Two-dimensional colloidal crystal in nonlinear Poisson-Boltzmann model

A two-dimensional hexagonal colloidal crystal of charged particles obeying the general nonlinear Poisson-Boltzmann equation is studied by the numerical method. Force constants and pressure in a system, as well as elastic constants of a crystal, are calculated on the basis of the solutions of the equation. Calculation procedures are described briefly and numerical data are reported. The effect of nonlinearity of charge distribution on the manifestation of many-body interactions and on the validity of the approximation of interaction of the nearest neighbors is considered.     

Internal structure of clusters from charge heteroaggregation

The internal structure of clusters formed by colloidal heteroaggregation of particles with opposite signs of charge is studied by means of computer simulations. Every particle is surrounded by a layer of particles of opposite sign, a second neighbors shell of particles mainly with the same sign, a third one of opposite sign, etc. As the distance from the particle increases, the system becomes more homogeneous and no difference between the numbers of particles with similar or opposite signs of charge can be noticed for distances larger than ten times the particle radius. For low ionic concentrations the local environment of particles is formed by quasi-straight branches, where the sign of charge alternates, and at high concentrations the structure of the cluster is typical of DLCA and the alternation is restricted to very short distances. However, this effect is not responsible for the low fractal dimensions observed in charge heteroaggregates.     

Colloidal stability of chitosan-modified poly(methyl methacrylate) latex particles

Experiments of coagulation kinetics were used to study the influence of the electrolyte concentration on the colloidal stability of cationic poly(methyl methacrylate) latex particles with various degrees of chitosan modification. For the chitosan-free latex products prepared by various levels of 2,2′ azobis(2-amidinopropane) dihydrochloride (V-50) at constant pH, the critical coagulation concentration (ccc) increases with increasing V-50 concentration, due to the enhanced particle surface charge density. On the other hand, the chitosan-modified latex products at constant pH do not exhibit very different values of ccc. This result is attributed to the counterbalance between two opposite effects related to the grafted chitosan, that is, the increased particle surface charge density and the enhanced shift of the particle's shear plane toward the aqueous phase with the chitosan content. The ccc of the latex products with various degrees of chitosan modification decreases significantly when the pH increases from 3 to 7. This is because the degree of ionization of the surface amino groups (the particle surface charge density) decreases with increasing pH. As a result, the stability of the colloidal system decreases significantly with increasing pH. The apparent Hamaker constant and diffuse potential were obtained from the coagulation kinetics data. These two parameters along with the zeta potential and particle size data for the latex samples taken immediately after the end of the coagulation experiments were also used to study the effect of ionic strength on the colloidal stability of the latex particles. Received: 10 October 1998 Accepted in revised form: 16 December 1998     

Particle Nucleation and Growth in the Emulsion Polymerization of Styrene: Effect of Monomer/Water Ratio and Electrolyte Concentration

This work is an extension of previous research results reported by our team (Colloid and Polymer Science 2013, 291: 2385-2398), where large scale and high solid content latexes of poly(n-butyl acrylate) were obtained with the particle coagulation method induced by the electrolyte. However, how to prepare controlled particle size distribution polymer latex has not been studied. Thus, in this study, the effect of the monomer/water ratios and electrolyte concentrations on particle formation and growth methods were studied by following the tracks of the evolutions of particle size, number and distribution as a function of reaction time or conversion. Experimental results showed that the length of time that particle nucleation occurred increased with increasing monomer charged for the systems without electrolyte. A point worthy of attention here is that homogeneous nucleation may occur at high monomer concentrations (30/70, 40/60). However, electrolyte added could be made the nucleation mechanism shift from micellar/homogeneous nucleation to micelle /coagulation nucleation. As a result, the final particle size distribution can be controlled by adding an appropriate electrolyte to regulate the nucleation mechanism. Spherical and uniformly sized particles could be obtained when electrolyte concentration is between 0.2 wt% and 0.4 wt% for water at the high monomer/water ratio (40/60). The effects of electrolyte concentration on nucleation mechanism mainly were expressed by decreasing the solubility of the monomer and interparticle potential, and then preventing homogeneous nucleation and enhancing particle coagulation.     

