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.     

Mean Particle Diameters. Part VIII. Computer Program to Decompose Mixtures of (Truncated) Lognormal Particle Size Distributions Using Differential Evolution to Generate Starting Values for Nonlinear Least Squares

Multimodal size distributions can result from a mixing of two or more component distributions and arise in quite different application areas. Physical and statistical approaches are described for decomposition of a multimodal particle size distribution into a number of lognormal components. These approaches, incorporated in the Fortran computer program FitDist, use a nonlinear least‐squares (NLLS) optimization, requiring initial parameter estimates. A hybrid deconvolution method has been developed. Differential Evolution (DE), is used for generation of initial parameter values, followed by an NLLS optimization to derive precise parameter values at the local optimum. The DE algorithm is required to decide on the proper number of modes to be fitted. Mathematical relationships have been derived to convert the parameter values of one multimodal lognormal moment distribution, e.g., a number distribution, to those of another moment distribution, e.g., a volume distribution. Moreover, mathematical relationships have been derived to compute mean diameters (Moment‐Ratio notation) from the parameters of a multimodal lognormal size distribution. Fitting a 1.5th moment distribution, being just in between a number and a volume distribution, has been introduced as an instrument to balance inaccuracies in both tails of a distribution due to sampling inaccuracies or truncation of these tails. The program fits a truncated size distribution by fitting its frequency density distribution, whereas a complete size distribution is fitted by fitting the cumulative distribution. Some guidelines are given for fitting Number, Diameter, Surface area, and Volume distributions to measured size distributions. Although fitting of multimodal normal distributions is an option, higher moment distributions will not be fitted as these distributions are not normally distributed. Practical examples demonstrate the validity of the method to decompose multimodal particle size distributions by use of DE.     

Elastic scattering of B on B in the energy range from 4 to 15 MeV

Angular distributions (at E_c.m. = 4, 6.5 and 10.5 MeV) and excitation functions (at 30°, 60° and 90°) are given for the elastic scattering of ¹⁰B on ¹⁰B. The results of an optical model (OM) analysis are presented and discussed. In the energy range covered the Sommerfeld parameter η varies from 4.4 to 2.3.     

A study of the level structure in Fe from the (d, p) reaction on Fe

The reaction ⁵⁶Fe(d, p)⁵⁷Fe is investigated at 12 MeV using the Aldermaston multi-channel magnetic spectrograph. The angular distributions of protons leading to various states in ⁵⁷Fe upto an excitation of 6.7 MeV are measured over an angular range 5°–175°. The data are analysed with the distorted wave Born approximation calculations; a satisfactory agreement is found in most cases upto about 100°. Spin, parity and the spectroscopic factors for various states are obtained and the positions of the single-quasiparticle energies determined. The results are compared with those for the isotonic nuclei ⁵⁵Cr and ⁵⁹Ni and with the pairing theory.     

Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization

As a part of resolving optical properties in atmosphere radiative transfer calculations, this paper focuses on obtaining aerosol optical thicknesses (AOTs) in the visible and near infrared wave band through indirect method by gleaning the values of aerosol particle size distribution parameters. Although various inverse techniques have been applied to obtain values for these parameters, we choose a stochastic particle swarm optimization (SPSO) algorithm to perform an inverse calculation. Computational performances of different inverse methods are investigated and the influence of swarm size on the inverse problem of computation particles is examined. Next, computational efficiencies of various particle size distributions and the influences of the measured errors on computational accuracy are compared. Finally, we recover particle size distributions for atmospheric aerosols over Beijing using the measured AOT data (at wavelengths λ=0.400, 0.690, 0.870, and 1.020 μm) obtained from AERONET at different times and then calculate other AOT values for this band based on the inverse results. With calculations agreeing with measured data, the SPSO algorithm shows good practicability.     

Particle sizing by multiangle light-scattering data using the high-order neural networks

The problem of retrieval of size and refractive index of a spherical particle by angular dependence of scattered light in scanning flow cytometry is considered. For its solution, the high-order neural networks are used. We restricted the range of angles available for measurement from 10° to 60°. The retrieval errors of characteristics of nonabsorbing particles were investigated at the ranges of the radius and relative refractive index 0.6–10.6 μm, and 1.02–1.38, respectively.     

Ion-implantation-induced structural modifications in Y1Ba2Cu3O7−δ superconductor

Ion-implantation-induced structural modifications in Y₁Ba₂Cu₃O_7−δ superconductor are examined by a grazing angle X- ray diffraction technique. By employing a range of grazing angles from 0.3° to 10° it is shown that 100 KeV Ar⁺ inplantation of the superconductor leads to amorphization as well as modification of grain size and orientation at dose values lower than 10¹⁶ ions/ cm². At the dose of 5 × 10¹⁶ ions/ cm² the X-ray diffraction intensity is a factor of 6 less as compared to the original pellet, though the lines themselves are sharp. This shows coexistence of perovskite grains and amorphous matrix.     

