椭球形粒子扩散动力学的研究进展

椭球形粒子作为一类重要的各向异性粒子,在生物、化工以及材料等领域有着广泛的应用。对椭球形粒子的扩散动力学进行深入地研究,不仅可以增进人们对各向异性粒子扩散动力学中基本科学问题的理解,而且可以为含各向异性粒子材料的设计与加工提供理论依据。因此,椭球形粒子的扩散问题一直是粒子扩散研究的焦点。虽然椭球形粒子扩散动力学的研究已经有一百多年的历史,其相关理论、实验和模拟研究工作很多,并取得了较大的进展,但是,系统的综述性文章相对较少。本文系统地总结了椭球形粒子扩散动力学的相关工作,包括:不同流体力学边界条件下椭球形粒子的扩散动力学和平动与转动扩散的耦合行为等。此外,本文还分析了椭球形粒子扩散动力学领域存在的关键科学问题,并对该领域研究方向进行了展望。     

Montmorillonite alignment induced by magnetic field: evidence based on the diffusion anisotropy of water molecules

Diffusion coefficients of water in Na-montmorillonite (Na-mon) suspensions have been determined by pulsed-field gradient spin-echo (PGSE) NMR spectroscopy for three directions (x, y, and z), where x and y mean the directions perpendicular to the static magnetic field, and z the direction parallel to it. Diffusion anisotropy was observed in the suspensions with Na-mon weight fractions of 0.63, 1.82, and 3.32%; i.e., the diffusivity of water in the z direction is faster than that in the x or y direction. The largest diffusion anisotropy of water was observed at the Na-mon fraction of 3.32%. However, diffusion anisotropy disappeared in the suspensions with Na-mon fraction more than 5.02%. The fast diffusivity in the z direction was slightly enhanced in a stronger static magnetic field (14.1 T). These results indicate that the platelike Na-mon particles are aligned with their platelike faces parallel to the static magnetic field of NMR. We also measured diffusion coefficients of water for the z direction in the temperature range from 24 to 85 degrees C. The plot of diffusion coefficients of water against reciprocal temperature showed a refraction point at 65 degrees C. This phenomenon explicitly means that the alignment is gradually relaxed at higher temperatures.     

Anisotropic magnetoresistance and piezoresistivity in structured Fe3O4-silver particles in PDMS elastomers at room temperature

Magnetorheological elastomers, MREs, based on elastic organic matrices displaying anisotropic magnetoresistance and piezoresistivity at room temperature were prepared and characterized. These materials are dispersions of superparamagnetic magnetite forming cores of aggregated nanoparticles inside silver microparticles that are dispersed in an elastomeric polymer (poly(dimethylsiloxane), PDMS), curing the polymer in the presence of a uniform magnetic field. In this way, the elastic material becomes structured as the application of the field induces the formation of filaments of silver-covered inorganic material agglomerates (needles) aligned in the direction of the field (parallel to the field). Because the magnetic particles are covered with silver, the MREs are not only magnetic but also electrical conductors. The structuration induces elastic, magnetic, and electrical anisotropic properties. For example, with a low concentration of particles in the elastic matrix (5% w/w) it is possible to obtain resistances of a few ohms when measured parallel to the needles or several megaohms in the perpendicular direction. Magnetite nanoparticles (Fe(3)O(4) NP) were synthesized by the coprecipitation method, and then agglomerations of these NPs were covered with Ag. The average size of the obtained magnetite NPs was about 13 nm, and the magnetite-silver particles, referred to as Fe(3)O(4)@Ag, form micrometric aggregates (1.3 μm). Nanoparticles, microparticles, and the MREs were characterized by XRD, TEM, SEM, EDS, diffuse reflectance, voltammetry, VSM, and SQUID. At room temperature, the synthesized magnetite and Fe(3)O(4)@Ag particles are in a superparamagnetic state (T(B) = 205 and 179 K at 0.01 T as determined by SQUID). The elastic properties and Young's modulus of the MREs were measured as a function of the orientation using a texture analysis device. The magnetic anisotropy in the MRE composite was investigated by FMR. The electrical conductivity of the MRE (σ) increases exponentially when a pressure, P, is applied, and the magnitude of the change strongly depends on what direction P is exerted (anisotropic piezoresistivity). In addition, at a fixed pressure, σ increases exponentially in the presence of an external magnetic field (H) only when the field H is applied in the collinear direction with respect to the electrical flux, J. Excellent fits of the experimental data σ versus H and P were achieved using a model that considers the intergrain electron transport where an H-dependent barrier was considered in addition to the intrinsic intergrain resistance in a percolation process. The H-dependent barrier decreases with the applied field, which is attributed to the increasing match of spin-polarization in the silver covers between grains. The effect is anisotropic (i.e., the sensitivity of the magnetoresistive effect is dependent on the relative orientation between H and the current flow J). In the case of Fe(3)O(4)@ Ag, when H and J are parallel to the needles in the PDMS matrix, we obtain changes in σ up to 50% for fields of 400 mT and with resistances on the order of 1-10 Ω. Magnetoresistive and magnetoelastic properties make these materials very interesting for applications in flexible electronics, electronic skins, anisotropic pressure, and magnetic field sensors.     

