Quasi-2D Monte Carlo simulations of the regime change in the aggregates of magnetic cubic particles on a material surface

We have investigated the aggregate structure of a suspension composed of magnetic particles with a cubic geometry by means of Monte Carlo simulations. From the viewpoint of application to the technology of surface modification, we have considered a quasi-two-dimensional suspension in thermodynamic equilibrium. As the magnetic interaction strength is increased, the effects of the thermal energy are reduced and the particles tend to aggregate together. These aggregates of cubic particles are not chain-like, but are designated as closely packed clusters. An applied magnetic field tends to enhance the formation of clusters along the field direction but does not significantly regularise the internal structure of the cluster. This is mainly due to the preference of a face-to-face contact configuration for the alignment of particles with cubic geometry. The regime of the internal structure of aggregates has a significant effect on the characteristics of the alignment of the magnetic moments with regard to the external magnetic field direction. Our simulations indicate that larger closely packed clusters are formed with increasing volumetric fraction, whereas the internal structure of the closely packed clusters is not found to be significantly influenced by the change in the volumetric fraction.     

Quasi-2D Monte Carlo simulations of phase transitions and internal aggregate structures in a highly dense suspension composed of magnetic plate-like particles

The phase transitions and the internal aggregate structures of a highly dense suspension composed of magnetic plate-like particles with a magnetic moment normal to the particle axis have been investigated by means of the Monte Carlo method. The present study considered a quasi-2D system in order to clarify the influences of the volumetric fraction of particles and the magnetic field strength on particle aggregations and phase transitions. The internal structures of particle aggregates have been discussed quantitatively in terms of pair correlation functions, orientational pair correlation functions, nematic and polar order parameters. The main results obtained here are summarized as follows. When the influence of the magnetic interaction between particles is of the same order of that of the perpendicular magnetic field strength, the particles form column-like clusters, and the internal structure of the suspension shows solid-like structures. For the case of a strong applied magnetic field, the internal structure is transformed from solid-like structures into isotropic ones. However, as the volumetric fraction increases, the particles form brick wall-like structures under the situation of a strong applied magnetic field, and the internal structure exhibits solid-like ones. The brick wall-like structures also appear for a relatively weak magnetic field applied along the in-plane direction despite a slightly smaller volumetric fraction compared with the case of the perpendicular applied magnetic field.     

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.     

Two-dimensional Monte Carlo simulations of structures of a suspension comprised of magnetic and nonmagnetic particles in uniform magnetic fields

The structures of suspensions comprised of magnetic and nonmagnetic particles in magnetic fields are studied using two-dimensional Monte Carlo simulations. The magnetic interaction among magnetic particles, magnetic field strength, and concentrations of both magnetic and nonmagnetic particles are considered as key influencing factors in the present work. The results show that chain-like clusters of magnetic particles are formed along the field direction. The size of the clusters increases with increasing magnetic interaction between magnetic particles, while it keeps nearly unchanged as the field strength increases. As the concentration of magnetic particles increases, both the number and size of the clusters increase. Moreover, nonmagnetic particles are found to hinder the migration of magnetic ones. As the concentration of nonmagnetic particles increases, the hindrance on migration of magnetic particles is enhanced.     

Quasi-2D Monte Carlo simulations of a colloidal dispersion composed of magnetic plate-like particles with magnetic moment normal to the particle axis

We have investigated aggregation phenomena of a colloidal dispersion composed of magnetic plate-like particles by means of Monte Carlo simulations. Such plate-like particles have been modelled as disk-like particles with magnetic moment normal to the particle axis at the particle centre, with the section shape of a spherocylinder. The main objective of the present study is to clarify the influences of the magnetic field strength and magnetic interactions between particles on particle aggregation phenomena. We have concentrated our attention on a quasi-2D system from an application point of view such as the development of surface quality changing technology using such magnetic plate-like particles. A magnetic field is applied along the direction perpendicular to the plane of the monolayer. Internal structures of particle aggregates are discussed quantitatively in terms of radial distribution and orientational pair correlation functions. For the case of strong magnetic interactions between particles, particles form long column-like clusters with their magnetic moments alternating in direction between the neighbouring particles. These tendencies appear under circumstances of a weak applied magnetic field. However, as the magnetic field strength increases, particles incline towards the magnetic field direction, so that particles do not form such clusters.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Two-dimensional Monte Carlo simulations of a suspension comprised of magnetic and nonmagnetic particles in gradient magnetic fields

