The effect of pH on aggregation kinetics of monodisperse silica sol in naCl solutions

The aggregation kinetics of monodisperse silica sols with a particle size of 220 nm in aqueous NaCl solutions is studied by flow ultramicroscopy in a pH range of 2.0–10.2. Slow coagulation of the sols is found to occur via the barrierless mechanism in the secondary potential minimum resulting from the summation of dispersion attractive and structural repulsive forces. The influence of pH and NaCl concentration on the parameters of the structural component of the energy of the interaction between SiO₂ particles is demonstrated.     

Influence of the Secondary Interaction Energy Minimum on the Early Stages of Colloidal Aggregation

The pair interaction energy of charged colloidal particles in electrolyte solutions can exhibit a large barrier as well as a pronounced secondary minimum. We discuss the effect of a secondary energy minimum on aggregation kinetics by modeling irreversible dimer formation as a two-step process in which charged colloidal particles in electrolyte solutions first aggregate reversibly into the secondary minimum before they can cross the energy barrier. In the classical regime of slow aggregation, the secondary minimum is seen to have a pronounced effect if either the ionic strength of the solution is high (e.g., 0.1 M for particles of 150-nm radius) or particles are large (>/=350-nm radius for an ionic strength of 0.01 M). Under these conditions, our calculations predict a transient period of fast aggregation into the secondary minimum followed by slow primary aggregation. The aggregation in this second regime is found to take place at a lower rate than what would be expected in the absence of the secondary minimum or from an earlier linearized model for secondary aggregation. The crossover time between the two regimes strongly depends on the particle size but not on the particle concentration, which however determines the degree of aggregation reached within the fast regime. We also conclude that a previously observed severe discrepancy between measured and predicted aggregation rate constants for submicron particles is not due to the neglect of secondary aggregation in the theoretical treatment. Copyright 2000 Academic Press.     

The Effect of Composition of Water-Ethanol Solutions on Coagulation Kinetics of Amorphous Monodisperse Silica Suspensions

The effect of the composition of water-ethanol solutions on the coagulation kinetics of dilute amorphous monodisperse silica suspensions is studied using flow ultramicroscopy technique. It is found that the suspensions prepared by the addition of an aliquot of concentrated and stored for more than 20 days suspension of the aforementioned silica in 96% ethanol to water-ethanol mixtures containing 96–80 vol % of ethanol are stable with respect to aggregation. A decrease in the alcohol concentration in a system leads to an ultrafast coagulation, whose characteristic time (coagulation period) is much smaller than the value corresponding to the Smoluchowski theory of fast coagulation. It is established that the highest coagulation rate is observed for the suspensions containing 40 vol % of ethanol. Mechanisms of the aggregation stability and ultrafast coagulation of the studied suspensions are discussed.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 475–478.Original Russian Text Copyright © 2005 by Zhukov, Zavarovskaya, Chernoberezhskii.     

Theoretical Analysis of Coagulation Kinetics in Brownian Disperse Systems

Analytical solution to the system of differential equations describing the coagulation kinetics in Brownian dilute disperse systems is obtained. The effect of the reversibility of aggregation in the secondary minimum on the coagulation kinetics in the primary minimum is analyzed. It is shown that experimental conditions can substantially affect the theoretical interpretation of experimental data.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 3, 2005, pp. 381–391.Original Russian Text Copyright © 2005 by Mishchuk.     

The model of cage reactions proceeding through the metastable term

A model of cage reactions in the solid state is examined in which the Franck-Condon prohibition is overcome by crossing two parabolic terms of the same curvature. Since the final term is considered to be of short half life, its width is significant and there exists a transition probability. The effects on the reaction kinetics by the Markovian migration over the initial terms modulating resonance detuning and therefore the transition probability has been studied (the interaction is considered to be independent of the reaction coordinate). The case where the point of term crossing coincides with the minimum of the initial term is examined in detail. The reaction kinetics passes three stages with increasing migration frequency. The process develops non-exponentially in the slowest, quasi-static stage. The reaction kinetics and rate depend on the manner of migration in the migration-accelerated stage. Only in the kinetic stage when the migration is very fast does the traditional quasi-classical theory of electron migration hold which implies exponential reaction kinetics with the rate being independent of the energy migration.     

