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The ferrofluid emulsion, made of kerosene-based ferrofluid droplets suspended in nonmiscible aviation oil, demonstrates experimentally the nonmonotonic dependence of the effective magnetic permeability as a function of the uniform static magnetic field. In weak fields the emulsion permeability rapidly grows; it reaches its maximum at fields on the order of 1 kA/m; after that, it decays to zero. The theoretical explanation of the effect, as we show here, could be based on the following idea: In a weak magnetic field the growth of the induced droplet magnetic moment is faster than the linear one due to the droplet elongation accompanied by the reduction of the demagnetizing field. Further increase of the external magnetic field strength cannot lead to a significant decrease of the demagnetizing field, as the droplets are already highly elongated. On the other hand, the magnetic susceptibility of the ferrofluid reduces with the field strength. Thus, the effective magnetic permeability of the ferrofluid suspension starts decreasing. The developed theoretical model describes well the experimental observations.

This work is devoted to the study of the thermodynamic properties of soft magnetic materials that are actively used in technology and medicine. The mathematical model assumes that magnetic nanoparticles are embedded in the nodes of a regular cubic lattice, so that the particle translational degrees of freedom are turned off and the mechanical Brownian rotation of particles is impossible. The response of the particles to the external magnetic field occurs by the Néel mechanism due to their magnetic moment rotation inside the nanoparticle. The easy axes are distributed according to the particular configuration: these are aligned (i) parallel or (ii) perpendicular to the direction of an external field. These models are investigated using both theory and computer simulation. The theoretical approach is based on a modification of the virial expansion method, which allows us to determine analytical expressions for the Helmholtz free energy, the static magnetization, and the initial magnetic susceptibility. These characteristics turned out in a good agreement with the numerical calculations in the region of low and moderate values of intensity of the dipole-dipole interparticle interactions and anisotropy energy barrier. [ABSTRACT FROM AUTHOR]

The active use of nanoparticles in modern biomedical applications and technologies requires reliable theoretical models capable of predicting physical properties. The effect of a static magnetic field on the orientational ordering of the easy magnetization axes in an ensemble of superparamagnetic nanoparticles (SNPs) is studied using a combination of statistical-mechanical theory and computer simulations. The magnetic dipole-dipole interaction between particles is taken into account within the framework of the modified mean-field approach. The alignment distributions of the easy magnetization axes of the SNPs and the static magnetic characteristics of the ferrocomposite are analyzed. The presence of even weak interparticle magneto-dipole interactions results in a notable enhancement of the magnetic susceptibility of the ferrocomposite. • Easy magnetization axes of superparamagnetic nanoparticles orient in magnetic field. • Solidification of liquid matrix maintains the induced orientation texture. • Textured ferrocomposite demonstrates enhanced magnetic response. • Particle interactions strengthen the effect of orientation texturing. • Theory is used to describe these effects for use in applications. [ABSTRACT FROM AUTHOR]

Anisotropic pair correlations in ferrofluids exposed to magnetic fields are studied using a combination of statistical-mechanical theory and computer simulations. A simple dipolar hard-sphere model of the magnetic colloidal particles is studied in detail. A virial-expansion theory is constructed for the pair distribution function (PDF) which depends not only on the length of the pair separation vector, but also on its orientation with respect to the field. A detailed comparison is made between the theoretical predictions and accurate simulation data, and it is found that the theory works well for realistic values of the dipolar coupling constant (λ = 1), volume fraction (φ <= 0.1), and magnetic field strength. The structure factor is computed for wavevectors either parallel or perpendicular to the field. The comparison between theory and simulation is generally very good with realistic ferrofluid parameters. For both the PDF and the structure factor, there are some deviations between theory and simulation at uncommonly high dipolar coupling constants, and with very strong magnetic fields. In particular, the theory is less successful at predicting the behavior of the structure factors at very low wavevectors, and perpendicular Gaussian density fluctuations arising from strongly correlated pairs of magnetic particles. Overall, though, the theory provides reliable predictions for the nature and degree of pair correlations in ferrofluids in magnetic fields, and hence should be of use in the design of functional magnetic materials. [ABSTRACT FROM AUTHOR]

