The simple procedure of the calculation of diffusion coefficient for adsorption on spherical and cylindrical adsorbent particles--experimental verification

A recently proposed simplified procedure for calculating the effective diffusion coefficient (D(e)) for adsorption on spherical and cylindrical adsorbent particles is now experimentally verified for adsorption systems: paracetamol-activated carbon. Adsorption kinetics was measured on nine carbons; for seven of them, measurements were taken at three temperatures. Since for adsorption on spherical adsorbent particles the approximate methods of D(e) calculation are already available in literature, only two systems have been studied, and the results of the new procedure are compared with those calculated from previously published methods. However, for cylinders the proposed method is the first simplification of this kind available in literature, thus, we focus our attention on the comparison of the results of the analytical approach with the simplified approaches for the systems where an adsorbent possesses cylindrically shaped granules. It is shown that for adsorption on spherical as well as on cylindrical adsorbent granules the proposed simplification leads to satisfactory results that, taking into account an experimental error, are practically the same as those obtained from exact time-consuming and mathematically advanced numerical fitting procedure. It is also shown that, for the studied carbons, the surface diffusion process dominates, and this explains the recently obtained correlation between the effective diffusion coefficient and the enthalpy of carbon immersion in water.     

Capillary forces between spherical particles floating at a liquid-liquid interface

We study the capillary forces acting on sub-millimeter particles (0.02-0.6 mm) trapped at a liquid-liquid interface due to gravity-induced interface deformations. An analytical procedure is developed to solve the linearized capillary (Young-Laplace) equation and calculate the forces for an arbitrary number of particles, allowing also for a background curvature of the interface. The full solution is expressed in a series of Bessel functions with coefficients determined by the contact angle at the particle surface. For sub-millimeter spherical particles, it is shown that the forces calculated using the lowest order term of the full solution (linear superposition approximation; LSA) are accurate to within a few percents. Consequently the many particle capillary force is simply the sum of the isolated pair interactions. To test these theoretical results, we use video microscopy to follow the motion of individual particles and pairs of interacting particles at a liquid-liquid interface with a slight macroscopic background curvature. Particle velocities are determined by the balance of capillary forces and viscous drag. The measured velocities (and thus the capillary forces) are well described by the LSA solution with a single fitting parameter.     

Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

粘结剂对形貌各异的石墨负极电化学性能的影响

As an important component in electrodes, the choice of an appropriate binder is significant when fabricating lithium-ion batteries (LIBs) with good cycle stability and rate capability, which are used in numerous applications, especially portable electronics and eco-friendly electric vehicles (EVs). Semi-crystalline poly(vinylidene fluoride) (PVDF), which is a traditional and widely used binder, cannot efficiently accommodate the volume changes observed in the anode during the charge-discharge process while binding all the components in the electrode together, which results in increased internal cell resistance, detachment of the electrode components, and capacity fading. Herein, we have investigated a highly polar and elastomeric polyacrylonitrile-butadiene (NBR) rubber for use as a binder in LIBs, which can accommodate graphite particles of different shapes compared to semi-crystalline PVDF. Prior to our electrochemical tests, NBR was analyzed using thermogravimetric analysis (TGA) and X-ray diffraction (XRD), showing good thermal stability and an amorphous morphology. NBR is more conformable to irregular surfaces, which results in the formation of a homogeneous passivation layer on both spherical and flaky graphite particles to effectively suppress any electrolyte side reactions, further allowing more uniform and fast Li ion diffusion at the electrolyte/electrolyte interface. As a result, the electrochemical performance of both spherical and flaky shape graphite electrodes was significantly improved in terms of their first cycle Coulombic efficiency (CE) and cycle stability. With comparative specific capacity, the first cycle CE of the NBR-based spherical and flaky graphite electrodes were 87.0% and 85.5%, compared to 85.3% and 82.6% observed for their corresponding PVDF-based electrodes, respectively. After 1000 discharge-charge cycles at 1C, the capacity retention of the NBR-based graphite electrodes was significantly higher than that of PVDF-based electrodes. This was attributed to the good stability of the solid electrolyte interphase (SEI) formed on the graphite electrodes and the high stretching ability of the elastomeric NBR binder, which help to accommodate the repeated volume fluctuation of graphite observed during long-term charge-discharge cycling. Electrochemical impedance spectroscopy (EIS) and microscopic analysis (SEM and TEM) were carried out to investigate the formation and evolution of the SEI layers formed on the spherical and flaky graphite electrodes. The results show that thin, homogeneous, and stable SEI layers are formed on the surface of both spherical and flaky graphite electrodes prepared using the NBR binder. When compared to the PVDF-based graphite electrodes, the graphite electrodes constructed using NBR showed decreased resistance in the SEI layer and faster charge transfer, thus enhancing the electrode kinetics for Li ion intercalation/deintercalation. Our study shows that the electrochemical performance of spherical and flaky graphite electrodes prepared using the NBR binder is significantly improved, demonstrating that NBR is a promising binder for these electrodes in LIBs.     

