Toward an understanding of the turbidity measurement of heterocoagulation rate constants of dispersions containing particles of different sizes

Our previous studies have shown that the determination of coagulation rate constants by turbidity measurement becomes impossible for a certain operating wavelength (that is, its blind point) because at this wavelength the change in the turbidity of a dispersion completely loses its response to the coagulation process. Therefore, performing the turbidity measurement in the wavelength range near the blind point should be avoided. In this article, we demonstrate that the turbidity measurement of the rate constant for coagulation of a binary dispersion containing particles of two different sizes (heterocoagulation) presents special difficulties because the blind point shifts with not only particle size but also with the component fraction. Some important aspects of the turbidity measurement for the heterocoagulation rate constant are discussed and experimentally tested. It is emphasized that the T-matrix method can be used to correctly evaluate extinction cross sections of doublets formed during the heterocoagulation process, which is the key data determining the rate constant from the turbidity measurement, and choosing the appropriate operating wavelength and component fraction are important to achieving a more accurate rate constant. Finally, a simple scheme in experimentally determining the sensitivity of the turbidity changes with coagulation over a wavelength range is proposed.     

Influence of the ionic strength in the heterocoagulation process between bare and surfactant-coated latexes

A novel and useful process of heterocoagulation between bare and surfactant-coated latexes is studied. Basically, this process consists of the heterocoagulation of two identical latexes, i.e. of the same size and with charges of the same sign, but distinguished by the degree of coverage by a nonionic surfactant (Triton X-100). The different critical coagulation concentrations (ccc) of this type of sample permitted us to analyze the influence of the ionic strength in the heterocoagulation process between both colloidal samples. Different ratios (2:1, 1:1 and 1:2) of the bare and surfactant-coated latexes were used during the experiments. In all cases, the heterocoagulation rate constants were lower than the homocoagulation rate constant in diffusion conditions; however, for an ionic strength higher than the ccc of both systems, similar values were found for the rate constants. Received: 18 January 1999 Accepted in revised form: 14 April 1999     

聚合物纳米微粒静电组装行为及其表征

使用2,2′-偶氮二异丁基脒二盐酸盐自由基引发剂,改变甲基丙烯酰氧乙基十六烷基二甲基溴化铵阳离子功能单体的量与苯乙烯进行乳液聚合获得不同粒径的阳离子乳胶粒,使用十二烷基硫酸钠为乳化剂和过硫酸钾为引发剂制备阴离子聚合物乳胶粒.采用基于静电相互作用的异凝聚法将以上2种带有相反电荷的乳胶粒组装,获得了表面粗糙程度不同的复合微粒.对异凝聚过程中复合液透光率和微粒大小及分布进行跟踪测试,并用透射电子显微镜表征了阳离子微粒、阴离子微粒以及复合微粒的形态和大小.结果表明,在一定范围内可以通过控制阴离子乳胶粒与阳离子乳胶粒的复合比例改变单个复合微粒表面阳离子小微粒的数目.     

Microflotation Suppression and Enhancement Caused by Particle/Bubble Electrostatic Interaction

The processes of attachment and detachment of small or medium-sized particles to relatively large bubbles during microflotation are considered in terms of the heterocoagulation theory. Calculations are made for the conditions that the surface potentials are of similar sign and constant, that one of the surface potentials is small, that hydrophobic attraction is absent, and that there are no surface deformations. Under these conditions bubble-particle aggregates may form as a result of an electrostatic attraction which exceeds the repulsive van der Waals force at intermediate distances. Next to electrostatic and van der Waals forces, hydrodynamic and gravitational forces are considered. These forces may overcome the electrostatic repulsion at large distances and promote particle bubble attachment. Strong electrostatic attraction at small distances, arising at a large difference of the surface potentials of the bubble and the particle and of low electrolyte concentrations, can prevent subsequent detachment by hydrodynamic and gravitational forces. With increasing electrolyte concentration the electrostatic barrier increases and the attractive electrostatic force diminishes. As a result, a critical electrolyte concentration for microflotation exists. Above this concentration attachment may still occur but it is followed by detachment. At lower electrolyte concentrations the electrostatic attractive force prevents the detachment. The dependence of the critical electrolyte concentration on the values of the bubble and particle potentials and the Hamaker constant is calculated. The critical concentration does not depend on particle or bubble size if the absolute values of the total detachment force and the total pressing force coincide, which is the case for Stokes and potential flow. For every electrolyte concentration lower than the critical value there are two critical particle sizes that limit the flotation possibility. For small particle sizes attachment is impossible because the pressing force is smaller than the electrostatic barrier. For large particle sizes detachment cannot be prevented because the detachment force exceeds the maximum electrostatic attraction. A microflotation domain of intermediate particle sizes exists in which irreversible heterocoagulation occurs. Copyright 2001 Academic Press.     