Thermodynamic Characteristics of a Spherical Molecular Surfactant Aggregate in a Quasi-Droplet Model

The model of spherical molecular aggregate of nonionic surfactant is proposed. This model allows for the maximal (in accordance with packing rules) penetration of water molecules into an aggregate and is an alternative to the droplet model of molecular aggregate. Necessary conditions for the applicability of a model named quasi-droplet model are formulated. Based on this model, the dependence of the work of molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that plays the key role for the theory of micellization is studied. The equation is derived for the coordinates of maximum and minimum of aggregate formation work on the aggregation number axis arising with an increase in the concentration of micellar solution. Model calculations of the thermodynamic characteristics of the kinetics of micellization are performed. The approximation of the work of molecular aggregate formation allowing for the analytical study is constructed.     

Analysis of the aggregation-fragmentation population balance equation with application to coagulation

Coagulation of small particles in agitated suspensions is governed by aggregation and breakage. These two processes control the time evolution of the cluster mass distribution (CMD) which is described through a population balance equation (PBE). In this work, a PBE model that includes an aggregation rate function, which is a superposition of Brownian and flow induced aggregation, and a power law breakage rate function is investigated. Both rate functions are formulated assuming the clusters are fractals. Further, two modes of breakage are considered: in the fragmentation mode a particles splits into w2 fragments of equal size, and in the erosion mode a particle splits into two fragments of different size. The scaling theory of the aggregation-breakage PBE is revised which leads to the result that under the negligence of Brownian aggregation the steady state CMD is self-similar with respect to a non-dimensional breakage coefficient theta. The self-similarity is confirmed by solving the PBE numerically. The self-similar CMD is found to deviate significantly from a log-normal distribution, and in the case of erosion it exhibits traces of multimodality. The model is compared to experimental data for the coagulation of a polystyrene latex. It is revealed that the model is not flexible enough to describe coagulation over an extended range of operation conditions with a unique set of parameters. In particular, it cannot predict the correct behavior for both a variation in the solid volume fraction of the suspension and in the agitation rate (shear rate).     

Kinetics of the Photodimerization of Anthracene in an Inhomogeneous Polymer Matrix

The photodimerization of anthracene in polyethylene was investigated. It was shown that the kinetics of photodimerization are not described in terms of nonstationary diffusion. A method is proposed for determining the probability of the existence a volume of inhomogeneous polymer layer with a specific diffusion coefficient of the impurity anthracene molecule. An equation describing the kinetics of photodimerization is derived, and the limiting values of the diffusion coefficient (minimum and maximum) are obtained. A probability distribution for the existence of regions of polymer layer with diffusion coefficient between D and D + dD is also obtained.     

The Effect of Composition of Water–Ethanol Solutions on the Kinetics of Coagulation of Fused Quartz Suspensions

The effect of composition of water–ethanol solutions containing 0–96 vol % alcohol on the coagulation kinetics of dilute fused quartz suspensions is studied using flow ultramicroscopy technique. It is established that, in both water and ethanol containing 4 vol % water, freshly prepared quartz suspensions are stable with respect to aggregation; at ethanol concentrations from 10 to 90 vol %, an ultrafast coagulation takes place, with characteristic time (coagulation period) being essentially smaller compared to a value corresponding to the Smoluchowski theory of fast coagulation kinetics. It was shown that the aging of the aforementioned suspensions for more than 24 h results in slow coagulation at high and low alcohol content, but its ultrafast character is retained in the ethanol concentrations range of 40–48 vol %. The probable reasons for the ultrafast coagulation in the disperse systems specified are discussed.     

