具有多体效应的胶体聚团的特征

考察了多体效应（用Ｓｔｕｔｔｏｎ－Ｃｈｅｎ势，ＳＣ）对胶体聚团的影响并与双体（ＬＪ）势下的结果作了比较。研究表明，ＳＣ和ＬＪ势下簇团的性质有其相似的一面，如：随着剪应力的增加，系统里颗粒的平均势能增加，而每个簇团的颗粒数减少；在较强的剪应力场里，簇团沿剪应力方向（Ｘ轴）被明显拉长且其主轴偏离Ｘ轴等。但它们间的差异也是明显的，在剪应力下ＳＣ系统内颗粒排列得更合理，从而使得平均位能比ＬＪ系统低约１－３     

AN ATOMIC FORCE MICROSCOPY STUDY ON THE AGGREGATION OF ISOTACTIC POLY（METHYL METHACRYLATE）

Aggregation process of isotactic poly(methyl methacrylate) (i-PMMA) has been studied extensively for many years, and considerable progress has been made in both experimental and theoretical studies. They are, however, seldom sustained by real-space observations of the underlying morphology. In this paper, the aggregation process of i-PMMA in concentrated acetone solutions and the fractal structure of the resulting three-dimensional clusters were characterized on the basis of real-space AFM observations of their two-dimensional projection. It was found that spherical multiple-chain particles formed upon collapse and aggregation of the involving chains as a whole during quenching the solution to room temperature. By keeping the solution at room temperature, the initially formed particles stick together upon contact to form larger particles through reassembling very slowly. The succeeding collision of the enlarged spherical particles leads to the formation of small clusters. These newly formed small clusters grow when they meet with other clusters or single Brownian particles. This leads to the formation of large clusters with fractal dimension of 1.95$±0.05, which suggest a reaction-limited cluster aggregation of i-PMMA in a concentrated acetone solution. This is in accordance with the conclusion obtained by light scattering measurements.     

Parameters of Equilibrium Spectrum of Particles in Coagulating System with Aggregate Disintegration

The formation of equilibrium spectrum of particles in a disperse system with the coagulation–fragmentation of aggregates at a steady-state shear flow was analyzed in terms of two-fraction model. It was suggested that an initial dispersed phase contains only small particles coagulating by the Brownian mechanism; the growth of larger aggregates proceeds by the gradient mechanism and is accompanied by the detachment of fragments. Parameters of equilibrium spectrum characterizing average masses and the number of particles in fine and coarse fractions were determined as functions of a flow shear rate, aggregate fractal dimension, parameters of particle interaction in aggregates, and the properties of the initial dispersed phase.     

Capillary force required to detach micron-sized particles from solid surfaces—Validation with bubbles circulating in water and 2 μm-diameter latex spheres

The adhesion forces holding micron-sized particles to solid surfaces can be studied through the detachment forces developed by the transit of an air–liquid interface in a capillary. Two key variables affect the direction and magnitude of the capillary detachment force: (i) the thickness of the liquid film between the bubble and the capillary walls, and (ii) the effective angle of the triple phase contact between the particles and the interface. Variations in film thickness were calculated using a two-phase flow model. Film thickness was used to determine the time-variation of the capillary force during transit of the bubble. The curve for particle detachment was predicted from the calculated force. This curve proved to be non-linear and gave in situ information on the effective contact angle developing at the particle–bubble interface during detachment. This approach allowed an accurate determination of the detachment force. This theoretical approach was validated using latex particles 2 μm in diameter.     

Estimation of the dynamic size of fractal aggregates

A model is presented for an aggregation act occurring between two aggregates of any mass and fractal dimension. The kinetics of aggregation is also analyzed, as well as some previous works concerning the structure of fractal aggregates. As a result, a generalized curve is derived describing the normalized dynamic radius of clusters of spherical character as dependent on both the aggregate fractal dimension and the space dimension. It is shown how the curve may be utilized to determine the dynamic size of anisotropic aggregates. The obtained dependence can be used to estimate the dynamic size of fractal aggregates, to evaluate the prefactor in mass–radius relation and to model the aggregation kinetics.     