Stability of a dispersion of particles covered by a charge-regulated membrane: effect of the sizes of charged species

The influence of the sizes of charged species on the stability of a colloidal dispersion is investigated theoretically. We consider the case where a particle comprises a rigid core and an amphoteric, charge-regulated membrane layer, which simulates biocolloids and particles covered by artificial membranes. A modified Poisson-Boltzmann equation, which takes the sizes of all the charged species into account, is adopted to describe the electrical field. The effects of other key parameters such as electrolyte concentration, pH, and the valence of counterions on the behavior of a dispersion are also examined. We show that the larger the effective size of the counterions, the greater the stability ratio, which is consistent with experimental observations in the literature.     

Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap

The application of optical tweezers (a single-beam gradient force optical trap) to the manipulation and characterisation of aerosol particles is discussed in this tutorial review. Optical tweezers allow not only the indefinite control over a single droplet, but control over arrays of particles. Typical particle sizes span the 1-10 microm diameter range. When coupled with spectroscopic techniques for probing evolving particle size (with nanometre accuracy), composition, phase and mixing state, detailed investigations of the thermodynamic properties of aerosol, the kinetics of particle transformation, and the nature of interparticle forces and coagulation can be undertaken.     

Numerical simulation and experimental verification of particle coagulation dynamics for a pulsed input

Mathematical simulation of particle coagulation dynamics was carried out using improved sectional modeling techniques for a system with a pulsed input of primary particles. The methodological improvement included the modification of the size density function based on a realistic assumption of particle size distributions, the application of a new and comprehensive curvilinear collision model, and special adjustment for the mass transfer of a doublet of particles that were very different in size. The simulation results demonstrated that the rectilinear model over-predicted the rate of particle coagulation and that the degree of over-prediction increased as the particles increased in size and the system became more heterogeneous. The coagulation rate increased remarkably as the fractal dimension of the particle aggregates decreased. The curvilinear model and the fractal scaling relationship in place of the rectilinear model and the Euclidean sizing geometry are two important modifications to the conventional Smoluchowski modeling approach. However, both modifications, rather than only one of them, should be applied together to produce more accurate and realistic simulations of coagulation dynamics. As indicated by the simulation, the importance of fluid shear rate to particle coagulation is reduced according to the curvilinear model compared to that previously described with the rectilinear model. As particles increased in size, the role of shear rate in coagulation became even less significant according to the curvilinear view of particle collisions. The results of numerical simulations in terms of the evolution of particle size distributions compared reasonably well with the observations of the jar-test coagulation experiments, which suggested the applicability of the modeling system, including the modified curvilinear-fractal approach, established in the present study.     

