Table of contents

We report a Monte Carlo simulation of deposition of magnetic particles on a one-dimensional substrate. Incoming particles interact with those that are already part of the deposit via a dipole–dipole potential. The strength of the dipolar interaction is controlled by an effective temperature T*, the case of pure diffusion-limited deposition being recovered in the limit T* → ∞. Preliminary results suggest that the fractal dimension of the deposits does not change with temperature but that there is a (temperature-dependent) crossover from regimes of temperature-dependent to universal behaviour. Furthermore, it was found that dipoles tend to align with the local direction of growth.

We investigate the structure and dynamics of ionic magnetic fluids (MFs), based on ferrite nanoparticles, dispersed at pH ≈ 7 either in H₂O or in D₂O. Polarized and non-polarized static small angle neutron scattering (SANS) experiments in zero magnetic field allow us to study both the magnetic and the nuclear contributions to the neutron scattering. The magnetic interparticle attraction is probed separately from the global thermodynamic repulsion and compares well to direct magnetic susceptibility measurements. The magnetic interparticle correlation is in these fluid samples independent of the probed spatial scale. In contrast, a spatial dependence of the interparticle correlation is evidenced at large Φ by the nuclear structure factor. A model of magnetic interaction quantitatively explains the under-field anisotropy of the SANS nuclear contribution.

In a quasi-elastic neutron spin-echo experiment, we probe the Brownian dynamics of translation of the nanoparticles in the range 1.3 ^≤qR_g^N≤ 10 (q, scattering vector; R_g^N, nuclear radius of gyration of the nanoparticles). For the first time in an MF, we determine the hydrodynamic function at large q vectors.

The model of an elastic magnetic chain is considered. By numerical simulation of the dynamics of rod shapes acted on by magnetic and elastic forces in viscous fluid, it is shown that the characteristic 'U'-like metastable shapes (hairpins) can be formed. The characteristic 'S'-like long-living shapes are formed at intermediate stages, depending on the initial perturbation of the rod, and finally relax to the global energy minima corresponding to the straight rod. Further extensions of the model will include long-range magnetic interactions between distant parts of a rod.

The process of miniemulsification allows the generation of small, homogeneous, and stable droplets containing monomer or polymer precursors and magnetite which are then transferred by polymer reactions to the final polymer latexes, keeping their particular identity without serious exchange kinetics involved. It is shown that the miniemulsion process can excellently be used for the formulation of polymer-coated magnetic nanoparticles which can further be used for biomedical applications. The use of high shear, appropriate surfactants, and the addition of a hydrophobe in order to suppress the influence of Ostwald ripening are key factors for the formation of the small and stable droplets in miniemulsion and will be discussed. Two different approaches based on miniemulsion processes for the encapsulation of magnetite into polymer particles will be presented in detail.

The rotational diffusion equation for a dipole in the presence of an oscillating field is solved by expansion of the orientational distribution function in terms of Legendre polynomials and harmonics. The nonlinear response of the average dipole moment is studied as a function of field strength and frequency. Outside the linear regime the in-phase and out-of-phase response as functions of frequency do not satisfy Kramers–Kronig relations. A comparison is made with the nonlinear response calculated from approximate macroscopic relaxation equations proposed by Shliomis and by Martsenyuk et al. The response of a macroscopic system of interacting dipoles is calculated in the mean-field approximation for a spherical sample.

In this paper, we report on how to take advantage of good knowledge of both the chemistry and the stability of an aqueous magnetic colloidal suspension to realize different magnetic composites. The osmotic pressure of the magnetic nanoparticles is set prior to the realization of the composite to a given value specially designed for the purpose for each hybrid material: magnetic particles in polymer networks, particles as probes for studying the structure of clay suspensions and shape modification of giant liposomes.

First, we show that the introduction of magnetic particles in polyacrylamide gels enhances their Young modulus and reduces the swelling caused by water. The particles cause both a mechanical and an osmotic effect. The latter is strongly dependent on the ionic strength and is attributed to an attraction between particles and the polymeric matrix.

In the second part, we determine the microscopic structure of suspensions of laponite as a function of concentration, by combining SANS and magneto-optical experiments with the probes. This study requires conditions suitable for including the magnetic particles as probes without disturbing the clay suspensions.

The third part presents giant magnetoliposomes, which encapsulate magnetic nanoparticles. Shape transitions are obtained with either a magnetic field or an osmotic stress.

