On the theory of phase transitions in magnetic fluids

Particles of magnetic fluids (ferrofluids), as is known from experiments, can condense to bulk dense phases at low temperatures (that are close to room temperature) in response to an external magnetic field. It is also known that a uniform external magnetic field increases the threshold temperature of the observed condensation, thus stimulating the condensation process. Within the framework of early theories, this phenomenon is interpreted as a classical gas-liquid phase transition in a system of individual particles involved in a dipole-dipole interaction. However, subsequent investigations have revealed that, before the onset of a bulk phase transition, particles can combine to form a chain cluster or, possibly, a topologically more complex heterogeneous cluster. In an infinitely strong magnetic field, the formation of chains apparently suppresses the onset of a gas-liquid phase transition and the condensation of magnetic particles most likely proceeds according to the scenario of a gas-solid phase transition with a wide gap between spinodal branches. This paper reports on the results of investigations into the specific features of the condensation of particles in the absence of an external magnetic field. An analysis demonstrates that, despite the formation of chains, the condensation of particles in this case can proceed according to the scenario of a gas-liquid phase transition with a critical point in the continuous binodal. Consequently, a uniform magnetic field not only can stimulate the condensation phase transition in a system of magnetic particles but also can be responsible for a qualitative change in the scenario of the phase transition. This inference raises the problem regarding a threshold magnetic field in which there occurs a change in the scenario of the phase transition.     

Structure formation in electromagnetically driven granular media

We report structure formation in submonolayers of magnetic microparticles subjected to periodic electrostatic and magnetic excitations. Depending on the excitation parameters, we observe the formation of a rich variety of structures: clusters, rings, chains, and networks. The dynamics and shapes of the structures are strongly dependent on the amplitude and frequency of the external magnetic field. We find that for pure ac magnetic driving the low-frequency magnetic excitation favors compact clusters, whereas high frequency driving favors chains and netlike structures. An abrupt phase transition from chains to a network phase was observed for a high density of particles.     

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.     

Rheological properties of polydisperse magnetic fluids. Effect of chain aggregates

A theoretical model of medium-density polydisperse magnetic fluids is proposed. The model takes into account that the major fraction of particles in typical ferrofluids is characterized by a magnetic core diameter of about 10 nm. In addition, there is a certain proportion of large particles with a core diameter of about 16 nm. As a result of the magnetic dipole interaction, the large particles form chain aggregates. Small particles, for which the magnetic dipole interaction energy (both with each other and with large particles) is smaller than the thermal energy, remain in the individual nonaggregated state. The distribution of chains with respect to the number of (large) particles and some rheological characteristics of the ferrofluids are determined. The proposed model is capable of explaining, in principle, the giant magnetoviscosity effect and a strong dependence of the rheological properties of ferrofluids on the shear rate observed in some recent experiments.     

Dynamic roughening and fluctuations of dipolar chains

Nonmagnetic particles in a carrier ferrofluid acquire an effective dipolar moment when placed in an external magnetic field. This fact leads them to form chains that will roughen due to Brownian motion when the magnetic field is decreased. We study this process through experiments, theory and simulations, three methods that agree on the scaling behavior over 5 orders of magnitude. The rms width goes initially as t(1/2), then as t(1/4) before it saturates. We show how these results complement existing results on polymer chains, and how the chain dynamics may be described by a recent non-Markovian formulation of anomalous diffusion.     

Synthesis and characterization of covalent diphenylalanine nanotube-folic acid conjugates

Traditionally, organosilica nanoparticles have been prepared inside micelles with an external silica shell for mechanical support. Here, we compare these hybrid core–shell particles with organosilica particles that are robust enough to be produced both inside micelles and alone in a sol–gel process. These particles form from octadecyltrimethoxy silane as silica source either in microemulsions, resulting in water-dispersible particles with a hydrophobic core, or precipitate from an aqueous mixture to form particles with both hydrophobic core and surface. We examine size and morphology of the particles by dynamic light scattering and transmission electron microscopy and show that the particles consist of Si–O–Si networks pervaded by alkyl chains using nuclear magnetic resonance, infrared spectroscopy, and thermogravimetric analysis.     