Dielectrophoretic choking phenomenon in a converging‐diverging microchannel for Janus particles

The dielectrophoretic (DEP) choking phenomenon is revisited for Janus particles that are transported electrokinetically through a microchannel constriction by a direct‐current (DC) electric field. The negative DEP force that would block a particle with a diameter significantly smaller than that of the constriction at its inlet is seen to be relaxed by the rotation of the Janus particle in a direction that minimizes the magnitude of the DEP force. This allows the particle to pass through the constriction completely. An arbitrary Lagrangian‐Eulerian (ALE) numerical method is used to solve the nonlinearly coupled electric field, flow field, and moving particle, and the DEP force is calculated by the Maxwell stress tensor (MST) method. The results show how Janus particles with non‐uniform surface potentials overcome the DEP force and present new conditions for the DEP choking by a parametric study. Particle transportation through microchannel constrictions is ubiquitous, and particle surface properties are more likely to be non‐uniform than not in practical applications. This study provides new insights of importance for non‐uniform particles transported electrokinetically in a microdevice.     

Interaction between poly(styrene-acrylic acid) latex nanoparticles and zinc oxide surfaces

Latex particles with an average diameter of 70 nm, functionalized at the surface with carboxylic groups, are chemically coated by layer-by-layer deposition onto a spherical probe attached on an atomic force microscope cantilever. The forces between poly(styrene-acrylic acid) latex nanoparticles and differently terminated zinc oxide surfaces are studied by a homemade atomic force microscope based apparatus. The results confirmed a preferred adhesion of the latex particles to zinc-terminated ZnO faces, 0001, compared to oxygen-terminated and apolar faces. The method proposed allows the measurement of the interaction between nanometric particles and planar surfaces, which may be of interest for different applications in surface and colloid sciences.     

The response of a colloidal suspension to an alternating electric field

This paper is concerned with the calculation of the complex conductivity K* of a suspension, a quantity which may be determined experimentally from the measurement of the alternating current which flows between a pair of electrodes in the suspension due to an alternating voltage difference. A semi-analytic formula is derived for the complex conductivity of a dilute suspension of spherical particles with small dielectric constant which is reasonably accurate for ?-potentials of less than 50 mV. For such suspensions this formula represents a very economical alternative to the exact computer calculation of K* described by DeLacey and White (ref. 2). Although the formula for K* is derived for particles with fixed surface charge, it is shown that the formula can also be applied to a more general class of suspensions, in which the surface charge arises from the dissociation of a single type of surface group.     

Calculation of the electric polarizability of a charged spherical dielectric particle by the theory of colloidal electrokinetics

Dielectrophoresis (DEP) is increasingly being explored as a means to manipulate or separate colloidal particles. The direction and strength of the DEP force depend strongly on the induced dipole strength, K, of a polarized particle, and predictions of DEP forces require carefully computed values for K. In this paper, we present the calculation of the dipole strength using the full electrokinetic theory of Mangelsdorf and White for both static and oscillating electric fields. The effects of particle zeta potential, radius, Debye length and electrolyte composition on the magnitude and sign of Re(K) are discussed. The full theory model is compared with the extended Maxwell-Wagner (EMW) model and the results show that the EMW model can fail to predict the full Re(K) variation with frequency, even predicting Re(K) with the incorrect sign depending on system parameters. A program for the dipole strength calculation shown in this paper is available from the authors.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

A Simple Model Incorporating the Effects of Deformation and Asperities into the van der Waals Force for Macroscopic Spherical Solid Particles