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.     

Influence of various monovalent cations and calcium ion on the colloidal fouling potential

The influence of various monovalent cations and of divalent calcium ions on colloidal fouling strength was investigated quantitatively on a bench-scale ultrafiltration device. A higher colloidal fouling potential (k) was consistently observed with lithium chloride compared to the same ionic strengths of chlorides of other monovalent cations (Na+, K+, and Cs+). This observation was attributed to the formation of an impervious layer around the colloidal particle by lithium ions that prevented the repulsive forces due to the interaction of the silica hairs formed on the particles in the presence of water. The impact of the divalent calcium ion on the fouling potential was more complex. The fouling potential first increased with calcium ion concentration and then decreased. The maximum value of fouling potential occurred at the ionic strength corresponding to the critical coagulation concentration, which decreased with increasing colloid concentration. The colloidal fouling potential was well correlated by a bilinear relationship with colloid concentration and ionic strength for all salts tested under the critical coagulation concentration.     

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.     

Ion distribution around electrostatically stabilized polystyrene latex particles studied by ellipsometric light scattering

The ion distribution around electrostatically stabilized polystyrene latex spheres for different ionic strengths is investigated by ellipsometric light scattering. This method is sensitive to the refractive index profile around colloidal particles, which is affected by the local salt content. At an average salt concentration of c* = 10(-4) mol L(-1), the ion concentration at the particle interface increases discontinuously, and a layer of high salt content with 20-30 nm thickness is built up. The observation cannot be explained within the framework of the Poisson-Boltzmann equation; it rather resembles a prewetting transition. Interactions that could possibly lead to a stabilization of the observed layer of high salt content are discussed.     

Automatic classification of chemical structure databases using a highly parallel array processor

This article describes the use of the ICL Distributed Array Processor (DAP) for the automatic classification of chemical structure databases using the Jarvis-Patrick clustering method. This method is based upon the calculation of a table containing the nearest neighbors for each of the molecules in the database which is to be clustered. These nearest neighbors can be identified very efficiently using the DAP since it allows up to 4096 molecules to be compared with a specified molecule in parallel. Experiments with files of 4096 and 8192 structures from the Fine Chemicals Database show that clustering with the DAP is up to 6.7 times as fast as using a highly efficient, inverted file algorithm on an IBM 3083 mainframe.     

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace??s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.     

Relative importance of hydrolyzed Al(III) species (Al(a), Al(b), and Al(c)) during coagulation with polyaluminum chloride: a case study with the typical micro-polluted source waters

The relative importance of three different Al species, Al(a) (monomeric species, instantaneous reacted species), Al(b) (medium polymer species, reacted less than 120 min), and Al(c) (colloidal or solid species, no reaction), defined by timed complexation reaction rate measured by using ferron reagent in polyaluminum chloride (PACl) was investigated in terms of DOC (dissolved organic carbon), UV(254), and turbidity removal efficiencies. Micro-polluted, typical North China, source waters were used to conduct the experiments. The results show that DOC removal is correlated well to the content of Al(b). Removal of UV(254) is determined by the content of Al(b) and Al(c), particularly Al(c). Turbidity removal is primarily related to the content of Al(c); however, Al(b) could destabilize particles efficiently, and the flocs formed by Al(b) are not as large as those formed by Al(c), which affected the settling efficiency. Unlike the preformed Al(b), the in situ formed Al(b) could remove turbidity more efficiently since Al(c) is the dominant final species formed during coagulation. Al(a) shows a strong ability to react with some unsatisfied coordinate bonds of organic matter to facilitate particle and DOC removal. The distinct coagulation feature of Al(a), Al(b), and Al(c) can be applied to develop tailor-made PACl (with the correct distribution of Al species) to match the characteristics of raw water for optimized coagulation.     

