Structure of soft-sphere dipolar fluids

Relating the length of a magnetic filament with solvophobic, superparamagnetic colloids to its properties in applied magnetic fields

The idea of creating polymer-like structures by crosslinking magnetic nanoparticles (MNPs) opened an alternative perspective on controlling the rheological properties of magnetoresponsive systems, because unlike suspensions of self-assembled MNPs, whose cluster sizes are sensitive to temperature, magnetic filaments (MFs) preserve their initial topology. Considering the length scales characteristic of single-domain nanoparticles used to create MFs, the MNPs can be both ferro- and superparamagnetic. Moreover, steric or electrostatic stabilization might not fully screen van der Waals interactions. In this paper, using coarse-grained molecular dynamics simulations, we investigate the influence of susceptibility of superparamagnetic MNPs-their number and central attraction forces between them-on the polymeric, structural, and magnetic properties of MFs with varied backbone rigidity. We find that, due to the general tendency of MFs with superparamagnetic monomers to bend, reinforced for colloids with a high susceptibility, properties of MFs vary greatly with chain length.

Noether-Constrained Correlations in Equilibrium Liquids

Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field Noether's theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate the fundamental role in the characterization of spatial structure.

How chains and rings affect the dynamic magnetic susceptibility of a highly clustered ferrofluid

The dynamic magnetic susceptibility, χ(ω), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1≤λ≤8), is examined using Brownian dynamics simulations. With increasing λ, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility χ(0) on λ and qualitative changes to the frequency spectrum. The behavior of χ(0) is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, τ_{B}, which depends on the particle size, carrier-liquid viscosity, and temperature. With λ≤5.5, the imaginary part of the spectrum, χ^{''}(ω), shows a single peak near ω∼τ_{B}^{-1}, characteristic of single particles. With λ≥5.75, the spectrum is dominated by the low-frequency response of chains. With λ≥7, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.

The structure of clusters formed by Stockmayer supracolloidal magnetic polymers

Unlike Stockmayer fluids, that prove to undergo gas-liquid transition on cooling, the system of dipolar hard or soft spheres without any additional central attraction so far has not been shown to have a critical point. Instead, in the latter, one observes diverse self-assembly scenarios. Crosslinking dipolar soft spheres into supracolloidal magnetic polymer-like structures (SMPs) changes the self-assembly behaviour. Moreover, aggregation in systems of SMPs strongly depends on the constituent topology. For Y- and X-shaped SMPs, under the same conditions in which dipolar hard spheres would form chains, the formation of very large loose gel-like clusters was observed (E. Novak et al., J. Mol. Liq. 271, 631 (2018)). In this work, using molecular dynamics simulations, we investigate the self-assembly in suspensions of four topologically different SMPs --chains, rings, X and Y-- whose monomers interact via Stockmayer potential. As expected, compact drop-like clusters are formed by SMPs in all cases if the central isotropic attraction is introduced, however, their shape and internal structure turn out to depend on the SMPs topology.

Polymer architecture of magnetic gels: a review

In this review article, we provide an introduction to ferrogels, i.e. polymeric gels with embedded magnetic particles. Due to the interplay between magnetic and elastic properties of these materials, they are promising candidates for engineering and biomedical applications such as actuation and controlled drug release. Particular emphasis will be put on the polymer architecture of magnetic gels since it controls the degrees of freedom of the magnetic particles in the gel, and it is important for the particle-polymer coupling determining the mechanisms available for the gel deformation in magnetic fields. We report on the different polymer architectures that have been realized so far, and provide an overview of synthesis strategies and experimental techniques for the characterization of these materials. We further focus on theoretical and simulational studies carried out on magnetic gels, and highlight their contributions towards understanding the influence of the gels' polymer architecture.

Self-assembly and rheology of dipolar colloids in simple shear studied using multi-particle collision dynamics

Magnetic nanoparticles in a colloidal solution self-assemble in various aligned structures, which has a profound influence on the flow behavior. However, the precise role of the microstructure in the development of the rheological response has not been reliably quantified. We investigate the self-assembly of dipolar colloids in simple shear using hybrid molecular dynamics and multi-particle collision dynamics simulations with explicit coarse-grained hydrodynamics, conduct simulated rheometric studies and apply micromechanical models to produce master curves, showing evidence of the universality of the structural behavior governed by the competition between the bonding (dipolar) and erosive (thermal and/or hydrodynamic) stresses. The simulations display viscosity changes across several orders of magnitude in fair quantitative agreement with various literature sources, substantiating the universality of the approach, which seems to apply generally across vastly different length scales and a broad range of physical systems.

