Charges and Fractal Properties of Nanoparticles — Combustion Products of Aluminum Agglomerates

The disperse, structural, and electrophysical characteristics of fine alumina produced by combustion of metal droplet agglomerates were studied experimentally. Data were obtained by transmission electron microscopy and video recording of aerosol particles moving in a homogeneous electric field. The aerosol particles are aggregates with sizes ranging from a fraction of a micrometer to a few micrometers and a fractal dimension of 1.60± 0.04 which consist of primary particles with sizes of a few to hundred nanometers. Most of the aggregates have electric charges, both positive and negative. The characteristic charge of the aggregates is equal to a few units of elementary charge. Some large aggregates rotate when the electric field polarity changes, i.e., they are dipoles.     

Determination of the characteristics of agglomerates in aqueous suspensions using nonlinear optimization

Measurement of characteristics of particles in suspensions without dilution has a practical interest in formulation, mineral processing, material sciences and environmental technologies.These characteristics are the size, shape, and surface properties of the primary particles, and also the size, structure and the number of primary particles in the agglomerates.In this work, the multiple light-scattering model through the optical analyzer, Turbiscan MA 2000 is used to determine the mean settling velocities of monodisperse glass beads and two polydisperse samples of powders, kaolin D and alumina, differing by their particle size distribution, their shape and their surface properties.Beyond the experimental validation of theoretical and empirical predictions, the nonlinear adjustment of experimental settling data gives the number of primary particles per agglomerate and the agglomerate size. These two characteristics lead to the determination of the fractal dimension of the agglomerates. The latter was found in the range of 2.5-2.7 for all suspensions examined. The calculation of permeability and spherical factor reveals the nonspherical impermeable agglomerates.     

On-Line Characterization of Morphology and Water Adsorption on Fumed Silica Nanoparticles

The first wetting layer on solid nanoparticles has direct implications on the roles these particles play in industrial processes and technological applications as well as in the atmosphere. We present a technique for online measurements of the adsorption of the first few water layers onto insoluble aerosol nanoparticles. Atomized fumed silica nanoparticles were dispersed from aqueous suspension and their hygroscopic growth factors (HGF) and number of the adsorbed water layers at subsaturated conditions were measured using a nanometer hygroscopic tandem differential mobility analyzer (HTDMA). Particle morphology was characterized by electron microscopy and particle density was determined by mobility analysis. The HGFs of the size-selected particles at mobility diameters from 10 to 50 nm at 90% relative humidity (RH) varied from 1.05 to 1.24, corresponding to 2–6 layers of adsorbed water. The morphology of the generated fumed silica nanoparticles varied from spheres at 8–10 nm to agglomerates at larger diameters with effective density from 1.7 to 0.8 g/cm³ and fractal dimension of 2.6. The smallest spheres and agglomerates had the highest HGFs. The smallest particles with diameters of 8 and 10 nm adsorbed two to three water layers in subsaturated conditions, which agreed well with the Frenkel, Halsey, and Hill (FHH) isotherm fitting. In comparison to the small spheres or large agglomerates, the compact agglomerate structure containing a few primary particles increased the number of adsorbed water layers by a factor of ～1.5. This was probably caused by the capillary effect on the small cavities between the primary particles in the agglomerate.     

一次大气颗粒物投影轮廓分维研究

构建了一次大气颗粒物投影轮廓分维模型,并以高精度数字光学显微系统为基础,测算了广州市3种一次大气颗粒物颗粒样品的投影轮廓分维,结果验证了颗粒投影轮廓分维数学模型的合理性,形成了一套简约的一次大气颗粒物投影轮廓分维分析方法。结果还表明一次大气颗粒物投影轮廓分维个数频率分布曲线呈＂S＂型,且一次大气颗粒物对数投影轮廓分维分布曲线呈对数正态分布;3种一次大气颗粒物样品中,柴油汽车排气管中沉积颗粒和餐饮过程产生的颗粒不规则程度相对低,其偏离圆的程度小,粗糙度较小;而粉煤灰颗粒的相反。     

A RECIPE FOR IMAGE CHARACTERIZATION OF FRACTAL-LIKE AGGREGATES

In the present paper a simple and straightforward recipe for characterizing the structural and fractal properties of aggregates from their projected images is presented. Starting from geometrical properties that are directly measured from the projected image—such as primary particle mean diameter, maximum projected length, projected area, and overlap coefficient—important threedimensional properties including number of primary particles in an aggregate, radius of gyration, aggregate surface, or fractal dimensions, D_f and k_g, can be inferred. Expressions proposed in the recipe to relate three dimensional with projected properties were obtained from an extensive investigation of the structure of numerically simulated cluster–cluster fractal-like aggregates. This involved the simulation of statistically significant populations of aggregates having appropriate fractal properties and prescribed numbers of primary particles per aggregate in order to characterize three-dimensional morphological properties of aggregates. Specific ranges of aggregate properties considered were as follows: number of primary particles per aggregate up to 512, fractal dimension, D_f≈1.78, overlap coefficient in the range 0–0.33 and fractal pre factor between 1.5 and 3.1.     

