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Following the coarse-grained molecular dynamics approach, we propose a model of a small ferrogel sample (containing up to 1000 magnetic nanoparticles), in which the polymer matrix is presented in t...

The effect of field-induced plasticity (magnetic shape memory) displayed by polymer composites filled with multi-domain ferromagnetic microparticles is discussed. Such a soft magnetic elastomer (SME) magnetizes, that is, the filler particles acquire magnetic moments only upon application of an external magnetic field. ‘Switching-on’ of interparticle magnetic interactions essentially affects the internal structure of SMEs since the magnetic forces by far exceed the high-elasticity ones due to attachment of the particles to the polymer matrix. According to the hypothesis, in a SME there self-organizes a network of clusters that gives birth to the effect of internal dry friction and by that imparts plasticity to the composite. Field-induced structuring, together with plasticity, disappears as soon as the external field is turned off. Under these conditions, elastic forces no longer experience any resistance and move the particles back to their initial spatial positions: the sample ‘recalls’ its initial shape. To account for the above-described plasto-elastic behavior of a magnetized SME, a structure-mechanical model (scheme) is proposed, which comprises the elastic elements (springs) and the entities (Saint-Venant elements) mimicking the dry-friction effect. The elements of the model are heuristically identified with two networks. One of them is related to the polymer matrix as itself, while another resembles the particle clusters formed due to the field-induced magnetic interactions. Both networks are interwoven and may deform only affinely. On the basis of the model, the tensile deformation cycles obtained in experiments on the two types of SMEs made of weakly-linked silicone rubber filled with carbonyl iron microparticles are interpreted. The tested SMEs differ by the dispersity of the filler. The samples of the first type contain only ‘fine’ iron particles with the size of 2-5 microns, while in the SME of the second type the filler consists of equal (by weight) amounts of ‘fine’ and ‘coarse’ (~70 microns) particles. The cycles measured under a number of external fields are presented. By fitting experimental data, the parameters of the theoretical scheme are evaluated, and their dependence on the applied field strength is determined. For the field dependencies of the scheme parameters of the isotropic SMEs examined here, the expressions borrowed from the phenomenology of textured SMEs are taken and tested, proving their applicability for this case.

The equilibrium structure and magnetic properties of a ferrogel object of small size (microferrogel(MFG)) are investigated by coarse-grained molecular dynamics. As a generic model of a microferrogel (MFG), a sample with a lattice-like mesh is taken. The solid phase of the MFG consists of magnetic (e.g., ferrite) nanoparticles which are mechanically linked to the mesh making some part of its nodes. Unlike previous models, the finite uniaxial magnetic anisotropy of the particles, as it is the case for real ferrogels, is taken into account. For comparison, two types of MFGs are considered: MFG-1, which dwells in virtually non-aggregated state independently of the presence of an external magnetic field, and MFG-2, which displays aggregation yet under zero field. The structure states of the samples are analyzed with the aid of angle-resolved radial distribution functions and cluster counts. The results reveal the crucial role of the matrix elasticity on the structure organization as well as on magnetization of both MFGs. The particle anisotropy, which plays insignificant role in MFG-1 (moderate interparticle magnetodipole interaction), becomes an important factor in MFG-2 (strong interaction). There, the restrictions imposed on the particle angular freedom by the elastic matrix result in notable diminution of the particle chain lengths as well as the magnetization of the sample. The approach proposed enables one to investigate a large variety of MFGs, including those of capsule type and to purposefully choose the combination of their magnetoelastic parameters.

The Monte Carlo method, which is a powerful tool for finding equilibrium states (and/or their corresponding characteristics) in systems of a different nature in many cases allows one to also describe the course of kinetic processes. This work presents the Monte Carlo modeling of magnetic relaxation and dynamics of induced magnetization of an ensemble of ferromagnetic nanoparticles. It is shown by comparison with the exact solution that in both problems there is a proportionality between the number of calculation steps and the physical duration of the transition or periodic process. On this basis, relationships are proposed making it possible to estimate the time interval corresponding to a single Monte Carlo step. For the process of magnetic relaxation the obtained result is a generalization of the well-known Nowak-Chantrell-Kennedy formula for the case of particles with finite magnetic anisotropy.