Network formation and gelation in telechelic star polymers

We investigate the efficiency of gelation and network formation in telechelic star polymer melt, where the tips of polymer arms are dipoles while the rest of the monomers are uncharged. Our work is motivated by the experimental observations [A. Kulkarni et al., Macromolecules 48, 6580 (2015)] in which rheological studies of telechelic star polymers of poly-(L-lactide), a bio-degradable polymer, showed a drastic increase in elastic properties (up to 2000 times) compared to corresponding star polymers without the telechelic arm ends. In contrast to previous studies, we avoid using effective attractive Lennard-Jones potentials or dipolar potentials to model telechelic interactions. Instead we use explicit Coulomb positive and negative charges at the tip of polymer-arms of our bead-spring model of star polymers. By our simulations we show that the dipoles at the tip of star arms aggregate together to form clusters of dipoles. Each cluster has contributions from several stars, and in turn each star contributes to several clusters. Thus the entire polymer melt forms a connected network. Network forming tendencies decrease with a decrease of the value of the effective charge constituting the dipole: this can be experimentally realized by choosing a different ionomer for the star tip. We systematically varied the value of dipole charges, the fraction of star-arms with dipoles at the tip, and the length of the arms. The choice of explicit charges in our calculations enables us to make better quantitative predictions about the onset of gelation; moreover we get qualitatively distinct results about structural organization of dipoles within a dipole-cluster.

Transport of particles in liquid crystals

Colloidal particles in a liquid crystal (LC) behave very differently from their counterparts in isotropic fluids. Elastic nature of the orientational order and surface anchoring of the director cause long-range anisotropic interactions and lead to the phenomenon of levitation. The LC environment enables new mechanisms of particle transport that are reviewed in this work. Among them the motion of particles caused by gradients of the director, and effects in the electric field: backflow powered by director reorientations, dielectrophoresis in LC with varying dielectric permittivity and LC-enabled nonlinear electrophoresis with velocity that depends on the square of the applied electric field and can be directed differently from the field direction.

Exact second virial coefficient for dipolar hard spheres

The second virial coefficient B2 for a fluid of dipolar hard spheres has been given several approximate forms valid in the limits of weak and strong interactions. They have been formulated as asymptotic expressions in a dimensionless interaction parameter λ. In this paper, B2 is determined exactly for all values of λ in both the three-dimensional case, where spheres may access the whole space and their dipole moments may be oriented in all directions, and in the quasi-two-dimensional case, where spheres have their centres bound to glide on a plane, while their dipole moments are still freely orientable in space.

Thermodynamics of ferrofluids in applied magnetic fields

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B(2) and B(3)) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B(3) for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ≤2. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.

Thermodynamics of a binary monolayer of Ising dipolar particles. II. Effect of relative moment

Thermodynamic behaviors of a binary monolayer of Ising dipolar particles are studied using particle dynamics simulation, varying the relative intensity between the upward and downward dipole moments. The orientational order of the solid phase changes from tetragonal to hexagonal as the moment ratio increases. On the basis of the arguments of the candidates for ground state structures, the energy of the structures are well estimated. The transition point is also determined theoretically, which is consistent with the value obtained from the simulation results. Critical condensation is also studied. While the system whose moment ratio is unity does not exhibit the gas-liquid critical condensation, the transition appears as the moment ratio changes. The local structure of the liquid phase is found to be characterized by the ground state of the tetramer. The above-mentioned results imply that the gas-liquid critical point comes close to the melting transition point as the local structure of the liquid phase becomes closer to the structure of the solid phase, and therefore, the critical condensation is vanished.

Influence of the colloidal environment on the magnetic behavior of cobalt nanoparticles

The magnetic properties of 10 nm diameter surfactant-coated cobalt (Co) nanoparticles in 1,2-dichlorobenzene (DCB) are investigated by a series of sequential magnetic moment (m) vs temperature (T) measurements. A rapid rise in magnetic moment around 250 K during warming and an abrupt drop at 234 K during cooling are observed when a nonsaturating external magnetic field is applied. Differential scanning calorimetry (DSC) measurements demonstrate that the rapid rise and abrupt drop in magnetization are associated with the melting and freezing of the solvent. Magnetic measurements of these Co nanoparticles in DCB are also used to probe their aging over a period of 70 days. The saturation magnetic moment of Co nanoparticles in DCB stored in air at room temperature decreases by nearly 40% over 70 days. Transmission electron microscopy (TEM) characterizations are reported to show the time evolution in the size, shape, and crystalline structures of DCB-immersed nanoparticles.