颗粒度对鞍山式铁矿反射光谱特征的影响研究

岩矿反射光谱的决定因素是其成分及含量,变异因素主要为颗粒度、粗糙度、观测角度、表面形态等。为明确颗粒度与鞍山式铁矿反射光谱之间的关系,采用SVC HR-1024便携式地物光谱仪对鞍山式铁矿的两种主要铁矿石(赤铁矿、磁铁矿)进行不同颗粒度下的可见光-近红外光谱测试,分析颗粒度对赤铁矿、磁铁矿反射光谱的影响规律,并明确颗粒度的敏感波段与稳定波段,为以后的定量反演工作提供参考。结果表明,颗粒度对赤铁矿、磁铁矿反射光谱的影响规律具有显著差异。当赤铁矿试样粒径由0.03 mm增加到1 mm时,光谱反射率随颗粒度增加而逐渐减小,二者呈现显著负相关关系。但是在不同的波段处,赤铁矿反射光谱受颗粒度的影响程度不同,在350~550 nm波段,反射光谱受颗粒度影响非常微弱,为赤铁矿反射光谱对颗粒度的稳定波段;在550~950 nm波段,反射光谱受颗粒度影响较微弱;在950~1 250 nm波段,反射光谱受颗粒度影响较显著;在1 250~2 500 nm波段,反射光谱受颗粒度影响非常显著,为赤铁矿反射光谱对颗粒度的敏感波段。当赤铁矿试样粒径大于1 mm之后,赤铁矿反射光谱多重叠,受颗粒度影响显著减弱,且二者无明显相关性。当磁铁矿试样粒径由0.03 mm增加到4 mm时,磁铁矿反射光谱对颗粒度的响应非常微弱,颗粒度引起的光谱反射率变化不超过3%,且颗粒度与磁铁矿反射光谱间无相关性,二者间联系微弱。该研究揭示了颗粒度对鞍山式铁矿反射光谱的影响规律,定量分析了颗粒度对赤铁矿、磁铁矿反射光谱的影响程度,并确定了颗粒度与试样反射率符合的函数分布关系,为提高鞍山式铁矿的品位反演精度奠定了良好基础。     

Cross section calculations of randomly oriented bispheres in the small particle regime

The T-matrix is used to calculate the extinction cross section of bispherical particle systems in random orientation for a monospherical size parameter x=0.01. Differences between bispherical and monospherical (Mie) results are shown for a range of values of the refractive index. It is found that the size of the T-matrix that needs to be calculated can be large, thus preventing simple dipole approximations from being used. Once the T-matrix is computed, however, only a small number of terms is needed to obtain cross section values.     

Application of the Model of Spheroidal Scatterers for Determination of Particles Sizes of Aqueous Suspensions by the Laser-Polarimetry and Dynamic-Light-Scattering Methods

Results of measurements of particle sizes of a dispersed medium by the methods of laser polarimetry and dynamic light scattering are presented for water suspensions of ZnO, CuO, TiO₂, and BaTiO₃ with particles of irregular shape. When using the laser-polarimetry method, the particle-size distributions within the framework of the spheroidal-scatterer model are reconstructed. The same model was used to correct data obtained by the method of dynamic light scattering. The data obtained are compared with results obtained by electron microscopy. It is shown that, at values of the size parameter of 2–5, correction of the results of measurements obtained by the dynamic-light-scattering method makes it possible to reduce the error in determining the average particle size by this method to no more than 11%.     

A V-curve criterion for the parameter optimization of the Tikhonov regularization inversion algorithm for particle sizing

The regularization parameter plays an important role in applying the Tikhonov regularization method to recover the particle size distribution from dynamic light scattering experiments. The so-called V-curve, which is a plot of the product of the residual norm and the norm of the recovered distribution versus all valid regularization parameters, can be used to estimate the result of inversion. Numerical simulation demonstrated that the resultant V-curve can be applied to optimize the regularization parameter. The regularization parameter is optimized corresponding to the minimum value of the V-curve. Simulation and experimental results show that stable distributions can be retrieved using the Tikhonov regularization with optimum parameter for unimodal particle size distributions.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

初始模型对含噪动态光散射数据正则化反演结果的影响

分别采用最小模型矩阵、最平坦模型矩阵、最光滑模型矩阵作为初始化模型,对加入5种不同水平随机噪声的90nm窄单峰、90nm宽单峰和250nm窄单峰、250nm宽单峰颗粒体系的模拟分布进行了正则化反演,并对反演结果进行比较。结果表明:当噪声水平为0时,正则化初始模型的选择对反演结果没有明显影响。随着噪声水平的增加,采用三种初始化模型反演得到的峰值误差和粒度分布误差都随之变大,但采用最平坦模型和最光滑模型反演得到的峰值和粒度分布误差明显小于采用最小初始模型的反演误差。当噪声水平大于0.01时,选择最平坦初始模型获得的粒度分布结果优于采用最光滑初始模型和最小初始模型获得的结果,而采用最光滑初始模型反演得到的峰值优于最平坦初始模型和最小初始模型的反演峰值。因此,采用正则化算法处理含噪动态光散射数据时,为得到最优的粒度分布信息,宜采用最平坦初始模型,若需要获取最准确的峰值信息,则应选择最光滑初始模型。     