A simple rheological model is introduced to describe the plasticity in soft magnetic elastomers induced by an external field. In addition to the elasticity of the polymer matrix, the effect of dry friction (plasticity), which is provided by the rearrangement of the spatial structure of a dispersed magnetic subsystem in the course of the deformation of the material by a sufficiently strong field, is taken into account in the model. Model parameters are estimated from the reported experimental data on the deformation of cylindrical samples based on a soft silicon elastomer filled with quasispherical microparticles of carbonyl iron.

The ground magnetic state of systems of finite number N of single-domain particles confined in a spherical monolayer is investigated by numeric simulations. Two model situations are considered. In the first, the particle positions are imposed and fixed, in the second, the particles are able to move freely within the layer; in the latter case the excluded volume effect is taken into account. It is found that in all the range studied ( N ⩽200) the ground state of the system retains a considerable extent of magnetic vorticity (toroid moment). Moreover, the magnetic and toroid moments are correlated: they are approximately perpendicular to one another.

Groups comprising few rigid magnetic dipoles (single-domain particles) organized in a regular flat N -polygon pattern are considered. The group is subjected to a constant magnetic field in the plane of the structure and responds to the field by magnetization in the same plane. In such a cluster, along with the magnetization, another order parameter does exist: the toroid moment. External field induces magnetization and suppresses the toroid moment. If the matrix of the cluster complies elastically to the interparticle forces, two types of behavior are possible. The particles may either slightly approach one another or undergo a collapse which results in their tight clotting.

A phase-field model with the two-component order parameter is proposed for describing the crystallization of a pure metal. The model is constructed on the basis of the Ginzburg-Landau theory of phase transitions using the principle of the positivity of entropy production in an open weakly nonequilibrium system. This makes it possible to use the proposed model for describing nonisothermal processes. A number of one-dimensional and two-dimensional problems associated with the simulation of a solidified structure under different temperature conditions are solved.

A numerical model is proposed for simulating the magnetic properties of a system (N-cluster) comprising a finite number N of monodomain particles uniformly distributed over a spherical surface. The calculation algorithm is based on the Monte Carlo method. In the absence of an external magnetic field, the magnetic moment of any spherical N-cluster vanishes due to the formation of vortex structures, with a measure of vorticity offered by the toroid moment Q. The results of model calculations show that the value of Q in N-clusters with 4 < N < 20 amounts to about 80% of the maximum and is virtually independent of N, while exhibiting weak even-odd oscillations.

Monte Carlo modeling of superparamagnetic kinetics is addressed with regard to quantification of the simulation steps in units of real time. For the classical N\'eel case (field-free relaxation of the magnetic moment in a single-domain uniaxial particle), a modification of the Nowak-Chantrell-Kennedy formula is proposed enabling the calculations with the variation amplitude of the magnetic moment independent of the particle anisotropy. This relation is obtained from comparison of the Monte Carlo simulated relaxation against the solution of the kinetic equation for the particle magnetic moment. The same idea is applied to a strongly nonequilibrium process: steady re-magnetization of a superparamagnetic particle under an ac field. It is found that in the latter case a linear relationship can be established between the number of simulation steps and the real-time scale (the field period) that holds fairly well in wide frequency and anisotropy parameter intervals.

The paper presents the system of analytical equations describing isothermal vortex flows induced in a plane magnetized ferrofluid layer by magnetophoresis of drop-like aggregates. Magnetophoresis of the aggregates is caused by configuration of a constant inhomogeneous magnetic field in the vicinity of a solid condensation core placed in the fluid. The vortex flow generated by inhomogeneous ponderomotive force drives the aggregates into the region of highest magnetic field intensity, which resembles condensation of drops at the surface of the core. The dynamic equations are written for the case of dilute magnetic fluids and take into account the dynamics of the drop-like aggregate growth. Numerical simulation based on the proposed system of equations is in qualitative agreement with the experimental data obtained in the Hele-Shaw cell.

A phenomenological model is proposed to describe the plasticity of soft magnetic elastomer composites under an external field. Along with high-elasticity, internal dry friction is introduced whose origin is attributed to the dipole-dipole interaction of the embedded particles. Numerical estimates of the model parameters are obtained from comparison with the measurements performed on iron carbonyl dispersions in soft silicon-rubber matrices.

Ferroelastic composites are smart materials with unique properties including large magnetodeformational effects, strong field enhancement of the elastic modulus and magnetic shape memory. On the basis of mechanical tests, direct microscopy observations and magnetic measurements we conclude that all these effects are caused by reversible motion of the magnetic particles inside the polymeric matrix in response to an applied field. The basic points of a model accounting for particle structuring in a magnetoactive elastomer under an external field are presented.