Distributions of particles in a suspension comprised of magnetic particles (MPs) and nonmagnetic particles (NPs) under gradient magnetic fields are vitally important for the preparation of magnetic-nonmagnetic functionally graded materials (FGMs). In the present study, the effects of magnetic field gradient, magnetic interaction between MPs and concentration of NPs on the distributions of particles in the suspension are investigated using a two-dimensional Monte Carlo simulation. The results show that a gradient distribution of MPs is formed under gradient magnetic fields and increases with increasing the field gradient. However, as the interaction between MPs increases, the distribution gradient decreases, accompanied by the formation of chain-like MP clusters. Moreover, NPs are found to hinder the translation of MPs along the field direction. As the NP concentration increases, the translation of MPs becomes difficult.     

Monte Carlo simulations of magnetic particle suspensions with a simple assessment method for the particle overlap between magnetic spheroids

We have developed a simple assessment method for the overlap between spheroidal particles, which neither requires the complex manipulation of vectors and matrices that is indispensable in the ordinary methods, nor is based on a model potential. Moreover, we have developed an evaluation method for the interaction energy arising from the overlap of the steric layer coating spheroidal particles. This is based on a sphere-connected particle model, but some modifications are introduced in order to express an appropriate repulsive interaction energy at the deepest overlapping position. We have investigated the phase change in a magnetic spheroidal particle suspension for a two-dimensional system by means of Monte Carlo simulations. In the case of no external magnetic field, if the magnetic particle-particle interaction is sufficiently strong to favour cluster formation, long raft-like clusters tend to be formed in a dilute situation. With decreasing values of area fraction, a chain-like structure in a dense situation transforms into a raft-like structure within a narrow range of the particle area fraction. Similarly, the raft-like clusters are preferred in a weak applied magnetic field, but an increase in the field strength induces a phase change from a raft-like into a chain-like structure.

Highlights of the present paper:

1. A simple assessment method has been proposed for the overlap between two spheroidal particles.

2. The particle overlap assessment is free from a complex mathematical manipulation regarding vectors and matrices.

3. A modified sphere-connected model has been proposed in order to more accurately evaluate a repulsive interaction due to the overlap of the steric layers coating spheroidal particles.

4. 2D Monte Carlo simulations have been performed to elucidate the phenomenon of a phase change by magnetic spheroidal particles on a material plane surface.

5. A phase change between a raft-like and a chain-like aggregate structure is able to be controlled by the area fraction of particles and an external magnetic field.

     

Computer simulation of structures and distributions of particles in MAGIC fluid

MAGIC (MAG-netic Intelligent Compound) is a solidified magnetic ferrofluid (MF) containing both magnetic particles (MPs) and abrasive particles (APs, nonmagnetic) of micron size. The distribution of APs in MAGIC can be controlled by applying a magnetic field during cooling process of MAGIC fluid. In this paper, the influences of magnetic field, size and concentration of particles on the final structures of MPs and the distributions of APs in MAGIC fluid are preliminarily investigated using Stokesian dynamic (SD) simulation method. Simulation results show that MPs prefer to form strip-like structures in MAGIC fluid, the reason for this phenomenon is mainly attributed to the strong dipolar interactions between them. It is also found that MPs prefer to form big agglomerations in weak magnetic field while chains and strip-like structures in strong magnetic field; no long chains or strip-like structures of MPs are observed in low-concentration MAGIC fluid; and for big-size MPs, pure wall-like structures are formed. Evaluation on the distribution of APs with uniformity coefficient shows that strong magnetic field, high concentration and small-size particles can induce more uniform distribution of APs in MAGIC fluid, the uniformity of APs in MAGIC is about 10% higher than that in normal grinding tools.     