Preparation and characterization of carboxylic-containing poly(methyl methacrylate) nanolatexes

Poly(methyl methacrylate) (PMMA)-based latex particles bearing carboxylic groups at the surface were prepared via emulsion polymerization. The polymerization recipe and process were optimized in order to target monodisperse particles with diameters around 100 nm. The polymerizations were performed using 4,4-azobis(4-cyanopentanoic) acid (ACPA) as initiator and sodium dodecyl sulphate (SDS) as surfactant. The polymerization conversion was determined by both gas chromatography and gravimetry. The final latexes were characterized with respect to particle size, size distribution, surface charge density, electrokinetic properties (i.e. electrophoretic mobility vs pH and ionic strength) and colloidal stability (i.e. coagulation rate constants vs pH and stability factor vs ionic strength).     

Note on One-Dimensional Lattice Gas in External Fields

Abstract

The fundamental equations of the scaled particle theory are derived for a one-dimensional lattice gas in an external potential. These equations relate the work required to add a particle, at a fixed point, to a N – 1 particle system to the activity and to a series of coordinate distribution functions. The equations hold in any dimension, and replacing sums by integrals, describe continuum fluids. The rigid lattice gas is solved by these means. When nearest neighbors interact, in a positive, increasing external potential, a formal solution is obtained by a matrix method. The grand partition function, in the infinite length limit, depends only on a single eigenvalue of an infinite product of matrices. The one-particle distribution, in this limit, is reduced to a series of terminating continued fractions, which is readily approximated in the high coordinate or low activity limit. Lastly, it is shown that the zeros of the grand partition function lie on the negative real axis of the complex activity plane when the nearest-neighbor interaction is positive.     

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.     

Phase transitions in two-dimensional colloidal particles at oil/water interfaces

Enhanced digital video microscopy is applied to study the equilibrium structure of a two-dimensional charged sulfate-polystyrene particle (2 mum in diameter) monolayer at decane/water interfaces. When the surface density is decreased, a sequential phase transition, pure solid phase-->pure hexatic phase-->liquid-hexatic-coexisting phase-->pure liquid phase, is observed. In addition, the transition between liquid and hexatic phases is first order, while the solid-hexatic phase transition is second order. The temperature effect on this two-dimensional melting transition is discussed by performing the experiments at three different temperatures. The Voronoi [J. Reine Angew. Math. 134, 198 (1908)] construction is applied to analyze the defect structure in the two-dimensional particle monolayer. The pair interaction potential of the two-dimensional colloidal particles is found to be a very long range repulsion and to decay with distance to the power of -3.     

熵驱大分子胶体粒子的柱状受限结晶

熵是物理化学的基本状态参量,在统计力学和热力学中处于核心位置.按照玻尔兹曼的微观解释,熵可以由孤立系统微观状态的数目(W)给出,即S=kBlnW,这里kB为玻尔兹曼常数[1,2].根据此公式,微观状态数越多,系统越混乱,熵越大,所以熵常被视作体系无序程度的度量.但熵增仅对应体系微观状态数的增加,与可观测的结构有序程度无关[3~5].在一些典型的软物质体系中,结构越有序熵反而越大,如胶体硬球在随机密堆积点的有序结晶[6]及描述各向异性棒状分子从各向同性相到向列相转变的Onsager原理[7].     