半结晶聚合物注射成型中结晶动力学的数值模拟

对半结晶聚合物注射成型过程及其结晶过程进行偶合模拟,分析了二者的相互影响.具体是在注射成型数值模拟中考虑结晶动力学效应,分别在本构方程、能量方程及材料物性参数方程中引入反映结晶效应的参数;同时在结晶动力学计算中考虑流动诱导效应,从能量的角度提出并使用修正的动力学模型,用材料流动过程的耗散能表征流动对结晶的影响.通过对等规聚丙烯(iPP)和聚对苯二甲酸乙二醇酯(PET)两种半结晶聚合物注射过程模拟结果的分析比较,证实成型过程具有加速结晶的作用.同时,材料的结晶也对注射成型加工过程,尤其是保压与冷却过程的温度场分布有较大的影响.     

Nanoparticle dynamics: a multiscale analysis of the Liouville equation

A theory of nanoparticle dynamics based on scaling arguments and the Liouville equation is presented. We start with a delineation of the scales characterizing the behavior of the nanoparticle/host fluid system. Asymptotic expansions, multiple time and space scale techniques, the resulting coarse-grained dynamics of the probability densities of the Fokker-Planck-Chandrasekhar (FPC) type for the nanoparticle(s), and the hydrodynamic models of the host medium are obtained. Collections of nanoparticles are considered so that problems such as viral self-assembly and the transition from a particle suspension to a solid porous matrix can be addressed via a deductive approach that starts with the Liouville equation and a calibrated atomic force field, and yields a generalized FPC equation. Extensions allowing for the investigation of the rotation and deformation of the nanoparticles are considered in the context of the space-warping formalism. Thermodynamic forces and dissipative effects are accounted for. The notion of configuration-dependent drag coefficients and their implications for coagulation and consolidation are shown to be natural consequences of the analysis. All results are obtained via formal asymptotic expansions in mass, size, and other physical and kinetic parameter ratios.     

Simple analytic solution of the rate equations for the early-stage aggregation kinetics of colloidal particles

The potential energy of the interaction between two approaching colloidal particles obtained by the DLVO theory can exhibit a maximum, a primary minimum, and a secondary minimum on the potential curve of the interparticle interaction energy. Behrens and Borkovec (J Colloid Interface Sci 225: 460, 2000) considered a set of coupled nonlinear differential rate equations for the early-stage aggregation kinetics of colloidal particles by taking into account the influence of the secondary minimum and derived an approximate solution to the rate equations as well as their exact numerical solutions. In the present article, an improved simple analytic solution is derived for these rate equations. The obtained solution, which involves two distinct (fast and slow) exponentially decay constants, is found to be in excellent agreement with numerical solutions to the rate equations with negligible errors.     

The effect of preparation procedure and composition of water-ethanol suspensions of amorphous silica on their aggregative stability and kinetics of coagulation

The method of flow ultramicroscopy is employed to study the effect of the composition and preparation procedure of dilute water-ethanol suspensions of two samples of amorphous silica (fractionated fused quartz and monodisperse amorphous silica) on the kinetics of their coagulation. It is revealed that all suspensions prepared by the addition of silica powders to water-ethanol mixtures with ethanol contents of 96 and 40 vol % are stable with respect to aggregation, as the suspensions prepared by the addition of aliquots of concentrated dispersions of the aforementioned silica samples in 96% ethanol aged for different time periods to water-ethanol mixtures containing 96 vol % ethanol. At a 40-vol % content of ethanol in the mixture, the coagulation whose character (including “superfast” coagulation) substantially depends on the time of aging of initial concentrated silica dispersions occurs. Furthermore, kinetic studies are performed for the coagulation of dilute silica suspensions prepared by the addition of silica powders to water-ethanol solutions containing 40 vol % of ethanol and traces (<1 ppm) of poly(ethoxysilane), poly(acrylic acid), and a supernatant prepared by the centrifugation of concentrated silica dispersion in 96% ethanol aged for more than 3 months. It is found that the addition of aliquots of the aforementioned ethanol solutions to silica suspensions in 40% ethanol, which are initially stable with respect to aggregation, causes their superfast coagulation.     