Structural Property Effect of Nanoparticle Agglomerates on Particle Penetration through Fibrous Filter

Most filtration studies have been conducted with spherical particles; however, many aerosol particles are agglomerates of small primary spheres. Filtration efficiency tests were conducted with silver NP agglomerates, with the agglomerate structure controlled by altering the temperature of a sintering furnace. The mobility diameter and mass of the silver NP agglomerates were measured using a differential mobility analyzer together with an aerosol particle mass analyzer. From these measurements, it was found that the fractal-like dimension, D _fm, varied from 2.07 to 2.95 as the sintering temperatures was increased from ambient to 600°C. The agglomerates were essentially fully coalesced at 600°C allowing direct comparison of the filtration behavior of the agglomerate to that of a sphere with the same mobility diameter. Other agglomerate properties measured include the primary diameter, the agglomerate length and aspect ratio, and the dynamic shape factor.

Agglomerate filtration modeling with no adjustable parameters has been investigated in terms of diffusion, impaction, and interception. The model results agree qualitatively with the experimental results in the particle size range of 50 to 300 nm. The results indicated that the larger interception length of agglomerates is responsible for the smaller penetration through a fibrous filter in comparison to spherical particles with the same mobility diameters.     

Evolution of the fractal dimension for simultaneous coagulation and sintering

Simulation results on the evolution of aggregate structure in aerosol processes with coagulation and sintering as the dominant mechanisms are presented. A model for simulation of the three-dimensional morphology of nano-structured aggregates formed by concurrent coagulation and sintering is applied. The model is based on a stochastic diffusion controlled cluster-cluster aggregation algorithm and sintering is modeled as a successive overlapping of spherical primary particles, which are allowed to grow in order to maintain mass conservation. This leads to computer simulated structured aggregates which are then subject to evaluation. Two different methods to determine the fractal dimension are presented which give comparable results. It is shown that even very small particles show the same fractal behavior. Furthermore, equilibrium structures assuming a constant ratio of the characteristic collision time to the characteristic fusion time are considered as well as the kinetics of structural changes due to a change in the ambient conditions.     

Measurement and simulation of soot agglomerates and aggregates

Soot clusters produced by partial oxidation of acetylene show three distinct phases - primary particles, agglomerates of the primary particles, and aggregates of the agglomerates. The dominant mode of soot formation can be controlled by the concentration of acetylene. Comparison of optical microscopy with inertial measurements indicate that the aggregates are not fractal (f_HB = 3) but porous with a density of 0.094. Those simulations for the smallest aerodynamic diameter suggest a transition from aggregates which are fractal to agglomerates. Algorithms based on generalized Menger sponges are developed to simulate the transition from agglomerates to aggregates.     

The Behavior of Constant Rate Aerosol Reactors

An aerosol reactor is a gaseous system in which fine particles are formed by chemical reaction in either a batch or flow process. The particle sizes of interest range from less than 10 Å (molecular clusters) to 10μm. Such reactors may be operated to study the aerosol formation process, as in a smog reactor, or to generate a product such as a pigment or a catalytic aerosol. Aerosol reactors can be characterized by three temporal or spatial zones or regions of operation for batch and flow reactors, respectively. In zone I, chemical reaction results in the formation of condensable molecular products which nucleate and form very high concentrations of small particles. The number density depends on the concentration of preexisting aerosol. Zone II is a transition region in which the aerosol number concentration levels off as a result of hetergeneous condensation by the stable aerosol. In zone III coagulation becomes sufficiently rapid to reduce the particle number concentration. There may be a zone IV in which agglomerates form. Chemical reaction may continue to generate condensable material throughout the various zones. This paper deals with reactors in which aerosol material is generated at a constant rate. Design parameters of interest are the particle size distribution, number density, surface area, and mass loadings. For ideal systems composed of spherical coalescing particles, these can be predicted theoretically for certain limiting cases. However, the irregular agglomerates which may form in zone IV are more difficult to characterize theoretically.     

