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.     

Assembly and photonic properties of superparamagnetic colloids in complex magnetic fields

Interparticle magnetic dipole force has been found to drive the formation of dynamic superparamagnetic colloidal particle chains that can lead to the creation of photonic nanostructures with rapidly and reversibly tunable structural colors in the visible and near-infrared spectrum. Although most studies on magnetic assembly utilize simple permanent magnets or electromagnets, magnetic fields, in principle, can be more complex, allowing the localized modulation of assembly and subsequent creation of complex superstructures. To explore the potential applications of a magnetically tunable photonic system, we study the assembly of magnetic colloidal particles in the complex magnetic field produced by a nonideal linear Halbach array. We demonstrate that a horizontal magnetic field sandwiched between two vertical fields would allow one to change the orientation of the particle chains, producing a high contrast in color patterns. A phase transition of Fe(3)O(4)@SiO(2) particles from linear particle chains to three-dimensional crystals is found to be determined by the interplay of the magnetic dipole force and packing force, as well as the strong electrostatic force. While a color pattern with tunable structures and diffractions can be instantly created when the particles are assembled in the form of linear chains in the regions with vertical fields, the large field gradient in the horizontal orientation may destabilize the chain structures and produces a pattern of 3D crystals that compliments that of initial chain assemblies. Our study not only demonstrates the great potential of magnetically responsive photonic structures in the visual graphic applications such as signage and security documents but also points out the potential challenge in pattern stability when the particle assemblies are subjected to complex magnetic fields that often involve large field gradients.     

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.     

Rheological properties and particle behaviors of a non-dilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow (analysis by means of mean-field approximation)

We have investigated the rheological properties and the orientational distributions of particles of a non-dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The mean-field approximation is applied to take into account the interactions between spherocylinder particles. The basic equation of the orientational distribution function has been derived from the balance of the torques (including the term due to the mean field approximation) acting on the particle in an applied magnetic field; this is an integrodifferential equation. Then, the governing equation has been solved by means of the method of successive approximation and Galerkin's method. The results obtained here are summarized as follows. For the case of strong magnetic interactions between particles, the particle exhibits a sharp peak of the orientational distribution even for a weak applied magnetic field. In this case, the mean magnetic moment of the particle becomes large, which leads to strong interactions between the applied magnetic field and the particle. Thus, the particle tends to point to the magnetic filed direction under these situations. Also, in this case, a large increase in viscosity is obtained due to such a restriction concerning the particle orientation.     

Tuning the Colloidal Crystal Structure of Magnetic Particles by External Field

Manipulation of the self‐assembly of magnetic colloidal particles by an externally applied magnetic field paves a way toward developing novel stimuli responsive photonic structures. Using microradian X‐ray scattering technique we have investigated the different crystal structures exhibited by self‐assembly of core–shell magnetite/silica nanoparticles. An external magnetic field was employed to tune the colloidal crystallization. We find that the equilibrium structure in absence of the field is random hexagonal close‐packed (RHCP) one. External field drives the self‐assembly toward a body‐centered tetragonal (BCT) structure. Our findings are in good agreement with simulation results on the assembly of these particles.     

Assembly behavior of iron oxide-capped Janus particles in a magnetic field

Three types of iron oxide Janus particles are obtained by varying the deposition rate of iron in a 3:1 Ar/O(2) atmosphere during physical vapor deposition. Each type of iron oxide Janus particle shows a distinct assembly behavior when an external magnetic field is applied, i.e., formation of staggered chains, double chains, or no assembly. A detailed deposition rate diagram is obtained to identify the relationship between deposition rate and assembly behavior. The extent of iron oxidation is identified as the key parameter in determining the assembly behavior. In addition, the effects of particle volume fraction, thickness of the iron oxide cap, and assembly time on the final assembly behavior are studied. Cap thickness is shown not to influence the assembly behavior, while particle volume fraction and assembly time affect the chain growth rate and the chain length, but not the overall assembly behavior. The samples are characterized by optical, scanning electron, and atomic force microscopies.     

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.     