The van der Waals interaction between perfectly spherical, infinitely hard spheres is well understood. Unfortunately, real powder particles are not infinitely hard and rarely spherical. Those particles that are approximately spherical are often covered in small asperities. It is often believed that the size of these asperities dominates the cohesive force between powder particles. This paper rigorously examines this phenomenon and demonstrates the regimes over which the asperities dominate the cohesive force and when the particle size dominates. Deformation of particles is also investigated with a simple model and is shown to produce a significant increase in cohesive force. We demonstrate that previous simple models for calculating the effect of deformation are inadequate, as they ignore effects that can be as large as the correction they suggest. This can lead to an underestimation of the cohesive force by a factor of approximately 2. Copyright 2000 Academic Press.     

Square‐Wave Voltammetry of Quasi‐Reversible CE Reactions at Spherical Microelectrodes

A mathematical model for the CE mechanism in which the chemical together with the electrochemical reactions are quasi‐reversible at the surface of spherical macro and micro‐electrodes is presented for the case of square‐wave voltammetry. The analysis of voltammometric responses considers the influence of rate and equilibrium constants, together with the electrode radius, and their dependence on the square‐wave frequency (f). Both kinetics and the sphericity effect act synergistically on the electrochemical response. Also, the apparent electrode sphericity and the reversibility of the chemical as well as the electrochemical reactions are jointly affected by the variation of f. Disregarding the sphericity contribution in the calculation of kinetic parameters at a microelectrode may introduce errors even higher than one order of magnitude. The model allows the analysis of a more realistic and complex electrochemical system that requires not only the dependence of experimental responses on f, but also their fit with theoretical voltammograms, in order to provide some useful mechanistic information. Finally, concentration profiles are also studied to realize how the chemical contribution is buffering the absences of oxidized species at the electrode surface, and how those profiles are modified for the case of spherical macro and micro‐electrodes.     

孪生球状碳酸钙的直接混合沉淀法制备及表征

以醋酸钙和碳酸钠为原料, 柠檬酸三钠为晶形控制剂, 利用液相直接混合沉淀法合成了分散性好、粒度约1.5~3.0 μm、长短轴比约2∶1的孪生球形碳酸钙晶体. 利用扫描电子显微镜(SEM)、X射线衍射仪(XRD)、傅里叶红外光谱仪(FTIR)、原子力扫描探针显微镜(ASPM)和粒度分析仪等对样品进行了表征. 结果表明, 在不添加柠檬酸三钠的溶液中得到微米级的立方状碳酸钙晶体, 而添加柠檬酸三钠(质量分数30%~40%)后则得到具有不同表面粗糙度的孪生球状碳酸钙晶体. 同时, 用分形生长理论和成核限制聚集(NLA)模型对孪生球状碳酸钙粒子的形成机理进行了分析.     

球胶体颗粒之间相互作用能的求解

根据线性迭加近似方法,定义了一个修正电位项,较详细地推导出用于中等电位条件下球形胶体颗粒相互作用能和力的公式,该公式较为简单、实用,然而,对其所做的改进主要是针对相互作用能而不是力,对其原因也作了简单的讨论.     

Brownian Motion and Large Electric Polarizabilities Facilitate Dielectrophoretic Capture of Sub-200 nm Gold Nanoparticles in Water

Dielectrophoresis can move small particles using the force resulting from their polarization in a divergent electric field. In liquids, it has most often been applied to micrometric objects such as biological cells or latex microspheres. For smaller particles, the dielectrophoretic force becomes very small and the phenomenon is furthermore perturbed by Brownian motion. Whereas dielectrophoresis has been used for assembly of superstructures of nanoparticles and for the detection of proteins and nucleic acids, the mechanisms underlying DEP of such small objects require further study. This work presents measurements of the alternating-current (AC) dielectrophoretic response of gold nanoparticles of less than 200 nm diameter in water. An original dark-field digital video-microscopic method was developed and used in combination with a microfluidic device containing transparent thin-film electrodes. It was found that the dielectrophoretic force is only effective in a small zone very close to the tip of the electrodes, and that Brownian motion actually facilitates transport of particles towards this zone. Moreover, the fact that particles as small as 80 nm are still efficiently captured in our device is not only due to Brownian transport but also to an effective polarizability that is larger than what would be expected on basis of current theory for a sphere in a dielectric medium.     