On hydrodynamic permeability of a membrane built up by porous deformed spheroidal particles

This paper concerns the slow viscous flow of an incompressible fluid past a swarm of identically oriented porous deformed spheroidal particles, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid region in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in a small parameter characterizing the deformation. The flow through the porous oblate spheroid is considered as the particular case of the porous deformed spheroid. The hydrodynamic drag force experienced by a porous oblate spheroid and permeability of a membrane built up by porous oblate spheroids having parallel axis are evaluated. The dependence of the hydrodynamic drag force and the hydrodynamic permeability on particle volume fraction, deformation parameter and viscosity of porous fluid are also discussed. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and hydrodynamic permeability have been verified. The model suggested can be used for evaluation of changing hydrodynamic permeability of a membrane under applying unidirectional loading in pressure-driven processes (reverse osmosis, nano-, ultra- and microfiltration).     

Theoretical studies of the early stage coagulation kinetics for a charged colloidal dispersion

We study the early stage coagulation kinetics for a charged colloidal dispersion which is here modeled by an effective two-body colloid-colloid potential. The colloidal system was physically prepared by choosing sets of colloidal parameters varying in particular the Hamaker constant and the particle's size. The kinetics of coagulation process was driven by the addition of an indifferent electrolyte and assumed to proceed in two quasi-steady steps. In the first step, colloidal particles are destabilized by the presence of a second potential minimum to diffuse from a bulk-stabilized liquid phase to a flocculated phase. In the second step, we assume that different entities are found in the second potential minimum. The entities comprise secondary dimers, secondary dimers undergoing redispersion, and monomers still in singlet states. If, under favorable condition, this kind of interaction-driven diffusive motion continues, a fraction of the secondary dimers will be induced to undergo primary dimers formation in the first deep minimum. Whether or not the latter process occurs is determined either energetically by the potential barrier falling below a prescribed value, say of 15k(B)T, or/and the second potential minimum becoming negligibly small (with a magnitude coagulation transition and would throw a fresh light on the use of both the energy and the kinetic criteria for understanding the colloidal stability such as those observed in the liquid-liquid coexistence.     

Aggregation kinetics of OX50 hydrosols in NaCl solutions studied by dynamic light scattering

The aggregation kinetics of OX50 sols in aqueous NaCl solutions (10^–4–2 × 10^–1 M) has been studied for 15 days or more by dynamic light scattering. The following set of characteristics has been considered to quantitatively estimate the coagulation intensity in the disperse systems: the particle size corresponding to the maximum in the differential particle size distribution curve, the height of the maximum, the polydispersity index, and the average diameter of the intensity distribution. It has been found that slow sol coagulation proceeds via the barrierless mechanism in secondary potential minimum, which arises from the predominance of the dispersion attractive forces over structural and electrostatic repulsive forces.     

A master equation investigation of coagulation reactions: Sol-gel transition

The kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration-dependent reaction kernels, K_ij = (ij)^ω, for clusters of mass i and j with 1/2 < ω ⩽ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol-gel transition.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Effect of pH on the Aggregation Stability of Microcrystalline Cellulose Dispersions in Aqueous 0.1 M NaCl Solutions

Effect of pH on the coagulation kinetics of microcrystalline cellulose dispersions in an aqueous 0.1 M NaCl solution is studied by the flow ultramicroscopy. The lowest coagulation rate is observed at pH 4.9. A decrease or an increase in pH gives rise to the coagulation rate approaching the rate of fast coagulation (according to Smoluchowski) at pH 1.0. Results of calculating the particle pair interaction energy in terms of the DLVO theory with allowance for only the molecular and ion electrostatic components suggest the dominance of attraction forces at any interparticle distances and cannot explain the data of experimental methods. The allowance for the structural component, which arises upon the overlap of water boundary layers surrounding hydrophilic particles of microcrystalline cellulose, makes it possible to treat the experimental results and estimate possible values of the K andl parameters of the equation for the structural component.     

Kinetics of the liquid-phase hydrochlorination of methanol

The kinetics of the liquid-phase hydrochlorination of methanol with hydrogen chloride in the absence of a catalyslt is reported. A kinetic equation is suggested for the reaction. The values of the preexponential factor, activation energy, and empiric coefficients characterizing the influence of the hydration of the chlorine anion on the rate of hydrochlorination have been.