We review, apply and compare diverse approaches to the theoretical understanding of the dynamical and rheological behaviour of ferrofluids and magnetorheological (MR) fluids subject to external magnetic and flow fields. Simple models are introduced which are directly solvable by nonequilibrium Brownian or molecular dynamics computer simulation. In particular, the numerical results for ferrofluids quantify the domain of validity of uniaxial alignment of magnetic moments (in and) out of equilibrium. A Fokker–Planck equation for the dynamics of the magnetic moments—corresponding to the Brownian dynamics approach—and its implications are analysed under this approximation. The basic approach considers the effect of external fields on the dynamics of ellipsoid shaped permanent ferromagnetic domains (aggregates), whose size should depend on the strength of flow and magnetic field, the magnetic interaction parameter and concentration (or packing fraction). Results from analytic calculations and from simulation are summarized for the anisotropy of the viscosity. In order to study the effect of flow on the anisotropic viscosities and shear-induced structures of MR fluids and ferrofluids subject to a strong external magnetic field, a simple model of perfectly oriented particles is considered.

This work reports the synthesis of iron oxide cores by coprecipitation of Fe²⁺ and Fe³⁺ ions with NaHCO₃ or NH₃. Depending on the experimental conditions, particles of two different sizes (13 or 130 nm diameter) were produced. X-ray diffractometry revealed Fe₃O₄ (magnetite) to be the main constituent. The smaller particles, which, in contrast to the larger ones, are superparamagnetic, were stabilized with a phospholipid bilayer consisting of a 9:1 molar ratio of dimyristoylphosphatidylcholine and dimyristoylphosphatidylglycerol, thereby creating so-called magnetoliposomes. In a subsequent step, poly(ethylene glycol)-(PEG-) derivatized dipalmitoylphosphatidylethanolamine was introduced into the lipid envelope by incubating the magnetoliposomes with pre-formed sonicated vesicles containing the PEGylated lipid. The mechanism by which lipid transfer occurred was determined from the kinetic profiles. The relevance of these observations to a wide range of biomedical applications is briefly discussed.

We have determined experimentally the parameters characterizing the structures formed in a magnetic colloidal suspension subjected to a unidirectional magnetic field and a rotating field for different cell thicknesses. In this latter case one observes the formation of a periodic structure in parallel sheets situated in the plane of rotation of the field. A theoretical model based on minimization of the energy allows one to find quantitatively the observations obtained in a unidirectional field. On the other hand, in a rotating field, the agreement is quantitative only if we take the surface energy as an adjustable parameter. We explain this fact on the basis of the existence of a substructure made of discs of particles. In a second part we show the influence of the structures on the rheological properties of the suspension by measuring the shear moduli for different kinds of structure. We find that for the same magnetic field, the shear moduli depend strongly on the structure and can be quite well predicted by a mean field theory; also the critical shear strain is determined and is in agreement with the model. Finally we show that, in a regime with a unidirectional oscillating field without shear flow, a new phenomenon appears if the confining walls are not parallel. In this case we observe the formation of anisotropic aggregates which undergo a collective chaotic rotation around the axis of the aggregates.

The particle structure of ferrofluids is studied in situ, by cryogenic electron microscopy, on vitrified films of iron and magnetite dispersions. By means of synthesis of iron colloids with controlled particle size and different types of surfactant, dipolar particle interactions can be varied over a broad range, which significantly influences the ferrofluid particle structure. Our experiments on iron dispersions (in contrast to magnetite dispersions) for the first time demonstrate, in ferrofluids in zero field, a transition with increasing particle size from separate particles to linear chains of particles (Butter K, Bomans P H, Frederik P M, Vroege G J and Philipse A P 2003 Nature Mater.2 88). These chains, already predicted theoretically by de Gennes and Pincus (de Gennes P G and Pincus P A 1970 Phys. Kondens. Mater.11 189), very much resemble the fluctuating chains found in simulations of dipolar fluids (Weis J J 1998 Mol. Phys.93 361, Chantrell R W, Bradbury A, Popplewell J and Charles S W 1982 J. Appl. Phys.53 2742). Decreasing the range of steric repulsion between particles by employing a thinner surfactant layer is found to change particle structures as well. The dipolar nature of the aggregation is confirmed by the alignment of existing chains and individual particles in the field direction upon vitrification of dispersions in a saturating magnetic field. Frequency-dependent susceptibility measurements indicate that particle structures in truly three-dimensional ferrofluids are qualitatively similar to those in liquid films.

A brief survey is given of recent simulation work of quasi-two-dimensional (Q2D) systems, monolayers and systems of finite thickness, involving dipolar interactions. Representative examples include colloidal particles at an interface, electrorheological fluids, magnetic thin films, nanocrystals deposited on a substrate etc. Methodological aspects related to the long range of the dipolar interaction and its directional nature (energy calculation, cluster moves) are summarized. Taking as an example a bilayer of dipolar hard spheres, we demonstrate that the energy and structural properties of a thin slab of dipolar particles periodic in two dimensions and finite in the third can be accurately calculated by means of the usual three-dimensional Ewald sum. Some new simulation results for the structural properties of Q2D dipolar hard spheres with additional attraction, in an external field or in bilayers, are presented.