Magnetic nanorods confined in a lamellar lyotropic phase

The dilute lamellar phase of the nonionic surfactant C 12EO 5 was doped with goethite (iron oxide) nanorods up to a fraction of 5 vol %. The interaction between the inclusions and the host phase was studied by polarized optical microscopy (with or without an applied magnetic field) and by small-angle X-ray scattering. We find that, when the orientation of the nanorods is modified using the magnetic field, the texture of the lamellar phase changes accordingly; one can thus induce a homeotropic-planar reorientation transition. On the other hand, the lamellar phase induces an attractive interaction between the nanorods. In more concentrated lamellar phases (under stronger confinement) the particles form aggregates. This behavior is not encountered for a similar system doped with spherical particles, emphasizing the role of particle shape in the interaction between doping particles and the host phase.     

Magnetic field induced synthesis and self-assembly of super paramagnetic particles in a protein matrix

Aqueous solution of a globular protein named bovine serum albumin was homogeneously mixed with ferrous and ferric ions and allowed to gel at ambient conditions. Gels were then oxidized using sodium hydroxide, in the presence of magnetic field of magnitude 0.13 T. The effect of magnetic field on the above biomimetic synthesis was a reduction in particle size and a directional assembly of synthesized super paramagnetic particles into a regular pattern in the protein film. The microstructural revelation was complimentary to Mossbauer results and magnetic measurement studies, i.e., an interesting variation in the magnetic behaviour of self-assembled super paramagnetic particles as a function of dc magnetic field induced ordering.     

Influence of magnetic interactions between clusters on particle orientational characteristics and viscosity of a colloidal dispersion composed of ferromagnetic spherocylinder particles: analysis by means of mean field approximation for a simple shear flow

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones that belong to the neighboring clusters, besides those that belong to its own cluster. The basic equation of the orientational distribution function, which is an integrodifferential equation, has approximately been solved by Galerkin's method and the method of successive approximation. Some of the main results obtained here are summarized as follows. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significant with increasing volumetric fraction of particles; the orientational distribution function exhibits a sharper peak in the direction nearer to the magnetic field one as the volumetric fraction increases. Such a significant inclination of the particle in the field direction induces the large increase in viscosity in the range of larger values of the volumetric fraction. The above-mentioned characteristics of the orientational distribution and viscosity come to appear more significantly when the influence of the applied magnetic field is not so strong compared with that of magnetic particle-particle interactions.     

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.     

Analytical magnetapheresis of magnetically susceptible particles

Analytical magnetapheresis is a newly developed technique for analyzing magnetic particles. The magnetically susceptible particles form deposition patterns after flowing through a separation channel in a magnetic field. The separation channel requirements for analytical magnetapheresis are an excellent seal for the carrier flow and ease of disassembly after magnetapheresis. Previously used separation channels often exhibit variable channel leakage and unstable flow velocities. We improved the separation channel assembly to ensure stable, high flow velocities and characterized the system with various magnetically susceptible and labeled particles. Our new separation channel featured silicone sealant with embedded nylon wires and met analytical magnetapheresis requirements. Characterization of this system was performed using several magnetically susceptible particles, and we studied a variety of diamagnetic sample labels with paramagnetic ions and magnetically susceptible particles at different flow-rates and solution pH values. The minimal labeling concentration for complete deposition was determined to be approximately 2.50 x 10(10) ions per particle for test samples at a flow velocity of 0.67 mm s(-1) and a magnetic field gradient of 2.8 T mm(-1). Silicas, yeasts and blood cells were used for these studies. We determined that the minimal difference in magnetic susceptibility (delta(chi)) for successful separation was approximately 2.00 x 10(-6) [SI]. The magnetic susceptibilities of Dynabeads M-450 at several separation distances and flow-rates were determined to be 0.25 [SI], within 2% of values published by other workers. The magnetic susceptibilities of various ion-labeled yeasts and cells were determined and most varied by less than 5% at different flow-rates. The results of this study provide very important references for analytical magnetapheresis applications.     