Effect of surfactants on shear-induced gelation and gel morphology of soft strawberry-like particles

The role of surfactant type in the aggregation and gelation of strawberry-like particles induced by intense shear without any electrolyte addition is investigated. The particles are composed of a rubbery core, partially covered by a plastic shell, and well stabilized by fixed (sulfate) charges in the end group of the polymer chains originating from the initiator. In the absence of any surfactant, after the system passes through a microchannel at a Peclet number equal to 220 and a particle volume fraction equal to 0.15, not only shear-induced gelation but also partial coalescence among the particles occurs. The same shear-induced aggregation/gelation process has been carried out in the presence of an ionic (sulfonate) surfactant or a nonionic (Tween 20) steric surfactant. It is found that for both surfactants shear-induced gelation does occur at low surfactant surface density but the conversion of the primary particles to the clusters constituting the gel decreases as the surfactant surface density increases. When the surfactant surface density increases above certain critical values, shear-induced gelation and eventually even aggregation do not occur any longer. For the sulfonate surfactant, this was explained in the literature by the non-DLVO, short-range repulsive hydration forces generated by the adsorbed surfactant layer. In this work, it is shown that the steric repulsion generated by the adsorbed Tween 20 layer can also protect particles from aggregation under intense shear. Moreover, the nonionic steric surfactant can also protect the strawberry-like particles from coalescence. This implies a decrease in the fractal dimension of the clusters constituting the gel from 2.76 to 2.45, which cannot be achieved using the ionic sulfonate surfactant.     

Thermal restructuring of fractal clusters: the case of a strawberry-like core-shell polymer colloid

Thermal restructuring of fractal styrene-acrylate copolymer clusters dispersed in water has been investigated experimentally in the temperature range between 313 and 363 K. The particles constituting the clusters are of strawberry-like core-shell structure with a soft core and a rigid shell grafted on the core polymer chains. Due to the incomplete coverage of the core, the rather soft core may "flow out" through the open areas of the shell, leading to coalescence with the neighboring particles. The clusters were generated under diffusion-limited cluster aggregation conditions, and the restructuring kinetics was monitored by small-angle light scattering. Two sets of thermal restructuring experiments have been performed at various temperatures: (1) restructuring of growing clusters during aggregation and (2) restructuring of preformed clusters in the absence of aggregation. It is found that restructuring occurs only at temperature values above 323 K. In the absence of aggregation, restructuring leads to an increase of the fractal dimension and a decrease of the radius of gyration of the clusters. At sufficiently long times, both quantities reach a plateau value due to the presence of the grafted rigid shell, which constrains the coalescence of the soft core. A simple model, based on coalescence theory of liquid droplets and accounting for the incomplete coalescence and its dependence on temperature, has been developed to interpret the restructuring kinetics in the absence of aggregation. It is found that the proposed model can represent the measured experimental data well.     

Aggregate restructuring by polymer solvency effects

This study investigates the aggregation in cyclohexane of silica particles initially stabilized by grafted polystyrene and destabilized by temperature reduction. It complements an earlier study by Zhu and Napper (P.W. Zhu, D.H. Napper, Phys. Rev. E 50 (1994) 1360) in which the aggregation of polystyrene latex particles with tethered poly(N-isopropyl acrylamide) (PNIPAM) in water was investigated. Their dynamic light scattering results showed that both the rate of aggregation and the aggregate fractal dimension increased with a sufficient decrease in the PNIPAM adlayer solvency, achieved by means of either salt (NaNO3) addition or temperature rise. This result stands in contrast to those obtained when an electrostatically stabilized colloid is destabilized, i.e., that the more rapidly aggregates are formed, the lower the resulting fractal dimension. The authors explained their results in terms of the effects of both salt effects and increased temperature on the extent of the hydrophobic interactions between the adlayer-covered surfaces in the water. The present study examines a sterically-stabilized colloid in a nonaqueous solvent, where neither salt effects nor hydrophobic effects play a role. Temperature is decreased to bring the system from better-than-theta-conditions to worse-than-theta-conditions. Power-law aggregation kinetics are observed at 15.7 degrees C by dynamic light scattering. The particles first undergo reduced rate aggregation, producing low-fractal-dimension aggregates, which after some time, restructure into more compact aged clusters. The fractal dimension of these aged clusters increases with increasing initial aggregation rate, consistent with results seen by Zhu and Napper, but without the presence of hydrophobic effects. The ability of the polymer-grafted particles to rearrange suggests aggregation into a secondary minimum, with the ability to slide over one another to achieve a more energetically favorable, denser configuration. The reversible nature of the aggregation is verified by additional experiments gradually bringing the system from worse-than-theta-conditions back to better-than-theta-conditions, with an attendant decrease in aggregate fractal dimension, and ultimately full redispersion.     

