Non-ergodic Internal Structures Research Articles

Heterogeneous materials: metastable and non-ergodic internal structures.

This issue is concerned with structural and phase transitions in heterogeneous and composite materials, the effects of external magnetic fields on these phenomena and the macroscopic properties and behaviour of materials with isotropic and anisotropic internal structures. Using experimental, theoretical and computer methods, these transitions are studied at the atomic and mesoscopic levels. The fundamental specific feature of structural transitions in many heterogeneous media consists of the fact that these transitions are stacked for a long time in non-equilibrium states that appear due to either macroscopic dissipative processes (an alternating magnetic field or hydrodynamic flow, for instance) or system lifetime in a metastable state. It is important to explain and describe these transitional states using the general approach of non-equilibrium physical mechanics. The review and research articles in the issue will cover the whole spectrum of scales (from nano to macro) and materials (from metastable liquids to biological polymers) in order to exhibit recently developed trends in the field of heterogeneous materials. Atomistic modelling, structuring induced by external magnetic fields and hydrodynamic flows, metastable and non-ergodic states, mechanical properties and phenomena in heterogeneous materials-all these are covered. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function.

In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integro-differential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddle-point methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

On the theory of the unsteady-state growth of spherical crystals in metastable liquids.

Motivated by a large number of applications, we consider the process of non-stationary growth of spherical crystals in a supercooled binary melt. The moving-boundary problem describing the unsteady-state distributions of temperature and impurity concentration around the growing crystal as well as the dynamics of its radius and growth rate is solved by means of the methods of small-parameter expansion and Laplace-Carson integral transform. We show that the growth rate of crystals contains the main contribution (which is proportional to the supercooling degree Δ) and the first correction (which is proportional to Δ2 t, where t is time). The second correction is also found. The non-stationary temperature and concentration fields are determined as power functions of Δ and t. We demonstrate that the first corrections to the dynamics of crystal radius R( t) and its growth rate V ( t) play an important role. It is shown that R( t) and V ( t) can change more than twice in comparison with the previously known steady-state solution with the course of time. Such a behaviour will significantly modify the dynamics of a polydisperse ensemble of crystals evolving in a metastable liquid. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

On anisotropic mechanical properties of heterogeneous magnetic polymeric composites.

This study is devoted to the magneto-mechanical characterization of heterogeneous magnetoactive elastomers based on an elastic polydimethylsiloxane matrix with embedded spherical magnetic soft microparticles and magnetic hard microparticles of irregular shape. An issue of the anisotropic mechanical properties of these smart composites is considered. Non-magnetized and pre-magnetized specimens are characterized using a planar shear and axial loading in an externally applied homogeneous magnetic field. The field direction differs relative to the direction of the field used for the specimens pre-magnetization. Results of the different methods allow comparison of the tensile shear moduli for the samples with an initially identical composition. Obtained results demonstrate a strong correlation between the composite behaviour and orientation of the magnetic field used for the pre-magnetization of the sample relative to the external field applied to a sample during the test. Composites pre-magnetized in the direction parallel to an applied mechanical force and external magnetic field show higher magnetorheological response than composites pre-magnetized transversally to the force and the field. Application of the external field directed opposite to the direction of the pre-magnetization reduces the observed stiffening. Moreover, in this situation a softening of the material can be observed, depending on the magnitude of the external field and the field used for pre-magnetization. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Mechanical properties of magnetic gels containing rod-like composite particles.

Magnetic gels (ferrogels) are heterogeneous systems structured at the nanoscale that contains magnetic particles dispersed in three-dimensional networks of polymer chains. In the present work, the magnetic particles were synthesized with a core-shell structure, consisting of sepiolite particles covered by magnetite nanoparticles. These composite particles had a rod-like shape with a high aspect ratio. The obtained sepiolite-magnetite particles showed a high enough susceptibility and saturation magnetization. The magneto-rheological (MR) properties, and the intensity of the MR effect, of aqueous suspensions of the synthesized particles were studied. The particles, functionalized by adsorption of alginate molecules, were imbedded in alginate hydrogels to get homogeneous soft materials. The particles were linked to the polymer chains as the knots in a network and dominated in a great extent the mechanical properties of the materials. After determining the optimal compositions of the ferrogels, their viscoelastic properties were measured in the absence/presence of magnetic fields. The results pointed out that the MR effect provided by the clay-magnetite particles was considerably more intense than those achieved in ferrogels that contain spherical magnetic microparticles. Therefore, the imbedding of rod-shaped magnetic particles in hydrogels allows controlling the mechanical properties in a wider range than in conventional ferrogels. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Diffusionless (chemically partitionless) crystallization and subsequent decomposition of supersaturated solid solutions in Sn-Bi eutectic alloy.