Simulation of structure and mobility of aggregates formed by simultaneous coagulation,sintering and surface growth

In this work, a new model for the simulation of nanostructured aggregates by simultaneous coagulation, sintering and surface growth is presented. Coagulation is treated as cluster–cluster agglomeration along the line connecting the center of mass of both agglomerates and is implemented using a Monte Carlo algorithm. Sintering is modeled as successive overlapping of spheres which cause reduction in the surface area based on a rate law for surface reduction. Surface growth is modeled as an increase in primary particle diameter, e.g. as a result of surface reactions. The evolved aggregates are analyzed by calculating their fractal dimension, radius of gyration, mobility diameter and mobility shape factor. It is found that the aggregates structure tends to be more compact when introducing the surface growth in shorter time comparing to the coagulation-sintering step only. Fractal dimension and the mobility shape factor of the resulting aggregates are correlated to an effective dimensionless time that combines the characteristic times of these three fundamental mechanisms. It is shown that the mobility diameter in the free molecular regime is not proportional to the radius of gyration. A power law relation that correlates the aggregates projected area and the equivalent number of primary particles is found to be in a very good agreement with estimates published in literature.     

Coagulation Coefficient of Agglomerates with Different Fractal Dimensions

A coagulation coefficient of agglomerates with different fractal dimensions has not been considered in the past, even though there is a possibility of variations in the fractal dimension of agglomerates at any instant. In this study, a Brownian dynamics simulation was performed with simultaneous collision and sintering, and variations in the fractal dimension of agglomerates were observed. A coagulation coefficient expression for agglomerates with two different fractal dimensions was proposed. The coagulation coefficient based on the different fractal dimensions was at most 140% higher than that based on the average fractal dimension. To determine an accurate coagulation coefficient of agglomerates, the fractal dimension of each agglomerate has to be considered.     

Study of the Sintering of Nanosized Titania Agglomerates in Flames Using In Situ Light Scattering Measurements

ABSTRACT

A premixed flame aerosol reactor was used to produce titania particles by oxidation of titanium isopropoxide vapor. The growth, aggregation of particles, and the agglomerate structure were determined as a function of height in the flame using in situ light scattering and transmission electron microscopy (TEM) measurements. A methodology to determine the sintering characteristic time using light scattering data was established. The light scattering data provided the evolution of the fractal dimension which was then related to the normalized surface area change using a computer simulation. The sintering equation was redeveloped in terms of the normalized surface area, thus not having to account for coagulation effects. Experimental results indicate that isolated titania particles were observed at the high temperatures due to fast sintering. An agglomerate was obtained at downstream locations with an associated change in fractal dimension due to sintering.     

Numerische und analytische Beschreibung der mechanischen Eigenschaften quasi‐tetraederförmiger Agglomerate

Quasi tetrahedral agglomerates consist of four primary particles, from which three primary particles generally form a base area on which the fourth primary particle is arranged centrally; in the regular case the primary particles having equal radii. The coordinates of the centers of the primary particles are derived for agglomerates exhibiting equal primary particles (regular tetrahedron) and primary particles of different radii (inclined tetrahedron). Moreover, an analytical model for elastic contact deformation is derived on the basis of the Hertz model. Subsequently, tetrahedral agglomerates are modeled using the discrete element method and the compression test between two rigid plates is simulated and compared with experimental results.     

Size Distribution Change of Titania Nano-Particle Agglomerates Generated by Gas Phase Reaction,Agglomeration, and Sintering

In the manufacturing of nanometer-sized material particlulates by aerosol gas-to-particle conversion processes, it is important to analyze how the gas-phase chemical reaction, nucleation, agglomeration, and sintering rates control the size distribution and morphology of particles. In this study, titania particles were produced experimentally by the thermal decomposition of titanium tetraisopropoxide (TTIP) and oxidation of titanium tetrachloride (TiCl 4 ) using a laminar flow aerosol reactor. The effect of reaction temperature on the size and morphology of the generated particles was investigated under various conditions. The size distributions of agglomerates were measured using a DMA/CNC system. The size distributions of primary particles were measured using TEM pictures of the agglomerates sampled by a thermophoretic aerosol sampler. In order to model the growth of both agglomerates and primary particles simultaneously, a two-dimensional discrete-sectional representation of the size distribution was employed, solving the aerosol general dynamic equation for chemical reaction, agglomeration, and sintering. Qualitative agreement between the experimentally observed results and the simulation are satisfactory for the large variations in reactor temperature explored.     