DIP angle dependence on track formation sensitivity in antioxidant doped CR-39 plates

Recently, space radiation dosimetry measurements were made by passive and active detectors inside the Spacelab [STS-47 (FMPT): 300km, 57°, STS-65 (IML-2 mission): 300km, 28.5°]. The LET distributions obtained by antioxidant doped CR-39 inside the Spacelab were compared with those measured by the tissue equivalent proportional counter (TEPC) and the real time radiation monitoring device (RRMD) consisting of eight silicon detectors. While both distributions by CR-39 are in good agreement with those obtained by active detectors over the region of LET of several tens to 200 keV/μm, a significant difference in the LET region of smaller than several tens keV/μm is seen. It is considered to be caused by the dip angle dependence of track formation sensitivity in CR-39. The track formation sensitivity for different dip angle were measured for several high heavy energy ions. Using these results, the correction for the dip angle was made for the LET distribution. The corrected result is consistent with the results obtained by active detectors.     

米氏理论的近似及在粒度测量中的应用

将夫琅禾费衍射理论与几何散射 (包括折射和反射 )相结合 ,给出平行光入射下圆形颗粒在前向大角度范围内的散射光强分布近似算法。由于考虑了衍射、折射和反射相互间的干涉效应和颗粒对光的吸收性 ,对于正常或非正常衍射状态下无因次参量α≥ 40的耗散颗粒 ,在前向 0°～ 60°散射之内 ,该方法对散射光强计算结果与米氏理论结果是吻合的。由于计算速度比米氏理论快 ,有效角度范围比夫琅禾费衍射理论宽 ,因而适合于大颗粒的前向光强计算。将这一计算方法应用到大角度采光时的激光粒度测量实验中 ,收到了良好的效果     

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.     

TiO2 颗粒紫外区Mie散射特性

应用Mie散射理论对紫外光下TiO₂微粒光散射特性进行了理论分析与数值计算,得到了散射强度分布、偏振度与散射角、散射强度与参数X以及光学截面与粒子半径的关系。结果表明,前向散射强度随着粒子半径的增大而增强;当粒子半径为50 nm左右,散射截面和吸收截面达到最大值。     

Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X‐Ray Scattering Curves

A method for recovering the size distribution of spherical particles from small angle scattering data by using a Monte Carlo interference function fitting algorithm is presented. The method is based on the direct simulation of the small angle scattering data upon the assumption of non‐interacting hard sphere ensembles (“dilute” solution approximation). The algorithm for retrieving the particle size distribution does not require any additional parameters apart from the input of the scattering data. The fitting strategy necessarily implies positive particle size distributions, while preserving the advantage of the indirect transformation method for data desmearing. Furthermore, the present approach does not use any regularisation procedures of the best fit solution and favours smooth particle size distributions. The Monte Carlo procedure has been tested against several simulated cases with various types of mono‐ and bi‐modal size distributions and different noise levels. In the special case of non‐interacting spheres, the Monte Carlo fitting algorithm had the same retrieving ability as the well assessed indirect transformation, structure interference and maximum entropy methods. Finally, the algorithm was applied to retrieve the distribution of spherical nanopowders produced by gas‐to‐particle conversion both as free powder and as reinforcing second‐phase agent in polymer nanocomposites.     

A Method for Increasing the Sensitivity of Phase Doppler Interferometry to seed particles in liquid spray flows

A method has been developed to increase the sensitivity of phase Doppler interferometry-based particle sizing systems to small particles in the presence of a spray containing large and small droplets; an important consideration when using seed particles to track the gas-phase velocity in multi-phase flows. The method, applicable to PDPA systems configured to operate in first and higher order refraction mode, involves doping the sprayed liquid with a dye that is strongly absorbing at the incident laser wavelengths. This results in greatly diminished scattered intensity from larger droplets, thus allowing the photomultiplier gain to be set to a level sufficient to easily detect small particles without saturation. Tests conducted indicate that, at a collection angle of 30° and droplet absorptivity of γ = 0.014/μm, the PDPA can accurately size absorbing droplets up to approximately 200 μm. This upper limit can be extended by changing selection angle. Tests performed with an actual spray demonstrated that the method allowed detection of 1 μm to 235 μm droplets; more than four times the instrument's usual range of 50: 1. A data correction scheme to determine the effective probe volume radius for each particle size class has been developed for absorbing particles, as standard correction schemes derived for non-absorbing droplets excessively weigh distributions toward smaller particles.