Cobalt particle size effects in the Fischer-Tropsch reaction studied with carbon nanofiber supported catalysts

The influence of cobalt particle size in the range of 2.6-27 nm on the performance in Fischer-Tropsch synthesis has been investigated for the first time using well-defined catalysts based on an inert carbon nanofibers support material. X-ray absorption spectroscopy revealed that cobalt was metallic, even for small particle sizes, after the in situ reduction treatment, which is a prerequisite for catalytic operation and is difficult to achieve using traditional oxidic supports. The turnover frequency (TOF) for CO hydrogenation was independent of cobalt particle size for catalysts with sizes larger than 6 nm (1 bar) or 8 nm (35 bar), while both the selectivity and the activity changed for catalysts with smaller particles. At 35 bar, the TOF decreased from 23 x 10(-3) to 1.4 x 10(-3) s(-1), while the C5+ selectivity decreased from 85 to 51 wt % when the cobalt particle size was reduced from 16 to 2.6 nm. This demonstrates that the minimal required cobalt particle size for Fischer-Tropsch catalysis is larger (6-8 nm) than can be explained by classical structure sensitivity. Other explanations raised in the literature, such as formation of CoO or Co carbide species on small particles during catalytic testing, were not substantiated by experimental evidence from X-ray absorption spectroscopy. Interestingly, we found with EXAFS a decrease of the cobalt coordination number under reaction conditions, which points to reconstruction of the cobalt particles. It is argued that the cobalt particle size effects can be attributed to nonclassical structure sensitivity in combination with CO-induced surface reconstruction. The profound influences of particle size may be important for the design of new Fischer-Tropsch catalysts.     

Colloidal stability of PVC primary particles in vinyl chloride

The electrostatic contribution to the colloidal stability of PVC primary particles (R=0.15 m) dispersed in vinyl chloride, was calculated using models based on the Coulombic interactions and the DLVO theory. The calculations were based on: a) the particle charge as obtained from literature data on the electrophoretic mobility of PVC primary particles in VCM and b) on estimates of the Debye length as obtained from measurements of the electrical conductivity of VCM and of solutions of Bu₄NBF₄ in VCM.The calculations showed that particle stability would decrease with particle size (experimentally-observed behaviour), only if the particle charge increased with size at a lower rate than in proportion to particle radius.The calculations also suggest that particle growth may be governed by a competitive growth mechanism of electrostatic origin. Particle growth is assumed to occur by absorption of many small, weakly charged basic particles from the monomer phase. According to the calculations, the electrostatic interaction between primary and basic particles may be such that the growth of the smaller primary particles is favoured over that of the larger ones.     

Computer Simulation of Bridging Flocculation Processes: The Role of Colloid to Polymer Concentration Ratio on Aggregation Kinetics

The flocculation of colloidal particles by adsorbing polymers is one of the central issues of colloid science and a very important topic in many industrial, biological, and environmental processes. We report a computer simulation study of a 2- and 3-dimensional model for bridging flocculation betweenlarge linear polymer chains and comparatively small colloidal particles,where the structure and growth kinetics of cluster formation are investigated. This model was developed within the framework of the cluster–cluster aggregation model using mass and fractal dimension dependent diffusion constants, where bridging flocculation is seen as a case of heterocoagulation in which, in addition, macromolecule configurations and lengths play an important role. The simulation of aggregate structure and formation kinetics obtained at different (i) relative particle concentrations, (ii) polymer chain conformations, and (iii) sticking probabilities are described from a qualitatively and quantitative point of view. The results suggest that the formation of large aggregates is a slow process, controlled by the reactivity of the clusters, even when the reaction between microcolloids and macrochains is very fast. Aggregation kinetics are strongly dependent on the particle/chain concentration ratio and on the configurational properties of the chains. It is shown that the scaling laws which are valid for homocoagulation processes are also applicable to the kinetics of bridging flocculation. The corresponding scaling exponents have been calculated.     

The effect of particle size on hydrolysis reaction rates and rheological properties in cellulosic slurries

