A theoretical model of the spatial density distribution of traces in a d.c. arc

A theoretical model of the spatial particle density distribution of traces in a d.c. arc plasma is established. The basic model is grounded on realistic estimations of transport velocities which indirectly include the influence of cathode layer phenomena on the particle distribution.     

Die Fehlordnung des Natriumazides und deren Einfluß auf die thermische Zersetzung, 4. Mitt.: Über die Programmierung von Zersetzungsreaktionen mit Hilfe von Korngrößenverteilungen

It is shown that in the case of thermal decomposition of sodium azide the overall kinetics can be predicted by defined particle size of the decomposed sodium azide crystals. This is always the case if the rate constant is a function of the particle size. Hence this special example can be generalized for similar decomposition reactions. It is necessary that the particles decompose independently which could be proved experimentally with sodium azide. If for this reason we state for true that the pressure/time-function of each particle size add together it is possible to set up a formula for the pressure/time-function of any particle size distribution. With the pressure/time function holding for sodium azide of uniform particle size, the total function for a Gauß distribution can be calculated exactly. Moreover, the trivial case of one single particle size and the case of two different particle sizes are discussed. Furthermore an approximation method for any arbitrary pressure/time-functions and distribution by means of “Schwerpunktdeutung” are discussed which can be carried out graphically as well as numerically. The numerical approximation is illustrated by an example. Pressure/time-functions then loose their characteristic form because of their dependence on the particle size distributions under consideration. In this case, reaction mechanism cannot be derived from pressure/time functions.     

Axial mass transport and distribution of particles in D.C. arc plasma

A model is proposed to establish the axial distribution of added substances in an arc plasma. Particles with a higher ionization degree in the plasma are retained by the cathode. This causes a decrease in the axial transport velocity of particles newly arriving in the vicinity of the cathode. Consequently, this decrease of transport velocity causes an increase in the density of particles and their radiation density. Such an assumption is confirmed by measurement of the axial transport velocities. The theoretical consideration here is based on the works of Boumans and Krinberg and Smirnova, and takes into account the stated phenomena of decrease of axial transport velocities near the cathode. Using the results of the experimentally determined axial radiation density distribution, the axial distribution of particle transport velocities was calculated. The proposed model to establish the axial distribution of added substances contributes to the explanation of cathode layer enrichment of radiation density.     

Prediction of emulsion particle sizes using a computational fluid dynamics approach

For many food products emulsification processes play an important role. Examples are ice cream, spreads, sauces, etc. As is well known, droplet break-up and coalescence phenomena are the local processes underlying the control of particle size in an emulsion process. Quite a number of studies have generated scaling laws which can be easily applied and which are useful in the design of a process. However, the prediction of particle sizes in an inhomogeneous flow, where the flow velocity is changing spatially in strength and direction and with time, is not yet well established. For one-phase flows computational fluid dynamics (CFD) methodologies are in use to predict details on the flow with quite some success. This methodology has been extended to capture the dispersed phase in an efficient way. The essence is that break-up and coalescence processes determine source terms in a transport equation for the moments of the particle size distribution, while velocity vectors as obtained in the one-phase CFD simulation determine the convective term. This method allows particle size prediction in any equipment. The approach is illustrated for the particle size evolution of an oil-in-water emulsion, for a phase-separated biopolymeric mixture (a so-called water-in-water emulsion) and for the escape of the included oil droplets from a double emulsion of the type oil-in-water-in-oil. In all cases experimental results are compared with simulation results, which match very well. This shows the strength of the method.     

基于随机行走的二维空间扩散模拟研究

分子的扩散行为是微观化学的重要研究领域. 影响扩散行为的因素很多,但是目前各个因素的具体影响效果还不明确. 作者基于随机行走理论建立了分子在二维空间的扩散模型,依据此模型自主开发了模拟软件以及数据分析系统,并利用该模拟软件系统研究了势垒尧横向速度等因素对扩散行为的影响,验证了该模型的可靠性,证明根据该模型可以得到和实验尧理论相吻合的结果. 该软件有望成为模拟微观化学扩散行为的潜在平台,如电化学以及膜过滤过程中的扩散.     

Transport coefficients and orientational distributions of spheroidal particles with magnetic moment normal to the particle axis (Analysis for an applied magnetic field normal to the shear plane)

We have investigated the influence of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. The rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the shear flow direction for a very strong magnetic field, such a peak is not restricted to the field direction alone, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.     