Synthesis and self-assembly of polymer-coated ferromagnetic nanoparticles

We describe the synthesis and characterization of polymer-coated ferromagnetic cobalt nanoparticles (CoNPs). The synthesis of end-functionalized polystyrene surfactants possessing amine, carboxylic acid, or phosphine oxide end-groups was accomplished using atom-transfer radical polymerization. This versatile synthetic method enabled the production of multigram quantities of these polymeric surfactants that stabilized ferromagnetic CoNPs when dispersed in organic media. An in-depth investigation into the synthesis of polystyrene-coated ferromagnetic CoNPs was also conducted using various combinations of these polymeric surfactants in the thermolysis of dicobaltoctacarbonyl (Co(2)(CO)(8)). Moreover, the application of a dual-stage thermolysis with Co(2)(CO)(8) allowed for the preparation of large samples (200-820 mg) per batch of well-defined and dispersable ferromagnetic nanoparticles. Characterization of these functionalized nanoparticle materials was then done using transmission electron microscopy, X-ray diffraction, vibrating sample magnetometry, and thermogravimetric analysis. Self-assembly of these dipolar nanoparticles was investigated in solutions cast onto supporting substrates, where local nematic-like ordering of nanoparticle chains was observed along with a tendency of adjacent chains to form "zippering" configurations, both phenomena having been predicted by recent simulations of dipolar fluids in conjunction with van der Waals interactions.

Thermodynamics of a binary monolayer of Ising dipolar particles

Thermodynamic behavior of a binary monolayer of Ising dipolar particles is studied using numerical simulation. The thermal equilibrium states of the system under the canonical ensemble are observed. The boundary of gas-liquid phase is determined from the power law growth of critical clusters. But that temperature is slightly lower than that of solidification. So it means that this system does not have a liquid phase. This system is also studied theoretically using virial expansion. The coefficients obtained from standard virial expansion, however, do not show any phase transition. An improvement of the virial expansion is also given by taking tetragonal local structures of alternate types of particles into consideration. Such structures are observed within critical clusters of our simulation. The thermodynamic state equation obtained from the improved virial expansion agrees well with the simulation result, and this expansion also shows that the critical point is almost at the same temperature with solidification. These results suggest that not simply the strength of attractive force by the dipole interaction but a typical configuration caused by the binary condition of this system plays a dominant role in phase transitions.

Analysis of chaining structures in colloidal suspensions subjected to an electric field

Structures formed by a colloidal suspension of silica particles in 4-methyl cyclohexanol have been analyzed in the presence of an electric field. The formation of chains of particles was detected using an elliptical mirror to collect scattered light and a nearly matched refractive index between particles and solvent. A numerical method has been developed to obtain the size distribution of chains and their kinetics of formation from the record of a two-dimensional map of scattered light. We have compared the experimental size distribution to the prediction of a statistical theory based on a minimization of the free energy of a gas of chains. This theory quite well reproduced the experimental results for small chains but overestimates the tail of the distribution at high field. A saturation of the average size of chains versus the electric field was observed experimentally instead of a continuous growth as would be expected from aggregation under dipolar forces. A kinetic model, taking into account both capture and escape rates of a particle at the extremity of a chain, was shown to reproduce well the experimental growth of the average size of chains with time.

Simple models of complex aggregation: vesicle formation by soft repulsive spheres with dipolelike interactions

Structural and thermodynamic properties of spherical particles carrying classical spins are investigated by Monte Carlo simulations. The potential energy is the sum of short range, purely repulsive pair contributions, and spin-spin interactions. These last are of the dipole-dipole form, with however, a crucial change of sign. At low density and high temperature the system is a homogeneous fluid of weakly interacting particles and short range spin correlations. With decreasing temperature particles condense into an equilibrium population of free floating vesicles. The comparison with the electrostatic case, giving rise to predominantly one-dimensional aggregates under similar conditions, is discussed. In both cases condensation is a continuous transformation, provided the isotropic part of the interatomic potential is purely repulsive. At low temperature the model allows us to investigate thermal and mechanical properties of membranes. At intermediate temperatures it provides a simple model to investigate equilibrium polymerization in a system giving rise to predominantly two-dimensional aggregates.

