ensure that growth was governed by diffusion limited aggregation alone. The fractal dimensions of the hematite aggregates changed from 1.73 to 2.23 ± 0.05 as the aggregation proceeded, indicating that restructuring occurred during aggregation. The fractal dimensions obtained from the small angle light scattering technique are compared with those obtained from the combination of volume fraction and floc size measurement. The steady state fractal dimensions (2.23 ± 0.05) obtained by small angle light scattering are comparable to the fractal dimensions obtained from determining the slope of the relationship between floc volume fraction and floc size (2.09 and 2.14 ± 0.05). The discrepancy between the fractal dimensions obtained by these techniques during the initial stages of aggregation is due to the fact that the latter method measures the average fractal dimensions, whilst the former method measures the fractal dimensions at any particular instant.     

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.     

Dynamic Light Scattering Measurement of Nanometer Particles in Liquids

Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.     

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。     

分形凝聚粒子的光散射特性研究

粒子的形状和凝聚对光散射特性有着很大的影响.基于分形生长的受限扩散(DLA)模型,模拟了凝聚粒子的三维空间分形结构,并采用回转半径法计算了凝聚粒子的分形维数.利用离散偶极子近似(DDA)方法研究了纳米石墨凝聚粒子的光散射特性,对于原始粒子数不同的凝聚粒子及分形结构不同的凝聚粒子,数值计算了散射强度和偏振度随散射角的分布...     

火灾烟颗粒的分形结构形状模拟与光散射计算

针对火灾烟颗粒的形状特点，提出并建立火灾烟颗粒分形结构凝团的形状模型，并对烟颗粒扫描电镜(SEM)图像进行分析，获取分形结构模型中的单个凝团中基本颗粒个数、凝团分形维数、基本颗粒半径等参数.利用该模型对火灾烟颗粒的形状进行模拟的结果表明，该模型能够较好反映出烟颗粒的形貌特征.利用形状模型对火灾烟颗粒散射进行初步计算表明，在其他参数相同的情况下，相对于同体积的球形颗粒，分形凝团具有前向散射较弱，后向散射较强的特征.     

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.     

The Fractal Characteristic of Particles in Granular Material Flows and Its Effect on Effective Thermal Conductivity

According to the fact that many pulverized particles possess fractal characteristic, a fractal model for studying fine particles in granular material flows is first proposed. An expression of particles' fractal distribution is derived to describe the relationship between the particle fractal dimensions and particle velocity distribution function. In accordance with this model, the theoretical particle effective thermal conductivity is derived. The analytical results show that for the small Biot-Fourier number, the effective thermal conductivity increases with the square root of the granular temperature. For very large Biot-Fourier number, the effective thermal conductivity linearly increases with the granular temperature. Numerically calculated results show that the thermal conductivity increases with the particle size fractal dimensions and decreases with the particle surface fractal dimensions.     

Simulation of light scattering by a particle on a film-coated substrate using coupled-dipole method

The intensity of light scattered by a submicron particle on a film-coated semiconductor substrate is calculated as a function of the thickness of the film using the coupled-dipole method. The result of calculation reproduces the experimentally observed features, i.e., the oscillatory dependence of the scattering intensity on the thickness and the enhancement of the scattering intensity for very thin films. The enhancement is reproduced only when the dipole-dipole interaction between the particle and the substrate is included in the calculation. Using the method we propose, the scattering intensity can be calculated for an arbitrary size and shape of particle on an arbitrary thickness of film.     

基于动态光散射研究pH值对茄红素胶囊粒径的影响

用微乳化技术结合复合团聚法制备了纳米及亚微米茄红素胶囊,基于动态光散射测量分析了环境p H值对胶囊的粒径大小及其分布的影响.结果表明,对纳米茄红素胶囊,当p H值为3.5、6.0及6.8时能稳定的分散,而p H值为7.4时则会出现明显的聚集现象;对亚微米茄红素胶囊,当p H值为3.5、6.0、6.8及7.4时其粒径分布均为双峰状态,其中粒径较大的为亚微米茄红素胶囊,粒径较小的为包覆不良的颗粒,且p H=7.4时的粒径明显小于其它三种p H值时的粒径.虽然亚微米胶囊在p H=7.4时粒径明显变小的结果与纳米胶囊相同,但亚微米胶囊并不像纳米胶囊那样出现聚集现象.     

Orientational averaging of integrated cross sections in the discrete dipole method

Using the discrete dipole method, exact and approximate analytical solutions for orientation-averaged cross sections for extinction, absorption, and scattering of light are obtained. The analytical solutions can be applied to the calculation of integrated cross sections of fractal clusters formed by primary particles with different optical properties (soot in air and aqueous suspensions of aggregates of polystyrene, gold, and silver nanoparticles). It is shown that two models of aggregates that differ only in trajectories (ballistic or Brownian) of primary particles and intermediate clusters and in average fractal dimensions give close values of averaged extinction cross sections.     