Particle Growth during the Polymerization of Olefins on Supported Catalysts. Part 2: Current Experimental Understanding and Modeling Progresses on Particle Fragmentation,Growth, and Morphology Development

The morphology of the growing polymer particles is important in olefin polymerisation on supported catalysts. It has a significant impact on the rate of mass and energy transport, and consequently on the polymerisation rate, comonomer incorporation, and the molecular weight distribution. The ability to quantify the evolution of morphology during the polymerisation process à priori would therefore be quite useful. The morphology itself is a direct product of the fragmentation step and concurrent/subsequent expansion of the particle, both caused by the build‐up and dissipation of hydraulic forces due to the accumulation of polymer in the particle. It is influenced by the initial morphology of the support, as well as the reaction conditions and local polymer properties. The single particle models developed to describe the morphology evolution in a growing particle are reviewed here. The main assumptions, abilities, and limitations of the models are evaluated and the issues which face developing a completely predictive model are finally discussed. Despite some very interesting attempts at morphology modelling in recent years, significant progress still needs to be made in order to develop a fully predictive model of the sort.     

Super-Monte Carlo: A photon/electron dose calculation algorithm for radiotherapy

Super-Monte Carlo (SMC) is a method of dose calculation for radiotherapy which combines both analytical calculations and Monte Carlo electron transport. Analytical calculations are used where possible, such as the determination of photon interaction density, to decrease computation time. A Monte Carlo method is used for the electron transport in order to obtain high accuracy of results. To further speed computation, Monte Carlo is used once only, to form an electron track kernel (etk). The etk is a dataset containing the lengths and energy deposition of each step of a number of electron tracks. The etk is transported from each incident particle interaction site, from which the dose is calculated. Dose distributions calculated in heterogeneous media show SMC results similar to those of Monte Carlo. For the same statistical uncertainty, SMC takes an order of magnitude less computation time than a full Monte Carlo simulation. SMC has only been implemented for photons and electrons, however the same basic method could be used for the transport of other particles. Current development includes the optimisation of the etks and the code in order to decrease computation time, and also the inclusion of SMC onto a clinical planning system.     

Diffusiophoretic mobility of charged porous spheres in electrolyte gradients

The diffusiophoretic motion of a polyelectrolyte molecule or charged floc in an unbounded solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is analytically studied. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration distributions (or electrochemical potential energies), and the fluid velocity field inside and outside the porous particle are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a charged porous sphere with the density of the fixed charges as the small perturbation parameter. An analytical expression for the diffusiophoretic mobility of the charged porous sphere in closed form is obtained from a balance between its electrostatic and hydrodynamic forces. This expression, which is correct to the second order of the fixed charge density of the particle, is valid for arbitrary values of kappaa and lambdaa, where kappa is the reciprocal of the Debye screening length, lambda is the reciprocal of the length characterizing the extent of flow penetration inside the particle, and a is the particle radius. Our result to the first order of the fixed charge density agrees with the corresponding solution for the electrophoretic mobility obtained in the literature. In general, the diffusiophoretic mobility of a porous particle becomes greater as the hindrance to the diffusive transport of the solute species inside the particle is more significant.     

Subdiffusion as a model of transport through the nuclear pore complex

Cargo transport through the nuclear pore complex continues to be a subject of considerable interest to experimentalists and theorists alike. Several recent studies have revealed details of the process that have still to be fully understood, among them the apparent nonlinearity between cargo size and the pore crossing time, the skewed, asymmetric nature of the distribution of such crossing times, and the non-exponentiality in the decay profile of the dynamic autocorrelation function of cargo positions. In this paper, we show that a model of pore transport based on subdiffusive particle motion is in qualitative agreement with many of these observations. The model corresponds to a process of stochastic binding and release of the particle as it moves through the channel. It suggests that the phenylalanine-glycine repeat units that form an entangled polymer mesh across the channel may be involved in translocation, since these units have the potential to intermittently bind to hydrophobic receptor sites on the transporter protein.     