Condensation of charged particles of a Bose-Einstein gas in a quantizing magnetic field

We determine the critical temperature of a degenerate bosonic gas of charged particles in the quantum limit for a magnetic field. We further determine the concentrations of the bosons that condense at the zero Landau level at temperatures below the critical temperature. We show that the degeneration of a bosonic gas can be suppressed when the magnetic field values are much greater than when particles begin to occupy the energy level having a nonzero value of the Landau quantum number.Brest Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 73–77, December, 1992.     

On the time evolution of transmittivity in magnetic fluids

When a magnetic fluid is subjected to a magnetic field, a part of the magnetic particles in the fluid agglomerates to form chains. Thus, the ferrofluid becomes optically anisotropic. In this work we describe optically observed patterns in some magnetic fluid films in applied parallel magnetic fields and optical effects of these, especially the optical transmittance. The most interesting experimental observation is that concerning the time dependence of relative transmittivity . For kerosene base ferrofluids relax rapidly at coupling and decoupling magnetic field, but for a transformer-oil magnetic fluid the relaxation times can attain (5–10) minutes, depending on the intensity of applied magnetic field.     

Yield stress in thin layers of ferrofluids

We present results of theoretical study of quasielastic behavior of ferrofluid filling a thin flat gap, placed into perpendicular magnetic field. When the field exceeds a certain critical magnitude, magnetic particles form dense discrete domains, elongated along the field, and linking the gap boundaries. Due to these bridges between the gap boundaries, the ferrofluid exhibits quasielastic properties with respect to shear strain in the plane of the gap. We estimated the elastic modules as well as the yield stress of the system, depending on magnetic field and concentration of magnetic particles in the ferrofluid. Analysis shows that there are at least two microscopical mechanisms of transition from the elastic to fluid behavior of the ferrofluid. The first one is connected with the loss of the mechanical equilibrium of the domains, slopped, under the shear stress, with respect to applied magnetic field. The second mechanism is connected with breakup of the “bridge” into two separate drops, when the shear strain exceeds some critical magnitude. Estimates show that for real ferrofluids the second mechanism is more probable.     

Reorientation phase transitions in planar arrays of dipolarly interacting ferromagnetic particles

Reorientation phase transitions (RPT) taking place in regular arrays of rectangular submicron-size ferromagnetic particles due to the competition between the external magnetic field of arbitrary direction and internal dipolar fields are analysed in this article. Dipolar interaction between particles is taken into account via real-space calculations of magnetometric demagnetizing factors. Long stripe arrays are also under consideration. I find that the direction of the external magnetic field determines the kind of the phase transition, while the dipolar interaction between particles can significantly change the values of RPT critical field. Calculations were presented for a set of submicron particles/stripe arrays, which were under experimental investigations recently.     

The structural instabilities in ferronematic based on liquid crystal with negative diamagnetic susceptibility anisotropy

The studied ferronematic is a nematic liquid crystal (ZLI1695) of low negative anisotropy of the diamagnetic susceptibility (χ_a<0) doped with the magnetic particles Fe₃O₄. Structural instabilities are interpreted within Burylov and Raikher's theory. The high magnetic fields were oriented perpendicular (Freedericksz transition) or parallel to the initial director. Using capacitance measurements the Freedericksz threshold magnetic field of the ferronematic B_FN, and the critical magnetic field B_max, at which the initial parallel orientation between the director and the magnetic moment of magnetic particles breaks down, have been determined. The values of these quantities have been used to estimate the surface density of the anchoring energy W of liquid crystal molecules on the surface of the magnetic particles. The obtained values indicate a soft anchoring of the liquid crystal on the magnetic particles with a preferred parallel orientation of the magnetic moment of magnetic particles and the director.     