The effect of varying initial particle sizes on enzymatic hydrolysis rates and rheological properties of sawdust slurries is investigated. Slurries with four particle size ranges (33 microm < x < or = 75 microm, 150 microm < x < or = 180 microm, 295 microm < x < or = 425 microm, and 590 microm < x < or = 850 microm) were subjected to enzymatic hydrolysis using an enzyme dosage of 15 filter paper units per gram of cellulose at 50 degrees C and 250 rpm in shaker flasks. At lower initial particle sizes, higher enzymatic reaction rates and conversions of cellulose to glucose were observed. After 72 h 50 and 55% more glucose was produced from the smallest size particles than the largest size ones, for initial solids concentration of 10 and 13% (w/w), respectively. The effect of initial particle size on viscosity over a range of shear was also investigated. For equivalent initial solids concentration, smaller particle sizes result in lower viscosities such that at a concentration of 10% (w/w), the viscosity decreased from 3000 cP for 150 microm < x < or = 180 microm particle size slurries to 61.4 cP for 33 microm < x < or = 75 microm particle size slurries. Results indicate particle size reduction may provide a means for reducing the long residence time required for the enzymatic hydrolysis step in the conversion of biomass to ethanol. Furthermore, the corresponding reduction in viscosity may allow for higher solids loading and reduced reactor sizes during large-scale processing.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

STUDY ON THE FORMATION MECHANISM OF MONODISPERSE PARTICLES IN THE EMULSIFIER-FREE EMULSION POLYMEAIZATION OF METHYL METHACRYLATE AND BUTYL ACRYLATE

The formation mechanism of monodisperse polymer latex particles in the emulsifier-free emulsion polymerizationof methyl methacrylate and butyl acrylate with potassium persulfate as initiator was investigated. A multi-step formationmechanism for the monodisperse polymer particles was proposed. The nucleation mechanism is considered to be thecoagulation of the precursor particles by homogeneous nucleation when the primary particles reach a critical size with highsurface charge density and sufficient stability. It had been proved by a special experiment that the early latex particles formedby the coagulation were stable. The primary particles grow by absorbing monomers and radicals in the polymerization systemand then become colloidally unstable again due to the understandable decrease of particle surface charge density, which leadsto the aggregation of the growing particles and the formation of larger latex pedicles therefrom. Aner the nucleation period,the preferential aggregation of the smaller particles in the propagation process leads to the change of the particles towards auniform size and narrower particle size distribution. The coexistence and competition of homogeneous nucleation,coagulation, propagation and aggregation result in the increase of the polydispersity index (U = D_(43)/D_(10)) in the first Stage,then its decrease in the later stage because of the competition of propagation and aggregation, and the gradual formation ofthe monodisperse particles.     

PARTICLE MORPHOLOGY OF POLY(VINYL CHLORIDE)RESIN PREPARED BY SUSPENDED EMULSION POLYMERIZATION

Suspended emulsion polymerization was used to prepare poly(vinyl chloride) (PVC) resin. Fine PVC particleswere formed at low polymerization conversions. The amount of fine panicles decreases as conversion increases anddisappears at conversions greater than 30%. Scanning electron micrographs show that PVC grains are composed of looselycoalesced primary particles, especially for PVC resins prepared in the presence of poly(vinyl alcohol) dispersant. The size ofprimary particles increases and porosity decreases with the increase of conversion. In view of the particle features of PVCresin, a particle formation mechanism including the formation of primary particles and grains is proposed. The formationprocess of primary particles includes the formation of particle nuclei, coalescence of particle nuclei to form primary particles,and growth of primary particles. PVC grains are formed by the coagulation of primary particles. The loose coalescence ofprimary particles is caused by the colloidal stability of primary particles and the low swelling degree of vinyl chloride in the primary particles.     

Rheology of PVC Plastisol: Particle Size Distribution and Viscoelastic Properties

Plastisols of poly(vinyl chloride), PVC, are suspensions of fine particles in plasticizer with about 50% resin volume fraction. Typically, the gross particle size ranges from 15 to 0.2 &mgr;m and smaller, where the common practice of spray-drying these resins and subsequent grinding of larger particles dictate the size ranges including agglomerates as well as the primary particles. The plastisol is a pastelike liquid, which may be spread to coat substrates. The coated substrates are heated in an oven to gel and fuse the material for producing uniform, rubbery products. Because the first step of processing is spreading the plastisol on a substrate, rheology at room temperature is obviously important. The material is thixotropic under very low stress. The flow behavior is pseudoplastic and exhibits dilatancy and fracture at high shear rate. This work is concerned with the pseudoplastic behavior but the dynamic mechanical measurements are employed instead of the usual steady-state shear flow measurements. This is because the steady shear may break up agglomerates. The dynamic measurements with small strain-amplitude avoid the break-up of the agglomerates. This is important, because this work is concerned with the effects of the particle size distribution on the material behavior. The frequency dependence of both viscous and elastic behavior is recorded and presented with samples varying in particle size distribution. Copyright 2001 Academic Press.     