• The dynamics in ferrofluids are analysed theoretically, including the effects of interactions, structure, and polydispersity. • The equilibrium magnetisation dynamics and non-equilibrium magnetic relaxation dynamics are compared and contrasted. • Interactions lead to strong differences between the two cases. • The influence of structure formation is summarised. • Polydispersity is included into the equations describing magnetic relaxation, and unusual effects are uncovered. Linear response theory relates the decay of equilibrium magnetisation fluctuations in a ferrofluid to the frequency-dependent response of the magnetisation to a weak ac external magnetic field. The characteristic relaxation times are strongly affected by interactions between the constituent particles. Similarly, the relaxation of an initially magnetised system towards equilibrium in zero field occurs on a range of timescales depending on the structure of the initial state, and the interactions between the particles. In this work, ferrofluids are modelled as colloidal suspensions of spherical particles carrying point dipole moments, and undergoing Brownian motion. Recent theoretical and simulation work on the relaxation and linear response of these model ferrofluids is reviewed, and the effects of interactions, structure formation, and polydispersity on the characteristic time scales are outlined. It is shown that: (i) in monodisperse ferrofluids, the timescale characterising the collective response to weak fields increases with increasing interaction strength and/or concentration; (ii) in monodisperse ferrofluids, the initial, short-time decay is independent of interaction strength, but the asymptotic relaxation time is the same as that characterising the collective response to weak fields; (iii) in the strong-interaction regime, the formation of self-assembled chains and rings introduces additional timescales that vary by orders of magnitude; and (iv) in polydisperse ferrofluids, the instantaneous magnetic relaxation time of each fraction varies in a complex way due to the role of interactions. [ABSTRACT FROM AUTHOR]

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 (B2 and B3) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter a. The formula for S3 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 A. and a 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. [ABSTRACT FROM AUTHOR]

We present a theoretical model for calculating the structure factor for ferrofluids with strong inter-particle magnetic dipole-dipole interactions, where chain aggregates are known to exist. Our analytical model is based on the minimization of a free energy density functional that allows us to explicitly construct the radial distribution functions of the ferroparticles. Both mono- and bi-disperse model systems have been investigated in the absence of an external magnetic field. We perform an extensive comparison of the theoretical model predictions with the results of molecular dynamic computer simulations for a wide range of ferroparticle densities and coupling parameters, and find encouraging agreement between the simulation data and theory. The behaviour of the structure factor in the region of the first peak and in the region of large wave vectors is studied in detail, and related to the observed microstructure. Our results demonstrate that the combined method developed in the present study is suitable for revealing the connection between microstructure and scattering images, and thus can help to interpret experimental results such as small angle neutron scattering images. [ABSTRACT FROM AUTHOR]

Abstract: The paper is devoted to the basic problem of chain aggregate structure in magnetic fluids under the influence of an external magnetic field. A traditional free-energy density functional approach is used, and the chain partition function of a flexible chain is calculated under the condition when both the interparticle dipole–dipole interaction between the nearest neighboring ferroparticles in a chain and the interaction of particle magnetic moments with an external field are taken into account with the help of rotational matrix techniques. [Copyright &y& Elsevier]

The response of ferrofluids to a high-amplitude AC magnetic field is important for several applications including magnetic hyperthermia and biodetection. In computer simulations of the dynamic susceptibility of a ferrofluid outside the linear response region, there are several problems associated with the fact that an increase in the frequency of the AC field leads to the appearance of additional computational errors, which can even lead to unphysical results. In this article, we study the dependence of the computational error arising in the computer simulation of the dynamic susceptibility on the input parameters of the numerical algorithm: the length of the time step, the total number of computer simulation periods, and averaging period. Computer simulation is carried out using the Langevin dynamics method and takes Brownian rotational relaxation of magnetic particles and interparticle interactions into account. The reference theory [Yoshida T.; Enpuku K. Jap. J. Ap. Phys. 2009] is used to estimate computational error. As a result, we give practical recommendations for choosing the optimal input parameters of the numerical algorithm, which make it possible to obtain reliable results of the dynamic susceptibility of a ferrofluid in a high-amplitude AC field in a wide frequency range. [ABSTRACT FROM AUTHOR]

Ferrofluids have attracted considerable interest from researchers and engineers due to their rich set of unique physical properties that are valuable for many industrial and biomedical applications. Many phenomena and features of ferrofluids' behavior are determined by internal structural transformations in the ensembles of particles, which occur due to the magnetic interaction between the particles. An applied magnetic field induces formations, such as linear chains and bulk columns, that become elongated along the field. In turn, these structures dramatically change the rheological and other physical properties of these fluids. A deep and clear understanding of the main features and laws of the transformations is necessary for the understanding and explanation of the macroscopic properties and behavior of ferrofluids. In this paper, we present an overview of experimental and theoretical works on the internal transformations in these systems, as well as on the effect of the internal structures on the rheological effects in the fluids. [ABSTRACT FROM AUTHOR]

