Dynamics in a one-dimensional ferrogel model: relaxation, pairing, shock-wave propagation

Abstract

Ferrogels are smart soft materials, consisting of a polymeric network and embedded magnetic particles. Novel phenomena, such as the variation of the overall mechanical properties by external magnetic fields, emerge consequently. However, the dynamic behavior of ferrogels remains largely unveiled. In this paper, we consider a one-dimensional chain consisting of magnetic dipoles and elastic springs between them as a simple model for ferrogels. The model is evaluated by corresponding simulations. To probe the dynamics theoretically, we investigate a continuum limit of the energy governing the system and the corresponding equation of motion. We provide general classification scenarios for the dynamics, elucidating the touching/detachment dynamics of the magnetic particles along the chain. In particular, it is verified in certain cases that the long-time relaxation corresponds to solutions of shock-wave propagation, while formations of particle pairs underlie the initial stage of the dynamics. We expect that these results will provide insight into the understanding of the dynamics of more realistic models with randomness in parameters and time-dependent magnetic fields.

arXiv comment17 pages, 9 figures

References in corpus (20)

• A continuum theory of phase separation kinetics for active Brownian particles
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Arrested phase separation in reproducing bacteria: a generic route to pattern formation?
• Microscopic theory for the phase separation of self-propelled repulsive disks
• Tuned, driven, and active soft matter
• Effective Cahn-Hilliard equation for the phase separation of active Brownian particles
• Freezing and phase separation of self-propelled disks
• Buckling of paramagnetic chains in soft gels
• Structural control of elastic moduli in ferrogels and the importance of non-affine deformations
• Hardening transition in a one-dimensional model for ferrogels
• Dynamic Elastic Moduli in Magnetic Gels: Normal Modes and Linear Response
• Tunable dynamic response of magnetic gels: impact of structural properties and magnetic fields
• Forces on rigid inclusions in elastic media and resulting matrix-mediated interactions
• Tailoring superelasticity of soft magnetic materials
• Forces and torques on rigid inclusions in an elastic environment: resulting matrix-mediated interactions, displacements, and rotations
• Superelastic stress-strain behavior in ferrogels of different types of magneto-elastic coupling
• Phase diagram for a single flexible Stockmayer polymer at zero field
• Model for Spreading of Liquid Monolayers
• Magnetomechanical response of bilayered magnetic elastomers
• Force-induced elastic matrix-mediated interactions in the presence of a rigid wall

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