Suspensions of magnetic nanoparticles exhibit normal liquid behaviour coupled with superparamagnetic properties. This leads to the possibility to control the properties and the flow of these liquids with moderate magnetic fields. The magnetic control enables various experiments in fluid mechanics and gives rise to the development of numerous technical and medical applications. Ferrofluids and their general properties will be introduced and, as examples for the magnetic control of their flow and properties, thermomagnetic convection and magnetoviscous effects will be discussed in some detail.

Liquid ferromagnets do not exist: all known ferromagnetic and ferrimagnetic materials undergo a change to a paramagnetic state at a temperature called the Curie temperature, which is below the melting temperature of the material. For example, for iron the Curie temperature is 770°C and the melting point is 1535°C. Nevertheless, fluids do exist which behave very much like a molten ferromagnet [1-4]. These magnetic fluids, also called ferrofluids, are actually stable colloidal suspensions of small magnetic particles with a typical diameter of about 10 nm. Materials such as magnetite (Fe₃O₄) or metallic iron generally contain magnetic multidomains, but when the particles are sufficiently small they can accommodate only one single domain. Such a single domain particle has a net magnetic moment (proportional to its volume) and a colloidal dispersion of the particles may be visualized as a collection of small permanent magnets which exhibit translational and rotational Brownian motion in the carrier solvent.

Usually Brownian motion in colloidal sols has to compete with an external force in the form of gravity, leading to the familiar sedimentation-diffusion (Boltzmann) distribution of colloids in a gravitational or centrifugal field. Equally familiar is the equilibrium shape of a conventional colloidal bulk fluid in the gravity field, namely a flat meniscus, parallel to the surface of the earth. A ferrofluid offers some refreshing changes: it responds to an external magnetic field gradient which deforms the meniscus of the fluid and may create exotic equilibrium shapes due to the balance between magnetic and gravitational forces [1]. Though this behaviour certainly mimics a liquid ferromagnet, we should realize that ultimately the colloidal stability of the suspended particles is responsible for this mimicry. If the particles aggregate into large clusters (by the addition of flocculating electrolyte or a poor solvent for the particle coatings) a magnet will drag out the dispersed material, leaving behind a clear supernatant. This is equivalent to the collapse of a sedimentation-diffusion equilibrium when (non-magnetic) colloids aggregate and settle to the bottom of the vessel. Clearly for applications of a ferrofluid as a liquid magnet (for example in an airtight seal between rotating parts [1]) colloidal stability is essential. Ferrofluids with long term stability have already been available for many years, giving a firm practical basis for the many studies on the continuum hydrodynamics of magnetic fluids [1]. However, the understanding of what happens on the level of the discrete colloidal particles is still very limited. What sort of spatial structures are present in a stable fluid in zero field; does chain formation really occur? What sort of phase transitions may take place; does a liquid-gas coexistence exist for pure dipolar interactions or does that require the (for real colloids ever present) Van der Waals attractions? What does the pair potential in a typical ferrofluid look like; below what particle size is magnetic interaction insignificant [5]? These are just some of the widely debated topics [6-11] and the reader will certainly identify more discussion topics in the contributions to this special issue, or the references therein. The reader will also notice that the joint focus of these contributions is actually much broader than the interaction of particles with each other or an external field. The field of magnetic colloids is becoming quite a colourful mix of disciplines, and meetings where, for example, chemical synthesis experts and theoretical physicists share a bench, are not uncommon.

The purpose of this special issue is certainly not to provide an overview of the field of dipolar colloids and ferrofluids which is large and diverse (see for example [1, 8, 11]). The aim is merely to illustrate this diversity with contributions on the preparation, experimental study, simulation and theory of dipolar particles. For didactic support the reader may wish to consult figure 1 which represents a dipolar hard sphere fluid, all be it one at zero temperature. I thank Peter de Graaf for the skilful manufacture of the marbles in figure 1 and Jan den Boesterd for the photography.

Figure 1: Glass marbles (radius 1 cm) with an embedded magnet. The magnet poles are slightly below the glass surface such that the magnetic interaction is fairly weak, modelling hard spheres with dipolar perturbation. The anisotropic attraction is nevertheless sufficiently strong to cause chain formation at low density (A) whereas the net attraction is too weak to orient dipoles in a random sphere packing (B). The dipole distribution can be observed more clearly when the glass marbles are optically matched by toluene (C).

A PhilipseGuest Editor

References

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