Simulation study on microstructure formations in magnetic fluids

We propose the Langevin-type microscopic equations of motion for magnetic fluids. Magnetic fluids are modeled as an ensemble of interacting ferromagnetic nanoparticles suspended in a viscous fluid. The present model is described in terms of position vectors of nanoparticles and orientation vectors of their magnetic dipole moments. In this model, forces and torques arising from the magnetic origin and the surrounding fluid flow are included. Effects of non-spherical particle shape are also taken into account. From the Brownian dynamics simulations of the model, it is found that the present model exhibits various microstructure formation processes in magnetic fluids.     

Brownian dynamics simulation of electrostatically interacting proteins

Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.     

Low-frequency complex magnetic susceptibility of magnetic composite microspheres in colloidal dispersion

A procedure is presented to determine the permanent magnetic dipole moment of composite microspheres containing magnetic nanoparticles with a blocked magnetic dipole moment. The composite particles are dispersed in a solvent, and the complex magnetic susceptibility is measured from 0.1 to 1000 Hz using a highly sensitive new setup. Composite particles with a permanent magnetic dipole moment are revealed by a characteristic frequency that corresponds to the Brownian rotation of the microspheres. From measured susceptibility spectra, we calculate the permanent magnetic dipole moment of recently developed cobalt ferrite-doped silica and latex microspheres.     

Measurement of the translational and rotational Brownian motion of individual particles in a rarefied gas

We measured the free Brownian motion of individual spherical and the Brownian rotation of individual nonspherical micrometer-sized particles in rarefied gas. Measurements were done with high spatial and temporal resolution under microgravity conditions in the Bremen drop tower so that the transition from diffusive to ballistic motion could be resolved. We find that the translational and rotational diffusion can be described by the relation given by Uhlenbeck and Ornstein [Phys. Rev. 36, 823 (1930)]. Measurements of rotational Brownian motion can be used for the determination of the moments of inertia of small particles.     

Field-variable magnetic domain characterization of individual 10 nm Fe_3O_4 nanoparticles

The local detection of magnetic domains of isolated 10 nm Fe_3O_4 magnetic nanoparticles(MNPs) has been achieved by field-variable magnetic force microscopy(MFM) with high spatial resolution.The domain configuration of an individual MNP shows a typical dipolar response.The magnetization reversal of MNP domains is governed by a coherent rotation mechanism, which is consistent with the theoretical results given by micromagnetic calculations.Present results suggest that the field-variable MFM has great potential in providing nanoscale magnetic information on magnetic nanostructures,such as nanoparticles, nanodots, skyrmions, and vortices, with high spatial resolution.This is crucial for the development and application of magnetic nanostructures and devices.     

Excitation of the orientation transition wave and chaotic dynamics in a lattice of magnetic nanoparticles

The propagation of the front of oscillatory dynamics of magnetic moments caused by the local perturbation of the lattice along a system is studied for planar three-row lattices of magnetic nanoparticles having cubic anisotropy and coupled by the dipole interaction. The propagation of both the transition between two equilibrium planar configurations and chaotic oscillations of magnetic moments in the case of their initial orientation perpendicular to the plane of the lattice is implemented. The possibility of controlling the velocity of propagation of the orientation transition wave and its stop is revealed. The appearance of the moving front of the chaotic dynamics is found at switching on and switching off the local external field and at the action of the alternating field pulse.     

Reciprocity of Faraday effect in ferrofluid: Comparison with magneto-optical glass

The transmission light intensity method is carried out on a classical platform to study the reciprocity of Faraday effect in water-based Fe₃O₄ ferrofluid and its diluents. Setting the polarization direction of the analyzer at an angle of 45° to that of the polarizer, the switchable DC magnetic field and the alternating magnetic field are imposed to ferrofluid. The ferrofluid film is replaced by magneto-optical glass for contrastive experiments. The results indicate that ferrofluid is different with magneto-optical glass. Even though the direction of magnetic field is reversed, the rotation direction of the polarized light does not change for ferrofluid. The theoretical model of magneto-optical rotation was used to describe the origin of the reciprocity of Faraday effect in ferrofluid and the non-reciprocity in magneto-optical glass. These findings suggest that the magnetic moments of nanoparticles in ferrofluid tend to the same orientation with the magnetic field because of the rotation of particles.     