An Analytical Solution to the Electrical Double Layer Potential for Spherical Particles: A Functional Theoretical Approach

Based on the Gouy-Chapman electrical double layer model, an analytical solution to the Poisson-Boltzmann equation describing the distribution of the electrical potential around spherical particles has been obtained. The advantage of this method is that it is not restricted to the Debye-Hückel approximation condition, where ze ψ ? kT. The present results compare favorably to results obtained under the ze ψ ? kT condition for spherical particles and to results obtained for the general solution for flat plate geometry. This approach provides an effective method for the iterative calculation of the electrical double layer potential for spherical particles.     

Surface modification of spherical nickel hydroxide for nickel electrodes

Electroless cobalt plating on spherical nickel hydroxide is tested in order to improve the conductivity of Ni(OH)₂ and the capacity of the electrode. The factors affecting the process of electroless cobalt plating are cobalt solution, temperature and pH, etc. The effects have been examined and the optimum process parameters have been obtained. The nickel hydroxide electrode which is made by nickel hydroxide deposited cobalt has excellent performance, the results showing that electroless cobalt plating on the surface of spherical nickel hydroxide particles is an effective method for modifying electrodes.     

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.     

Microphase separation and rheology of a semicrystalline poly(ether-ester) multiblock copolymer

A microphase separation transition (MST) of a thermoplastic elastomer based on soft segments of poly(tetra methylene oxide) and hard crystalline segments of poly(tetra methylene terephthalate) has been studied by means of rheological measurements, differential scanning calorimetry (DSC), and wide-angle X-ray scattering (WAXS), showing that the MST is entirely caused by melting/crystallization, and that no separate segmental mixing/demixing transition is involved. DSC and WAXS measurements show that melting starts at 190°C, leading to crystal reorganization effects up to above 200°C, and that a gradual decrease in crystallinity occurs from below 210°C up to 224°C, above which temperature no crystals are left. Rheological measurements reveal a wide MST (207–224°C) upon heating, which coincides perfectly with the melting range. From this coincidence together with the Maxwell fluid behavior directly following the MST, it is concluded that melting leads to a one-phase liquid, and that no separate segmental mixing transition occurs. Similar results are obtained upon cooling, indicating that crystallization is the driving force for phase separation and that no separate segmental demixing step precedes crystallization. The wide MST implies a large processing window over which the rheological properties change from highly elastic, with a distinct yield stress, to normal pseudoplastic, enabling application in preparation of structured blends. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1795–1804, 1998     

Underpotential deposition and involved alloy formation of cadmium on silver particles modified HOPG substrates

Cadmium underpotential deposition (UPD) on Ag particles modified highly ordered pyrolytic graphite (HOPG) surfaces, and the involved alloy formation were studied by conventional electrochemical techniques. Voltammetric results indicated that the Cd UPD followed an adsorption behavior different from that observed for massive Ag electrodes and Ag particles supported on vitreous carbon. Nanometer-sized bimetallic Cd–Ag particles were characterized by ex situ atomic force microscopy (AFM). Initially, AFM images show Ag deposits of similar size distributed preferably on HOPG step edges. No remarkable morphological changes are observed on the surface after the subsequent Cd deposition, suggesting that the Cd particles are deposited selectively over the Ag crystals. From the analysis of desorption spectra, employing different polarization times, and density functional theory (DFT) calculations, the formation of a Cd–Ag surface alloy could be inferred.     

Quantitative measurement of friction between single microspheres by friction force microscopy

The sliding friction between single silica microspheres was examined by applying friction force microscopy to probe the interaction between spherical silica particles glued to a tipless atomic force microscopy (AFM) cantilever and another particle glued to a glass slide. A three-dimensional model handling the complex contact geometry between spherical particles was established to compute friction and normal forces at the sliding interface from measured deflections of the AFM cantilever. Results obtained at different loads show a linear relationship between friction and normal force, with a friction coefficient of 0.4 between silica spheres. Friction in this system occurs at multi-asperity contacts. The results show that the macroscopic friction law of Amontons can be used to model the friction behavior of micrometer-sized granular matter. For plasma-treated silica particles, increased friction as well as wear could be observed during sliding.