Branched networks by directed assembly of shape anisotropic magnetic particles

The directed assembly of shape anisotropic magnetic particles into targeted macrostructures requires judicious particle design. We present a framework to understand the self-assembly of magnetic non-Brownian H-shaped particles and the formation of branched networks under an applied magnetic field. A finite element integration (FEI) method is developed to identify the preferred particle orientation (relative to the applied field) at different values of the geometric parameters defining H shapes, and used to construct a phase diagram to generalize the results. Theoretical predictions are validated by comparing with experiments performed using magnetic hydrogels synthesized using stop-flow lithography (SFL). We demonstrate the ability of H-shaped particles to form chains parallel to the field that can thicken in a direction orthogonal to the field, and in some cases with branching. The assembly of a suspension containing H-shaped particles, or rods, or a combination of both, is reported.     

Transport coefficients and orientational distributions of rodlike particles with magnetic moment normal to the particle axis under circumstances of a simple shear flow

We have investigated the influences of the magnetic field strength, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. This dispersion is composed of ferromagnetic spheroidal particles with a magnetic moment normal to the particle axis. In the present analysis, these spheroidal particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the rodlike particle is significantly restricted in the field direction, so that the particle points to a direction normal to the flow direction (and also to the magnetic field direction). However, the present particle does not exhibit a strong directional characteristic, which is one of the typical properties for the previous particle with a magnetic moment parallel to the particle axis. That is, the particle can rotate around the axis of the magnetic moment, although the magnetic moment nearly points to the field direction. The viscosity significantly increases with the field strength, as in the previous particle model. The particle of a larger aspect ratio leads to the larger increase in the viscosity, since such elongated particles induce larger resistance in a flow field. The diffusion coefficient under circumstances of an applied magnetic field is in reasonable agreement between theoretical and experimental results.     

Structural properties of charge-stabilized ferrofluids under a magnetic field: a Brownian dynamics study

We present Brownian dynamics simulations of real charge-stabilized ferrofluids, which are stable colloidal dispersions of magnetic nanoparticles, with and without the presence of an external magnetic field. The colloidal suspensions are treated as collections of monodisperse spherical particles, bearing point dipoles at their centers and undergoing translational and rotational Brownian motions. The overall repulsive isotropic interactions between particles, governed by electrostatic repulsions, are taken into account by a one-component effective pair interaction potential. The potential parameters are fitted in order that computed structure factors are close to the experimental ones. Two samples of ferrofluid differing by the particle diameter and consequently by the intensity of the magnetic interaction are considered here. The magnetization and birefringence curves are computed: a deviation from the ideal Langevin behaviors is observed if the dipolar moment of particles is sufficiently large. Structure factors are also computed from simulations with and without an applied magnetic field H: the microstructure of the repulsive ferrofluid becomes anisotropic under H. Even our simple modeling of the suspension allows us to account for the main experimental features: an increase of the peak intensity is observed in the direction perpendicular to the field whereas the peak intensity decreases in the direction parallel to the field.     

Forming chainlike filaments of magnetic colloids: the role of the relative strength of isotropic and anisotropic particle interactions

The influence of the interplay between anisotropic magnetic and isotropic electrostatic interactions on the aggregation behavior of aqueous suspensions of electric double layered magnetic particles was studied. Therefore, the particles were aggregated under the action of an external magnetic field and in the presence of different amounts of an indifferent 1:1 electrolyte. After removing the field, linear aggregates remained in the sample. Static light scattering and electron micrographs confirmed the chainlike cluster morphology. Dynamic light scattering was used for monitoring the average diffusion coefficient of these magnetic filaments. A theoretical model that allows the experimental mean diffusion coefficient to be related to the average chain length was successfully employed. The results show that, at fixed exposure time and field strength, the average filament size is proportional to the amount of electrolyte added. The light scattering data and transmission electron microscopy micrographs prove that permanent chains coexist with a relatively large fraction of individual particles when no or little electrolyte was added to the samples. A plausible explanation for this "selective aggregation" phenomenon could be given in terms of surface charge heterogeneities. The chain growth was found to follow a power law with a similar exponent for all the electrolyte concentrations studied. Scaling theories were employed for estimating the ratio of particles taking part in the aggregation process.     