Influence of nonwetting on the aggregation dynamics of micronic solid particles in a turbulent medium

The aim of this work was to determine and to interpret the influence of nonwetting on the aggregation dynamics of micronic solid particles in a turbulent medium. Two silica granular samples were studied: one was naturally hydrophilic; the other was made hydrophobic. Aggregation in an aqueous ethanol solution was followed by in situ turbidimetry. The influence of stirring rate and deaeration was determined. Aggregates of hydrophilic particles were small and fragile, whereas aggregates of hydrophobic particles were large and solid. Moreover, they differred greatly in optical properties. Within the proposed approach, different features of the aggregate morphology were identified: fractal dimension, maximum size, and gas content of the hydrophobic clusters. These elements are taken into account in the models of aggregation dynamics proposed here.     

Structure and Adsorption Properties of Nanocrystalline Silicon

The structure of the particles of nanocrystalline silicon synthesized in argon plasma with added oxygen is studied. An amorphous shell composed of silicon oxide is formed on the surface of silicon nanoparticles. The particles form clusters with a fractal structure. The adsorption of nitrogen on a powder of nanocrystalline silicon at 77 K is studied, and adsorption isotherms obtained for nanocrystalline silicon and nonporous silica adsorbents with identical specific surface areas are compared. The values of surface fractal dimension of powdered nanocrystalline silicon are calculated using the Frenkel-Halsey-Hill equation for multilayer adsorption under the dominant contribution of van der Waals or capillary forces. It is shown that surface fractal dimension is a structure-sensitive parameter characterizing both the morphology of clusters and the structure (roughness) of the surface of particles and their aggregates.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 541–547.Original Russian Text Copyright © 2005 by Tutorskii, Belogorokhov, Ishchenko, Storozhenko.     

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.     

Clustering properties of partly charged superfine particles in a light medium

This paper investigated average cluster sizes （ACS） and cluster size distributions （CSD） at different shear rates by Brownian dynamics in non-, bi-, and uni-polar systems with partly charged superfine particles, The investigation indicates that clusters in non- polar systems are the weakest and easiest to be damaged by increasing shear stresses; charged particles play important and different roles： in bi-polar system, it intends to strengthen clusters to some extent provided that the sign-like ions homogeneously arranged; in uni-polar system charged particles cracked the clusters into smaller ones, but the small clusters are strong to stand with larger shear stress. The relationship between ACS and shear rates follows power law with exponents in a range 0.18-0.28, these values are in a good agreement with experiment range but at the lower limit compared with other systems of non-metallic cluster particles.     

Numerical computations of molecular reactions in associated systems caused by the formation of fractal structures

The interaction between particles in a system containing fractal clusters has been computationally simulated. The fractal structure of the system has been demonstrated to determine the kinetic characteristics of particle interaction. If a system in an N-dimensional space (N = 2, 3, 4) contains fractal clusters with the fractal dimension D > N-1, the rate of interaction of a free particle with particles belonging to clusters depends on their concentration according to the power law. The exponent gamma of this power law formally corresponds to the kinetic order of the reaction with respect to the concentration of particles belonging to the clusters. Its value is determined by the free surface of the clusters and depends on its fractal dimension D. The results of simulation qualitatively agree with the data on high, non-integral orders of many liquid phase molecular reactions characterized by self-organization of the medium via weak intermolecular interactions, such as hydrogen bonds.     