On the influence of the hydrodynamic interactions on the aggregation rate of magnetic spheres in a dilute suspension

Magnetostatic attraction may lead to formation of aggregates in stable colloidal magnetic suspensions and magneto-rheological suspensions. The aggregation problem of magnetic composites under differential sedimentation is a key problem in the control of the instability of non-Brownian suspensions. Against these attractive forces are the electrostatic repulsion and the hydrodynamic interactions acting as stabilizing effects to the suspension. This work concerns an investigation of the pairwise interaction of magnetic particles in a dilute sedimenting suspension. We focus attention on suspensions where the Péclet number is large (negligible Brownian motion) and where the Reynolds number (negligible inertia) is small. The suspension is composed of magnetic micro-spheres of different radius and density immersed in a Newtonian fluid moving under the action of gravity. The theoretical calculations are based on direct computations of the hydrodynamic and the magnetic interactions among the rigid spheres in the regime of low particle Reynolds number. From the limiting trajectory in which aggregation occurs, we calculate the collision efficiency, representing the dimensionless rate at which aggregates are formed. The numerical results show clear evidence that the hydrodynamic interactions are of fundamental relevance in the process of magnetic particle aggregation. We compare the stabilizing effects between electrostatic repulsion and hydrodynamic interactions.     

Structural properties of complex (dusty) plasma upon crystallization and melting

A change in the local order of a bounded complex (dusty) plasma in the process of its crystallization and melting has been examined by molecular dynamics simulations. The dynamics of microparticles is considered in the framework of a Langevin thermostat, the pair interaction between charged particles is described by a screened Coulomb potential (Yukawa potential) with the hard wall potential as a confinement. It has been shown that the beginning of the crystallization of such a system is accompanied by the formation of clusters with the hexagonal close packed (hcp) structure; a noticeable number of these clusters are then transformed to the face centered cubic (fcc) phase. A plasma crystal formed after crystallization consists of the metastable hcp phase, fcc clusters, and a small number of clusters with a body centered cubic (bcc) crystal lattice. Beginning with a certain threshold value of the thermostat temperature, the number of fcc/bcc clusters decreases sharply with increasing temperature, which is an important signature of the beginning of the melting of the plasma crystal.     

Numerical micromagnetics of interacting superparamagnetic nanoparticles assembled in clusters with different dimensionalities

We analyze here the equilibrium magnetization state of densely packed interacting superparamagnetic nanoparticles assembled in clusters of various sizes and dimensionalities by comparison with the non-interacting case. We demonstrate that the average magnetization of individual particles is strongly increased in linear chains aligned parallel with the external magnetic field. Two-dimensional (2D) distributions of superparamagnetic nanoparticles present weaker increases of their average magnetization with respect to the non-interacting approximation whereas volume distributions (3D) are almost equivalent with the non-interacting case. A large number of nanoparticles densely packed in 2D superparamagnetic clusters present almost the same magnetic moment as infinite superparamagnetic chains. The effect of mutual interactions on the total magnetic moment of 3D surfaces (spheroids with various aspect ratios) uniformly covered with densely packed monolayers of superparamagnetic nanoparticles is also investigated.     

Single-domain magnetic nanoparticles as force generators for the nanomechanical control of biochemical reactions by low-frequency magnetic fields

The dynamics of single-domain magnetic nanoparticles cross-linked into multiparticle aggregates by organic ligands is considered. Mechanical factors of the effect of low frequency magnetic field on macromolecules attached to magnetic nanoparticles/aggregates within a suspension or gel are analyzed. The optimum conditions ensuring the best control over biochemical reactions in suspension by an external magnetic field (i.e., the ranges of frequency and magnetic field intensities, and the size of magnetic nanoparticles and shells covering them) are determined.     

Ultrasound and light scattering from a suspension of reversible fractal clusters in shear flow

Shear break-up of reversible fractal clusters is investigated by ultrasound and multiple light scattering in the low shear regime. We consider a dense suspension of Rayleigh scatterers (particles or clusters) with acoustic properties close to those of the surrounding liquid so that the attenuation of the ultrasonic coherent field is weak and multiple scattering is negligible. The concept of variance in local particle volume fraction is used to derive an original expression of the ultrasound scattering cross-section per unit volume for Rayleigh fractal clusters. On the basis of a scaling law for the shear break-up of aggregates, then we derive the shear stress dependence of the ultrasound scattered intensity from a suspension of reversible fractal clusters. In a second part, we present rheo-acoustical experiments to study the shear break-up of hardened red cell aggregates in plane-plane flow geometry and we examine both the self consistent field approximation and the scaling laws used in microrheological models. We further compare the ability of acoustical backscattering and optical reflectometry techniques to estimate the critical disaggregation shear stress and the particle surface adhesive energy. Finally, the microrheological model from Snabre and Mills [#!ref5!#] based on a fractal approach is shown to describe the non Newtonian behavior of a dense distribution of hardened red cell aggregates. Received 12 November 1998 and Received in final form 17 May 1999     

