Influences of magnetic particle–particle interactions on orientational distributions and rheological properties for a colloidal dispersion composed of rod-like particle with a magnetic moment normal to the particle axis

We have investigated mainly the influences of magnetic particle–particle interactions on the orientational distribution and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane since the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the increase in the viscosity because the mean-field vector has only a component along the magnetic field direction.     

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.     

Phase field simulation of spinodal decomposition under external magnetic field

A computational model was developed to simulate the spinodal decomposition process of ferromagnetic alloys under an external magnetic field. In this model, the temporal evolution of the modulated structure was described by a phase field method, and the magnetic configuration was solved by using a micromagnetic method. The spinodal decomposition and coarsening processes of a single magnetic particle and an A-B hypothetical system under an external magnetic field were simulated using the proposed model. The simulation results show that the precipitated particles were elongated along the direction of the external magnetic field. The dependence of the modulated structure of an A-B hypothetic system on external magnetic field is much more sensitive than that of the single particle structure. The simulation results also demonstrate that the modulation of the external magnetic field is effective even if the spinodal decomposition has been completed and a stable modulated structure was formed.     

Elasticity,fracture and thermoreversible gelation of highly filled physical gels<Superscript>⋆</Superscript>

We describe a physically associating triblock copolymer-based gel that exhibits a reversible transition between solid and liquid states at a temperature of approximately 55^°C. The thermal transition of the gel enables us to compare the properties of liquid suspensions and elastic composites with identical particle loadings, with particle volume fractions as large as 0.55. The suspension viscosity and the composite elasticity scale in a similar manner with the overall particle volume fraction, a result that is rationalized in terms of an effective strain amplification factor that depends only on the particle loading. Measured values of the strain amplification factor are in good agreement with the expected form for well-dispersed spheres. We also find that the elastic composites are exceptionally strong, with fracture strengths that exceed the modulus of the base gel by a factor of 100 or more. Deviations from purely elastic behavior became important for high particle volume fractions, and were probed by stress relaxation experiments.     

两个非磁性颗粒在磁流体中的沉降现象研究

在磁场作用下,在磁流体里添加非磁性颗粒(non-magnetic particles,NPs),可以使得NPs形成不同的结构,操控NPs的运动从而影响磁流体的特性,这种应用逐渐受到了研究者的关注.为了更好地操控磁流体里NPs的运动,本文采用一种多物理模型研究在外加磁场作用下,磁流体中两个NPs沉降的运动过程.其中,用格子玻尔兹曼方法模拟磁流体的运动,外加磁场对磁流体的影响用一种自修正方法求解泊松方程,这个自修正方法可以使欧姆定律满足守恒定律.NPs之间的偶极干扰力采用偶极力模型,同时采用一种相对过渡平滑的共轭边界条件处理NPs与磁流体交界面的流固干扰以避免磁场密度过渡的突变.本文主要探究两个NPs在磁流体中的沉降,揭示磁场作用下NPs的相互干扰原理;同时,对控制NPs运动时的参数进行调节,得到NPs不同的运动轨迹,达到操控颗粒运动的目的.本研究可对NPs在磁流体中的应用提供定量的分析结果,对NPs在工业上的应用提供有力的理论支撑.     

Brownian dynamics simulations of a cubic haematite particle suspension with a more effective treatment of steric layer interactions

We have proposed a new repulsive layer model for describing the interaction between steric layers of coated cubic particles. This approach is an effective technique applicable to particle-based simulations such as a Brownian dynamics simulation of a suspension composed of cubic particles. 3D Brownian dynamics simulations employing this repulsive interaction model have been performed in order to investigate the equilibrium aggregate structures of a suspension composed of cubic haematite particles. It has been verified that Brownian dynamics employing the present steric interaction model are in good agreement with Monte Carlo results with respect to particle aggregate structures and particle orientational characteristics. From the viewpoint of developing a surface modification technology, we have also investigated a regime change in the aggregate structure of cubic particle in a quasi-2D system by means of Brownian dynamics simulations. If the magnetic particle–particle interaction strength is relatively strong, in zero applied magnetic field the particles aggregate in an offset face-to-face configuration. As the magnetic field strength is increased, the offset face-to-face structure is transformed into a more direct face-to-face contact configuration that extends throughout the whole simulation region.     

