Magnetooptical studies of aggregates of nanoparticles in colloidal solutions of magnetite

The birefringence in a colloidal solution of nanosized magnetite particles in kerosene exposed to constant, alternating, and pulsed magnetic fields is studied. Data on the birefringence kinetics in nonstationary magnetic fields is used to determine the hydrodynamic radius of particle aggregates in solutions. The permanent dipole moment of aggregates and the anisotropy of the magnetic susceptibility are calculated based on the data of magnetooptical experiments. It is shown that the induced dipole moment plays a significant role in an orientation of aggregates of magnetic nanoparticles under the effect of a field.     

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.     

Hydrodynamics of Brownian particles

When considering the hydrodynamics of Brownian particles, one is confronted to a difficult closure problem. One possibility to close the hierarchy of hydrodynamic equations is to consider a strong friction limit. This leads to the Smoluchowski equation that reduces to the ordinary diffusion equation in the absence of external forces. Unfortunately, this equation has infinite propagation speed leading to some difficulties. Another possibility is to make a Local Thermodynamic Equilibrium (L.T.E) assumption. This leads to the damped Euler equation with an isothermal equation of state. However, this approach is purely phenomenological. In this paper, we provide a preliminary discussion of the validity of the L.T.E assumption. To that purpose, we consider the case of free Brownian particles and harmonically bound Brownian particles for which exact analytical results can be obtained [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)]. For these systems, we find that the L.T.E. assumption is not unreasonable and that it can be improved by introducing a time dependent kinetic temperature T_kin(t)=γ(t)T instead of the bath temperature T. We also compare hydrodynamic equations and generalized diffusion equations with time dependent diffusion coefficients.     

Simulating (electro)hydrodynamic effects in colloidal dispersions: Smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent (Phys. Rev. E 71, 036707 (2005)). An improved formulation called the “Smoothed Profile (SP) method” is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids.     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

混沌半导体激光器的弛豫振荡频率对随机序列速率的影响

利用光反馈半导体激光器产生的混沌激光作为随机数发生器的物理熵源, 分析了混沌信号自相关系数与随机序列游程数之间的联系, 在此基础上研究了激光器的弛豫振荡频率f_r与随机序列速率f_n在不同比值时, 序列游程数的变化情况. 研究发现, 当f_r/f_n=(2k+1)/4时, 随机序列的游程数容易满足NIST SP800-22随机数测试标准的要求. 当k=1时, 得到随机序列最大速率为f_n=4f_r/3.     

Light scattering from colloids

This paper presents a review of light scattering results on static and dynamic properties of ordered colloidal suspensions of charged polystyrene particles and fractal colloidal aggregates. Our studies on static structure factor,S(Q), of ordered monodisperse colloidal suspensions and binary mixtures of particles with different particle diameters, measured by angle-resolved Rayleigh scattering will be discussed. This will include determination of bulk modulus using gravitational compression and observation of colloidal glass (inferred from splitting of the second peak inS(Q)). Dynamic light scattering, with real time analysis of scattered intensity fluctuations, is used to get information about Brownian dynamics of the particles. Recent advances in the field of light scattering from colloidal aggregates which show fractal geometry will also be discussed.     

A statistical-mechanical theory of self-diffusion in colloidal suspensions — application to colloidal glass transitions

A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama–Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.     

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.     

Hydrodynamic Stress Tensor in Inhomogeneous Colloidal Suspensions: an Irving-Kirkwood Extension *

Based on statistical mechanics for classical fluids, general expressions for hydrodynamic stress in inhomogeneous colloidal suspension are derived on a molecular level. The result is exactly an extension of the Iving-Kirkwood stress for atom fluids to colloidal suspensions where dynamic correlation emerges. It is found that besides the inter-particle distance, the obtained hydrodynamic stress depends closely on the velocity of the colloidal particles in the suspension, which is responsible for the appearance of the solvent-mediated hydrodynamic force. Compared to Brady's stresslets for the bulk stress, our results are applicable to inhomogeneous suspension, where the inhomogeneity and anisotropy of the dynamic correlation should be taken into account. In the near-field regime where the packing fraction of colloidal particles is high, our results can reduce to those of Brady. Therefore, our results are applicable to the suspensions with low, moderate, or even high packing fraction of colloidal particles.     

