Particle Size Distributions from Static Light Scattering with Regularized Non‐Negative Least Squares Constraints

Simulated data from static light scattering produced by several particle size distributions (PSD) of spherical particles in dilute solution is analyzed with a regularized non‐negative least squares method (r‐NNLS). Strong fluctuations in broad PSD's obtained from direct application of NNLS are supressed through an averaging procedure, as introduced long ago in the inversion problem in dynamic light scattering. A positive correlation between the best PSD obtained from several averaging schemes and the condition number of the respective data transfer matrices was obtained. The performance of the method is found to be similar to that of constrained regularization (CONTIN), which uses also NNLS as a starting solution, but incorporates another regularizing strategy.     

Particle Systems Characterization Using a Flat Cell Static Light Scattering Apparatus

In this work a light scattering apparatus for the study of heterogeneous liquid systems of evolving morphology is presented. A Fraunhofer configuration consisting of a linear array of photodiodes is used to detect the light scattered by thin samples illuminated by a He‐Ne laser light. Temperature control is available. The instrument is tested with the polymerization induced phase separation of a thermosetting polymer formulated with a divinylester resin copolymerized with styrene and modified with poly(methylmethacrylate). The system is successfully modeled as an arrangement of particles growing in size and number, and varying in composition. The ability of the experimental setup to provide results that can be quantitatively analyzed is checked using microspherical polystyrene standards. Different samples with nominal sizes of 0.5, 1 and 2 μm are used in different combinations of sample thickness and concentration. The analysis of the light scattering spectra is performed using inverse techniques to estimate the particle size distribution of the microspheres. The results agree with previous knowledge of the parameters of the samples.     

动态光散射测量粒径分布的格雷码编码遗传算法反演运算

采用格雷码编码的遗传算法对动态光散射测量的粒径分布进行反演运算,数字测试结果表明,对于无噪声的分布,算法能精确的反演出各种粒子分布图像;对于加了一定噪声的分布,算法显示出较好的稳定性,能反演出主峰的分布图像.聚苯乙烯乳球的实验结果表明,该算法能反演双分布的粒径分布图像.与标准遗传算法和反演蒙特卡罗算法相比,该算法具有较高的搜索效率,能够用较少的计算时间快速搜索到最优解.格雷码编码遗传算法是一种更有效的随机反演算法.     

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.     

多角度动态光散射加权贝叶斯反演算法

研究加权贝叶斯算法在多角度动态光散射法测量单峰分布颗粒体系的颗粒粒度分布中的应用.采用颗粒粒度信息分布为底数、调节参数为指数的权重系数给各个角度下的光强自相关函数曲线加入不同的权重系数,再利用传统的贝叶斯算法反演.模拟与实验结果表明,加权后的贝叶斯算法能获得分布误差更小的反演结果,有效地抑制了数据噪声的影响,提高颗粒粒度分布反演的准确性.     

Resolving Concentrated Particle Size Mixtures Using Dynamic Light Scattering

Dynamic light scattering (DLS) is a technique used for measuring the size of molecules and particles undergoing Brownian motion by observing time‐dependent fluctuations in the intensity of scattered light. The measurement of samples using conventional DLS instrumentation is limited to low concentrations due to the onset of a phenomenon called multiple scattering. The problems of multiple scattering have been addressed in a light scattering instrument incorporating non‐ invasive backscatter optics (NIBS). This novel optic arrangement maximizes the detection of scattered light while maintaining signal quality and allows for measurements of turbid samples. This paper discusses the ability of backscatter detection to accurately determine particle sizes at 1 %w/v sample concentrations and demonstrates the correct resolution of different size populations using a series of latex standard mixtures with known volume ratios. The concentration of 1 %w/v is much higher than can be measured on conventional dynamic light scattering instruments.     

