Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels

TL;DR

This paper extends a density functional approach to three-dimensional magnetic gels, linking microscopic particle arrangements to macroscopic elastic properties, and explores how magnetic interactions influence the material's shape and elasticity.

Contribution

It introduces a 3D density functional framework for magnetic gels, incorporating magnetic dipole interactions and shape effects, bridging mesoscopic particle configurations with macroscopic elasticity.

Findings

Magnetostrictive effects depend on particle configuration and sample shape.

Elastic and rotational coefficients relate mesoscopic properties to macroscopic behavior.

Implications for real systems with random particle arrangements are discussed.

Abstract

Magnetic gels are composite materials, consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles, to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction, and consider the approximate incompressibility of the embedding media, and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.