# A density functional approach to ferrogels

## TL;DR

This paper introduces a density functional approach to model ferrogels, capturing the interplay of magnetic and elastic interactions, and predicts their elastic properties through a novel pseudopotential mapping and simulations.

## Contribution

It presents a new classical density functional framework for ferrogels, using a pseudopotential to simplify interactions and enabling predictions of bulk elastic properties.

## Key findings

- The pseudopotential mapping is validated by Monte-Carlo simulations.
- The approach predicts the bulk elastic modulus under various conditions.
- It extends to inhomogeneous situations using external pseudopotentials.

## 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.