Chemical reaction dynamics within anisotropic solvents in time-dependent fields

The dynamics of low-dimensional Brownian particles coupled to time-dependent driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have been described through the use of a variant of the stochastic Langevin equation. The rotational motion of the mesogens is assumed to follow the motion of an external driving field in the linear response limit. Reaction dynamics have also been probed using a two-state model for the Brownian particles. Analytical expressions for diffusion and reaction rates have been developed and are found to be in good agreement with numerical calculations. When the external field driving the mesogens is held at constant rotational frequency, the model for reaction dynamics predicts that the applied field frequency can be used to control the product composition.     

Influence of perpendicular external magnetic field on microstructures of monolayer composed of ferromagnetic particles: analysis by means of quasi-two-dimensional Monte Carlo simulation

We investigated the influences of the magnetic field strength and particle areal density on the microstructure of a quasi-two-dimensional monolayer composed of ferromagnetic particles by means of a Monte Carlo simulation. The magnetic field was applied along a direction perpendicular to the plane of the monolayer. Microstructures of the monolayer obtained in the simulations were analyzed in terms of radial distribution and orientational distribution functions. Formation of the microstructures is discussed from the perspective of particle-particle interaction energy and the perpendicular magnetic susceptibility of the monolayer was calculated from simulated magnetization curves. The obtained results are summarized as follows. For small areal density of particles, formation of chain-like structures is prevented by the repulsive magnetic interaction between particles due to orientations of the magnetic moments in the particles along the magnetic field direction. For intermediate areal density of particles, the chain-like structures remain even when a relatively strong magnetic field is applied, because contributions of the attractive magnetic interactions increase. For large areal density of particles, mixtures of chain-like and locally ordered structures appear due to the anisotropic attractive magnetic interactions in the absence of the magnetic field. However, when a sufficiently strong magnetic field is applied, the magnetic interactions between particles change to isotropic repulsive interactions, which results in the short-range repulsive steric interactions between particles becoming dominant with the appearance of hexagonal close packed structures.     

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.     

Directed assembly of BaFe12O19 particles and the formation of magnetically oriented films

We have studied the preparation of oriented BaFe(12)O(19) films produced using electrophoretic deposition (EPD). Highly anisotropic, platelike BaFe(12)O(19) particles were synthesized under hydrothermal conditions, and from these particles, stable suspensions were prepared in 1-butanol by the addition of dodecylbenzene sulfonic acid as a surfactant. The interplay of the interaction forces between the suspended particles and the forces acting on the particles during the EPD directed the particles' assembly in the plane of the substrate. The most significant effect on the orientation of the films was the diameter-to-thickness ratio of the particles, which was experimentally confirmed with X-ray analyses, electron microscopy, and magnetic measurements. The abnormal grain growth that accompanied the sintering at 1150 °C further improved the overall orientation of the films, which showed highly anisotropic magnetic behavior with a remanent-to-saturation magnetization ratio exceeding 0.8.     

Rheology and orientational distributions of rodlike particles with magnetic moment normal to the particle axis for semi-dense dispersions (analysis by means of mean field approximation)

We have considered a semi-dense dispersion composed of ferromagnetic rodlike particles with a magnetic moment normal to the particle axis to investigate the rheological properties and particle orientational distribution in a simple shear flow as well as an external magnetic field. We have adopted the mean field approximation to take into account magnetic particle-particle interactions. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the magnetic moment of the rodlike particle is strongly restricted in the field direction, so that the particle points to directions normal to the flow direction (and also to the magnetic field direction). This characteristic of the particle orientational distribution is also valid for the case of a strong particle-particle interaction, as in the strong magnetic field case. To the contrary, for a weak interaction among particles, the particle orientational distribution is governed by a shear flow as well as an applied magnetic field. When the magnetic particle-particle interaction is strong under circumstances of an applied magnetic field, the magnetic moment has a tendency to incline to the magnetic field direction more strongly. This leads to the characteristic that the viscosity decreases with decreasing the distance between particles, and this tendency becomes more significant for a stronger particle-particle interaction. These characteristics concerning the viscosity are quite different from those for a semi-dense dispersion composed of rodlike particles with a magnetic moment along the particle direction.     