Quantitative real-space analysis of self-assembled structures of magnetic dipolar colloids

We present the first real-space analysis on a single-particle level of the dipolar chains and branched clusters self-assembling in magnetic fluids in zero field. Spatial correlations and chain-length distributions directly obtained from tracked particle positions in vitrified films of synthetic magnetic (Fe3O4) dispersions provide a quantitative test for simulations and theory of dipolar fluids. A pertinent example is the cluster-size distribution that can be analyzed with a one-dimensional aggregation model to yield a dipolar attraction energy that agrees well with the dipole moment found from independent magnetization measurements.

Are dipolar liquids ferroelectric?

VH and HV depolarized hyper-Rayleigh scattering spectra were measured for liquid solutions of dipolar CH3CN in nondipolar C2Cl4 at T=300 K. The VH spectrum contains a strong narrow peak due to a slowly relaxing longitudinal orientation mode. This peak is absent in the HV spectrum, and it disappears from the VH spectrum when the CH3CN concentration is reduced to 8%. This observation is consistent with a ferroelectric phase transition predicted to occur when rho mu0(2)=9epsilon0kT=49 D2 M.

The ferroelectric transition of dipolar hard spheres

We investigate by Monte Carlo simulation the size dependence of the variation of the polarization and the dielectric constant with temperature for dipolar hard spheres at the two densities rho sigma3=0.80 and 0.88. From the crossing of the fourth-order cumulant for different system sizes first more precise estimates of the ferroelectric transition temperatures are obtained. Theoretical approaches, when predicting an ordering transition, are shown to generally overestimate the critical temperature.

Computer simulations of the structure of colloidal ferrofluids

The structure of a ferrofluid under the influence of an external magnetic field is expected to become anisotropic due to the alignment of the dipoles into the direction of the external field, and subsequently to the formation of particle chains due to the attractive head to tail orientations of the ferrofluid particles. Knowledge about the structure of a colloidal ferrofluid can be inferred from scattering data via the measurement of structure factors. We have used molecular-dynamics simulations to investigate the structure of both monodispersed and polydispersed ferrofluids. The results for the isotropic structure factor for monodispersed samples are similar to previous data by Camp and Patey that were obtained using an alternative Monte Carlo simulation technique, but in a different parameter region. Here we look in addition at bidispersed samples and compute the anisotropic structure factor by projecting the q vector onto the XY and XZ planes separately, when the magnetic field was applied along the z axis. We observe that the XY-plane structure factor as well as the pair distribution functions are quite different from those obtained for the XZ plane. Further, the two-dimensional structure factor patterns are investigated for both monodispersed and bidispersed samples under different conditions. In addition, we look at the scaling exponents of structure factors. Our results should be of value to interpret scattering data on ferrofluids obtained under the influence of an external field.

Equilibrium polymerization in the Stockmayer fluid as a model of supermolecular self-organization

A diverse range of molecular self-organization processes arises from a competition between directional and isotropic van der Waals intermolecular interactions. We conduct Monte Carlo simulations of the Stockmayer fluid (SF) with a large dipolar interaction as a minimal self-organization model and focus on basic thermodynamic properties that are needed to characterize the polymerization transition that occurs in this fluid. In particular, we determine the polymerization transition lines from the maximum in the specific heat, C(v), and the inflection point in the extent of polymerization, Phi. We also characterize the geometry (radius of gyration R(g), chain length L, chain topology) of the clusters that form in this associating fluid as a function of temperature, T, and concentration, rho . The pressure, P, and the second virial coefficient, B2, were determined, since these properties contain essential information about the strength of the isotropic (van der Waals) interactions. Our simulations indicate that the locations of the polymerization lines are quantitatively consistent with a model of equilibrium polymerization with the enthalpy of polymerization ("sticking energy") fixed by the minimum in the intermolecular potential. The polymerization transition in the SF is accompanied by a topological transition from predominantly linear to ring polymers upon cooling that is driven by the minimization of the dipolar energy of the clusters. We also find that the basic interaction parameters describing polymerization and phase separation in the SF can be estimated based on the existing theory of equilibrium polymerization, but the theory must be refined to account for ring formation in order to accurately describe the configurational properties of this model self-organizing fluid.

Ferrofluid aggregation in chains under the influence of a magnetic field

The theory of particle association in flexible chains in dilute ferrofluids is generalized to the case of an arbitrarily strengthened magnetic field. The chain distribution in dynamic equilibrium is obtained on the basis of free energy minimization method under the neglect of interchain interaction. The chain partition function is calculated analytically with the help of the rotation matrix technique under the condition when the interparticle dipole-dipole interaction between the nearest neighboring ferroparticles in each chain is taken into account. At weak fields, the chain distribution and the initial susceptibility are shown to be dependent on the value of the correlation coefficient describing the zero field mutual orientational correlations between the magnetic moments of two neighboring ferroparticles in a chain. The internal chain orientational correlations and the field dependent chain lengthening result in higher magnetization of the aggregated ferrofluid in comparison with the Langevin magnetization.