Determination of magnetic susceptibility of various ion-labeled red blood cells by means of analytical magnetapheresis

Analytical magnetapheresis is a newly developed technique for separating magnetically susceptible particles. The magnetically susceptible particles are deposited on a bottom plate after flowing through a thin (< 0.05 cm) separation channel under a magnetic field applied perpendicular to the flow. Particles with various magnetic susceptibilities can be selectively deposited and separated by adjusting the applying magnetic force and flow rates. Magnetic susceptibility is an important parameter for magnetic separation. Magnetic susceptibility determination of various ion-labeled red blood cells (RBCs) using analytical magnetapheresis with a simple theoretical treatment is reported in this study. Susceptibility determination is based on the balance between maximal channel flow rate and magnetically induced flow rate for deposition. We tried a new approach to determine particle magnetic susceptibilities using a balance of magnetic and drag forces to control magnetically induced particle velocities. The Er3+, Fe3+, Cu2+, Mn2+, Co2+, and Ni2+ ions were used to label RBC at various labeling concentrations for susceptibility determination. The susceptibilities determined for various ion-labeled RBC under two magnetic field intensities fell within a 10% range. The average viabilities of various ion-labeled RBCs were 96.1 +/- 0.8%. The susceptibility determination generally took less than 10 min. Determined susceptibilities from analytical magnetapheresis differed by 10% from reference measurements using a superconducting quantum interference device (SQUID) magnetometer. The cost and time for analysis is much less using analytical magnetapheresis. This technique can provide a simple, fast, and economical way for particle susceptibility determinations.     

Labeled magnetic nanoparticles assembly on polypyrrole film for biosensor applications

In recent years, conducting polymers combined with metallic nanoparticles have been paid more attention due to their potential applications in microelectronics, microsystems, optical sensors and photoelectronic chemistry. The work presented in this paper describes the preparation and characterization of a nanocomposite composed by a thin polypyrrole (PPy) film covered with an assembly of magnetic nanoparticles (NPs). The magnetic particles were immobilized on PPy films under appropriate magnetic field in order to control their organization on the PPy film and finally to improve the sensitivity of the system in potential sensing applications. The electrical properties and morphology of the resulting PPy film and the PPy film/NPs composite were characterized with cyclic voltammetry, impedance spectroscopy (IS), scanning electron microscopy (SEM), atomic force microscopy (AFM) and infra-red spectroscopy (IR). By using streptavidin labeled magnetic particles it was possible to functionalize the NPs assembly with biotin-Fab fragment K47 antibody. The designed biosensor had been successfully applied in rapid, simple, and accurate measurements of atrazine concentrations, with a significantly low detection limit of 5 ng/ml.     

Rheological Properties and Orientational Distributions of Dilute Ferromagnetic Spherocylinder Particle Dispersions

We have investigated the rheological properties and the orientational distributions of particles of a dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The governing equation of an orientational distribution function has been derived from the balance of the torques acting on a particle in an applied magnetic field. After a spherical harmonic expansion, an approximate solution to the governing equation has been found by Galerkin's method. The results obtained are summarized as follows. The orientational distribution function has a sharper peak for a stronger magnetic field, and the position of the peak changes from the flow direction to the magnetic field direction as the magnetic field comes to govern the shear flow. Since the orientation of the particle is highly restricted in the field direction as the magnetic field becomes strong, the viscosity increases significantly. The particles with a larger aspect ratio lead to the larger increment in the viscosity, since they induce a larger resistance in a flow field. Copyright 2001 Academic Press.     

Magnetic particle‐loaded polymer brushes induced by external magnetic field: A Monte Carlo simulation

The effects of applied magnetic field on the system composed of polymer brushes and magnetic particles are studied by means of Monte Carlo simulation. The direction of the applied magnetic field is chosen to be perpendicular to the substrate plane. Polymer brushes and magnetic particles are attracted to each other. The average heights of polymer brushes depend not only on the strength of applied magnetic field (H) but also on the brush grafting density (σ) and the chain length (N). The applied magnetic field influences the arrangement of magnetic particles, and in turn, the arrangement of magnetic particles affects the spatial distribution of polymer brush monomers. When the strength of the magnetic field is increased, the average height of polymer brushes will be increased accordingly. The reason is that the orientations of the magnetic moments of particles must be along the magnetic field direction, and this leads polymer brushes to rearrange along the magnetic field direction. At the same time, the chain length and the grafting density of polymer brushes have also effects on the properties of the magnetic particles, such as the magnetic particles distribution, magnetic susceptibility, and pair correlation functions. Comparisons with the experimental ones are also made, and this investigation can provide some insights into statistical properties of magnetic particle‐loaded brushes induced by external magnetic field. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1873–1881, 2010     