Video-frequency scanning transmission electron microscopy of moving gold nanoparticles in liquid

Immobilized gold nanoparticles were imaged in a liquid containing water and 50% glycerol with scanning transmission electron microscopy (STEM). The specimen was enclosed in a liquid compartment formed by two silicon microchips with electron transparent windows. A series of images was recorded at video frequency with a spatial resolution of 1.5nm. The nanoparticles detached from their support after imaging them for several seconds at a magnification of 250,000. Their movement was found to be much different than the movement of nanoparticles moving freely in liquid as described by Brownian Motion. The direction of motion was not random-the nanoparticles moved either in a preferred direction, or radially outwards from the center of the image. The displacement of the gold nanoparticles over time was three orders of magnitude smaller than expected on the basis of Brownian Motion. This finding implies that nanoscale objects of flexible structure or freely floating, including nanoparticles and biological objects, can be imaged with nanoscale resolution, as long as they are in close proximity to a solid support structure.     

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.     

Ultrafast Faraday effect and the dynamics of the antiferromagnet-paramagnet phase transition in FeBO3

The optical pump-probe technique using ultrashort laser pulses with a photon energy of 1.55 eV was used to study the dynamics of the antiferromagnet-paramagnet phase transition in FeBO₃. The Faraday magneto-optical effect was measured with a time resolution of 100 fs, and signal transients were observed as functions of sample temperature. The rate of photoinduced phase transition was shown to be limited by the phonon-magnon relaxation rate with a characteristic time of 700 ps. The subpicosecond dynamics of Faraday rotation is not associated with the destruction of magnetic order but is caused by electron photoexcitation and recombination.     

The verification of the Taylor-expansion moment method for the nanoparticle coagulation in the entire size regime due to Brownian motion

The closure of moment equations for nanoparticle coagulation due to Brownian motion in the entire size regime is performed using a newly proposed method of moments. The equations in the free molecular size regime and the continuum plus near-continuum regime are derived separately in which the fractal moments are approximated by three-order Taylor-expansion series. The moment equations for coagulation in the entire size regime are achieved by the harmonic mean solution and the Dahneke??s solution. The results produced by the quadrature method of moments (QMOM), the Pratsinis??s log-normal moment method (PMM), the sectional method (SM), and the newly derived Taylor-expansion moment method (TEMOM) are presented and compared in accuracy and efficiency. The TEMOM method with Dahneke??s solution produces the most accurate results with a high efficiency than other existing moment models in the entire size regime, and thus it is recommended to be used in the following studies on nanoparticle dynamics due to Brownian motion.     

A direct method for numerical analysis of relaxation of the statistical characteristics of brownian motion

We propose a numerical method for analyzing the relaxation of coordinate moments of the Brownian motion of a system described by a stochastic Liouville equation of the 1st or 2nd order with moderate-order polynomial nonlinearity. Using exact or approximate recurrence relations for the stationary values, at a certain step, we break the chain of equations for the moments of the Brownian motion. The evolution of the model probability distribution of coordinates is found from the numerical solution of the differential equations of relaxation of moments. This method is used for analyzing the nonstationary probability characteristics of a system with nonlinear rigidity described by a third-degree polynomial. The relaxation of moments and of the model probability distribution is plotted and tabulated. The results obtained allow us to draw certain conclusions on the statistical dynamics of the Brownian motion of the systems studied. Nizhny Novgorod Architecture and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 922–930, September 1999     

Dependence of the metastability of the magnetic states of two-phase nanoparticles on mechanical stress

The influence of mechanical stress on the magnetic states of multiaxial heterophase magnetic materials is investigated using a model of two-phase nanoparticles. The range of critical fields for the reversal of the magnetic moments of phases is calculated and phase diagrams are built to assess the effect of interface exchange interaction and mechanical stress on the metastability of the magnetic states of two-phase nanoparticles.     

1H NMR Detection of superparamagnetic nanoparticles at 1T using a microcoil and novel tuning circuit

Magnetic beads containing superparamagnetic iron oxide nanoparticles (SPIONs) have been shown to measurably change the nuclear magnetic resonance (NMR) relaxation properties of nearby protons in aqueous solution at distances up to approximately 50 microm. Therefore, the NMR sensitivity for the in vitro detection of single cells or biomolecules labeled with magnetic beads will be maximized with microcoils of this dimension. We have constructed a prototype 550 microm diameter solenoidal microcoil using focused gallium ion milling of a gold/chromium layer. The NMR coil was brought to resonance by means of a novel auxiliary tuning circuit, and used to detect water with a spectral resolution of 2.5 Hz in a 1.04 T (44.2MHz) permanent magnet. The single-scan SNR for water was 137, for a 200 micros pi/2 pulse produced with an RF power of 0.25 mW. The nutation performance of the microcoil was sufficiently good so that the effects of magnetic beads on the relaxation characteristics of the surrounding water could be accurately measured. A solution of magnetic beads (Dynabeads MyOne Streptavidin) in deionized water at a concentration of 1000 beads per nL lowered the T(1) from 1.0 to 0.64 s and the T2 * from 110 to 0.91 ms. Lower concentrations (100 and 10 beads/nL) also resulted in measurable reductions in T2 *, suggesting that low-field, microcoil NMR detection using permanent magnets can serve as a high-sensitivity, miniaturizable detection mechanism for very low concentrations of magnetic beads in biological fluids.     

