Structural phase transitions in isotropic magnetic elastomers
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DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Structural Phase Transitions in Isotropic Magnetic Elastomers E. Z. Meilikhov* and R. M. Farzetdinova National Research Center “Kurchatov Institute”, pl. Kurchatova 1, Moscow, 123182 Russia *e-mail: [email protected] Received September 17, 2015
Abstract—Magnetic elastomers represent a new type of materials that are “soft” matrices with “hard” magnetic granules embedded in them. The elastic forces of the matrix and the magnetic forces acting between granules are comparable in magnitude even under small deformations. As a result, these materials acquire a number of new properties; in particular, their mechanical and/or magnetic characteristics can depend strongly on the polymer matrix filling with magnetic particles and can change under the action of an external magnetic field, pressure, and temperature. To describe the properties of elastomers, we use a model in which the interaction of magnetic granules randomly arranged in space with one another is described in the dipole approximation by the distribution function of dipole fields, while their interaction with the matrix is described phenomenologically. A multitude of deformation, magnetic-field, and temperature effects that are described in this paper and are quite accessible to experimental observation arise within this model. DOI: 10.1134/S1063776116060170
1. INTRODUCTION Magnetic elastomers represent a new type of materials that are “soft” rubber-like matrices with “hard” magnetic nano- or microgranules embedded in them. They possess a small elastic modulus (of the order of several tens of kilopascals), so that the elastic forces of the polymer matrix and the magnetic forces acting between magnetic-filler granules turn out to be comparable in magnitude. As a result, these materials acquire a number of new properties. In particular, their mechanical and/or magnetic characteristics can depend strongly on the polymer matrix filling with magnetic particles and can change under the action of an external magnetic field, pressure, and temperature [1]. The softer the polymer matrix, the more pronounced the corresponding effects. The magnetostrictive effect, the magnetic fieldinduced deformation accompanied by a change in the elastic modulus of the material, is most important (and interesting for applications) [2]. Two approaches are mostly used in the theoretical works devoted to the investigation of this effect: the continuum approximation and the microscopic model. The latter describes most adequately the magnetic interaction between granules, which, to a first approximation, may be considered as a dipole interaction between point rigid magnetic dipoles immersed in a nonmagnetic elastic matrix. In this case, it is important whether the spatial distribution of these granules is isotropic or they are grouped into highly anisotropic chains [1, 3—5].
In this paper, we study the elastic properties of magnetic elastomers in a simple model that admits an analytical solution [6]. More specifically, the magnetic granule
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