On the behavior of an oblate spheroidal hematite particle in a simple shear flow under a uniform magnetic field applied in the flow direction

We discuss the orientational properties of an oblate spheroidal hematite particle and also its influence on the rheological characteristics of a dilute suspension of these magnetic particles, by means of an analytical approach based on the orientational distribution function. A hematite particle with oblate spheroidal shape has an important characteristic; that is, it is magnetized in a direction normal to the particle axis. From the balance of the torques acting on a particle, we have developed the basic equation of the orientational distribution function. This basic equation has been numerically solved in order to investigate the dependence of the orientational distribution on the various factors. If both the magnetic field and the shear flow are weak, the particle does not exhibit specific directional characteristics. If the magnetic field is more dominant, the particle inclines such that the oblate surface is parallel to the magnetic field direction. If the shear flow becomes more dominant, the particle shows a sharper peak of the orientational distribution in the shear flow direction. The viscosity due to the magnetic torque increases and finally converges to a constant value as the magnetic field increases. In a sedimentation process under the gravitational field, the translational diffusion coefficient decreases with increasing magnetic field strength in the present case of the magnetic field direction.     

3D Monte Carlo simulations of a magnetic disk-like particle dispersion

We have investigated the aggregate structures of a colloidal dispersion composed of ferromagnetic disk-like particles with a magnetic moment normal to the particle axis at the particle center, by means of 3D Monte Carlo simulations. Such disk-like particles have been modeled as a circular disk-like particle with the side section shape of spherocylinder. We have attempted to clarify the influences of the magnetic field strength, magnetic interactions between particles and volumetric fraction of particles. In order to discuss quantitatively the aggregate structures of clusters, we have focused on the radial distribution and orientational pair correlation functions, etc. For no applied magnetic field cases, long column-like clusters come to be formed with increasing magnetic particle–particle interactions. The internal structures of these clusters clearly show that the particles incline in a certain direction and their magnetic moments alternate in direction between the neighboring particles in the clusters. For applied magnetic field cases, the magnetic moment of each particle inclines in the magnetic field direction and therefore the column-like clusters are not formed straightforwardly. If the magnetic field is much stronger than magnetic particle–particle interactions, the particles do not have a tendency to form the clusters. As the influence of magnetic particle–particle interactions is significantly strong, thick chain-like clusters or column-like clusters or brick-wall-like clusters come to be formed along the magnetic field direction.     

Dynamically corrected transition state theory calculations of self-diffusion in anisotropic nanoporous materials

We apply the dynamically corrected transition state theory to confinements with complex structures. This method is able to compute self-diffusion coefficients for adsorbate-adsorbent systems far beyond the time scales accessible to molecular dynamics. Two example cage/window-type confinements are examined: ethane in ERI- and CHA-type zeolites. In ERI-type zeolites, each hop in the z direction is preceded by a hop in xy direction and diffusion is anisotropic. The lattice for CHA-type zeolite is a rhombohedral Bravais lattice, and diffusion can be considered isotropic in practice. The anisotropic behavior of ERI-type cages reverses with loading, i.e., at low loading the diffusion in the z direction is two times faster than in the xy direction, while for higher loadings this changes to a z diffusivity that is more than two times slower. At low loading the diffusion is impeded by the eight-ring windows, i.e., the exits out of the cage to the next, but at higher loadings the barrier is formed by the center of the cages.     

Evaluation of translational friction coefficients of macroscopic probes in nematic liquid crystals

We present a study of the translational friction coefficients of spherical and ellipsoidal probes in nematic liquid crystalline fluids, based on the numerical treatment of Leslie-Ericksen equations [Q. J. Mech. Appl. Math. 19, 357 (1966); Adv. Liq. Cryst. 4, (1979); Trans. Soc. Rheol. 5, 23 (1961); Adv. Liq. Cryst. 2, 233 (1976)] for incompressible nematic fluids. Simulations of director dynamics in a local environment surrounding the moving probe are presented, and the dependence of translational diffusion on liquid crystal viscoelastic parameters is discussed. The time evolution of the director field is studied in the presence of an orienting magnetic field in two characteristic situations: Directors of motion parallel and perpendicular with respect to the field. In the particular case under investigation, a detailed analysis is given for the case of spherical, prolate, and oblate ellipsoidal probes in rectilinear motion in nematic (4-methoxibenzylidene-4'-n-butylaniline), together with a comparison with other nematogens, namely, 4,4'-dimethoxuazoxy benzene and (4'-n-pentyl-4-cyanobiphenil). A discussion of the general methodology presented in this work is given for the case of colloidal dispersions in nematic liquid crystals, which are considered as model systems of dispersions of particles in host media with anisotropic physical properties.     