On the properties of “short” granular magnets with disordered chains of grains: A field between grains

The values and functional exponential form of the demagnetizing factor of “short” cylindrical samples of the polyspherical medium and samples (elements) of this medium, i.e., chains of spheres, have been established. The tortuosity factor of chains formed by spheres (as effective elementary conductors of the magnetic flux in a magnetized granular medium) has been analyzed. It has been demonstrated that the tortuosity factor for chains in a filling medium is insignificant. The strength of the field between spheres in the chain, like the magnetic permeability of the effective magnetization channel, has an extremum (bell-shaped) profile. It has been revealed (by using magnetophoresis of finely dispersed ferroparticles) that the gradient of this strength exhibits a two-extremum profile.     

Efficient simulation of chemical potentials and phase equilibria in associating fluids: monomer/dimer insertion versus gradual particle insertion in primitive water models

Widom's test particle method for simulation of chemical potentials fails for associating (network forming) fluids. Therefore we study more sophisticated insertion methods, such as gradual particle insertion and the recent unbonded particle insertion of Tripathi and Chapman. We model strongly associating fluids by short-ranged primitive models (PMs) due to Nezbeda and co-workers. Recently, we showed that gradual insertion, in principle, is applicable to PM water. Here, we study systematically subcritical chemical potential isotherms, determine vapour–liquid coexistence densities and estimate the critical point density and temperature. For comparison we implement two variants of the Tripathi–Chapman algorithm. In the first case we use as unbonded test particles only particles which remain single molecules (monomers), when inserted and in the second case such test particles which remain as single molecules or form a two-particle cluster with an existing free molecule (monomer/dimer), when inserted. While monomer insertion improves Widom's method slightly, monomer/dimer insertion extends substantially the range of application to the subcritical temperatures studied by gradual insertion. But, for low temperatures monomer/dimer insertion requires extremely long Markov chains and significantly more computer time than gradual insertion. The Tripathi–Chapman algorithm—a direct extension of Widom's method—is much simpler than gradual insertion and therefore should be preferred at supercritical and critical conditions.     

A molecular dynamics study of the microstructure of the liquid-gas interphase surface

Numerical experiments showed that the number-of-bonds distribution of particles that form a fairly large molten argon-like cluster was bimodal. This result was interpreted as a consequence of the formation of two “phases, ” namely, particles inside the cluster and a monolayer of particles lying above the others. Particle chains were shown to be formed near the surface of the cluster. Splitting off of separate particles from them was the most probable mechanism of vaporization. Model concepts that described the dependences observed in numerical experiments were developed.     

Dynamical arrest in attractive colloids: the effect of long-range repulsion

We study gelation in suspensions of model colloidal particles with short-ranged attractive and long-ranged repulsive interactions by means of three-dimensional fluorescence confocal microscopy. At low packing fractions, particles form stable equilibrium clusters. Upon increasing the packing fraction the clusters grow in size and become increasingly anisotropic until finally associating into a fully connected network at gelation. We find a surprising order in the gel structure. Analysis of spatial and orientational correlations reveals that the gel is composed of dense chains of particles constructed from face-sharing tetrahedral clusters. Our findings imply that dynamical arrest occurs via cluster growth and association.     

Particles with Magnetic Patches: Synthesis,Morphology Control,and Assembly

The concept of patchy particles is revolutionizing the research field of colloidal assembly, by the design of particles whose surface is purposely patterned to promote attractive interactions with their neighbors in limited number, and in privileged and programmed directions. The idea of magnetic patches makes it possible to imagine assemblies not only spontaneous by simple magnetic coupling but also triggered and canceled at will due to external magnetic fields. This review shows that studies published until now mainly deal with particles with a single magnetic patch, often called Janus particles. The very diverse synthetic routes have been brought together into four main strategies, covering the size range from 100 nm to 100 µm. Their assembly capacity is described both from experimental and simulation viewpoints. The orientation of the magnetic moment of the patch and its decentering extent with respect to the particle are the key parameters for controlling the morphology of clusters, loops, staggered chains, double chains, helices, microtubes, etc. The review offers some perspectives to generalize these studies to multipatch particles, examples of which are still too rare, and to make assemblies sustainable, especially after the removal of the structuring magnetic fields.     