Studies of trapped strontium ions in low magnetic fields

The effect of weak magnetic fields ( 1 mT) on small clouds and single ions of strontium has been studied. The fluorescence rate and hence the cooling efficiency is sharply reduced for fields of less than around 0.2 mT. The magnetic field also splits the various levels involved through the Zeeman effect. In particular, the² S _1/2–² D _5/2 transition at 674 nm, which is the basis for a potential optical frequency standard, is split into a maximum of 10 components, depending upon the experimental geometry. This is studied for various configurations of the magnetic field and 674 nm laser polarization. The implication for frequency-standards work is that the standard will need to be operated in a small but highly stable field.     

Citric-acid-coated magnetite nanoparticles for biological applications

Water-based magnetic fluids, generally intended for biomedical applications, often have various coating molecules that make them stable and compatible with biological liquids. Magnetic fluids containing iron oxide particles have been prepared by a co-precipitation method, using citric acid as stabilizer. The magnetic particles of the magnetic fluids were obtained by chemical precipitation from ferric ( FeCl₃) and ferrous salts ( FeSO₄ or FeCl₂) in alkali medium (ammonia hydroxide). Citric acid was used to stabilize the magnetic-particle suspension. Physical tests were performed in order to determine various microstructural and rheological features. Transmission electron microscopy was the main investigation method for assessing the magnetic-particle size. The dimensional distribution of the magnetic-particle physical diameter was analyzed using the box-plot statistical method while infrared absorption spectra were used to study the colloidal particle structure. The magnetic-fluid density (picnometric method), viscosity (capillary method) and surface tension (stalagmometric method) were measured using standard methods.     

A comparative study on the effect of hydrodynamic interactions in the non-sequential deposition of concentrated colloidal dispersions: stochastic rotation dynamics and Brownian dynamics simulations

Irreversible adsorption of particles onto a flat surface as a consequence of sedimentation colloidal suspension has been studied by two simulation techniques: Brownian dynamics (BD) and stochastic rotation dynamics (SRD). The purpose of using both methods is to investigate the effect of hydrodynamic interactions on adsorption kinetics and structure of the first monolayer of sediment obtained from the sedimentation of a concentrated and monodisperse colloidal suspension. Three systems were studied, characterised by the Péclet numbers: 0.1, 1.0 and 10. To physically understand the kinetic behaviour, simulation results were analysed using a kinetic model based on chemical reactions. High values of jamming limit (θ_∞ > 0.61) were obtained for both simulation techniques, with the SRD showing the highest figures (0.631) due to the hydrodynamics effect that takes into account the fluid backflow produced on particle sedimentation. A two-step adsorption mechanism was proposed based on the observed kinetic behaviour.     

Allgemeine Berechnung der Elektronenverteilungsfunktion von schwach ionisierten Plasmen in beliebig zeitabhängigen elektromagnetischen Feldern

The behaviour of a weakly ionized plasma in external, arbitrarily time-dependent, electromagnetic fields is treated within the framework of kinetic theory. The Boltzmann kinetic equation is solved using the Lorentz ansatz, taking into account elastic collisions between electrons and neutral particles and assuming that the collision frequency is independent of the electron velocity. The drift velocity of electrons enters into the isotropic part f₀ and into the direction-dependent part f₁ of the electron distribution function. A method is given for the calculation of the drift velocity, which is calculated explicitly for the important but difficult case of a sinusoidal electric field in the presence of a magnetic switching field. f₀ and f₁ are calculated; f₀ is investigated generally. f₀ consists of an expansion in generalized Laguerre polynomials. The influence of the electromagnetic fields on the distribution function and its time variation is discussed and the relaxation behaviour is shown. The following two special cases are calculated explicitly: a linear rising electric field and a sinusoidal electric field, both in the presence of a constant magnetic field.     