Role of the secondary minimum on the flocculation rate of nondeformable droplets

The kinetic stability of suspensions is usually associated with a decrease in the flux of flocculating particles due to the action of a repulsive potential. However, previous calculations on bitumen drops suggest the possible occurrence of relatively fast aggregation rates in systems with large electrostatic barriers for primary minimum flocculation. This indicates a strong effect of the secondary minimum in the process of aggregation. Here, emulsion stability simulations (ESS) are used to study the aggregation behavior of 11 systems showing different depths of the secondary minimum and three particle sizes. Micron size drops (as those of Bitumen emulsions) usually exhibit deep secondary minima, which rarely occur between nanometer size particles. At high surfactant concentrations, these drops do not coalesce but can still show fast aggregation rates caused by irreversible secondary-minimum flocculation. On the other hand, the extent of coalescence in nanometer-size systems markedly depends on the height of the repulsive barrier. Furthermore, the secondary minimum of these smaller particles is usually shallow, causing reversible aggregation or no aggregation at all. In this article, the consequences of the referred behaviors on the magnitude of the stability ratio are discussed.     

Fragmentation and erosion of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates containing glass particles trapped at a water/oil or water/air interface. Two modes for aggregate break-up are observed: break-up by fragmentation into a few parts and break-up by erosion of single particles. We have studied the critical shear rate for these modes as a function of the aggregate size. Two different particle sizes were used. The smaller particles, with a radius of 65 microm, form aggregates that break up predominantly by erosion at a shear rate between 0.5 and 0.7 s(-1). This value hardly depends on the size of the aggregates. The larger particles, with a radius of 115 microm, form aggregates that break by erosion or by fragmentation. In both modes, the critical shear rate again depends only weakly on the size of the aggregates and ranges between 1.6 and 2.2 s(-1). Also the structural changes inside the aggregate before break-up were studied. The aggregate behavior at the water/air and water/oil interfaces is quite similar. The critical shear rate for break up was also modeled. The model shows in both modes a weak dependence of the critical shear rate on the aggregate size, which is consistent with the experimental observations. The kinetics of the erosion process was also modeled and compared with the experimentally obtained time dependence of the aggregate size. The differences in the large and small particle systems can be attributed to the occurrence of friction forces between the particles, which one expects to be much larger for the large particle system, due to the stronger two-particle interaction.     

Interaction between an ion-penetrable particle and a solid particle. II. Criteria for heterocoagulation

The potential energy of the total interaction between two spherical colloidal particles of different nature is calculated, i. e., of an ion-penetrable particle and an ion-impenetrable solid particle having a constant surface potential or constant surface charge density. The criteria for heterocoagulation are derived. The obtained results suggest a possibility of selective coagulation in the mixed system.     

The effect of particle coalescence on the surface area of a coagulating aerosol

The initial stage of particle formation in high temperature processes is characterized by a high density of very small particles undergoing rapid coagulation. When these particles are solid this leads to agglomerates with a high specific surface area. However, at high gas temperatures particle coalescence which is very sensitive to the temperature may reduce the surface area and increase the size of the primary particles. In this paper we generalize the Smoluchowski equation to incorporate the coalescence rate into the aerosol dynamics. Individual agglomerates are characterized by their volume, v, and surface area, a. A Liouville term is added to the coagulation equation determining the movement of the distribution function through a-space due to coalescence. For the rate of coalescence a simple two sphere model has been used. Results for the surface area and the average diameter of the individual primary particles are presented for the case of a collision kernel which is independent of the particle structure. As an example, the theory is applied to fine particle formation in combustion processes under nonisothermal conditions.