Measurement of Metal Nanoparticle Agglomerates Generated by Spark Discharge Using the Universal Nanoparticle Analyzer (UNPA)

Nanoparticle agglomerates play an essential role in the manufacturing of many nanomaterials and are commonly found in combustion products. Conventional aerosol instruments based on equivalent spheres are not directly applicable to the measurement of nanoparticle agglomerates. The increasing interest in real-time assessment of the structure of engineered nanoparticle agglomerates and the mass concentration of potentially hazardous agglomerates (e.g., diesel soot, welding fume) makes an instrument devoted to online structure and mass measurements for nanoparticle agglomerates highly desirable. A recently developed instrument, universal nanoparticle analyzer (UNPA), utilizes the close relation between agglomerate structure and unipolar charging properties and infers agglomerate structure from measurement of the average charge per agglomerate. It was used in this study to characterize in situ the structure of metal nanoparticle agglomerates generated by spark discharge, to study the effects of sintering on the structure of these agglomerates, and to make real-time assessment of their airborne mass concentration. The primary particles sizes measured by UNPA for the gold (Au), silver (Ag), and nickel (Ni) agglomerates are in reasonable agreement with the TEM (transmission electron microscopy) sizing results, d _p = 7.9 ± 1.5, 11.8 ± 3.2, and 6.6 ± 1.0 nm, respectively. In addition, findings from the study of agglomerate structural change during sintering using the UNPA sensitivity coincide with results from TEM and mobility analyses. With regard to the mass concentration of silver agglomerates at room temperature, good agreement was found under our experimental conditions between results given by UNPA, the effective density, and the gravimetric measurement.

Copyright 2012 American Association for Aerosol Research     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

Application of fractal theory to estimation of equivalent diameters of airborne carbon nanotube and nanofiber agglomerates

Understanding transport characteristics of airborne nanotubes and nanofibers is important for assessing their fate in the respiratory system. Typically, diffusion and aerodynamic diameters capture key deposition mechanisms of near-spherical particles such as diffusion and impaction in the submicrometer size range. For nonspherical particles with high aspect ratios, such as aerosolized carbon nanotubes, these diameters can vary widely, requiring their independent measurement. The objective of this study was to develop an approach to provide approximate estimates of aerodynamic- and diffusion-equivalent diameters of airborne carbon nanotubes (CNTs) and carbon nanofibers (CNFs) using their morphological characteristics obtained from electron micrographs. The as-received CNT and CNF materials were aerosolized using different techniques such as dry dispersion and nebulization. Mobility and aerodynamic diameters of test aerosol were directly deduced from tandem measurement of particle mobility and mass. The same test aerosol was mobility-classified and subsequently collected on a microscopy grid for transmission electron microscopy (TEM) analysis. TEM micrographs were used to obtain projected area, maximum projected length, and two-dimensional (2-D) radius of gyration of test particles. Estimates of the aerodynamic diameter and the diffusion diameter were obtained by applying the fractal theory developed for aerosol agglomerates of primary spherical particles. After accounting for the particle dynamic shape factor, estimated aerodynamic diameters agreed with those from the direct measurements (using tandem mobility-mass technique) within 30–40% for the agglomerates with relatively open structures while the diffusion diameters agreed within 40–50%. The uncertainty of these estimates mainly depends on degree of overlapping structures in the microscopy image and nonuniformity in tube diameter. The approach could be useful in calculating approximate airborne properties from microscopy images of CNT and CNF agglomerates with relatively open structures.

This article not subject to US copyright law     

Fractal Dimensions of Model Particle Packings Having Multiple Generations of Agglomerates

We examine a simple model for a powder having multiple generations of agglomerates. Over the size range over which the generations span, this structure is shown to be fractal. An equation expressing the fractal dimension for any Euclidean dimension is derived.     

Calculating the Parameters of the Fractal Aggregates Formed in a Bidisperse Suspension

The fractal properties of aggregates (clusters) formed in a bidisperse (two-phase) suspension through the attachment of fine particles to a coarse fraction, taking the dependency of the fractal dimension of the aggregate on its size into account, are studied. The correlation coupling parameters of the initial and limiting states of the suspension (for the complete aggregation of the primary particles) is obtained based on the balance of the number of particles. The influence of the key parameters of the suspension, as well as of the factor of variable fractal dimension on the typical characteristics of fractal clusters, is analyzed.