Results of a study on microstructural evolution of eutectic Sn-57 wt.% Bi processed with cooling rates of 10-2, 1 K s-1 and approximately 105 K s-1 are presented. In order to distinguish different mechanisms of microstructure formation, a comparison with microstructures of different hypoeutectic alloys with compositions down to below the maximum solubility of Bi in Sn-Bi is undertaken. It is found that at the cooling rates of 10-2 and 1 K s-1, coupled eutectic growth occurs, leading to lamellar structures with different length scales. At the rapid quenching rates of approximately 105 K s-1, structure formation in the eutectic alloy is qualitatively different. Partitionless solidification resulting in a supersaturated solid solution with the initial composition is observed in both eutectic and hypoeutectic alloys. It is shown that the observed microstructure of the rapidly solidified alloys forms by the decomposition of the supersaturated solid solution. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Liquid phase separation in undercooled Cu-Co alloys under the influence of static magnetic fields.

Undercooling of Cu-based alloys often induces metastable liquid phase separation followed by rapid solidification of separated liquids. The rapid solidification can help freeze in the morphology of a higher-melting liquid and eases difficulties in studies of liquid phase separation kinetics. In the present work, the influence of static magnetic fields on liquid phase separation in bulk Cu84Co16 composition was investigated. Inductively melted samples were glass-fluxed, undercooled and solidified under uniform and non-uniform magnetic fields generated by a superconducting magnet. Solidification microstructure of the phase-separated samples was examined using an optical microscope. The imposition of the magnetic fields, both uniform and non-uniform, altered the morphology, segregation pattern and size distribution of Co-rich droplets due to liquid phase separation. The imposition of the non-uniform magnetic fields with positive and negative gradients brought about segregation of the Co-rich droplets at the top and the bottom side of the samples, respectively. Such influence of the static magnetic fields is interpreted by assuming intensification of convective flow and Kelvin force-controlled migration of the Co-rich droplets. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Anisotropic magnetic hydrogels: design, structure and mechanical properties.

Anisotropy is an intrinsic feature of most of the human tissues (e.g. muscle, skin or cartilage). Because of this, there has been an intense effort in the search of methods for the induction of permanent anisotropy in hydrogels intended for biomedical applications. The dispersion of magnetic particles or beads in the hydrogel precursor solution prior to cross-linking, in combination with applied magnetic fields, which gives rise to columnar structures, is one of the most recently proposed approaches for this goal. We have gone even further and, in this paper, we show that it is possible to use magnetic particles as actuators for the alignment of the polymer chains in order to obtain anisotropic hydrogels. Furthermore, we characterize the microstructural arrangement and mechanical properties of the resulting hydrogels. This article is part of a theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

A review on computational modelling of phase-transition problems.

Phase-transition problems are ubiquitous in science and engineering. They have been widely studied via theory, experiments and computations. This paper reviews the main challenges associated with computational modelling of phase-transition problems, addressing both model development and numerical discretization of the resulting equations. We focus on classical phase-transition problems, including liquid-solid, gas-liquid and solid-solid transformations. Our review has a strong emphasis on the treatment of interfacial phenomena and the phase-field method. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Experimental and modelling studies for solidification of undercooled Ni-Fe-Si alloys.

We present experimental results, analytical calculations and phase-field simulations for undercooled Ni-Fe-Si alloy system. Undercooling experiments are performed using flux encapsulation along with in situ measurement of recalescence speed using a high-speed camera followed by microstructural characterization. Dendrite growth calculations are performed using a modified Boettinger, Coriell and Trivedi theory to incorporate constitutional undercooling due to multiple segregating elements and a modified kinetic undercooling term. Phase-field simulations are performed using a multi-component phase-field model to generate dendrites in this alloy. High growth velocities are observed and the analytical calculations are in good agreement with experiments. The microstructure evolution from the phase-field simulations indicates that there is a difference in solute segregation during growth of dendrites. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

On the theory of crystal growth in metastable systems with biomedical applications: protein and insulin crystallization.