利用低相干光纤动态光散射法测量浓悬浮液中多分散颗粒粒径分布

本文针对高浓度散射介质,用低相干光纤动态光散射技术测量浓悬浮液中多分散颗粒系的粒径及其粒径分布。利用迭代CONTIN算法对实验数据进行反演运算,得到多分散颗粒系的粒径分布结果。结果表明,浓悬浮液中多分散颗粒系的峰值粒径测量值与给定的两种标准粒径值相吻合,其误差在4%之内,粒径分布曲线中各散射颗粒所反映的散射体光强分布与根据Mie散射计算得到的理论值相吻合。实验结果证明低相干光纤动态光散射实验系统能准确测量浓悬浮液中多分散颗粒粒径及粒径分布。     

激光散射法对尿液中纳米微晶粒径及其分布的研究

泌尿系结石已经成为威胁人类健康的一种常见病、多发病,目前对其形成的机制尚不清楚。文章采用激光散射法测定了正常人尿液和尿石症患者尿液中纳米粒子的粒径和粒径分布,该方法快速准确、经济、容易操作。正常人尿液比尿石症患者尿液的稳定性好,归因于正常人尿液中纳米微晶尺寸分布均匀,不容易聚集,而尿石症患者尿液的纳米微晶尺寸分布不均匀,粒子间容易聚集而沉降。通过分析尿样稀释、离心或者用微孔滤膜过滤后体系的光强-自相关函数曲线,得到了制备稳定的尿样悬浮液的方法：尿样先稀释20%,然后离心或用1.2 μm微孔滤膜过滤,可得到稳定的尿液悬浮液。激光散射法结果与TEM检测结果一致。从尿液中存在的范德华力、尿液粘度、酸碱性、离子强度、尿液中纳米微晶的表面电荷和Zeta电位等方面解释了尿液稳定的原因。     

Particle Size Distribution by Combined Elastic Light Scattering and Turbidity Measurements. A Novel Method to Estimate the Required Normalization Factor

Turbidity (T) and Elastic Light Scattering (ELS) measurements can be combined to estimate the particle size distribution (PSD) of a polymer latex. To this effect a “normalization factor” must be employed to adequately scale both measurements. In a real application, such factor is a priori unknown, and it must be estimated for determining the PSD. In a previous publication, a method was proposed to simultaneously estimate the normalization factor and the PSD by solving an inverse nonlinear problem. In this work, a simpler technique is presented which estimates the normalization factor and the PSD by sequentially solving two inverse linear problems. To evaluate the proposed technique, a synthetic example based on a polystyrene latex sample with a bimodal PSD was solved. It is shown that, for slight noise measurements, the errors in the estimation of the normalization factor are quite small and have a low effect on the PSD recovery.     

激光散射法测试超细颗粒粒度分布的研究

本文系统研究了样品制备条件对激光散射法测试超细颗粒粒度的影响,例如:分散介质的选择、分散剂的类型和浓度、分散颗粒的浓度、超声分散的时间和强度等。并与其他TEM结果进行了对比。研究表明:只有将各种条件最优化,获得高度分散和稳定的悬浮体系或胶体体系,才能最终精确地得到颗粒的粒度分布结果。     

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。     

可见-红外波段光全散射法颗粒粒径测量范围的研究

在光全散射法颗粒粒径测量中,采用独立模式算法在可见-红外波段对粒径测量范围进行了深入的研究。通过对多种R-R分布函数反演结果进行分析,比较,以确定光全散射法颗粒粒径测量范围。同时在消光系数计算中,采用修正的消光系数代替原始的消光系数,以便得到更准确的粒径测量范围。仿真计算结果表明,在可见-红外光谱区,相对折射率m=1.235时的粒径测量范围为0.05～18 μm。在此区域内测量粒径分布,反演结果与真值基本吻合。随着颗粒相对折射率、波长范围的变化,粒径测量范围也随之发生改变。采用限制最小二乘算法能够最大限度地克服随机噪声对测量结果的影响,使测量的精度和可靠性明显提高。对测量的消光值加入±1%随机噪声时,颗粒粒径分布的反演均能得到满意的结果。     

Determination of Soot Particle Size in a Premixed Flame: a Static and Dynamic Light Scattering Study

In this contribution we report upon our static and dynamic light scattering experiments to characterize soot particles in flames. We studied sooting laminar premixed flame with acetylene as fuel mixed with air as oxidizer. The air equivalence ratio of the combustion was larger than one. We used a Kaskan type burner with circular geometry and a stabilizing flow of nitrogen around the flame. We focused on the determination of the size of the soot particles in the center of the flame as a function of height above burner. In addition we investigated the influence of the mixing ratio of the gases on the size of the particles. Our results show that static light scattering is better suited than dynamic light scattering for a fast and reliable characterization of soot particles in flames. The latter needs detailed a priori information about the flame to allow the unique determination of sizes from the diffusion measurements. The soot particles grow monotonously with height above burner and with decreasing air equivalence ratio. The aggregates have a fractal dimension lower than two.     