Chain aggregate structure and magnetic birefringence in polydisperse ferrofluids

The theory of particle association in chains in dilute ferrofluids and dipole fluids is generalized to the case of polydisperse systems. The chains could be formed by ferroparticles of different sizes, so various types of chain aggregates are considered. The probabilities of chain structure appearance are calculated, and the phase diagram, allowing to find the most probable structure with only the continuous particle size distribution known, is built. Our results demonstrate that in spite of a very weak dipole-dipole interaction between the small size fraction particles, their presence exerts a decisive influence on the ferrofluid microstructure. The chain shortening caused by the small particles sticking to the edges of chains formed by large particles is discovered theoretically. The latter effect is proved to exist by the recent computer simulations on bidisperse ferrofluid makeup. The application of the developed model to the description of magnetic birefringence phenomena in weak external magnetic fields shows a very good agreement with experimental data.

Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study

We study by Langevin molecular dynamics simulations systematically the influence of polydispersity in the particle size, and subsequently in the dipole moment, on the physical properties of ferrofluids. The polydispersity is in a first approximation modeled by a bidisperse system that consists of small and large particles at different ratios of their volume fractions. In the first part of our investigations the total volume fraction of the system is fixed, and the volume fraction phiL of the large particles is varied. The initial susceptibility chi and magnetization curve of the systems show a strong dependence on the value of phiL. With the increase of phiL, the magnetization M of the system has a much faster increment at weak fields, and thus leads to a larger chi. We performed a cluster analysis that indicates that this is due to the aggregation of the large particles in the systems. The average size of these clusters increases with increasing phiL. In the second part of our investigations, we fixed the volume fraction of the large particles, and increased the volume fraction phiS of the small particles in order to study their influence on the chain formation of the large ones. We found that the average aggregate size formed by large particles decreases when phiS is increased, demonstrating a significant effect of the small particles on the structural properties of the system. A topological analysis of the structure reveals that the majority of the small particles remain nonaggregated. Only a small number of them are attracted to the ends of the chains formed by large particles.

Spontaneous ferromagnetic ordering in magnetic fluids

This paper is devoted to the theoretical justification of spontaneous orientational order in magnetic fluids. We study the self-consistent solutions of the Bogoliubov-Born-Green-Kirkwood-Yvon equation connecting the one-particle distribution function with the pair correlation function. This self-consistent approach is used in the specific density functional method and proves to be equivalent to the mean field theory. On the basis of the second-order perturbation method over the intensity of dipole-dipole interparticle interaction the following effect is discovered: the self-consistent density functional approach leads to the spontaneous "ferrimagnetic" state of the magnetic fluid induced by the dipole-dipole interaction. This strange result seems to be physically meaningless and prejudices the validity of the density functional methods and mean field theories applied to orientational microstructure in ferrofluids.

Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids

We investigate in detail the initial susceptibility, magnetization curves, and microstructure of ferrofluids in various concentration and particle dipole moment ranges by means of molecular dynamics simulations. We use the Ewald summation for the long-range dipolar interactions, take explicitly into account the translational and rotational degrees of freedom, coupled to a Langevin thermostat. When the dipolar interaction energy is comparable with the thermal energy, the simulation results on the magnetization properties agree with the theoretical predictions very well. For stronger dipolar couplings, however, we find systematic deviations from the theoretical curves. We analyze in detail the observed microstructure of the fluids under different conditions. The formation of clusters is found to enhance the magnetization at weak fields and thus leads to a larger initial susceptibility. The influence of the particle aggregation is isolated by studying ferro-solids, which consist of magnetic dipoles frozen in at random locations but which are free to rotate. Due to the artificial suppression of clusters in ferrosolids the observed susceptibility is considerably lowered when compared to ferrofluids.

Quasi-two-dimensional dipolar fluid at low densities: Monte Carlo simulations and theory

We studied a quasi-two-dimensional dipolar fluid in the chaining regime using Monte Carlo canonical simulations and theoretical analyses. The self-assembled clusters were characterized by measuring their internal energy, conformational properties, and equilibrium length distributions. We generalized and used equilibrium polymer theory to describe the structure of the chains and rings observed in the simulations. The scaling forms of the length distribution functions predicted by theory were found to describe adequately the simulation results. Finally, we discuss how this type of analysis may be used to establish the existence and mechanisms of phase transitions in dilute dipolar fluids.