A generalized theory of nucleation and growth of crystals in a metastable (supercooled or supersaturated) liquid is developed taking into account two principal effects: the diffusion mechanism of the particle-size distribution function in the space of particle radii and the unsteady-state growth rates of individual crystals induced by fluctuations in external temperature or concentration field. A system of the Fokker-Planck and balance integro-differential equations is formulated and analytically solved in a parametric form for arbitrary nucleation kinetics and arbitrary growth rates of individual crystals. The particle-size distribution function and system metastability are found in an explicit form. The Weber-Volmer-Frenkel-Zel'dovich and Meirs kinetic mechanisms, as well as the unsteady-state growth rates of nuclei (Alexandrov & Alexandrova 2019 Phil. Trans. R. Soc. A 377, 20180209 ( doi:10.1098/rsta.2018.0209 )), are considered as special cases. Some potential biomedical applications of the present theory for crystal growth from supersaturated solutions are discussed. The theory is compared with experimental data on protein and insulin crystallization (growth dynamics of the proteins lysozyme and canavalin as well as of bovine and porcine insulin is considered). The hat-shaped particle-size distribution functions for lysozyme and canavalin crystals as well as for bovine and porcine insulin are found. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Effect of internal chain-like structures on magnetic hyperthermia in non-liquid media.

This paper deals with a theoretical study of the effect of chain-like aggregates on magnetic hyperthermia in systems of single-domain ferromagnetic particles immobilized in a non-magnetic medium. We assume that the particles form linear chain-like aggregates and the characteristic time of the Néel remagnetization is much longer than the time of medium heating (time of process observation). This is applicable to magnetite particles when the particle diameter exceeds 20-25 nm. Our results show that the appearance of the chains significantly decreases the intensity of heat production. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Phase transformations in metastable liquids combined with polymerization.

This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space-time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Thermal dependence of large-scale freckle defect formation.

The fundamental mechanisms governing macroscopic freckle defect formation during directional solidification are studied experimentally in a Hele-Shaw cell for a low-melting point Ga-25 wt.% In alloy and modelled numerically in three dimensions using a microscopic parallelized Cellular Automata Lattice Boltzmann Method. The size and distribution of freckles (long solute channels, or chimneys) are shown to be strongly dependent on the thermal profile of the casting, with flat, concave and convex isotherms being considered. For the flat isotherm case, no large-scale freckles form, while for concave or convex isotherms, large freckles appear but in different locations. The freckle formation mechanism is as expected buoyancy-driven, but the chimney stability, its long-term endurance and its location are shown to depend critically on the detailed convective transport through the inter-dendritic region. Flow is generated by curved isopleths of solute concentration. As solute density is different from that of the bulk fluid, gravity causes 'uphill' or 'downhill' lateral flow from the sample centre to the edges through the mush, feeding the freckle. An excellent agreement is obtained between the numerical model and real-time X-ray observations of a solidifying sample under strictly controlled temperature conditions. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Discontinuous shear thickening in concentrated suspensions.

The flow of concentrated suspensions of solid particles can be suddenly blocked by the formation of a percolated network of frictional contacts above a critical value of the applied stress. Suspensions of magnetic particles coated with a superplastifier molecule were shown to produce a strong jamming transition. We find that, for these suspensions with an abrupt discontinuous shear thickening, a model using the divergence of the viscosity at a volume fraction that depends on the applied stress does not well describe the observed behaviour both below and above the critical stress. At a constant applied stress above the critical one, we have a stick-slip behaviour of the shear rate whose period can be predicted and scaled as the square root of the relaxation time of the frictional contacts. The application of a small magnetic field allows us to continuously decrease the critical shear rate, and it appears that the yield stress induced by the magnetic field does not contribute to the jamming transition. Finally, it is shown that this jamming transition also appears in the extrusion of a suspension through a die, but with a much slower dynamics than in the case of stress imposed on a rotational geometry. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Effect of interparticle interaction on magnetic hyperthermia: homogeneous spatial distribution of the particles.

The paper deals with the theoretical study of the effect of magnetic interparticle interaction on magnetic hyperthermia, produced by the particles under the action of a linearly polarized oscillating field. The particles are homogeneously distributed and immobilized in a rigid medium. The supposed size of the magnetite particles is about 20-30 nm. For these particles, the characteristic time of the Neel remagnetization is much longer than the time of observation. This is why we concluded that the dissipation occurs as a result of the particle magnetic moment oscillation in the pit of energy of magnetic anisotropy. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.