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.     

Theoretical study of the magnetic moments and anisotropy energy of CoRh nanoparticles

The role of size, structure and chemical order on the magnetic moments and magnetic anisotropy energy (MAE) of CoRh nanoparticles are studied in the framework of a self-consistent real-space tight-binding method. Our results show that a Rh core in a geometry having a large surface/volume ratio and with Co–Rh mixing at the interface is the most likely chemical arrangement. A local analysis reveals that the orbital and spin moments at the Co–Rh interface are largely responsible for the increase of the magnetic moments and magnetic anisotropy. Moreover, the local moments induced at the Rh atoms, which amount to about 20% of the moment per Co atom [ μ_Rh = (0.2–0.3) μ_B] and the orbital moments of Co atoms play a crucial role on the interpretation of experiment. The results are discussed in the context of the interplay between chemical order and magnetic properties.     

Self-assembly in the systems of magnetic anisotropic nanoparticles

This paper presents the complex investigation of the system of magnetic anisotropic nanoparticles using computer simulations in a wide range of the system’s parameters. The cluster analysis was made, various average characteristics of the formed clusters were calculated and the initial magnetic susceptibility and the radial distribution function were computed. It was shown that via changing the nanoparticles characteristics (their shape and the values of the magnetic moments) it’s possible to change macroscopic response of the system, that implements the idea of tuning and design new materials with controllable properties.     

Optomagnetically Controlled Microparticles Manufactured with Glancing Angle Deposition

Optical trapping and magnetic trapping are common micromanipulation techniques for controlling colloids including micro‐ and nanoparticles. Combining these two manipulation strategies allows a larger range of applied forces and decoupled control of rotation and translation; each of which are beneficial properties for many applications including force spectroscopy and advanced manufacturing. However, optical trapping and magnetic trapping have conflicting material requirements inhibiting the combination of these methodologies. In this paper, anisotropic microscaled particles capable of being simultaneously controlled by optical and magnetic trapping are synthesized using a glancing angle deposition (GLAD) technique. The anisotropic alignment of dielectric and ferromagnetic materials limits the optical scattering from the metallic components which typically prevents stable optical trapping in three dimensions. Compared to the current state of the art, the benefits of this approach are twofold. First, the composite structure allows larger volumes of ferromagnetic material so that larger magnetic moments may be applied without inhibiting the stability of optical trapping. Second, the robustness of the synthesis process is greatly improved. The dual optical and magnetic functionality of the synthesized colloids is demonstrated by simultaneously optically translating and magnetically rotating a magnetic GLAD particle using a custom designed optomagnetic trapping system.     

Uniaxial Diffusional Narrowing of NMR Lineshapes for Membrane Proteins Reconstituted in Magnetically Aligned Bicelles and Macrodiscs

Structure and dynamics of membrane proteins can be effectively studied by oriented-sample solid-state nuclear magnetic resonance (NMR) techniques when the lipid bilayers are macroscopically aligned with respect to the main magnetic field. Magnetic alignment of the protein-containing membrane bilayer results from the negative susceptibility anisotropy of the lipid hydrocarbon interior yielding perpendicular sample alignment. At this orientation, while the uniformity of alignment represents an essential prerequisite for obtaining high-quality NMR spectra, further line narrowing is obtained by uniaxial motional averaging of the azimuthal parts of the chemical shift anisotropies and dipolar couplings. The motional averaging is brought about by uniaxial rotational diffusion of the protein molecules about the normal to the membrane surface, which is perpendicular to the magnetic field. Uniaxial averaging is efficient when the motion about the axis of alignment becomes sufficiently fast (on the timescale of the dipolar couplings and chemical shift anisotropies). Line narrowing under uniaxial rotation can be theoretically modeled using the stochastic Liouville equation. In this mini-review, we illustrate the method of uniaxial averaging for the relatively small Pf1 coat protein which exhibits excellent resolution in magnetically aligned bicelles due to its fast uniaxial diffusion and even superior resolution in large (30 nm) nanodiscs (macrodiscs) stabilized by a belt peptide. Spectra of Pf1 coat protein in polymer-stabilized macrodiscs, an alternative and more robust alignment media, are presented. We also report on preliminary spectra of a much larger protein—uniformly ¹⁵N labeled M1-M4 domain for the human acetylcholine receptor. While some spectral resolution is apparent, significantly broader linewidths emphasize the need for creating fast rotating discoidal membrane mimetics.