Alexey O. Ivanov

Equilibrium properties of ferrocolloids

Abstract We consider a thermodynamic model of a stable macroscopically homogeneous ferrocolloid containing identical spherical particles with permanent moments suspended in a non-dissociated liquid on the basis of the hard sphere perturbation theory. Magnetostatic properties and the phase diagram of the ferrocolloid are shown to agree very well with experimental evidence. Dipole interparticle interactions result in an effective attraction between the particles which increase, as the strength of an externally applied magnetic field grows, favours the phase separation and cause a reduction in the coefficient of mutual Brownian diffusion of the particles.

Equilibrium properties of a bidisperse ferrofluid with chain aggregates: theory and computer simulations

In this paper we investigate a bidisperse model ferrofluid, where the aggregates are treated as flexible chains, under the influence of an arbitrary valued external magnetic field. An extensive comparison of the theoretical predictions to the results of the computer simulations is provided. Both magnetostatic properties and structural observables are investigated with the help of the newly developed theoretical approach and molecular dynamic simulations. It is shown that the results of the cluster analysis are very sensitive to the cluster definition. Here we use two different criteria for the particles to be bound: an energy criterion which is slightly different in the theory and simulations due to technical problems, and an entropy criterion which is the same for the molecular dynamics and theoretical model. This enables us to compare qualitatively and quantitatively theoretical and numerical microstructural observables, as well as the macro properties of the bidisperse ferrofluids. Finally, an answer to the question which chain criterion should actually be used is provided in this paper.

Phase separation in bidisperse ferrocolloids

Abstract The peculiarities of the phase separation of polydisperse ferrocolloids have been investigated using thermodynamic perturbation theory for the analysis of a model bidisperse system. The phase stability region is determined completely by a small number of large particles present in the system.

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.

Non-linear evolution of a system of elongated droplike aggregates in a metastable magnetic fluid

We study the evolution of a system of drop-like aggregates suspended in a macroscopically homogeneous magnetic fluid made metastable by strengthening of an external magnetic field with account of both the reduction in metastability and the continuing initiation of new nuclei in the metastable surroundings. The growing aggregates are highly elongated ellipsoidal shaped and are distributed over volume. The distribution density is governed by a kinetic equation which neglects of fluctuations in the growth rate of a single aggregate. The approximate solutions for supersaturation and diverse characteristics of the distribution density has been found as functions of time. An influence of emerging aggregates on the macroscopic ferrocolloid properties is illustrated by the example of the time dependence of magnetization and effective viscosity.

Kinetics of phase separation in colloids II. Non-linear evolution of a metastable colloid

Abstract We study the evolution of a system of dropwise aggregates suspended in a macroscopically homogeneous metastable colloid with account of both the reduction in metastability (the decrease in the parent colloid supersaturation) and the continuing initiation of new nuclei in the metastable surroundings. The growing aggregates are distributed over size and the distribution density is governed by an equation of the Fokker-Planck type with allowance for variations in the growth rate of a single aggregate. A complementary equation relates the supersaturation to the total rate of absorption of colloidal particles by the aggregates. A method of solving those equations is worked out. It permits the supersaturation and diverse characteristics of the distribution density to be found as functions of time. The former quantity is monotonously declining to zero and the dispersion of the latter one is either decreasing or increasing with time depending on the level of random fluctuations of the growth rate. If the fluctuations are absent, the evolving system of the aggregates is tending to a monodisperse one, what calls in question the validity of underlying assumptions inherent to the classical theory of Ostwald ripening.

Magnetophoresis, sedimentation, and diffusion of particles in concentrated magnetic fluids

A dynamic mass transfer equation for describing magnetophoresis, sedimentation, and gradient diffusion of colloidal particles in concentrated magnetic fluids has been derived. This equation takes into account steric, magnetodipole, and hydrodynamic interparticle interactions. Steric interactions have been investigated using the Carnahan-Starling approximation for a hard-sphere system. In order to study the effective interparticle attraction, the free energy of the dipolar hard-sphere system is represented as a virial expansion with accuracy to the terms quadratic in particle concentration. The virial expansion gives an interpolation formula that fits well the results of computer simulation in a wide range of particle concentrations and interparticle interaction energies. The diffusion coefficient of colloidal particles is written with regard to steric, magnetodipole and hydrodynamic interactions. We thereby laid the foundation for the formulation of boundary-value problems and for calculation of concentration and magnetic fields in the devices (for example, magnetic fluid seals and acceleration sensors), which use a concentrated magnetic fluid as a working fluid. The Monte-Carlo methods and the analytical approach are employed to study the magnetic fluid stratification generated by the gravitational field in a cylinder of finite height. The coefficient of concentration stratification of the magnetic fluid is calculated in relation to the average concentration of particles and the dipolar coupling constant. It is shown that the effective particle attraction causes a many-fold increase in the concentration inhomogeneity of the fluid if the average volume fraction of particles does not exceed 30%. At high volume concentrations steric interactions play a crucial role.

How to analyse the structure factor in ferrofluids with strong magnetic interactions: a combined analytic and simulation approach

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.

Formation of chain aggregates in magnetic fluids: an influence of polydispersity

Abstract The formation of chain-like aggregates in polydisperse ferrofluids is studied theoretically on the basis of the model bidisperse system, consisting of two fractions of small and large ferroparticles. Various topological structures of chains, containing the particles of both fractions, are considered. The equilibrium chain distribution is obtained with the help of the density functional approach. It was found that in real conditions the majority of large particles and the minority of small particles are connected in short chains of 1–3 large particles in the middle and 1–2 small particles at the edges. The chain distribution is greatly dependent on the mole portion of the large particle fraction.

Branching points in the low-temperature dipolar hard sphere fluid

In this contribution, we investigate the low-temperature, low-density behaviour of dipolar hard-sphere (DHS) particles, i.e., hard spheres with dipoles embedded in their centre. We aim at describing the DHS fluid in terms of a network of chains and rings (the fundamental clusters) held together by branching points (defects) of different nature. We first introduce a systematic way of classifying inter-cluster connections according to their topology, and then employ this classification to analyse the geometric and thermodynamic properties of each class of defects, as extracted from state-of-the-art equilibrium Monte Carlo simulations. By computing the average density and energetic cost of each defect class, we find that the relevant contribution to inter-cluster interactions is indeed provided by (rare) three-way junctions and by four-way junctions arising from parallel or anti-parallel locally linear aggregates. All other (numerous) defects are either intra-cluster or associated to low cluster-cluster interaction energies, suggesting that these defects do not play a significant part in the thermodynamic description of the self-assembly processes of dipolar hard spheres.