Ekaterina A. Elfimova

Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields

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.

The effects of polydispersity on the initial susceptibilities of ferrofluids.

The effects of particle-size polydispersity on the initial susceptibilities of concentrated ferrofluids are analyzed using a combination of theory and computer simulation. The study is focused on a model ferrofluid with a prescribed magnetic-core diameter distribution, a fixed non-magnetic surface layer (corresponding to a demagnetized layer and adsorbed surfactant) and a combination of dipolar and hard-core interactions. The non-trivial effects of polydispersity are identified by comparing the initial susceptibilities of monodisperse and polydisperse ferrofluids with the same Langevin susceptibility. The theory is based on a correction to the second-order modified mean-field theory arising from a formal Mayer-type cluster expansion; this correction is dependent on a parameter similar to the normal dipolar coupling constant, except that it contains a complicated double average over the particle-size distribution, which means that the initial susceptibility should depend significantly on polydispersity. Specifically, the theory predicts that the initial susceptibility is enhanced significantly by polydispersity. This prediction is tested rigorously against results from Monte Carlo simulations and is found to be robust. The qualitative agreement between theory and simulation is already satisfactory, but the quantitative agreement could be improved by a systematic extension of the cluster expansion. The overall conclusion is that polydispersity should be accounted for carefully in magnetogranulometric analyses of real ferrofluids.

Thermodynamics of the Stockmayer fluid in an applied field

The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ4, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ3, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.

Influence of dipolar interactions on the magnetic susceptibility spectra of ferrofluids

The frequency-dependent magnetic susceptibility of a ferrofluid is calculated under the assumption that the constituent particles undergo Brownian relaxation only. Brownian-dynamics simulations are carried out in order to test the predictions of a recent theory [A. O. Ivanov, V. S. Zverev, and S. S. Kantorovich, Soft Matter 12, 3507 (2016)1744-683X10.1039/C5SM02679B] that includes the effects of interparticle dipole-dipole interactions. The theory is based on the so-called modified mean-field approach and possesses the following important characteristics: in the low-concentration, noninteracting regime, it gives the correct single-particle Debye-theory results; it yields the exact leading-order results in the zero-frequency limit; it includes particle polydispersity correctly from the outset; and it is based on firm theoretical foundations allowing, in principle, systematic extensions to treat stronger interactions and/or higher concentrations. The theory and simulations are compared in the case of a model monodisperse ferrofluid, where the effects of interactions are predicted to be more pronounced than in a polydisperse ferrofluid. The susceptibility spectra are analyzed in detail in terms of the low-frequency behavior, the position of the peak in the imaginary (out-of-phase) part, and the characteristic decay time of the magnetization autocorrelation function. It is demonstrated that the theory correctly predicts the trends in all of these properties with increasing concentration and dipolar coupling constant, the product of which is proportional to the Langevin susceptibility χ_{L}. The theory is in quantitative agreement with the simulation results as long as χ_{L}≲1.

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) − 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.

The initial magnetic susceptibility of polydisperse ferrofluids: A comparison between experiment and theory over a wide range of concentration.

Temperature dependencies of the static initial magnetic susceptibility for ferrofluids at various concentrations are studied using experiment and statistical-mechanical theories. Magnetic susceptibility measurements are carried out for twelve samples of magnetite-based fluids stabilized with oleic acid over a wide range of temperatures (210 K ≲T ≲ 390 K); all samples have the same granulometric composition but different volume ferroparticle concentrations (0.2 ≲ φ ≲ 0.5). Experimental results are analyzed using three theories: the second-order modified mean-field theory (MMF2) [A. O. Ivanov and O. B. Kuznetsova, Phys. Rev. E 64, 41405 (2001)]; its correction for polydisperse ferrofluids arising from Mayer-type cluster expansion and taking into account the first terms of the polydisperse second virial coefficient [A. O. Ivanov and E. A. Elfimova, J. Magn. Magn. Mater 374, 327 (2015)]; and a new theory based on MMF2 combined with the first terms of the polydisperse second and third virial contributions to susceptibility. It turns out that the applicability of each theory depends on the experimental sample density. If twelve ferrofluid samples are split into three groups of strong, moderate, and low concentrated fluids, the temperature dependences of the initial magnetic susceptibility in each group are very precisely described by one of the three theories mentioned above. The determination of a universal formula predicting a ferrofluid susceptibility over a broad range of concentrations and temperatures remains as a challenge.

Modified mean-field theory of the magnetic properties of concentrated, high-susceptibility, polydisperse ferrofluids

The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)1063-651X10.1103/PhysRevE.64.041405] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids. Comparisons have been made between systems with the same Langevin susceptibility and the same saturation magnetization. In all cases, the new theoretical magnetization curve shows better agreement with simulation data than does the MMF2 theory. As for the initial susceptibility, MMF2 theory is most accurate for the monodisperse model, while the new theory works best for polydisperse systems with a significant proportion of large particles. These results are important for the analysis and characterization of recently synthesized polydisperse ferrofluids with record-breaking values of the initial magnetic susceptibility.

Thermodynamics of Bidisperse Ferrofluids in Zero External Magnetic Field: Theory and Simulations

The thermodynamic properties of a ferrofluid modeled by a bidisperse system of dipolar hard spheres in the absence of external magnetic field are investigated using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy in terms of particle volume concentration. Comparison between the theoretical predictions and simulation data shows a great agreement of the results.

Structure Properties in a Bidisperse Ferrofluid in the Absence of an External Magnetic Field

The structure properties of a ferrofluid modeled by a bidisperse system of dipolar hardspheres are studied theoretically for the case of zero external field. Analytical expressions are providedfor the pair distribution function (PDF) and structure factor (SF) to within the first order in numberdensity and the second order in dipole-dipole interaction strength. The influence of the granulometriccomposition on the behavior of the PDF and the position of the first peak of the SF is analyzed.