Structural and thermal properties of orientationally ordered dipolar fluids

Force density functional theory in- and out-of-equilibrium

When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In-equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

Ferrofluids and bio-ferrofluids: looking back and stepping forward

Ferrofluids investigated along for about five decades are ultrastable colloidal suspensions of magnetic nanoparticles, which manifest simultaneously fluid and magnetic properties. Their magnetically controllable and tunable feature proved to be from the beginning an extremely fertile ground for a wide range of engineering applications. More recently, biocompatible ferrofluids attracted huge interest and produced a considerable increase of the applicative potential in nanomedicine, biotechnology and environmental protection. This paper offers a brief overview of the most relevant early results and a comprehensive description of recent achievements in ferrofluid synthesis, advanced characterization, as well as the governing equations of ferrohydrodynamics, the most important interfacial phenomena and the flow properties. Finally, it provides an overview of recent advances in tunable and adaptive multifunctional materials derived from ferrofluids and a detailed presentation of the recent progress of applications in the field of sensors and actuators, ferrofluid-driven assembly and manipulation, droplet technology, including droplet generation and control, mechanical actuation, liquid computing and robotics.

Energy dissipation of rigid dipoles in a viscous fluid under the action of a time-periodic field: The influence of thermal bath and dipole interaction

Ferrofluid heating by an external alternating field is studied based on the rigid dipole model, where the magnetization of each particle in a fluid is supposed to be firmly fixed in the crystal lattice. Equations of motion, employing Newton's second law for rotational motion, the condition of rigid body rotation, and the assumption that the friction torque is proportional to angular velocity are used. This oversimplification permits us to expand the model easily: to take into account the thermal noise and interparticle interaction that allows us to estimate from unified positions the role of thermal activation and dipole interaction in the heating process. Our studies are conducted in three stages. The exact expressions for the average power loss of a single particle are obtained within the dynamical approximation. Then, in the stochastic case, the power loss of a single particle is estimated analytically using the Fokker-Planck equation and numerically using the effective Langevin equation. Finally, the power loss for the particle ensemble is obtained using the molecular dynamics method. Here, the local dipole fields are calculated approximately based on the Barnes-Hut algorithm. The revealed trends in the behavior of both a single particle and the particle ensemble suggest the way of choosing the conditions for obtaining the maximum heating efficiency. The competitiveness character of the interparticle interaction and thermal noise is investigated in detail. Two situations, when the thermal noise rectifies the power loss reduction caused by the interaction, are described. The first of them is related to the complete destruction of dense clusters at high noise intensity. The second one originates from the rare switching of the particles in clusters due to thermal activation, when the noise intensity is relatively weak. In this way, the constructive role of noise appears in the system.

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.

Polar-solvation classical density-functional theory for electrolyte aqueous solutions near a wall

A precise description of the structural and dielectric properties of liquid water is critical to understanding the physicochemical properties of solutes in electrolyte solutions. In this article, a mixture of ionic and dipolar hard spheres is considered to account for water crowding and polarization effects on ionic electrical double layers near a uniformly charged hard wall. As a unique feature, solvent hard spheres carrying a dipole at their centers were used to model water molecules at experimentally known concentration, molecule size, and dipolar moment. The equilibrium ionic and dipole density profiles of this electrolyte aqueous model were calculated using a polar-solvation classical density-functional theory (PSCDFT). These profiles were used to calculate the charge density distribution, water polarization, dielectric permittivity function, and mean electric potential profiles as well as differential capacitance, excess adsorptions, and wall-fluid surface tension. These results were compared with those corresponding to the pure dipolar model and unpolar primitive solvent model of electrolyte aqueous solutions to understand the role that water crowding and polarization effects play on the structural and thermodynamic properties of these systems. Overall, PSCDFT predictions are in agreement with available experimental data.

