Structure/Property Relationships for Poly(Vinylidene Fluoride)/Doped Polyaniline Blends

Poly(vinylidene fluoride) (PVDF) and its blends with polyaniline (PANI) doped with dodecylbenzene sulfonic acid (DBSA) were characterized by electrical conductivity, differential scanning calorimetry (DSC) and X‐ray scattering techniques.

The onset of an infinite cluster (InC) of conducting, highly anisometric PANI/DBSA particles in PVDF/(PANI/DBSA) blends was observed at the percolation threshold as low as w*≈3.5 wt.%. The small angle X‐ray scattering (SAXS) data confirmed the expected spatial organization of PANI/DBSA needles into fractal‐like structures above w*. A slight decrease of both the DSC and the wide‐angle X‐ray scattering (WAXS) degrees of crystallinity of PVDF with the PANI/DBSA mass content w was explained by strong interactions at the PVDF/(PANI/DBSA) interface resulting in the loss of crystallizability of a fraction of sterically immobilized chains of PVDF in boundary layers around PANI/DBSA particles. The available data suggest that the conductive paths within InC of PANI/DBSA in PVDF/(PANI/DBSA) blends were formed primarily by the end‐to‐end contacts of PANI/DBSA fibrils.     

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.     

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.     

The Effect of Polydispersity in Primary Particle Size on Measurement of the Fractal Dimension of Aggregates

The use of the mass fractal dimension has become a popular method of characterising the structure of aggregates of fine particles. This parameter is often inferred from scattering experiments that exhibit a power law correlation between scattered intensity and the scattering vector. In this paper we demonstrate deviations from this behaviour that occur when the particles making up the aggregate are not monodisperse, even though the aggregate maintains the same fractal structure as observed in the monodisperse case. We have performed light scattering experiments with aggregating colloidal haematite and performed DLCA computer simulations to explain the observed behaviour. The behaviour can influence the determination of the mass fractal dimension, as can other factors such as scattering effects from primary particles.     

Light scattering from colloids

This paper presents a review of light scattering results on static and dynamic properties of ordered colloidal suspensions of charged polystyrene particles and fractal colloidal aggregates. Our studies on static structure factor,S(Q), of ordered monodisperse colloidal suspensions and binary mixtures of particles with different particle diameters, measured by angle-resolved Rayleigh scattering will be discussed. This will include determination of bulk modulus using gravitational compression and observation of colloidal glass (inferred from splitting of the second peak inS(Q)). Dynamic light scattering, with real time analysis of scattered intensity fluctuations, is used to get information about Brownian dynamics of the particles. Recent advances in the field of light scattering from colloidal aggregates which show fractal geometry will also be discussed.     

Small angle neutron scattering and small angle X-ray scattering studies of platinum-loaded carbon foams

The morphology of carbon nanofoam samples comprising platinum nanoparticles dispersed in the matrix was characterized by small angle neutron scattering (SANS) and small angle X-ray scattering (SAXS) techniques. Results show that the structure of pores of carbon matrix exhibits a mass (pore) fractal nature and the average radius of the platinum particles is about 2.5 nm. The fractal dimension as well as the size distribution parameters of platinum particles varies markedly with the platinum content and annealing temperature. Transmission electron micrographs of the samples corroborate the SANS and SAXS results.      

Response of Laser Diffraction Particle Sizer to Anisometric Particles

This study deals with the size measurement of non-spherical particles by the laser diffraction technique. Size analyses of three sets of identical metallic bodies (cubes, tablets and cylinders) were performed by means of a Malvern 2600 instrument. The results prove that under the operating conditions chosen and in the case of anisometric objects, the mean total surface area is not measurable either because the Malvern software, strictly valid for spheres, is not applicable to such particles or because the particles adopt preferential orientations in the measurement cell. Further, a way of processing diffraction data is proposed in order to determine two characteristic dimensions of identical anisometric particles. It is based on the measurement of the minimum and maximum projected surface areas of the particles. The experimental results obtained with our particles show the procedure to be reliable.     