Rheo-acoustical study of the shear disruption of reversible aggregates. Ultrasound scattering from concentrated suspensions of red cell aggregates

Shear-induced disruption of reversible aggregates or clusters in a concentrated suspension is investigated by ultrasound backscattering in the low shear regime. Fractal aggregates are considered as non-Brownian scatterers much smaller than the wavelength with acoustic properties close to those of the surrounding liquid, so that the attenuation of the coherent field is weak and multiple scattering can be neglected. The concept of variance in local particle volume fraction is used to deduce a first-order expression of the ultrasound scattering cross section per unit volume for Rayleigh scatterers in a dense suspension. On the basis of a scaling law for the shear-induced disruption of aggregates, the shear stress dependence of the ultrasonic scattered intensity from a dense suspension of clusters is derived. In a second part, the shear breakup of hardened red blood cell aggregates is investigated in plane-plane flow geometry by ultrasound scattering. Rheo-acoustical experiments are analyzed within the framework of the self-consistent field approximation and the scaling laws currently used in microrheological models. Finally, the ability of ultrasonic, light reflectometry and viscometry methods to provide quantitative information about red blood cell aggregation and membrane adhesiveness is discussed.     

Magnetophoresis and diffusion of colloidal particles in a thin layer of magnetic fluids

Experimental and theoretical studies were carried out to investigate the spatial distribution of colloidal particles in magnetic fluids formed under the influence of magnetophoresis and gradient diffusion in a strong magnetic field. Several theoretical models, describing the equilibrium concentration profiles for rigid chain-like and quasispherical aggregates, are discussed. The experiment was made for four samples of magnetic fluids, differing in the average diameter of magnetic particles and the width of the particle size distribution. The analysis of the experimental data shows that the aggregates essentially change the concentration profile, making it nonlinear even in small (2 mm) magnetic fluid samples. Good agreement between the experimental and theoretical curves is observed in the case when the aggregates contain on the average 40-50 particles. The average diameter of single particles, calculated from the concentration profile curves, coincides with the average diameter, found from the magnetogranulometric analysis.     

Rotating spin-1/2 Bose-Einstein condensates in a gradient magnetic field with spin-orbit coupling

We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ≥1 and is nonlinear with λ<1. In the relatively strong rotation regime, in addition to the unstable phase and the single vortex-line phase, the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation. The vortex-ring phase shows the giant and hidden vortex structures at the center of ring. The strong magnetic field gradient makes the number of the vortices around the ring unchanged.     

优化磁共振纳米医学中磁性纳米粒子的热疗效率

磁共振热疗(magnetic resonance hyperthermia)是近年来新兴的一种纳米医学治疗方法,由磁共振的硬件架构产生特定交变磁场,有效地加热磁性纳米粒子,以直接或间接地杀死癌细胞,体现诊疗一体化。提高磁性纳米粒子的加热效率是当前磁共振热疗领域亟待解决的难题之一。磁性纳米粒子的加热效率不仅与粒子本身的大小、性质以及尺寸分布有关,还和聚集状态有关。该研究利用3D Metropolis蒙特卡罗模拟方法,模拟了不同温度下磁性纳米粒子的磁共振热动力学行为及其团聚与分离现象;并通过修正过的郎之万方程,建立了相变临界温度与外加磁场频率的函数关系。模拟结果显示,磁性纳米粒子悬浮液中多聚体的相对含量随着温度的升高而降低,达到临界温度后,多聚体完全分离成单体;而提高交变磁场频率可以显著降低临界温度,且存在临界频率,高于此临界频率后临界温度不再受外加磁场频率影响,达到稳定。因而在临界频率下预热磁性纳米粒子悬浮液,使得多聚体分离成单体,可优化磁性纳米粒子的热疗效率。     

酞菁钴/铁纳米填充母粒组成的磁流变液性能

采用有机／无机原位（ｉｎ ｓｉｔｕ）复合方法制备得出本菁钴／铁纳米填充母粒，与甲基硅油组成磁流变液（ＭＲＳ）。ＭＲＳ的附加动态剪切应力（△τ）与分散介质浓度、外加磁场强度呈正比例关系；剪切速率对△τ的影响表明磁致流变为链状结构特征；△τ的对温度不敏感；ＭＲＳ对外加磁场有可逆的开／关变化特征，无记忆效应，磁流变响应时间小于０．１ｓ。