Dynamic susceptibility of soft ferrogels. Effect of interparticle interaction.

We present the results of theoretical analysis of the dynamic susceptibility of soft elastic-viscous ferrogels with embedded single-domain ferromagnetic particles chaotically distributed in the host medium. The magnetic anisotropy of the particle is supposed to be strong. The effect of magnetic interparticle interaction is a focus of our attention. A differential equation for the statistically averaged (measured) magnetic moment of the particle is derived. Our analysis shows that in the case of a weak applied field, the interparticle interaction increases the composite magnetization and decreases the rate of its remagnetization.

A kinetic model for magnetostriction of a ferrogel with physical networking.

Kinetics of magnetostriction of ferrogel with physical networking based on natural polysaccharide guar gum with embedded strontium hexaferrite magnetic particles were studied in the uniform magnetic field 420 mT. An ellipsoidal sample was elongated by 37% along the applied field and contracted by 15% in the transverse direction, while its volume was kept constant. The characteristic time of magnetostriction was 440 s. Dynamic mechanical analysis in an oscillatory mode showed that the deformation of ferrogel is mostly elastic rather than viscous. Its storage modulus was almost constant in a frequency range of 0.1-100 Hz and by at least an order of magnitude larger than the loss modulus. Meanwhile, a developed theoretical model based on the elasto-viscous behaviour of the ferrogel failed to estimate correctly the experimental value of its magnetostriction. Calculated values of the elongation of ferrogel in the field were several orders of magnitude lower than those observed in the experiment for the ferrogel with physical networking. Consistency between the experiment and the theory was achieved using the alternative consideration based on the deformation of a liquid droplet of ferrofluid. The applicability of such an approach was discussed concerning structural relaxation properties of the ferrogel with physical networking. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Magnetic hyperthermia in a system of immobilized magnetically interacting particles.

This paper deals with the theoretical study of magnetic hyperthermia, induced by a system of immobilized single-domain ferro- (ferri-) magnetic particles under the action of an oscillating magnetic field. It is supposed that the particles are randomly distributed in a host medium. The effect of magnetic interparticle interaction on the intensity of the heat production is the focus of our attention. The results show that interparticle interaction enhances the thermal effect.

Shear elasticity of isotropic magnetic gels.

The paper deals with a theoretical study of the effective shear modulus of a magnetic gel, consisting of magnetizable particles randomly and isotropically distributed in an elastic matrix. The effect of an external magnetic field on the composite modulus is the focus of our consideration. We take into account that magnetic interaction between the particles can induce their spatial rearrangement and lead to internal anisotropy of the system. Our results show that, if this magnetically induced anisotropy is insignificant, the applied field reduces the total shear modulus of the composite. Strong anisotropy can qualitatively change the magnetomechanic effect and induce an increase of this modulus with the field.

Kinetics of doublet formation in bicomponent magnetic suspensions: The role of the magnetic permeability anisotropy.

Micron-sized particles (microbeads) dispersed in a suspension of magnetic nanoparticles, i.e., ferrofluids, can be assembled into different types of structures upon application of an external magnetic field. This paper is devoted to theoretical modeling of a relative motion of a pair of microbeads (either soft ferromagnetic or diamagnetic) in the ferrofluid under the action of applied uniform magnetic field which induces magnetic moments in the microbeads making them attracting to each other. The model is based on a point-dipole approximation for the magnetic interactions between microbeads mediated by the ferrofluid; however, the ferrofluid is considered to possess an anisotropic magnetic permeability thanks to field-induced structuring of its nanoparticles. The model is tested against experimental results and shows generally better agreement with experiments than the model considering isotropic magnetic permeability of ferrofluids. The results could be useful for understanding kinetics of aggregation of microbeads suspended in a ferrofluid. From a broader perspective, the present study is believed to contribute to a general understanding of particle behaviors in anisotropic media.

Hysteresis of the magnetic properties of soft magnetic gels.

We present results of an experimental and theoretical study of the magnetic properties of soft magnetic gels consisting of micron-sized magnetizable particles embedded in a polymer matrix. Experiments demonstrate hysteretic dependences of composite magnetization on an applied magnetic field and non-monotonic, with maximum, dependence of the sample susceptibilities on the field. We propose a theoretical approach which describes the main physical features of these experimental results.

Shear thickening of dense suspensions due to energy dissipation in lubrication layers between particles.

This paper deals with a theoretical study of the shear thickening effects in concentrated suspensions of non-Brownian particles. Our analysis shows that an increase of the shear rate of the suspension flow leads to a decrease of the mean thickness of the gaps between the nearest particles in dense suspensions. In turn, this leads to the growth of energy dissipation in these gaps, which means an increase of the suspension effective viscosity with the shear rate.

Viscoelastic properties of ferrofluids.