Collective effects in doped nematic liquid crystals

We studied the collective elastic interaction in a system of many macroparticles embedded in a nematic liquid crystal. A theoretical approach to the interaction of macroparticles via deformation of the director field [1] is developed. It is found that the director field distortion induced by many particles leads to the screening of the elastic pair interaction potential. This screening strongly depends on the shape of the embedded particles: it exists for anisotropic particles and is absent for spherical ones. Our results are valid for the homeotropic and the planar anchoring on the particle surface and for different Frank constants. We apply our results to cylindrical particles in a nematic liquid crystal. In a system of magnetic cylindrical grains suspended in a nematic liquid crystal, the external magnetic field perpendicular to the grain orientation results in inclining the grains to the director and induces an elastic Yukawa-law attraction between the grains. The appearance of this elastic attraction can explain the cellular texture in magnetically doped liquid crystals in the presence of the magnetic field [2].     

驻波声场中单分散细颗粒的相互作用特性

利用外加声场促进悬浮在气相中的细颗粒发生相互作用,进而引起颗粒的碰撞和凝并,使得颗粒平均粒径增大、数目浓度降低,是控制细颗粒排放的重要技术途径.为探究驻波声场中单分散细颗粒的相互作用,建立包含曳力、重力、声尾流效应的颗粒相互作用模型,采用四阶经典龙格-库塔算法和二阶隐式亚当斯插值算法对模型进行求解.将数值模拟得到的颗粒声波夹带速度和相互作用过程与相应的解析解和实验结果进行对比,验证模型的准确性.进而研究颗粒初始条件和直径对相互作用特性的影响.结果表明,初始时刻颗粒中心连线越接近声波波动方向、颗粒位置越接近波腹点,颗粒间的声尾流效应就越强,颗粒发生碰撞所需要的时间就越短.研究还发现,颗粒直径对颗粒相互作用的影响取决于初始时刻颗粒中心连线偏离声波波动方向的程度.当偏离较小时,颗粒直径越大,颗粒发生碰撞所需要的时间越短;当偏离很大时,直径较小的颗粒能够发生碰撞,而直径较大的颗粒则无法发生碰撞.     

基于伊辛模型的Fe0.5Mn0.1Al0.4 合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序 合金的磁化强度和磁熵变。首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场（温度）的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对 合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场h=0.14时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变 达到了正向最大值,极值的位置对应于体系的相变温度。     

基于伊辛模型的Fe_(0.5)Mn_(0.1)Al_(0.4)合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序Fe0.5Mn0.1Al0.4合金的磁化强度和磁熵变.首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场(温度)的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对Fe0.5Mn0.1Al0.4合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场H=0.14(a.u.)时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变ΔS(0.1,0.14)达到了正向最大值,极值的位置对应于体系的相变温度.     

Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

Coupling of ferromagnetic nanoparticles through dipolar interactions

We consider two ferromagnetic nanoparticles coupled via long-range dipolar interactions. We model each particle by a three-dimensional array of classical spin vectors, with a central spin surrounded by a variable number of shells. Within each particle only ferromagnetic coupling between nearest neighbor spins is considered. The interaction between particles is of the dipolar type and the magnetic properties of the system is studied as a function of temperature and distance between the centers of the particles. We perform Monte Carlo simulations for particles with different number of shells, and the magnetic properties are calculated via two routes concerning the dipolar contribution: one assuming a mean-field like coupling between effective magnetic moments at the center of the particles, and other one, where we take into account interactions among all the pairs of spins, one in each particle. We show that the dipolar coupling between the particles enhances the critical temperature of the system relative to the case in which the particles are very far apart. The dipolar energy between the particles is smaller when the assumption of effective magnetic moment of the particles is used in the calculations.     

3D Arrangement of Magnetic Particles in Thin Polymer Films Assisted by Magnetically Patterned Exchange Bias Layer Systems

The possibility to arrange and embed magnetic micro- and nanoparticles in thin polymer film systems using flat magnetically patterned substrate templates is investigated. In contrast to self-organized particle rows forming by applying a homogeneous magnetic field, particles adapt to the magnetic field landscape of the substrate's magnetic pattern prior to polymer crosslinking. Crosslinking then fixes the particle positions in the polymer. The process is tested for composites of hydrophobic polydimethylsiloxane (PDMS) and maghemite nanoparticles as well as for hydrophilic polyvinyl alcohol (PVOH) and hydrophilic functionalized, superparamagnetic core–shell microspheres. The substrate template is an exchange bias layer system magnetically patterned into parallel-stripe domains with in-plane magnetizations and head-to-head/tail-to-tail remanent magnetization orientation in adjacent magnetic domains. A high occupancy percentage of magnetic beads on a domain wall as well as anisotropic actuation of the composite is achieved.     