A review of the numerical investigation on the scattering of Gaussian beam by complex particles

The study of light scattering by various particles is an active and important subject of research with myriad practical applications. During the years the scattering of plane wave by various particles has been investigated extensively. In recent years, with the development of laser sources and the tremendous expansion of their application, there has been a growing interest in the study of light scattering by various particles illuminated by a focused Gaussian beam. Since the analytical methods are only suitable for the analysis of Gaussian beam scattering by some regular particles, for complex particles with arbitrary shape and structure, one has to resort to the numerical methods. In this article, we review the recent numerical investigation on the scattering of Gaussian beam by systems of complex particles, including arbitrarily shaped conducting particles, dielectric particles, composite particles with inclusions, as well as random discrete particles and fractal soot aggregates. The essential formulations of the proposed numerical methods are outlined and the numerical results for some complex particles are also presented. This review is expected to provide useful help for the study of the interaction between the laser beams and the complex particles.     

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.     

Particle Growth in an Experimental Dusty Plasma System

The coagulation and growth process of dust particles is investigated through laboratory experiment in a plasma system. A large number of dust particles with different sizes and shapes are formed. The growth process is characterized by the scattering laser intensity and fractal dimension. The comparisons of dust particles and scattering laser intensity obtained at different rf powers are presented. The three-dimensional distribution of dust particles is also given. These results provide an experimental basis for dust growth investigation.     

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.     

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...     

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。     

Coupling of velocity gradients to orientation densities

Velocity gradients and orientation densities are coupled in liquids composed of anisometric molecules, as is evidenced by flow birefringence and by the Rytov dip observed in VH depolarized light scattering. The coupling strength can be related to a dimensionless parameter R which can be expressed in terms of correlations over molecular quantities or, when evaluated by a hydrodynamic model, in terms of geometric factors. Both cases are discussed. Although R depends on the temporal behaviour of molecular quantities, i.e. it is a dynamic factor, it is actually a ratio of dynamic factors and can be approximated by static or equilibrium quantities. In the hydrodynamic limit, i.e. for brownian particles, this approximation is rigorously valid.     

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.     

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.     

Discrete dipole approximation simulations of light reflection from flat non-transparent particles with rough surfaces

We study light reflection from flat particles with rough surfaces and fractal statistics of topography. Discrete dipole approximation method is used to solve the problem of light scattering. Refractive indices corresponding to a metal and a transient material with conductive properties are taken. The sizes of particles are much larger than the wavelength of incident light and the roughness scales are larger, comparable to and smaller than the wavelength. The influence of the fractal dimension parameter and the amplitude of heights of random topography on reflectance and on the angular profile of the specular reflection peak is considered. Our calculations demonstrate that topography amplitude is very important for reflectance and fractal dimension is responsible for the angular dispersion of the specular reflection peak.     

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.     

火灾烟颗粒分形模型和球形模型光散射的比较研究

对烟颗粒的光散射进行模拟计算是研究火灾烟颗粒光散射特性的重要手段,目前对于火灾烟颗粒光散射的数值计算多采用球形或椭球模型.实际上,火灾烟颗粒的形貌与球形和椭球均存在着显著差异.扫描电子显微镜图像表明,烟颗粒具有近似分形的结构.本文利用离散偶极近似方法计算了随机取向的火灾烟颗粒分形凝团以及同体积的球形颗粒的光散射Muller矩阵,并对两者的归一化Muller矩阵元素随散射角的分布进行了比较.研究表明:火灾烟颗粒分形模型和球形模型的归一化矩阵元素F₁₁(θ)/     

Fractal model of transport: Low-angle approximation

Multiple scattering of particles by a stochastic fractal, a set of point targets (atoms) randomly distributed in a space with a power correlation function, is considered. The energy and angular distributions that generalize the known Landau, Fermi, and Molière distributions are found in the low-angle approximation. The analytical results are checked by Monte Carlo numerical simulation.