The paper deals with theoretical study of non linear viscoelastic phenomena in ferrofluids placed in magnetic field. Our attention is focused on the study of nonstationary flow and Maxwell-like relaxation of the macroscopical viscous stress after alternation of the shear rate. We propose that these phenomena can be explained by finite rate of evolution of chainlike aggregates, consisting of the ferrofluid particles. Statistical model of the chains growth-disintegration is suggested. In this model the chain-single particle mechanism of the chains evolution is considered, the effects of the chain-chain interaction are ignored. The proposed model allows us to estimate the time-dependent function of distribution over number of particles in the chain. Having determined this function and using methods of hydromechanics of ferrofluids with chainlike aggregates, we have studied evolution of the ferrofluid viscosity after stepwise alternation of the fluid shear rate. The estimated time of relaxation is in a reasonable agreement with experimental results. Thus, our analysis shows that the observed macroscopical viscoelastic phenomena in ferrofluids can be provided by evolution of the chain ensemble.

Theoretical study of the magnetization dynamics of nondilute ferrofluids.

The paper is devoted to the theoretical investigation of the magnetodipolar interparticle interaction effect on magnetization dynamics in moderately concentrated ferrofluids. We consider a homogenous (without particle aggregates) ferrofluid consisting of identical spherical particles and employ a rigid dipole model, where the magnetic moment of a particle is fixed with respect to the particle itself. In particular, for the magnetization relaxation after the external field is instantly switched off, we show that the magnetodipolar interaction leads to the increase of the initial magnetization relaxation time. For the complex ac susceptibility chi(omega)=chi'(omega)+ ichi''(omega) we find that this interaction leads to an overall increase of chi''(omega) and shifts the chi''(omega) peak towards lower frequencies. Comparing results obtained with our analytical approach (second order virial expansion) to numerical simulation data (Langevin dynamics method), we demonstrate that the employed virial expansion approximation gives a good qualitative description of the ferrofluid magnetization dynamics and provides a satisfactory quantitative agreement with numerical simulations for the dc magnetization relaxation, up to the particle volume fraction phi approximately 10% , and for the ac susceptibility, up to phi approximately 5%.

Condensation phase transitions in ferrofluids.

Experiments show that under suitable conditions magnetic particles in ferrofluids and other polar suspensions undergo condensation phase transitions and form dense liquidlike or solidlike phases. The problem of fundamental features and scenarios of the phase transitions is one of the central problems of the physics of these systems. This work deals with the theoretical study of scenarios of condensation phase transitions in ferrofluids, consisting of identical magnetic particles. Our results show that, unlike the classical condensation phase transitions, the appearance of the linear chains precedes the magnetic particle bulk condensation. The effect of the chains on the diagrams of the equilibrium phase transitions is studied.

Internal structures in two-dimensional ferrofluids.

We present the results of a theoretical study of internal microstructures in two-dimensional ferrofluids without an external magnetic field. Recent experiments with these systems demonstrate the appearance of linear chains and ringlike and various branched clusters. We consider linear chains, rings, and branched Y-like "forks." In the model of an ideal gas of noninteracting clusters, taking into account interactions only between nearest particles, we estimate the equilibrium distribution functions of the chains, forks, and rings over a number of particles in them. Our results show that for experimentally realistic situations the majority of particles are united into chains and forks, the number of particles in the rings being relatively small. The results of calculations are in qualitative agreement with experiments.

Structural transformations in ferrofluids.

We present results of theoretical study of internal structural transformations in magnetic liquids consisting of identical spherical magnetic particles suspended in a carrier liquid. As the results show, when the dimensionless characteristic energy of magnetic interaction epsilon between particles is less than a certain critical value epsilon('), the system of particles is in spatially homogeneous state with linear chainlike aggregates. When epsilon exceeds epsilon('), bulk droplike aggregates, consisting of large number of particles, can occur in this system. The critical parameter epsilon(') decreases when external magnetic field increases. This means that, in accordance with all known experiments, magnetic field stimulates the phase separation. Our estimates of epsilon(') are in agreement with magnitudes of the parameter of interaction between particles in typical ferrofluids where these phase transitions have been observed experimentally. Analysis shows that the bulk dense structures can occur provided that the total number N of particles in the system exceeds a threshold value N', which is about a thousand by order of magnitude. We think that this result explains why the bulk dense clusters, observed in many real experiments, have never been observed in three-dimensional computer simulations of ferrofluids-the total number of particles in these simulations was too small to provide the formation of bulk structures.

Effect of interaction between chains on their size distribution: strong magnetic field.

We consider ferrofluid consisting of identical spherical particles with permanent magnetic moment. Under the assumption that linear chains can appear in the ferrofluid, we estimate the distribution function of a number of the particles inside the chains. The main new moment of our consideration is that we estimate the influence of interaction between the chains on the size distribution as well as on the mean number of the particles in the chain. The analysis is done and simple expressions for an the size distribution function are obtained for infinitely strong magnetic field in asymptotics of strong magnetic interaction between the particles inside one chain.

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.