切比雪夫雾霾粒子的紫外光散射偏振特性研究

雾霾天气已严重影响人们的日常生活,通过检测雾霾粒子的紫外光散射偏振特性可以有效分析雾霾成因。矿物粒子、灰尘粒子等雾霾颗粒均有小规模表面粗糙度的形态学特征,因此可用切比雪夫粒子作为模型分析。“日盲”紫外光与切比雪夫雾霾粒子相互作用发生散射,散射光偏振特性可反演切比雪夫雾霾颗粒物理性质(如粒子尺寸参数、复杂折射率、粒子形变、波纹参数)。采用紫外光单次散射模型和T矩阵方法,仿真分析切比雪夫雾霾粒子物理参数与散射光偏振特性(Stokes矢量和偏振度)之间的关系,结果表明：粒径对散射光Stokes矢量Is和Qs随散射角的变化趋势影响很大,粒子的粒径和复杂折射率虚部的变化会造成散射光偏振度随散射角的变化趋势的改变;具体分析散射角度为10°时,得到粒径对Is和Qs的数值影响最大,当粒径r<1 μm时,Is随粒径呈现抛物线趋势;切比雪夫粒子形变的增大,Is呈现先增大后减小的趋势。     

双峰分布颗粒体系的多角度动态光散射数据反演

采用多角度动态光散射和加权正则化反演方法,对4组模拟的双峰分布颗粒体系(100/600 nm,200/600 nm,300/600 nm和350/600 nm)分别选取1、3、6和10个散射角进行测量.粒度反演结果表明,采用加权正则化方法反演双峰颗粒体系的多角度动态光散射测量数据,可获得峰值位置比小于2∶1且含有大粒径(＞350 nm)颗粒的双峰颗粒粒度分布.采用标准聚苯乙烯乳胶颗粒进行实测的结果验证了这一结论.得到含大粒径颗粒的双峰粒度分布反演结果的原因在于,多角度动态光散射能提供更多的大粒径颗粒的粒度信息,加权正则化反演方法能减少测量数据中的噪声,因而多角度动态光散射测量数据的加权反演能实现峰值位置比小于2∶1且含有大粒径颗粒的双峰颗粒体系的测量.     

颗粒溶液颗粒尺寸及浓度的差分偏振弹性散射光谱在线分析方法

偏振弹性散射光谱技术的基本原理为在偏振光入射条件下,根据出射光的偏振特性不同可以筛选出浅表层组织的单次散射光信息和深层组织的漫散射光信息。该研究的创新点在于将这种方法应用于颗粒溶液检测,目的是在颗粒溶液原始状态下实现对颗粒尺寸及浓度的同时检测。设计了一个共轴笼式光学系统,测量了聚苯乙烯微球颗粒溶液某一角度的背向散射信号,通过控制入射端和收集端偏振片的偏振方向获得了颗粒溶液的偏振平行光谱与偏振垂直光谱,两者之差即偏振差分光谱对应颗粒的单次散射信息,将该单次散射信息与Mie散射数据库进行比对获得颗粒的尺寸,然后在颗粒尺寸作为已知的条件下进一步分析偏振垂直光谱,将该垂直光谱对应的颗粒溶液的漫散射信息代入光漫散射下的近似表达式拟合得到颗粒的浓度信息。将实验结果与样品提供值进行了比对,并进一步分析了在获取颗粒数浓度时,颗粒直径的方差分布对结果的影响,最终验证了该实验方法的可行性。该方法的潜在应用包括对标准颗粒制造厂商的产品在线检测以及对牛奶制品中脂肪和蛋白质的浓度检测研究。     

Scattered Light Photometer for On-Line monitoring of size distribution parameters and particle number concentration

A scattered light photometer which monitors the particle number concentration of aerosols is described. The photometer measures the scattered light from illuminated submicron particle clouds with known material properties at certain scattering angles. Intensity ratios in combination with the degree of polarization are used to determine the mean particle diameter and the geometric standard deviation of an assumed log-normal particle size distribution. The determination of the particle size distribution is based on an algorithm which compares the measured and calculated (Mie theory) relative intensity quantities described. Furthermore, the particle number concentration is monitored from a single absolute intensity measurement at one scattering angle. In order to obtain quantitative results a spherical particle shape is required.     