Frequency-domain performance of a femtosecond laser with carrier-envelope phase stabilized by the direct locking method

We analyzed frequency-domain characteristics of a femtosecond laser whose carrier-envelope phase (CEP) was stabilized by the direct locking method (DLM). To evaluate the CEP-stabilized laser with zero carrier-envelope-offset frequency (f _ceo), as imposed by DLM, a self-referencing f-to-2f interferometer with a shifted frequency comb by an acousto-optic modulator was employed in an out-of-loop. The measurement of the square root of triangle variance confirmed that DLM is a phase-locking method. The tight locking was verified from a narrow bandwidth of f _ceo, measured using the out-of-loop interferometer, and from a small frequency jitter measured with a frequency counter referenced to a Rb-clock. The femtosecond laser with CEP stabilized by DLM is, thus, well suited for applications in the frequency domain as well as in the time domain.     

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。     

A study of various intraband processes inn-InSb by means of stimulated spin-flip raman scattering

The spin-flip Raman (SFR) laser is shown to be an excellent tool to investigate different processes in the conduction band of the SFR laser crystal itself. For the case ofn-InSb, intracavity spectroscopy of inter-Landau transitions is demonstrated to be much more sensitive than conventional transmission spectroscopy. Data on cyclotron harmonic transitions, both free and LO-phonon assisted, are obtained from the output power characteristics of the SFR laser versus magnetic field. The spin-splitting energy and the effectiveg-factor up to 14 T are derived from the SFR laser frequency. The influence of temperature on SFR laser power, threshold and frequency is investigated. The relaxation following the SFR laser pulse is observed in the electrical conductivity. This yields in a direct way the spin-lattice relaxation time at high magnetic fields, which is of the order of 200 ns.     

On Different Approaches to Estimate the Mass Fractal Dimension of Coal Aggregates

Several methods to measure the structures of coal aggregates are compared. Loose and compact coal aggregates were generated through flocculation of ultrafine coal particles (mean volume diameter of 12 μm) under specific shearing conditions. Aggregate structure in terms of mass fractal dimension, D_f, was determined using various methods; namely 2D and 3D image analysis, interpretation of intensity patterns from small angle light scattering, changes in aggregation state through light obscuration, and settling behavior. In this study, the measured values of D_f ranged from 1.84–2.19 for coal aggregates with more open structures, and around 2.27–2.66 for the compact ones. All of these approaches could distinguish structural differences between aggregates, albeit with variation in D_f values estimated by the different techniques. The discrepancy in the absolute values for fractal dimension is due to the different physical properties measured by each approach, depending on the assumptions used to infer D_f from measurable parameters. In addition, image analysis and settling techniques are based on the examination of individual aggregates, such that a large number of data points are required to yield statistically representative estimations. Light scattering and obscuration measure the aggregates collectively to give average D_f values of the particulate systems; consequently ignoring any structural variation between the aggregates, and leaving possible small contaminations undetected (e.g. by dust particles or air bubbles). Appropriate utilization of a particular method is thus largely determined by system properties and required data quality.     

Laser frequency stabilization using a balanced bi-polarimeter

We report on a Doppler-free polarization spectroscopy based technique of laser frequency stabilization using a balanced bi-polarimeter set-up. Two linearly polarized weak laser beams are used to probe birefringence induced by two oppositely circularly polarized strong pump beams in a vapour cell. Subtraction of balanced polarimeter signals obtained from the two probe beams results in a background-free dispersion-like reference signal without frequency modulation. The dispersion-like signal corresponding to the closed transition 5 ² S _1/2 (F=2) →5 ² P _3/2 (F^′=3) of ⁸⁷Rb was used for frequency locking of a diode laser. The frequency fluctuations and the drift were measured to be less than 0.25 MHz and 0.02 MHz, respectively, for an observation period of more than 10 hours. PACS 42.62.Fi; 42.55.Px; 32.30.-r