Analysis of Particle Size Distribution by Particle Tracking

Particle tracking is performed using a combination of dark field or fluorescence video microscopy with automatic image analysis. The optical detection together with the image analysis software allows for the time resolved localization of individual particles with diameters between 100 and 1000 nm. Observation of their Brownian motion over a set of time intervals leads to the determination of their mean square displacements under the given room temperature and viscosity. Hereby, the radii of a set of particles visible within a given optical frame are derived simultaneously. Rapid data analysis leads to reliable particle size histograms. The applicability of this method is demonstrated on polystyrene latices and PMMA nanospheres with radii between 51 nm and 202 nm.     

光复散射对消光法粒径测量的影响:复散射模型与数值模拟

复散射效应在光散射颗粒测量中不仅重要．且尚未得到很好解决。采用蒙特卡罗方法,对不同的光波长,颗粒浓度以及收接器条件下的光复散射进行了数值模拟．数值算法程序经与四通量模型进行对比验证,数值结果与单散射条件的郎伯-比尔模型进行比较．进而讨论了复散射效应对消光法颗粒粒径测量影响。表明复散射对消光法颗粒测量的影响不仅取决于颗粒系自身的浓度．而且接收器的几何尺寸和接收位置起着非常重要的作用,减小颗粒介质层厚度和减小光接收器接收面积．增大接收距离以及减小接收角都能减小复散射效应对消光法粒径测量的影响。     

分段自相关动态光散射法测量亚微米粒度

介绍了动态光散射法测量微粒尺度的原理，通过对相关函数相对的分析，提出了分段自相关的方法，该方法解决了高速，大数据量采集的困难，又不显著影响相关函数的精度，给出了实验装置及实验结果，测量结果与标准样品的标称值相符。     

Size and Shape Prediction of Colloidal Metal Oxide MgBaFeO Particles from Light Scattering Measurements

The size and structure of colloidal metal oxide (MgBaFeO) particles are determined using an Elliptically Polarized Light Scattering (EPLS) technique. The approach is based on a hybrid experimental/theoretical study where the experimental data are compared against predictions obtained using a T-Matrix model that accounts for particle shape irregularities. A power-law distribution function with two parameters is employed to account for the particle size distribution. The refractive index of the particles in ethyl alcohol is calculated based on the Maxwell-Garnet formula. The experiments are conducted using a second-generation nephelometer. It is shown that the current EPLS measurements can effectively be used for identification of both the shape and the size of the colloids.     

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.     

光散射检测微粒直径分布的实验装置的研制

论述光散射检测微粒直径分布的实验装置的原理及其设计,并给出装置的实验结果。     

非独立模式算法下粒径分布反演及分类的研究

在光全散射法颗粒粒径测量中,提出一种非独立模式算法下粒径分布反演及分类的方法。对被测颗粒系分别按照不同的粒径分布函数同时进行反演,并依据反演误差大小判断被测颗粒系符合哪种分布函数。仿真实验结果表明,在非独立模式下,完全可以利用已知的不同分布函数的反演误差作为分类依据,从而更准确地确定被测颗粒系的粒径分布。采用的遗传反演算法能够在3个可见光波长下得到较准确的粒径分布,反演结果稳定可靠,最大限度地减少了多个波长的使用,从而对光源有更大的选择余地。对透射消光测量结果加入5%随机噪声时,单峰分布颗粒系的反演误差小于5%,多峰分布颗粒系的反演误差小于10%。整个算法运行时间小于2 s。该方法具有原理简单,计算速度快等优点,能够满足颗粒粒径在线测量的要求。