Flocculation of hematite particles by a comparatively large rigid polysaccharide: schizophyllan

We studied the flocculation kinetics and structure of hematite aggregates induced by a large rigid extracellular polysaccharide, schizophyllan. Transmission electron microscopy (TEM), atomic force microscopy (AFM), photon correlation spectroscopy (PCS), and static light scattering (SLS) were used to characterize hematite particles, schizophyllan chains, and their flocs, to follow the time evolution of floc sizes, and to determine floc fractal dimensions. A maximum flocculation rate was found at a certain schizophyllan/hematite ratio. The maximum rate was considerably smaller than the rate of diffusion-limited aggregation (DLA) of hematite particles induced by simple electrolytes. To interpret the experimental results and to reveal various factors affecting the optimal dosage, Monte Carlo simulations were performed on the flocculation of small colloidal particles by relatively long, monodisperse linear polymers. The existence of the maximum flocculation rate was confirmed by computer simulation. However, a higher optimal dosage of schizophyllan was obtained in the experiments. The difference in the optimal dosage can be attributed mostly to the higher adsorption affinity of the hematite on schizophyllan aggregates present in the initial solution and the presence of a large fraction of free polymer chains which do not participate in the flocculation process. Both experiments and computer simulations demonstrated the fractal nature of the schizophyllan-hematite flocs. The fractal dimensions of the flocs at the optimal dosage were determined. A higher fractal dimension was obtained from experiments than from computer simulations, suggesting a reconstruction of the floc structure. Finally, a two-stage flocculation mechanism for hematite particles in the presence of a relatively long schizophyllan polymer was proposed. In the first flocculation stage, the hematite particles are preferentially adsorbed onto the schizophyllan aggregates in solution. The second stage consists of the association of these reactive entities with each other and also with naked chains to form fractal flocs by a bridging mechanism, where the hematite particles play the role of ligands.     

Fractal Characterization of Silica Sol Prepared by the Sol-Gel Method: From the Sol Formation to the Flocculation Process

The fractal characterization of silica particles prepared by the sol-gel method was obtained; from the beginning of the sol-gel synthesis to the aggregation process of these particles by adding metal ions in solution, the fractal dimension was determined. At the beginning of the sol-gel process, unstable structures were formed due, essentially, to the auto-catalytic nature of the sol-gel condensation reactions; these particles are fractal structures with a fractal exponent corresponding to a reaction limited aggregation regime. As the time proceeds, the reactants are consumed approaching the system to equilibrium, stabilizing the size of the silica particles. The silica sol can be flocculated by adding metal ions in solution. The fractal exponent for the aggregation process was determined, obtaining a value corresponding to a diffusion limited aggregation regime.     

Breakage rate of colloidal aggregates in shear flow through stokesian dynamics

We study the first breakage event of colloidal aggregates exposed to shear flow by detailed numerical analysis of the process. We have formulated a model, which uses stokesian dynamics to estimate the hydrodynamic interactions among the particles in a cluster, van der Waals interactions and Born repulsion to describe the normal interparticle interactions, and the tangential interactions through discrete element method to account for contact forces. Fractal clusters composed of monodisperse spherical particles were generated using different Monte Carlo methods, covering a wide range of cluster masses (N(sphere) = 30-215) and fractal dimensions (d(f) = 1.8-3.0). The breakup process of these clusters was quantified for various flow magnitudes (γ), under both simple shear and extensional flow conditions, in terms of breakage rate constant (K(B)), mass distribution of the produced fragments (FMD, f(m,k)), and critical stable aggregate mass (N(c)), defined as the largest cluster mass that does not break under defined flow conditions. The breakage rate K(B) showed a power law dependence on the product of the aggregate size and the applied stress, with values of the corresponding exponents depending only on the aggregate fractal dimension and the type of flow field, whereas the prefactor of the power law relation also depends on the size of the primary particles comprising a cluster. The FMD was fitted by Schultz-Zimm distribution, and the parameter values showed an analogous dependence on the product of the aggregate size and the applied stress similar to the rate constant. Finally, a power law relation between the applied stress and corresponding largest stable aggregate mass was found, with an exponent value depending on the aggregate fractal dimension. This unique and detailed analysis of the breakage process can be directly utilized to formulate a breakage kernel used in solving population balance equations.     

