Hardening transition in a one-dimensional model for ferrogels

Abstract

We introduce and investigate a coarse-grained model for quasi one-dimensional ferrogels. In our description the magnetic particles are represented by hard spheres with a magnetic dipole moment in their centers. Harmonic springs connecting these spheres mimic the presence of a cross-linked polymer matrix. A special emphasis is put on the coupling of the dipolar orientations to the elastic deformations of the matrix, where a memory effect of the orientations is included. Although the particles are displaced along one spatial direction only, the system already shows rich behavior: as a function of the magnetic dipole moment, we find a phase transition between "soft-elastic" states with finite interparticle separation and finite compressive elastic modulus on the one hand, and "hardened" states with touching particles and therefore diverging compressive elastic modulus on the other hand. Corresponding phase diagrams are derived neglecting thermal fluctuations of the magnetic particles. In addition, we consider a situation in which a spatially homogeneous magnetization is initially imprinted into the material. Depending on the strength of the magneto-mechanical coupling between the dipole orientations and the elastic deformations, the system then relaxes to a uniaxially ferromagnetic, an antiferromagnetic, or a spiral state of magnetization to minimize its energy. One purpose of our work is to provide a largely analytically solvable approach that can provide a benchmark to test future descriptions of higher complexity. From an applied point of view, our results could be exploited, for example, for the construction of novel damping devices of tunable shock absorbance.

Tunable dynamic response of magnetic gels: Impact of structural properties and magnetic fields

“…For such a straight magnetic chain we had previously observed three qualitatively different energetic ground states [9]. They occur for a memorized directionm We determined the corresponding relaxation spectra and depict them in Fig.…”

“…See Ref. [9] for further explanations. In the following we only consider situations and parameter values for which a collapse due to the dipolar attractions does not occur; we thus can neglect steric repulsion between the particles.…”

“…In the next section, we review the simplified dipolespring model that we recently introduced to investigate equilibrium ground states of simple model systems [9]. We expand it by formulating the corresponding relaxation dynamics.…”

“…We expand it by formulating the corresponding relaxation dynamics. Our approach contains memory terms to include a possible orientational coupling of the magnetic particles to the polymer network [9]. We then demonstrate and analyze the impact of three different factors on the dynamic relaxatory modes.…”

“…Then, restoring torques hinder reorientations of the particles. We use the term "orientational memory" to refer to this situation [9].…”