Linear and nonlinear magnetic properties of ferrofluids

Within a high-magnetic-field approximation, employing Ruelle's algebraic perturbation theory, a field-dependent free-energy expression is proposed which allows one to determine the magnetic properties of ferrofluids modeled as dipolar hard-sphere systems. We compare the ensuing magnetization curves, following from this free energy, with those obtained by Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] as well as with new corresponding Monte Carlo simulation data. Based on the power-series expansion of the magnetization, a closed expression for the magnetization is also proposed, which is a high-density extension of the corresponding equation of Ivanov and Kuznetsova. From both magnetization equations the zero-field susceptibility expression due to Tani et al. [Mol. Phys. 48, 863 (1983)] can be obtained, which is in good agreement with our MC simulation results. From the closed expression for the magnetization the second-order nonlinear magnetic susceptibility is also derived, which shows fair agreement with the corresponding MC simulation data.

Size effect and stability of polarized fluid phases

The existence of a ferroelectric fluid phase for systems of 1000-2000 dipolar hard or soft spheres is well established by numerical simulations. Theoretical approaches proposed to determine the stability of such a phase are either in qualitative agreement with the simulation results or disagree with them. Experimental results for systems of molecules or particles with large electric or magnetic dipole moments are also inconclusive. As a contribution to the question of existence and stability of a fluid ferroelectric phase this simulation work considers system sizes of the order of 10 000 particles, thus an order of magnitude larger than those used in previous studies. It shows that although ferroelectricity is not affected by an increase of system size, different spatial arrangements of the dipolar hard spheres in such a phase are possible whose free energies seem to differ only marginally.

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.

Vapor-liquid coexistence of the Stockmayer fluid in nonuniform external fields

We investigate the structure and phase behavior of the Stockmayer fluid in the presence of nonuniform electric fields using molecular simulation. We find that an initially homogeneous vapor phase undergoes a local phase separation in a nonuniform field due to the combined effect of the field gradient and the fluid vapor-liquid equilibrium. This results in a high-density fluid condensing in the strong field region. The system polarization exhibits a strong field dependence due to the fluid condensation.

Isotropic-polar phase transitions in an amphiphilic fluid: density functional theory versus computer simulations

We investigate the critical line separating isotropic from polar phases in an amphiphilic bulk fluid by means of density functional theory (DFT) and Monte Carlo (MC) simulations in the isothermal-isobaric ensemble. The intermolecular interactions are described by a Lennard-Jones potential in which the attractive contribution is modified by an orientation-dependent function. The latter consists of two terms: The first one has the orientation dependence of a classical three-dimensional Heisenberg interaction, whereas, the second one has the orientation dependence of a classical dipole-dipole interaction. However, both contributions are short range. Employing DFT together with a modified mean-field (MMF) approximation for the orientation-dependent pair correlation function, we derive an analytical expression for the critical line separating isotropic from polar liquidlike phases. In parallel MC simulations, we locate the line of critical points through an analysis of Binder's second-order cumulant of the polar-order parameter. Comparison with DFT shows that the dipolelike contribution is irrelevant for the isotropic-polar phase transition. As far as the Heisenberg contribution is concerned, the MC data are in semiquantitative agreement with the DFT predictions for sufficiently strong coupling between molecular orientations. For weaker coupling, the variation in the ratio of critical density and temperature ρ(c)/T(c) with the Heisenberg coupling constant ε(H) is underestimated by the MMF treatment. The MC results suggest that this is because ρ(c) increases with decreasing ε(H) such that the assumption on which the MMF approach rests becomes less applicable in the weaker-coupling limit.

Magnetization of multicomponent ferrofluids

The solution of the mean spherical approximation (MSA) integral equation for isotropic multicomponent dipolar hard sphere fluids without external fields is used to construct a density functional theory (DFT), which includes external fields, in order to obtain an analytical expression for the external field dependence of the magnetization of ferrofluidic mixtures. This DFT is based on a second-order Taylor series expansion of the free energy density functional of the anisotropic system around the corresponding isotropic MSA reference system. The ensuing results for the magnetic properties are in quantitative agreement with our canonical ensemble Monte Carlo simulation data presented here.

Steric effects in a mean-field model for polar nematic liquid crystals

The existence of uniaxial liquid crystals comprising polar molecules, with all the dipoles aligned in a parallel pattern, is classically ruled out. Generally, there are two different avenues to a mean-field theory for liquid crystals: one is based on short-range, repulsive, steric forces, and the other is based on long-range, globally attractive, dispersion forces. Purely polar steric interactions have been shown to have the potential of inducing unexpected orientationally ordered states. In real molecules, anisotropies both in shape and in polarizability coexist; it has been shown that dispersion forces interaction can be combined with hard-core repulsion in a formal theory, based on a steric tensor. Starting from this, we build an interaction Hamiltonian featuring the average electric dipolar energy exchanged between molecules with the same excluded region. Under the assumption that the molecular shape is spheroidal, we propose a mean-field model for polar nematic liquid crystals which can exhibit both uniaxial and biaxial polar phases. By means of a numerical bifurcation analysis, we discuss the stability of the equilibrium against the choice of two model parameters, one describing the degree of molecular shape biaxiality and the other describing the relative orientation of the electric dipole within each molecule. We find only uniaxial stable phases, which are effectively characterized by a single scalar order parameter.

Dipolar particles in an external field: Molecular dynamics simulation and mean field theory

Using molecular dynamics computer simulation we compute gas-liquid phase coexistence curves for the Stockmayer fluid in an external electric field. We observe a field-induced shift of the critical temperature DeltaTc. The sign of DeltaTc depends on whether the potential or the surface charge density is held constant assuming that the dielectric material fills the space between capacitor plates. Our own as well as previous literature data for DeltaTc are compared to and interpreted in terms of a simple mean field theory. Despite considerable errors in the simulation results, we find consistency between the simulation results obtained by different groups including our own and the mean field description. The latter ties the sign of DeltaTc to the outside constraints via the electric field dependence of the orientation part of the mean field free energy.

Magnetization and susceptibility of ferrofluids

A second-order Taylor series expansion of the free energy functional provides analytical expressions for the magnetic field dependence of the free energy and of the magnetization of ferrofluids, here modeled by dipolar Yukawa interaction potentials. The corresponding hard core dipolar Yukawa reference fluid is studied within the framework of the mean spherical approximation. Our findings for the magnetic and phase equilibrium properties are in quantitative agreement with previously published and new Monte Carlo simulation data.

Phase diagram for stimulus-responsive materials containing dipolar colloidal particles

Dipolar colloidal particles self-assemble into a rich variety of microstructures ranging from co-crystals of unusual symmetry, to open networks (gels) of cross-linked chains of particles. We use molecular dynamics computer simulation to explore the self-assembly, structure, crystallization and/or gelation of systems of colloid particles with permanent dipole moments immersed in a high-dielectric solvent. Particle-particle interactions are modeled with a discontinuous potential. The phase diagram in the temperature-packing fraction plane is calculated. Several types of phases are found in our simulations: ordered phases including face-centered-cubic, hexagonal-close-packed, and body-centered-tetragonal at high packing fractions, and fluid, string-fluid, and gel phases at low packing fractions. The very low volume fraction gel phases and the well-ordered crystal phases are promising for advanced materials applications.

Capillary condensation and orientational ordering of confined polar fluids

The phase behavior and the orientational structure of polar model fluids confined to slit pores is investigated by means of density functional theory in a modified mean-field approximation. We focus on fluid states and further assume a uniform number density throughout the pore. Our results for spherical dipolar particles with additional van der Waals-like interactions (Stockmayer fluids) reveal complex fluid-fluid phase behavior involving condensation and first- and second-order isotropic-to-ferroelectric phase transitions, where the ferroelectric ordering occurs parallel to the confining walls. The relative importance of these phase transitions depends on two "tuning" parameters, that is the strength of the dipolar interactions (relative to the isotropic attractive ones) between fluid particles, and on the pore width. In particular, in narrow pores the condensation transition seen in bulk Stockmayer fluids is entirely suppressed. For dipolar hard spheres, on the other hand, the impact of confinement consists in a decrease of the isotropic-to-ferroelectric transition temperatures. We also demonstrate that the local orientational structure is inhomogeneous and anisotropic even in globally isotropic systems, in agreement with computer simulation results.

Ordering in linear multipolar colloids driven by an external field

An approach to describe a linear multipolar colloid driven by an external field is developed by considering a colloid which in absence of the field is low structured and its coupling potential is axially symmetric. The equilibrium correlation of one component of the orientation tensor, self and collective, is computed up to linear order in density, which can be measured in an appropriate light scattering experiment. The self-correlation is written in terms of the second and fourth order parameters. All the equilibrium quantities are computed up to two-body level. This is done by assuming that the two-body equilibrium density function is given by the Boltzmann distribution, whereas the one-body density function is computed as solution of the equilibrium N-body Smoluchowski equation in the absence of hydrodynamic interactions. These observables, self and collective, as well as the second and fourth order parameters are able to describe when the colloid would evolve to an orientationally ordered phase. Explicit results for the dipole and quadrupole moments are reported. These results predict a different alignment with the external field for each moment. A relationship is provided between second and fourth order parameters, predicting the critical value of the external field in which the colloid goes into an axially symmetric phase.

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.

Density-functional study of model bidisperse ferrocolloids in an external magnetic field

We present phase diagrams of a model bidisperse ferrocolloid consisting of a binary mixture of dipolar hard spheres (DHSs) under the influence of an external magnetic field. The dipole moments of the particles are chosen proportional to the particle volume to mimic real ferrocolloids, and we focus on dipole-dominated systems where isotropic attractive interactions are absent. Our results are based on density-functional theory in the modified mean-field (MMF) approximation. For one-component DHS fluids in external fields, and for corresponding mixtures dominated by one of the components, MMF theory predicts the tricritical point of the transition between an isotropic gas and a ferromagnetic liquid occurring at zero field to be changed into a critical point separating two magnetically ordered phases of different density. The corresponding critical temperature displays a nonmonotonic dependence on the field strength. Completely different behavior is found for the critical temperature related to the demixing phase transitions appearing in strongly asymmetric mixtures [G. M. Range and S. H. L. Klapp, Phys. Rev. E 70, 061407 (2004)]. For such systems, we find a monotonic decrease of the demixing critical temperature with increasing field. The field strength dependence of the critical temperature can therefore be tuned between nonmonotonic and monotonic behaviors just by changing the composition of the mixture--e.g., by adjusting the chemical potentials. This allows us to efficiently control the influence of external magnetic fields on the phase behavior over a large temperature interval.

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.

Heat capacity in a model polydisperse ferrofluid with narrow particle size distribution

The influence of polydispersity on the phase equilibrium properties and the heat capacity of a dipolar system with additional short-range (repulsive + attractive) interactions (modeled by a shifted Lennard-Jones pair potential) is studied by means of a Monte Carlo scheme. The particle distribution of the investigated system is realized in the semigrand ensemble by tuning appropriately the underlying particle distribution density. The phase coexistence and heat capacity data are calculated with and without an applied magnetic field, and the obtained results are compared with the data determined in a monodisperse equivalent of the system.

Density functional study of the phase behavior of asymmetric binary dipolar mixtures

Using density functional theory in the modified mean-field (MMF) approximation we study the phase behavior of asymmetric binary mixtures of equisized dipolar hard spheres with different dipole moments in the fluid phase regime. We focus on "dipole-dominated" systems where isotropic attractive interactions are absent. Despite these restrictions our results reveal complex fluid-fluid phase behavior involving demixing and first- and second-order isotropic-to-ferroelectric phase transitions the relative importance of which depends on two "tuning" parameters, that is, the parameter Gamma measuring the ratio of the dipolar coupling strengths, and the chemical potential difference Deltamu controlling the composition. The interplay of these effects then yields three different types of phase behavior differing in the degree to which demixing dominates the system. A generic feature of the resulting diagrams is that the isotropic-to-ferroelectric transition is shifted towards significantly higher densities compared to the one-component case, and is therefore destabilized. Furthermore, demixing in the MMF approach turns out to be always accompanied by spontaneous ferroelectricity, which is in contrast to recent integral equation and simulation results for the limiting case of a mixture of dipolar and pure hard spheres (Gamma=0).

Effect of external electric field on the bulk and interfacial properties of weakly dipolar fluid in slab-shaped and sphere-shaped systems

The effect of a uniform electric field on the bulk and interfacial properties of a model dipolar fluid is investigated by using a modified mean-field density functional theory. Particular attention is given to the dependence of the vapor-liquid phase coexistence in a slab-shaped system on the direction of the electric field with respect to the slab surfaces, as well as in the sphere-shaped system on the surrounding dielectric permittivity. For planar vapor-liquid interfaces, the interfacial profiles of the orientation order parameters and components of the dielectric-permittivity tensor are calculated. Analytical expressions for these interfacial profiles and their dependence on the electric field are obtained. When the electric field is normal to the interface we find that the thermodynamic surface tension is lowered compared to that in zero field, and that when the electric field is parallel to the interface the surface tension is enhanced. In contrast, the mechanical surface tension at the equimolar dividing surface is always enhanced by the field regardless of the field direction, and it assumes its highest value when the field is parallel to the interface.

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.

Bulk and interfacial properties of a dipolar-quadrupolar fluid in a uniform electric field: a density-functional approach

We have studied the bulk and interfacial properties of a dipolar-quadrupolar fluid based on an extended modified mean-field density-functional theory. Effects of a uniform electric field on the bulk and interfacial properties are also studied. Results of the coexisting vapor-liquid densities, interfacial profiles of the density and orientation order parameters, the surface tension, and their dependence on the temperature, magnitude of molecule dipole and quadrupole moment, and the applied field are obtained. In general, we find that the applied field increases the critical temperature, broadens the vapor-liquid coexistence curves, and reduces the surface tension. We also find that if the quadrupole moment is positive, the reduction in the surface tension is greater when the applied field is in the direction from the vapor to the liquid phase than the reduction when the field is in the opposite direction. This apparent symmetry breaking by reversing the field direction may offer a molecular mechanism to explain the phenomenon of the sign preference in liquid droplet formation on charged condensation centers.

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.

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.

Dipole orientational order at the critical interface

We present experimental evidence that dipoles exhibit orientational order at the critical interface of mixtures of polar plus nonpolar liquids using the technique of ellipsometry. In this technique the ellipticity rho; at the critical interface for all nonpolar or weakly polar fluids or fluid mixtures diverges as t(beta-nu) where t=(Tc-T)/Tc is the reduced temperature relative to the critical temperature Tc and beta=0.328, nu=0.632 are critical exponents. For polar fluids, however, the dipole-image dipole interaction at the interface can cause long-range orientational order resulting in deviations from this power-law divergence. Theoretical results predict that the surface orientational order parameter alpha2(z) approximately m(*4)[d2v(z)/dz2], where m(*) is the reduced dipole moment and v(z) is the local composition at position z within the interface. We find quantitative agreement with these predictions for two different critical binary liquid mixtures composed of a highly polar plus nonpolar component.

Comment on "Algebraic perturbation theory for polar fluids: A model for the dielectric constant"

Kalikmanov [Phys. Rev. E 59, 4085 (1999)] proposed a perturbation theory method to calculate the dielectric constant of dipolar hard sphere fluids using an infinitely long cylindrical container to avoid the depolarization. We demonstrate that while the method is very helpful, his theory appears to be incomplete because of the incorrect calculation of the corresponding three-body integrals. It is shown that with the correct consideration of these terms the theory is consistent with the results of earlier work in low-density limit, and at high densities the method yields the equation of Tani et al. [Mol. Phys. 48, 863 (1983)] for the dipolar hard sphere fluid dielectric constant.

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.