In this study, we derived the equations describing the dynamics of a magnetic fluid in crossed magnetic fields (bias and alternating probe fields), considering the field dependence of the relaxation times, interparticle interactions, and demagnetizing field has been derived. For a monodisperse fluid, the dependence of the output signal on the bias field and the probe field frequency was constructed. Experimental studies were conducted in a frequency range up to 80 kHz for two samples of fluids based on magnetite nanoparticles and kerosene. The first sample had a narrow particle size distribution, low-energy magneto dipole interactions, and weak dispersion of dynamic susceptibility. The second sample had a broad particle size distribution, high-energy magneto dipole interactions, and strong dispersion of dynamic susceptibility. In the first case, the bias field led to the appearance of short chains. In the second case, we found quasi-spherical clusters with a characteristic size of 100 nm. The strong dependence of the output signal on the particle size allowed us to use the crossed field method to independently estimate the maximum diameter of the magnetic core of particles. [ABSTRACT FROM AUTHOR]

The dynamic magnetic response of a ferrofluid to a weak ac magnetic field is studied using statistical mechanical theory and Brownian dynamics simulations, taking account of dipole-dipole interactions between the constituent ferromagnetic colloidal particles, and the presence of a range of particle sizes. The effects of interactions and polydispersity on the frequency dispersion are shown to be substantial: the amplitude of the response can be about twice that of a noninteracting system; the frequency for peak power loss can be reduced by about one half; and polydispersity effects can even change the qualitative appearance of the susceptibility spectrum. [ABSTRACT FROM AUTHOR]

Abstract: The paper is devoted to the basic problem of chain aggregate formation in magnetic fluids under the influence of an external magnetic field. Chain distribution in dynamic equilibrium is obtained on the basis of free energy minimization method under the condition when the interparticle dipole–dipole interaction between the nearest neighboring ferroparticles in each chain is taken into account. The modified mean field approach is used for considering the dipole–dipole interaction between all particles in a ferrofluid. The model describes well the molecular dynamics simulations of magnetostatic properties for monodisperse ferrofluids containing chain aggregates. [Copyright &y& Elsevier]

A method for calculation of the free energy of dipolar hard spheres under the presence of an applied magnetic field is presented. The method is based on the virial expansion in terms of density as well as the dipolar coupling constant λ , and it uses diagram technique. The formulas and the diagrams, needed to calculate the second B 2 and third B 3 virial coefficients, are derived up to the order of ∼ λ 3 , and compared to the zero-field case. The formula for B 2 is the same as in the zero-field case; the formula for B 3 , however, is different in an applied field, and a derivation is presented. This is a surprising result which is not emphasized in standard texts, but which has been noticed before in the virial expansion for flexible molecules (Caracciolo et al., 2006; Caracciolo et al., 2008). To verify the correctness of the obtained formulas, B 2 and B 3 were calculated within the accuracy of λ 2 , which were applied to initial magnetic susceptibility. The obtained expression fully coincides with the well-known theories (Morozov and Lebedev, 1990; Huke and Lücke, 2000; Ivanov and Kuznetsova, 2001), which used different methods to calculate the initial magnetic susceptibility. [ABSTRACT FROM AUTHOR]

The dynamic magnetic response of ferrofluid in a static uniform external magnetic field to a weak, linear polarized, alternating magnetic field is investigated theoretically. The ferrofluid is modeled as a system of dipolar hard spheres, suspended in a long cylindrical tube whose long axis is parallel to the direction of the static and alternating magnetic fields. The theory is based on the Fokker-Planck-Brown equation formulated for the case when the both static and alternating magnetic fields are applied. The solution of the Fokker-Planck-Brown equation describing the orientational probability density of a randomly chosen dipolar particle is expressed as a series in terms of the spherical Legendre polynomials. The obtained analytical expression connecting three neighboring coefficients of the series makes possible to determine the probability density with any order of accuracy in terms of Legendre polynomials. The analytical formula for the probability density truncated at the first Legendre polynomial is evaluated and used for the calculation of the magnetization and dynamic susceptibility spectra. In the absence of the static magnetic field the presented theory gives the correct single-particle Debye-theory result, which is the exact solution of the Fokker-Planck-Brown equation for the case of applied weak alternating magnetic field. The influence of the static magnetic field on the dynamic susceptibility is analyzed in terms of the low-frequency behavior of the real part and the position of the peak in the imaginary part. [ABSTRACT FROM AUTHOR]

A theory for the frequency-dependent magnetic susceptibility of a ferrofluid in a static uniform magnetic field is developed, including the dipolar interactions between the constituent particles. Interactions are included within the framework of modified mean-field theory. Predictions are given for the linear responses of the magnetization to a probing ac field both parallel and perpendicular to the static field and are tested against results from Brownian dynamics simulations. The effects of the particle concentration and dipolar coupling constant on the field-dependent static susceptibilities and the frequency dispersions are shown to be substantial, which justifies taking proper account of the interactions between particles. The theory is reliable provided that the volume concentration and dipolar coupling constant are not too large and within the range of values for real ferrofluids. [ABSTRACT FROM AUTHOR]