ESR line shape of paramagnetic particles in a magnetic liquid. Theory and experiment

A basic model has been proposed to describe the resonance spectra of the paramagnetic sensor particles in dispersions of magnetic nanoparticles aggregated in chains. A theory of the line shape of low-mobility sensors has been developed in the case of chains of a sufficiently homogeneous length. A specific line shift has been shown to appear in such systems and the spectrum may be asymmetric. The ESR spectra of a magnetite-based magnetic liquid have been measured and the main parameters of the chains have been determined.     

Effect of dipolar interaction on the magnetization state of chains of rectangular particles located either head-to-tail or side-by-side

Magnetostatic coupling in arrays of closely spaced magnetic elements is becoming an important issue in the path to the fabrication of spintronic devices. Dense chains of rounded-corners rectangular particles (dots) of lateral size 1025 × 450 nm², with interdot spacing variable in the range between 55 and 700 nm, have been patterned by deep UV lithography, followed by the lift-off of two permalloy films of thickness 20 and 40 nm. Magneto-optical Kerr effect (MOKE) and magnetic force microscopy (MFM) experiments, together with micromagnetic simulations, were performed to study the dependence of the magnetization configuration on the dipolar coupling. Both MOKE measurements and MFM images clearly show that, at remanence, the magnetic state of isolated particles of thickness 20 nm takes the form of a distorted single domain (C-state or S-State configurations). Instead, when the particle thickness is double (40 nm), closure states characterized by one, two or three vortices occur at remanence. However, when the 40 nm thick dots are placed in chains along the easy axis (head to tail), as the separation is progressively reduced, the single domain state is stabilized at remanence. On the other hand, when the 40 nm thick particles are placed side by side in chains the effect of dipolar interactions is to favour the nucleation of vortex states. For small inter-element separation, there is only one vortex per particle and it has the same chirality in adjacent particles, due to the dipolar interaction. Different from this, for the 20 nm thick samples and sub-100 nm separation, adjacent particles are single-domain but with antiparallel magnetization in neighbour elements, like in an artificial antiferromagnet.     

Scaling of the viscoelasticity of weakly attractive particles

The rheological data of weakly attractive colloidal particles are shown to exhibit a surprising scaling behavior as the particle volume fraction, straight phi, or the strength of the attractive interparticle interaction, U, are varied. There is a critical onset of a solid network as either straight phi or U increase above critical values. For all solidlike samples, both the frequency-dependent linear viscoelastic moduli, and the strain-rate dependent stress can be scaled onto universal master curves. A model of a solid network interspersed in a background fluid qualitatively accounts for this behavior.     

Properties of Josephson junctions in the inhomogeneous magnetic field of a system of ferromagnetic particles

The effect of a system of ferromagnetic particles on the field-dependent critical current of a Josephson junction is experimentally studied for junctions of different geometries. For edge junctions, the effect of commensurability between the periodic magnetic field of the particles and the Josephson vortex lattice is observed. The effect manifests itself in additional maxima of the field-dependent critical current. For overlap junctions, giant (greater than sixfold) variations of the maximum critical current are observed depending on the magnetic state of the particles. The changes in the “Fraunhofer” pattern of the overlaped Josephson junctions are attributed to the formation of Abrikosov vortices due to the effect of uniformly magnetized particles. The effects revealed in the experiments can be used to analyze the inhomogeneous magnetic field of a system of submicron particles and to control the transport properties of Josephson junctions.