Microstructure Evolution of Nonhydrolytic Alumina Gels

Nonhydrolitic sol-gel processes of aluminum chloride and aluminum bromide with isopropyl ether and aluminum sec-butoxide were performed at various temperatures. Based on the Arrhenius type variation of the gelation time with temperature, activation energies for the gelation were found to be in the range 19–25 Kcal/mol range. The energies were found to be sensitive to the nature of the aluminum ligands and the chemical scheme. Due to the large activation energy, it is possible to stop the reaction at any time before gelation by cooling the sol to room temperature. Small angle X-ray scattering (SAXS) of sols from the AlClAlCl₃/Pr O system shows unique development of a fractal like structure with nanometer scale order, demonstrated by discrete peaks in the SAXS data. A fractal dimension D = 1.64 was found. An aggregation scheme is proposed to explain this phenomenon. A fractal dimension of 2.4 without small scale ordering found for xerogels prepared from the AlCl₃/ASB system reflects the effect of the different precursors on the microstructure of nonhydrolytic gels.     

Phase-field modeling of two-dimensional solute precipitation∕dissolution: solid fingers and diffusion-limited precipitation

Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the chemical reaction at the solid-liquid interface has similarities with diffusion-limited aggregation (DLA). The diffusion-limited precipitation is attained by setting the chemical reaction rate much larger compared to the solute diffusion to eliminate the effect of the interface growth kinetics. The phase-field simulation results were in reasonable agreement with the analytical solutions. The fractal solid fingers can be formed in the diffusion-limited precipitation and have a fractal dimension measured d(f)=1.68, close to 1.64, the fractal dimensionality of large square lattice DLA clusters.     

Aggregation-fragmentation in a model of DNA-mediated colloidal assembly

We present results from an off-lattice Monte Carlo simulation of DNA-mediated colloidal assembly. In this simulation, the aggregation-fragmentation of a binary mixture of DNA-coated colloidal particles is studied through a simplified model of base-pair hybridization. Bonding between monomers is modeled as a simple temperature-sensitive A/B-type interaction, where type A and B monomers can bond to only the opposite type (no A/A or B/B attachments are allowed). The actual chemistry of base-pair hybridization is not included in the model. The morphological structures of the clusters formed as well as the kinetics of growth are analyzed in our 2D simulations. The fractal dimension and kinetic growth exponents for clusters formed near the DNA "melting" temperature agree with those seen previously for 2D diffusion-limited cluster aggregation (DLCA) models. The clusters appear more compact, exhibiting signs of local order at intermediate temperature values. At higher temperatures, the formation of large clusters is not favorable under the action of temperature-dependent fragmentation, and the system eventually reaches a steady state as a collection of small aggregates. The temperature profile for this dissolution of the colloidal assembly is sharp, indicating that the selective hybridization process provides a highly sensitive measurement tool. At high temperatures, we analyze the steady-state behavior of the average cluster size in terms of an aggregation-fragmentation model.     

Multi-fractal imaging and structural investigation of silica hydrogels and aerogels

In this work, we report on the preparation of TEOS gels by means of the sol–gel method employing different TEOS/ethanol/water ratios at room temperature. Small-angle X-ray scattering (SAXS) measurements provide the first-generation structural parameters, which indicate that particle size and fractal dimension are synthesis and depth dependent. These results are supported by the second- and third-generation aggregates observed using atomic force microscopy (AFM) and scanning electron microscopy (SEM). The fiber-like first-generation clusters aggregate as spherical second-generation particles which, in turn, in the third generation rearrange into complex structures.