Alignment of carbon nanotubes under low magnetic fields through attachment of magnetic nanoparticles

The alignment of multiwalled carbon nanotubes (MWNTs) has been accomplished through deposition of uniform layers of magnetite/maghemite nanoparticles (diameter = 6-10 nm) and use of an external magnetic field. The coating of CNTs with magnetic nanoparticles was performed by combining the polymer wrapping and layer-by-layer (LbL) assembly techniques. The particle-coated MWNTs are superparamagnetic and can be aligned at room temperature on any substrate by deposition from an aqueous solution in an external field B = 0.2 T. The volume magnetization of the particle coated MWNTs is found to be enhanced by 17% compared to the pure particles in a powder indicating that either the adsorption process onto the CNTs changes the particle magnetization, or the MWNTs carry an intrinsic magnetization due to remaining Ni used as a catalyst for the growth process.     

Polarization and interactions of colloidal particles in ac electric fields

Micrometer-sized polystyrene particles form two-dimensional crystals in alternating current (ac) electric fields. The induced dipole-dipole interaction is the dominant force that drives this assembly. We report measurements of forces between colloidal particles in ac electric fields using optical tweezers and find good agreement with the point dipole model. The magnitude of the pair interaction forces depends strongly on the bulk solution conductivity and decreases as the ionic strength increases. The forces also decrease with increasing field frequency. The salt and frequency dependences are consistent with double layer polarization with a characteristic relaxation frequency omega(CD) approximately a(2)/D, where a is the particle radius and D is the ion diffusivity. This enables us to reinterpret the order-disorder transition reported for micrometer-sized polystyrene particles [Lumsdon et al., Langmuir 20, 2108 (2004)], including the dependence on particle size, frequency, and ionic strength. These results provide a rational framework for identifying assembly conditions of colloidal particles in ac fields over a wide range of parameters.     

Digital microfluidics and delivery of molecular payloads with magnetic porous silicon chaperones

Digital microfluidics involves the manipulation of molecules and materials in discrete packages. This paper reviews our work using amphiphilic magnetic microparticles constructed from porous silicon. An individual porous particle can be used to carry a nanomole or smaller quantities of a reagent, and assemblies of the particles can encapsulate and transport microliter droplets of liquid containing inorganic, organic, or biological molecules. The tracking and identification of each particle can be accomplished with spectral labels that are encoded into the particles during their synthesis. When used to chaperone liquid droplets, the labels can identify the separate droplets prior to mixing and also the combined droplets after mixing. Magnetic iron oxide nanoparticles encapsulated in the porous matrix allow the manipulation of the particles or whole droplet assemblies with a magnetic field, and they also allow heating of the particle's payload by means of an externally applied RF field. Examples of organic, inorganic, and biomolecular addition reactions, catalytic reactions, and thermolysis reactions are described.     

Dielectrophoretic assembly of metallodielectric Janus particles in AC electric fields

"Janus" particles with two hemispheres of different polarizability or charge demonstrate a multitude of interesting effects in external electric fields. We reported earlier how particles with one metallic hemisphere and one dielectric hemisphere self-propel in low-frequency alternating current (AC) electric fields. Here, we demonstrate the assembly of such Janus particles driven by AC electric fields at frequencies above 10 kHz. We investigated the relation between field-induced dielectrophoretic force, field distribution, and structure of the assemblies. The phase space for electric field intensity and frequency was explored for particle concentrations large enough to form a monolayer on a glass surface between two gold electrodes. A rich variety of metallodielectric particle structures and dynamics were uncovered, which are very different from those obtained from directed assembly of plain dielectric or plain conductive particles under the action of fields of similar frequency and intensity. The metallodielectric particles assemble into new types of chain structures, where the metallized halves of neighboring particles align into lanes along the direction of the electric field, while the dielectric halves face in alternating direction. The staggered chains may assemble in various orientations to form different types of two-dimensional metallodielectric crystals. The experimental results on the formation of staggered chains are interpreted by means of numerical simulations of the electric energy of the system. The assembly of Janus metallodielectric particles may find applications in liquid-borne microcircuits and materials with directional electric and heat transfer.