Diffusion in coiled pores - learning from microrelease and microsurgery

The anisotropic diffusion in coiled pore systems of SBA-3-type microparticles has been studied by the release of guest molecules. The diffusion turns out as an example of the influence of hierarchical structuring on physical properties. Two modes of diffusion, associated with transport along and across the mesopores, can be identified and measured using optical microscopy. Redistribution between the two modes has been achieved by mesopore opening using two methods of "microsurgery"-either focused ion beams (FIB) or mechanical tools. The particles trimmed by FIB have revealed risks of misinterpretation of sample preparation with this tool. Instead of pure pore opening, the cutting by FIB resulted in simultaneous sealing of the mesopores.     

Self-diffusion in two-dimensional hard ellipsoid suspensions

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with subpixel resolution. The translational and rotational diffusions were measured in both the laboratory frame and the body frame along the long and short axes. The long-time and short-time diffusion coefficients of translational and rotational motions were measured as functions of the particle concentration. We observed the nondiffusive crossover region in the intermediate time regime due to the caging of neighboring particles. Both the beginning and the ending times of the intermediate regime exhibit power-law dependence on concentration. The long-time and short-time diffusion anisotropies change nonmonotonically with concentration and reach minima in the semidilute regime because the motions along long axes are caged at lower concentrations than the motions along short axes. The time derivatives of mean-square displacements change linearly with the inverse of time in the intermediate time regimes at various particle densities. This indicates that their relaxation functions decay as 1/t which provides new challenges in theory. The effects of coupling between rotational and translational Brownian motions were demonstrated and the two time scales corresponding to anisotropic particle shape and anisotropic neighboring environment were measured.     

Anisotropic diffusion in confined colloidal dispersions: the evanescent diffusivity

We employ an analogy to traditional dynamic light scattering to describe the inhomogeneous and anisotropic diffusion of colloid particles near a solid boundary measured via evanescent wave dynamic light scattering. Following this approach, we generate new expressions for the short-time self- and collective diffusivities of colloidal dispersions with arbitrary volume fraction. We use these expressions in combination with accelerated Stokesian dynamics simulations to calculate the diffusivities in the limit of large and small scattering wave numbers for evanescent penetration depths ranging from four particle radii to one-fifth of a particle radius and volume fractions from 10% to 40%. We show that at high volume fractions, and larger penetration depths, the boundaries have little effect on the dynamics of the suspension parallel to the wall since, to a first approximation, the boundary acts hydrodynamically much as another nearby particle. However, near and normal to the wall, the diffusivity shows a strong dependence on penetration depth for all volume fractions. This is due to the lubrication interactions between the particles and the boundary as the particle moves relative to the wall. These results are novel and comprehensive with respect to the range of penetration depth and volume fraction and provide a complete determination of the effect of hydrodynamic interactions on colloidal diffusion adjacent to a rigid boundary.     

Oil-in-water emulsification induced by ellipsoidal hematite colloids: evidence for hydrolysis-mediated self-assembly

We report on the preparation of a novel type of particle-stabilized oil-in-water emulsions. The emulsification mechanism comprises partial hydrolysis of the oil phase promoted by the alkaline surface of ellipsoidal hematite colloids stabilized by tetramethylammonium hydroxide. This mechanism yields monodisperse oil droplets with embedded single ellipsoidal particles. The emulsions, which are stable for at least several months, can be polymerized by radical initiation, to yield latex-like particles with interesting optical and magnetic properties due to their anisotropic hematite cores. Moreover, we show that complex composite core-shell colloids can be prepared by PMMA growth and silica deposition on polymerized emulsion droplets. Finally, as an example of a possible application for our system, we have measured translational and rotational diffusion coefficients of hematite-stabilized oil droplets by depolarized dynamic light scattering. The latter technique can also be employed to monitor the spontaneous emulsification in time.