A rotating disk electrode study of the particle size effects of Pt for the hydrogen oxidation reaction

By using a catalyst-lean thin-film RDE method, the fast kinetics of the hydrogen oxidation reaction (HOR) on highly dispersed Pt nanoparticle electrocatalysts can be determined, free from the interference of the mass transport of H(2) molecules in solution. Measurements with carbon-supported Pt nanoparticles of different sizes thus allow revealing the particle size effect of Pt for the HOR. It is shown that there is a "negative" particle size effect of Pt on the kinetics of HOR, i.e., the exchange current density j(0) decreases with the increased dispersion (i.e. decreased mean particle size). A maximum mass activity of Pt for the HOR is found at particle sizes of 3-3.5 nm. The observed particle size effect is interpreted in terms of the size dependent distribution of surface atoms on the facets and edges, which is implied by the voltammetric responses of Pt/C catalysts with differently sized Pt particles. The accompanied decrease in the HOR activity with the increase in the edge atom fraction suggests that the edge atoms on the surface of Pt nanoparticles are less active for the HOR than those on the facets.     

Switching between laser-induced thermophoresis and thermal convection of liquid suspension in a microgap with variable dimension

Phoretic motion of particles along a temperature gradient formed in a fluid, known as thermophoresis, often takes place under the influence of bulk motion caused by thermal convection. In this paper, using a laser heating method, the significance of two competing effects, that is, thermophoresis and thermal convection, for the particle transport in a liquid phase confined in a microgap is investigated experimentally by changing the gap size as a control parameter. It is found that there is a threshold of the gap size, above which the particles tend to accumulate around the heated spot, forming a ring-like particle distribution. On the contrary, if the gap size is below the threshold, the particles are depleted from the heated spot. Switching between these accumulation and depletion modes is expected to develop novel manipulation techniques.     

A general gel layer model for the transport of colloids and macroions in dilute solution

A general boundary element methodology for studying the dilute solution transport of rigid macroions that contain gel layers on their outer surfaces is developed and applied to several model systems. The methodology can be applied to particles of arbitrary size, shape, charge distribution, and gel layer geometry. Account is also taken of the steady state distortion of the ion atmosphere from equilibrium, which makes it applicable to the transport of highly charged structures. The coupled field equations (Poisson, ion-transport, low-Reynolds-number Navier-Stokes, and Brinkman) are solved numerically and from this, transport properties (diffusion constants, electrophoretic mobilities, excess viscosities) can be computed. In the present work, the methodology is first applied to a gel sphere model over a wide range of particle charge and the resulting transport properties are found to be in excellent agreement with independent theory under those conditions where independent theory is available. It is then applied to several prolate spheroidal models of a particular silica sol sample in an attempt to identify possible solution structures. A single model, that is able to account simultaneously for all of the transport behavior, which does not undergo significant conformational change with salt concentration, could not be found. A model with a thin (相似文献   

Two-dimensional Monte Carlo simulations of a colloidal dispersion composed of rod-like ferromagnetic particles in the absence of an applied magnetic field

Influences of the magnetic interaction between particles and the aspect ratio of particles on aggregate structures in a colloidal dispersion composed of rod-like ferromagnetic particles were investigated by means of the cluster-moving Monte Carlo method. The internal structures of the aggregates obtained in simulations were analyzed in terms of the number density distribution of the clusters and radial distribution functions. The results show that as the magnetic interaction between particles increases, many small clusters such as anti-parallel particle pairs, raft-like clusters, and small loop-like clusters are formed; these gather to form larger aggregates. In the case of a relatively strong magnetic interaction between particles, solid-like rectangular clusters are formed when the aspect ratio is approximately 2, since the suitable distance between magnetic charges enables particles to form a fundamental structure of two normal anti-parallel particle pairs. As the aspect ratio increases beyond 2, many more stable raft-like clusters are formed, since the increase in distance between magnetic charges makes the two normal anti-parallel particle pair structures unstable. For a significantly larger aspect ratio, large network microstructures are produced by the formation of many chain-like and loop-like structures.     