Theory of structural transformations in ferrofluids: chains and "gas-liquid" phase transitions

We consider a ferrofluid consisting of identical spherical particles with a permanent magnetic moment. Under the assumption that linear flexible chains can appear in the ferrofluid, we estimate the distribution function of the number of particles inside the chain. The analysis is done and simple expressions for the size distribution function are obtained in asymptotics of a strong magnetic interaction between the particles inside one chain. We studied the influence of the linear chains on conditions and scenarios of bulk "gas-liquid" phase transition in the ensemble of the particles under an infinitely strong magnetic field. In order to study the influence of the chains on bulk "gas-liquid" phase transition in the ensemble of the particles, their chemical potential mu is calculated in the model of separate interacting particles as well as in the model with chains, taking into account the interaction between them. When the temperature is low enough, van der Waals loops appear on the plots of mu versus volume concentration phi of the particles in the first model; function mu(phi) increases monotonically in the second model for all examined temperatures. This means that the condensation "gas-liquid" phase transition can take place in the model of individual particles; however, formation of the chains in real ferrofluids prevents the appearance of this transition.

Phase transitions in a ferrofluid at magnetic-field-induced microphase separation

In the presence of a magnetic field applied perpendicular to a thin sample layer, a suspension of magnetic colloidal particles (ferrofluid) can form spatially modulated phases with a characteristic length determined by the competition between dipolar forces and short-range forces opposing density variations. We introduce models for thin-film ferrofluids in which magnetization and particle density are viewed as independent variables and in which the nonmagnetic properties of the colloidal particles are described either by a lattice-gas entropy or by the Carnahan-Starling free energy. Our description is particularly well suited to the low-particle-density regions studied in many experiments. Within mean-field theory, we find isotropic, hexagonal and stripe phases, separated in general by first-order phase boundaries.

Crystal structures and freezing of dipolar fluids

We investigate the crystal structure of classical systems of spherical particles with an embedded point dipole at T=0. The ferroelectric ground state energy is calculated using generalizations of the Ewald summation technique. Due to the reduced symmetry compared to the nonpolar case the crystals are never strictly cubic. For the Stockmayer (i.e., Lennard-Jones plus dipolar) interaction three phases are found upon increasing the dipole moment: hexagonal, body-centered orthorhombic, and body-centered tetragonal. An even richer phase diagram arises for dipolar soft spheres with a purely repulsive inverse power law potential approximately r(-n). A crossover between qualitatively different sequences of phases occurs near the exponent n=12. The results are applicable to electro- and magnetorheological fluids. In addition to the exact ground state analysis we study freezing of the Stockmayer fluid by density-functional theory.

Magnetization of ferrofluids with dipolar interactions: A born-mayer expansion

For ferrofluids that are described by a system of hard spheres interacting via dipolar forces we evaluate the magnetization as a function of the internal magnetic field with a Born-Mayer technique and an expansion in the dipolar coupling strength. Two different approximations are presented for the magnetization, considering different contributions to a series expansion in terms of the volume fraction of the particles and the dipolar coupling strength.

Structure and scattering in colloidal ferrofluids

The structure of a model colloidal ferrofluid, the dipolar hard-sphere fluid, at low temperature has been investigated using Monte Carlo simulations. Extensive particle association into chainlike and ringlike clusters is observed at low density. The structure factors have been calculated, and are analyzed with the aid of simple scaling arguments. We describe the progression of fluid structures from the low-density associated phase, to the high-density liquid phase. This paper may be of help in obtaining an experimental observation of a fluid-fluid transition in colloidal ferrofluids.

Ferromagnetic liquid thin films under applied field

Theoretical calculations, computer simulations, and experiments indicate the possible existence of a ferromagnetic liquid state, although definitive experimental evidence is lacking. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture. Since liquid droplets are deformable, the droplet shape is coupled with the magnetization texture. In a thin-film geometry in zero applied field, the droplet has a circular shape and a rotating magnetization texture with a point vortex at the center. We calculate the elongation and magnetization texture of such a ferromagnetic thin-film liquid droplet confined between two parallel plates under a weak applied magnetic field. The vortex stretches into a domain wall and exchange forces break the reflection symmetry. This behavior contrasts qualitatively and quantitatively with the elongation of paramagnetic thin films.