Vertical motion of a charged colloidal particle near an AC polarized electrode with a nonuniform potential distribution: theory and experimental evidence

Electroosmotic flow in the vicinity of a colloidal particle suspended over an electrode accounts for observed changes in the average height of the particle when the electrode passes alternating current at 100 Hz. The main findings are (1) electroosmotic flow provides sufficient force to move the particle and (2) a phase shift between the purely electrical force on the particle and the particle's motion provides evidence of an E2 force acting on the particle. The electroosmotic force in this case arises from the boundary condition applied when faradaic reactions occur on the electrode. The presence of a potential-dependent electrode reaction moves the likely distribution of electrical current at the electrode surface toward uniform current density around the particle. In the presence of a particle the uniform current density is associated with a nonuniform potential; thus, the electric field around the particle has a nonzero radial component along the electrode surface, which interacts with unbalanced charge in the diffuse double layer on the electrode to create a flow pattern and impose an electroosmotic-flow-based force on the particle. Numerical solutions are presented for these additional height-dependent forces on the particle as a function of the current distribution on the electrode and for the time-dependent probability density of a charged colloidal particle near a planar electrode with a nonuniform electrical potential boundary condition. The electrical potential distribution on the electrode, combined with a phase difference between the electric field in solution and the electrode potential, can account for the experimentally observed motion of particles in ac electric fields in the frequency range from approximately 10 to 200 Hz.     

Synthesis of Microporous Silica Spheres

Spherical microporous silica powders with a narrow size distribution have been prepared by a precipitation technique involving the hydrolysis reaction of a silicon alkoxide in ethanol. The formation of the important microporosity has been investigated following two templating methods: the co-hydrolysis and condensation of two alkoxides, one of which presents porogen function, and the adsorption of an organic compound (glycerol) as the porogen. In both processes, the organic porogen is removed by a simple calcination. In the first method, the addition of more than 20 mol% of the porogen alkoxide, necessary for generating enough microporosity, disturbs completely the condensation process resulting in microporous, nonuniform silica particles of large size distribution. The best result has been obtained with the glycerol method where submicrometer-sized silica spheres with a very narrow size distribution and about 40 vol% porosity have been synthesized. The presence of glycerol during the synthesis considerably affects the precipitation mechanism, resulting in a larger mean particle size. The use of an aggregative growth model has successfully been employed to explain the effect of the porogen during particle formation. The precipitation mechanism of silica involves the aggregation between particles of similar size until a critical size is reached, resulting in a uniform particle size distribution. In the presence of glycerol, it has been shown that a second aggregative growth between still-nucleating primary particles and large particles occurred with increasing reaction time. This second aggregative growth appears at an intermediate stage of the precipitation process and is due to both the precipitation of smaller primary particles and the destabilization of the colloidal stability of the system. This explains why the final particle size reached in this system is larger compared to silica particles synthesized without glycerol and shows how glycerol is incorporated in the silica particles. The synthesis of silica microporous spheres of narrow size distribution, by varying particle size and porosity, should yield a wide range of aqueous silica slurries for particular chemical mechanical polishing applications. Copyright 2000 Academic Press.     

Colloidal stability of dextran-modified latex particles toward adsorption of concanavalin A

The colloidal stability of the dextran-modified poly(methyl methacrylate) (PMMA) latex particles toward adsorption of a carbohydrate-binding protein, concanavalin A (Con A), is primarily controlled by the charge neutralization mechanism. Formation of a crosslinked network structure via the specific affinity interactions between the dimeric Con A molecules and the dextran molecules anchored onto different latex particles may also have an impact on the coagulation kinetics. Judging from the data of coagulation kinetics, the colloidal stability of the latex particles toward added Con A in the decreasing order is: latex particles without dextran modification>latex particles with a dextran content of 2.15%>latex particles with a dex-tran content of 1.24% based on total polymer weight (PMMA+grafted dextran). The coagulation mechanisms involved in the adsorption of Con A onto the latex particles have been proposed to explain these experimental data. Charge neutralization of the negatively charged latex particles by adsorption of the positively charged Con A is the predominant destabilization mechanism. The ratio of the number of dextran active sites to that of Con A molecules plays an important role in the formation of the crosslinked network structure. The electrolytes in water cause a reduction in the electrostatic repulsion force among the interactive latex particles, but this ionic strength effect is not significant in comparison with charge neutralization. Received: 22 October 1997 Accepted: 24 December 1997