Measurements of Silica Aggregate Particle Growth Using Light Scattering and Thermophoretic Sampling in a Coflow Diffusion Flame

The evolution of silica aggregate particles in a coflow diffusion flame has been studied experimentally using light scattering and thermophoretic sampling techniques. An attempt has been made to calculate the aggregate number density and volume fraction using the measurements of scattering cross section from 90° light scattering with combination of measuring the particle size and morphology from the localized sampling and a TEM image analysis. Aggregate or particle number densities and volume fractions were calculated using Rayleigh–Debye–Gans and Mie theory for fractal aggregates and spherical particles, respectively. Using this technique, the effects of H₂ flow rates on the evolution of silica aggregate particles have been studied in a coflow diffusion flame burner. As the flow rate of H₂ increases, the primary particle diameters of silica aggregates have been first decreased, but, further increase of H₂ flow rate causes the diameter of primary particles to increase and for sufficiently larger flow rates, the fractal aggregates finally become spherical particles. For the cases of high flame temperatures, the particle sizes become larger and the number densities decrease by coagulation as the particles move up within the flame. For cases of low flame temperatures, the primary particle diameters of aggregates vary a little following the centerline of burner and for the case of the lowest flame temperature in the present experiments, the sizes of primary particles even decrease as particles move upward.     

Sh-matrices method applied to light scattering by finite circular cylinders

We present a rigorous analytical solution describing light scattering by a finite circular cylinder of arbitrary dimensions. This solution uses a modification of the extended boundary condition method (EBCM) that is based on the introduction of the so-called Sh-matrices. The Sh-matrices depend only on the shape of particles and do not depend on the particle size or optical constants. The Sh-matrices can be used to find the transition-matrix (T-matrix), that contains all the scattering information from the particle system. The solution is confirmed by corresponding discrete-dipole approximation (DDA) and traditional EBCM calculations.     

Model of light scattering by dust particles in the solar system: Applications to cometary comae and planetary regoliths

We analyze both the intensity and linear polarization of cosmic dust particles by using the physically exact superposition T-matrix method in a fixed orientation for various aggregates of spheres and DDA for the aggregates of Gaussian random spheres. We study both the spherical geometry (in cometary comae) and cylindrical slabs (for regoliths) up to 2000 monomers with size parameters less than ∼3. It is straightforward to produce the observed linear polarization in both geometries while the typically convex and strong opposition spike seems to require wide regolith geometries. The dependence of various parameters on light scattering has also been studied in a rather detailed form. In applications to the cometary polarization we can fit the data in six colors from UV to the J band at a very good accuracy. We, however, emphasize that we do not claim our model to be unique. The most important parameters here are the refractive index and the size distribution of submicron particles. Rest of the parameters has only a minor role. We also found that it is critically important to use several realizations from any assumed particle geometry model because corresponding scattering characteristics can vary quite a lot.     

降雨粒子的无线紫外光散射特性

紫外光与降雨粒子相互作用发生散射,散射光特性改变能够反映降雨粒子的相关物理特性（如粒子尺寸参数、浓度、形态）,因此研究粒子的物理参数对散射光特性的影响对有效提高光谱法定量探测降水的精度有很大意义。由于雨滴在非球形降水粒子中具有代表性,以群雨滴粒子为例,采用T矩阵理论,利用紫外光直视和非直视单次散射模型,分析了入射光波长、群雨滴粒子形态、降雨强度、粒径大小与散射光强之间的关系。并用蒙特卡洛方法仿真分析了非球形群雨滴粒子在不同降雨强度和粒径下散射角与散射光强之间的关系,以及降雨环境中的风切变对紫外光散射特性的影响。通过理论及仿真分析,得到了不同群雨滴粒子形态下的路径损耗,不同降雨强度、风切变率和粒径下的散射光强分布。仿真结果表明：在紫外光直视与非直视通信方式下,降雨环境中的通信质量比晴天条件下的通信质量差,即路径损耗增大。当粒径分布已知时,随着降雨强度的增大,衰减系数增大,路径损耗增加,且直视通信方式的路径损耗比非直视降低7 dB左右。随着降雨强度、风切变率和粒子粒径的增大,散射光强曲线整体呈下降趋势,其中,降雨强度的变化对散射光强分布影响程度最大。相同通信距离时,不同降雨强度下的紫外光散射光强分布均随着散射角的增大而减小,当散射角继续增大到90°时,有效散射体体积逐渐减小,接收到的光子能量减小,暴雨中的散射光强衰减程度最大。相同降雨强度下考虑风切变时,相比较无风时的路径损耗增大5 dB左右。除此之外,还研究了椭球形和切比雪夫形粒子对紫外光散射光强的影响,结果表明当粒子粒径分布相同时,椭球形粒子的散射光强衰减较广义切比雪夫形粒子大。根据散射粒子的散射光强分布以及路径损耗能够区分雨滴粒子是否由相同粒径及形态组成,为粒子测量提供理论基础。分析降水中群雨滴粒子的光散射特性,为提高光谱法评估降水衰减的数值模拟方面提供理论依据,为光学技术在探测识别降水现象等气象领域的广泛应用提供了设计参考。