On Suhl's approach to the Kondo problem

A model for the Kondo problem is studied in which the impurities are envisaged as a gas of infinitely heavy particles embedded in the gas of conduction electrons. Fors-wave interactions and low impurity concentrations the electron self-energy is expressed by the impurity-electron scattering matrix which is also shown to determine the thermodynamic potantial. Using standard Goldstone diagrams Suhl's equation is derived by the summation of leading singular graphs. For a special density of states, vanishing magnetic field, and no potential scattering the dispersion equation is solved exactly.     

Magnetic interactions and media noise in rigid disks

This paper discusses the relationship between media-noise and magnetic properties. Two topics in longitudinal barium ferrite (Ba-ferrite) particulate rigid disks are mainly investigated; the relationship between media-noise characteristics and interparticle magnetic interactions, and the particle-size effect in read/write properties. For the first topic, a series of longitudinal Ba-ferrite disks with a variation in volumetric particle-packing densities are investigated. The magnetomotive force dependences or reverse DC-erase noise are measured and compared with interaction field factor. For the second topic, the particle-size effect in read/write properties of Ba-ferrite particulate disks are described compared with the those of Co–γFe₂O₃ particulate disks. The magnetic interactions in Ba-ferrite disks consist of two mechanisms: the interparticle positive interactions in stacks of Ba-ferrite particles, and the negative interactions between the stacks in which the magnetic moments of the Ba-ferrite platelet particles are aligned in the stack direction. H_c and switching field distribution values depend on interparticle interactions and extra stack-like particle interactions. Media noise depends on particle size. These ideas are effective for thin film media without exchange of magnetic interactions.     

Anisotropy in elastic modulus of hydrogel containing magnetic particles

We derive the analytic expression of elastic modulus for a gel containing magnetic particles with a magnetic dipole moment. The obtained elastic modulus is anisotropic and the modulus increases and decreases with the density of magnetic particle when the direction of strain is perpendicular and parallel to the direction of magnetization, respectively. This behavior is qualitatively in good agreement with previous experimental data [T. Mitsumata, et al., Macromol. Rapid Commun. 23, (2002) 178].     

Magnetic behavior of iron and iron-oxide nanoparticle/polymer composites

An inert gas condensation technique was used to prepare nanometer-sized particles of metallic iron and iron oxide. The particles were passivated by the controlled oxidation of the particle surface leading to an Fe-oxide shell-Fe core structure. Nanoparticle–polymer composites were obtained by spin casting mixtures of nanoparticles and polymethylmethacrylate films. The magnetic properties of the nanoparticles compressed into pellets and dispersed in the composites were both studied. The particles were observed to exhibit increased coercivity and exchange bias. The exchange bias was observed to increase with oxide shell thickness. The magnetism in the nanoparticle composites was studied as a function of nanoparticle loading. It was observed that when the particles were dispersed into the nanocomposite the coercivity was increased, suggesting a heightened anisotropy barrier. Similarly, the magnetic relaxation results indicate that the composites exhibit significantly reduced relaxations through the entire temperature range, as compared to the compressed pellet. This observation supports the possibility of heightened anisotropy barriers due to reduced dipolar interactions.     

Elastic property of multiphase composites with random microstructures

We propose a computational method with no ad hoc empirical parameters to determine the elastic properties of multiphase composites of complex geometries by numerically solving the stress–strain relationships in heterogeneous materials. First the random microstructure of the multiphase composites is reproduced in our model by the random generation-growth method. Then a high-efficiency lattice Boltzmann method is employed to solve the governing equation on the multiphase microstructures. After validated against a few standard solutions for simple geometries, the present method is used to predict the effective elastic properties of real multiphase composites. The comparisons between the predictions and the existing experimental data have shown that the effects of pores/voids in composites are not negligible despite their seemingly tiny amounts. Ignorance of such effects will lead to over-predictions of the effective elastic properties compared with the experimental measurements. When the pores are taken into account and treated as a separate phase, the predicted Young’s modulus, shear modulus and Poisson’s ratio agree well with the available experimental data. The present method provides an alternative tool for analysis, design and optimization of multiphase composite materials.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)