Molecular weight distribution in emulsion polymerization. II. The copolymer case

A model for evaluating instantaneous degree of polymerization distribution and the chain composition distribution of copolymers produced in emulsion is developed. The approach adopted is based on the mathematics of Markov processes and represents an extension of the one developed for homopolymers in Part I. As in the homopolymer case, the main aspect of the theoretical treatment is the definition of the proper one step transition probability matrix through the so called subprocess-main process procedure. The model accounts for monomolecular and bimolecular termination (both by combination and disproportionation) and, in principle, it can be applied to any number of reacting monomer species as well as to any number of active chains per particle. However, only the 0–1–2 and 0–1–2–3 emulsion copolymerization systems are discussed in detail. In the case of the chain composition distribution, the model allows the calculation of its moments only, through the method of the Generating Function associated with the probability density function. The expression obtained for the instantaneous probability density functions, as well as for the corresponding cumulative distributions, are all in explicit form and involve only algebraic operations among matrices. Efficient numerical procedure for their application are reported in the Appendix. Illustrative calculations are reported for a 0–1–2–3 copolymerization system, simulating the copolymer styrene–methylmethacrylate. The effect of the various termination mechanisms on the distribution of degrees of polymerization and on the first two moments of the chain composition distribution is discussed in detail. Finally, the three dimensional overall distribution function of both chain length and composition is shown under the assumption of Gaussian type chain composition distribution.     

Sedimentation analysis using a magnetic fluid

An improved sedimentation method for analyzing particle size distribution is described. The method is primarily distinguished by the application of a magnetic fluid as a medium in which particles move. This circumstance makes it possible to measure particle velocities and sizes with magnetic sensors. The theory of the method and experimental data are discussed.     

The peculiarities of homogeneous nucleation of reactive Cu0 colloidal particles in the presence of functional oligoperoxides

A method is proposed that combines the stage of formation of colloidal metal and metal-oxide particles with the stage of their surface modification by functional surface-active oligoperoxides (FSAP), which are sorbed irreversibly. Investigation of copper particle homogeneous nucleation kinetics witnesses the significant influence of supermolecular micelle-like structures formed by FSAP in solution on the reduction rate of Cu2+ cations caused by a phenomenon analogous to micellar catalysis. The rate constants of copper reduction in different local zones of the process have been determined. Particle homogeneous nucleation kinetics in the presence of surface-active oligoperoxides has been found to correspond to the main regularities of the Michaelis-Menten equation describing micellar catalysis. The carrying out of copper particle formation in distinct zones correlates well with the particle size distribution. The presence of reactive ditertiary peroxidic fragments on the particle surface as a result of FSAP sorption confers reliable protection from oxidation, hydrophobicity, and ability to form free radicals and participate in elementary stages of radical processes.     

Brownian Coagulation of Fractal Agglomerates: Analytical Solution Using the Log-Normal Size Distribution Assumption

An analytical solution to Brownian coagulation of fractal agglomerates in the continuum regime that provides time evolution of the particle size distribution is presented. The theoretical analysis is based on representation of the size distribution of coagulating agglomerates with a time-dependent log-normal size distribution function and employs the method of moments together with suitable simplifications. The results are found in the form that extends the spherical particle solution previously obtained by K. W. Lee (J. Colloid Interface Sci. 92, 315-325 (1983)). The results show that the mass fractal dimension has a significant effect on the size distribution evolution during coagulation. When the obtained solution was compared with numerical results, good agreement was found. The self-preserving size distribution of nonspherical agglomerates is discussed. Copyright 2000 Academic Press.     

Evaluation of the Chain Length Distribution in Free‐Radical Polymerization, 1. Bulk Polymerization

A method for the direct computation of the chain length distribution in a bulk polymerization is developed, based on the discretization procedure introduced by Kumar and Ramkrishna (Chem. Eng. Sci. 1996 , 51, 1311) in the context of particle size distribution. The overall distribution of chain lengths is partitioned into a finite number of classes which are supposed to be concentrated at some appropriate pivotal chain lengths. Several of the involved reactions lead to the formation of chain whose length differs from the pivotal values. Rules have been introduced in order to share chains between two contiguous classes, which have been designed so as to preserve two well‐defined properties of the distribution, such as, for example, two of its moments. The method has been applied to a polymerization system including propagation, bimolecular terminations and two different chain branching mechanisms: chain transfer to polymer and crosslinking. In addition, complex systems such as one with chain length‐dependent kinetic constants or a two‐dimensional distribution of chain length and number of branches have been considered.     

Measurement of particle size distribution in the discrete phase of high-impact polystyrene. I. Errors in direct coulter counter techniques

The published Coulter Counter method for measuring particle size distribution of the discrete phase in rubber-modified polystyrene is shown to be subject to serious limitations, especially when the data generated are used to compute discrete phase volume fractions. The source of error is time-dependent swelling of the particles in DMF which is used to isolate them from the polystyrene matrix for the counting operation.