A density functional approach to ferrogels

Abstract

Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a "pairwise pseudopotential". Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an "external pseudopotential" when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.

14 pages, 14 figures

References in corpus (10)

• Tuned, driven, and active soft matter
• Magneto-sensitive elastomers in a homogeneous magnetic field: a regular rectangular lattice model
• Structural control of elastic moduli in ferrogels and the importance of non-affine deformations
• 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
• Bridging from particle to macroscopic scales in uniaxial magnetic gels
• 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
• Pseudospectral methods for density functional theory in bounded and unbounded domains

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• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
• Classical density functional theory for a two-dimensional isotropic ferrogel model with labeled particles
• Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels