Ferrogels cross-linked by magnetic particles: Field-driven deformation and elasticity studied using computer simulations

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

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.

Functional Thermoresponsive Hydrogel Molecule to Material Design for Biomedical Applications

Temperature-induced, rapid changes in the viscosity and reproducible 3-D structure formation makes thermos-sensitive hydrogels an ideal delivery system to act as a cell scaffold or a drug reservoir. Moreover, the hydrogels’ minimum invasiveness, high biocompatibility, and facile elimination from the body have gathered a lot of attention from researchers. This review article attempts to present a complete picture of the exhaustive arena, including the synthesis, mechanism, and biomedical applications of thermosensitive hydrogels. A special section on intellectual property and marketed products tries to shed some light on the commercial potential of thermosensitive hydrogels.

Elastically-mediated collective organisation of magnetic microparticles

Gels are soft elastic materials made of a three-dimensional cross-linked polymer network and featuring both elastic and dissipative responses under external mechanical stimuli. Here we investigate how such gels mediate the organization of embedded magnetic microparticles when driven by an external field. By constructing a continuum theory, we demonstrate that the collective dynamics of the embedded particles result from the delicate balance between magnetic dipole-dipole interactions, thermal fluctuations and elasticity of the polymer network, verified by our experiments. The proposed model could be extended to other soft magnetic composites in order to predict how the elastic interactions mediate the aggregation of the embedded elements, fostering technological implications for multifunctional hydrogel materials.

Magnetic field controlled behavior of magnetic gels studied using particle-based simulations

This contribution provides an overview of the study of soft magnetic materials using particle-based simulation models. We focus in particular on systems where thermal fluctuations are important. As a basis for further discussion, we first describe two-dimensional models which demonstrate two deformation mechanisms of magnetic gels in a homogeneous field. One is based on the change of magnetic interactions between magnetic particles as a response to an external field; the other is the result of magnetically blocked particles acting as cross-linkers. Based on the qualitative behavior directly observable in the two-dimensional models, we extend our description to three-dimensions. We begin with particle-cross-linked gels, as for those, our three-dimensional model also includes explicitly resolved polymer chains. Here, the polymer chains are represented by entropic springs, and the deformation of the gel is the result of the interaction between magnetic particles. We use this model to examine the influence of the magnetic spatial configuration of magnetic particles (uniaxial or isotropic) on the gel’s magnetomechanical behavior. A further part of the article will be dedicated to scale-bridging approaches such as systematic coarse-graining and models located at the boundary between particle-based and continuum modeling. We will conclude our article with a discussion of recent results for modeling time-dependent phenomena in magnetic-polymer composites. The discussion will be focused on a simulation model suitable for obtaining AC-susceptibility spectra for dilute ferrofluids including hydrodynamic interactions. This model will be the basis for studying the signature of particle–polymer coupling in magnetic hybrid materials. In the long run, we aim to compare material properties probed locally via the AC-susceptibility spectra to elastic moduli obtained for the system at a global level.

Review on the advancements of magnetic gels: towards multifunctional magnetic liposome-hydrogel composites for biomedical applications

Magnetic gels have been gaining great attention in nanomedicine, as they combine features of hydrogels and magnetic nanoparticles into a single system. The incorporation of liposomes in magnetic gels further leads to a more robust multifunctional system enabling more functions and spatiotemporal control required for biomedical applications, which includes on-demand drug release. In this review, magnetic gels components are initially introduced, as well as an overview of advancements on the development, tuneability, manipulation and application of these materials. After a discussion of the advantages of combining hydrogels with liposomes, the properties, fabrication strategies and applications of magnetic liposome-hydrogel composites (magnetic lipogels or magnetolipogels) are reviewed. Overall, the progress of magnetic gels towards smart multifunctional materials are emphasized, considering the contributions for future developments.

Modeling and theoretical description of magnetic hybrid materials—bridging from meso- to macro-scales

Magnetic gels and elastomers consist of magnetic or magnetizable colloidal particles embedded in an elastic polymeric matrix. Outstanding properties of these materials comprise reversible changes in their mechanical stiffness or magnetostrictive distortions under the influence of external magnetic fields. To understand such types of overall material behavior from a theoretical point of view, it is essential to characterize the substances starting from the discrete colloidal particle level. It turns out that the macroscopic material response depends sensitively on the mesoscopic particle arrangement. We have utilized and developed several theoretical approaches to this end, allowing us both to reproduce experimental observations and to make theoretical predictions. Our hope is that both these paths help to further stimulate the interest in these fascinating materials.

Magneto-mechanical coupling of single domain particles in soft matter systems

Combining inorganic magnetic particles with complex soft matrices such as liquid crystals, biological fluids, gels, or elastomers, allows access to a plethora of magnetoactive effects that are useful for sensing and actuation perspectives, allowing inter alia to explore and manipulate material properties on the nanoscale. The article provides a comprehensive summary of recent advancement on employing magnetic nanoparticles either as tracers for dynamic processes, or as nanoscopic actuating units. By variation of the particle characteristics in terms of size, shape, surface functionality, and magnetic behavior, the interaction between the probe or actuator particles and their environment can be systematically tailored in wide ranges, giving insight into the relevant structure–property relationships.

Rheological, Microstructural and Thermal Properties of Magnetic Poly(Ethylene Oxide)/Iron Oxide Nanocomposite Hydrogels Synthesized Using a One-Step Gamma-Irradiation Method

Magnetic polymer gels are a new promising class of nanocomposite gels. In this work, magnetic PEO/iron oxide nanocomposite hydrogels were synthesized using the one-step γ-irradiation method starting from poly(ethylene oxide) (PEO) and iron(III) precursor alkaline aqueous suspensions followed by simultaneous crosslinking of PEO chains and reduction of Fe(III) precursor. γ-irradiation dose and concentrations of Fe³⁺, 2-propanol and PEO in the initial suspensions were varied and optimized. With 2-propanol and at high doses magnetic gels with embedded magnetite nanoparticles were obtained, as confirmed by XRD, SEM and Mössbauer spectrometry. The quantitative determination of γ-irradiation generated Fe²⁺ was performed using the 1,10-phenanthroline method. The maximal Fe²⁺ molar fraction of 0.55 was achieved at 300 kGy, pH = 12 and initial 5% of Fe³⁺. The DSC and rheological measurements confirmed the formation of a well-structured network. The thermal and rheological properties of gels depended on the dose, PEO concentration and initial Fe³⁺ content (amount of nanoparticles synthesized inside gels). More amorphous and stronger gels were formed at higher dose and higher nanoparticle content. The properties of synthesized gels were determined by the presence of magnetic iron oxide nanoparticles, which acted as reinforcing agents and additional crosslinkers of PEO chains thus facilitating the one-step gel formation.

Ultrasound-Driven Two-Dimensional Ti3C2Tx MXene Hydrogel Generator

Ultrasound is a source of ambient energy that is rarely exploited. In this work, a tissue-mimicking MXene-hydrogel (M-gel) implantable generator has been designed to convert ultrasound power into electric energy. Unlike the present harvesting methods for implantable ultrasound energy harvesters, our M-gel generator is based on an electroacoustic phenomenon known as the streaming vibration potential. Moreover, the output power of the M-gel generator can be improved by coupling with triboelectrification. We demonstrate the potential of this generator for powering implantable devices through quick charging of electric gadgets, buried beneath a centimeter thick piece of beef. The performance is attractive, especially given the extremely simple structure of the generator, consisting of nothing more than encapsulated M-gel. The generator can harvest energy from various ultrasound sources, from ultrasound tips in the lab to the probes used in hospitals and households for imaging and physiotherapy.

Smart Hydrogels in Tissue Engineering and Regenerative Medicine

The field of regenerative medicine has tremendous potential for improved treatment outcomes and has been stimulated by advances made in bioengineering over the last few decades. The strategies of engineering tissues and assembling functional constructs that are capable of restoring, retaining, and revitalizing lost tissues and organs have impacted the whole spectrum of medicine and health care. Techniques to combine biomimetic materials, cells, and bioactive molecules play a decisive role in promoting the regeneration of damaged tissues or as therapeutic systems. Hydrogels have been used as one of the most common tissue engineering scaffolds over the past two decades due to their ability to maintain a distinct 3D structure, to provide mechanical support for the cells in the engineered tissues, and to simulate the native extracellular matrix. The high water content of hydrogels can provide an ideal environment for cell survival, and structure which mimics the native tissues. Hydrogel systems have been serving as a supportive matrix for cell immobilization and growth factor delivery. This review outlines a brief description of the properties, structure, synthesis and fabrication methods, applications, and future perspectives of smart hydrogels in tissue engineering.

Surface relief of magnetoactive elastomeric films in a homogeneous magnetic field: molecular dynamics simulations

The structure of a thin magnetoactive elastomeric (MAE) film adsorbed on a solid substrate is studied by molecular dynamics simulations. Within the adopted coarse-grained approach, a MAE film consists of magnetic particles modeled as soft-core spheres, carrying point dipoles, connected by elastic springs representing a polymer matrix. MAE films containing 20, 25 and 30 vol% of randomly distributed magnetic particles are simulated. Once a magnetic field is applied, the competition between dipolar, elastic and Zeeman forces leads to the restructuring of the layer. The distribution of the magnetic particles as well as elastic strains within the MAE films are calculated for various magnetic fields applied perpendicular to the film surface. It is shown that the surface roughness increases strongly with growing magnetic field. For a given magnetic field, the roughness is larger for the softer polymeric matrix and exhibits a nonmonotonic dependence on the magnetic particle concentration. The obtained results provide a better understanding of the MAE surface structuring as well as possible guidelines for fabrication of MAE films with a tunable surface topology.

Polymer architecture of magnetic gels: a review

In this review article, we provide an introduction to ferrogels, i.e. polymeric gels with embedded magnetic particles. Due to the interplay between magnetic and elastic properties of these materials, they are promising candidates for engineering and biomedical applications such as actuation and controlled drug release. Particular emphasis will be put on the polymer architecture of magnetic gels since it controls the degrees of freedom of the magnetic particles in the gel, and it is important for the particle-polymer coupling determining the mechanisms available for the gel deformation in magnetic fields. We report on the different polymer architectures that have been realized so far, and provide an overview of synthesis strategies and experimental techniques for the characterization of these materials. We further focus on theoretical and simulational studies carried out on magnetic gels, and highlight their contributions towards understanding the influence of the gels' polymer architecture.

Hindered nematic alignment of hematite spindles in poly(N-isopropylacrylamide) hydrogels: a small-angle X-ray scattering and rheology study

Field-induced changes to the mesostructure of ferrogels consisting of spindle-shaped hematite particles and poly(N-isopropylacrylamide) are investigated by means of small-angle X-ray scattering (SAXS). Related field-induced changes to the macroscopic viscoelastic properties of these composites are probed by means of oscillatory shear experiments in an external magnetic field. Because of their magnetic moment and magnetic anisotropy, the hematite spindles align with their long axis perpendicular to the direction of an external magnetic field. The field-induced torque acting on the magnetic particles leads to an elastic deformation of the hydrogel matrix. Thus, the field-dependent orientational distribution functions of anisotropic particles acting as microrheological probes depend on the elastic modulus of the hydrogel matrix. The orientational distribution functions are determined by means of SAXS experiments as a function of the varying flux density of an external magnetic field. With increasing elasticity of the hydrogels, tunedviathe polymer volume fraction and the crosslinking density, the field-induced alignment of these anisotropic magnetic particles is progressively hindered. The microrheological results are in accordance with macrorheological experiments indicating increasing elasticity with increasing flux density of an external field.

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

Based on theory and simulations, we elucidate the relaxation dynamics of a one-dimensional ferrogel model and provide classification scenarios.

Self-propelled ion gel at air-water interface

We report on a self-propelled gel using ionic liquid as a new type of self-propellant that generates a powerful and durable motion at an air-water interface. The gel is composed of 1-ethyl-3-methylimidazolium-bis(trifluoromethylsulfonyl)imide (EMIM-TFSI) and poly(vinylidene fluoride-co-hexafluoropropylene) (P(VDF-co-HFP)). A long rectangular ion gel piece placed on the interface shows rapid rotation motion with maximum frequency close to 10 Hz, corresponding to the velocity over 300 mms⁻¹ at an outmost end of the piece. The rotation continues for ca. 10² s, followed by a reciprocating motion (<~10³ s) and a nonlinear motion in long-time observations (>~10³ s). The behaviours can be explained by the model considering elution of EMIM-TFSI to the air-water interface, rapid dissolution into water, and slow diffusion in an inhomogeneous polymer gel network. Because the self-propellants are promptly removed from the interface by dissolution, durable self-propelled motions are observed also at limited interface areas close in size to the gel pieces. A variety of motions are induced in such systems where the degree of freedom in motion is limited. As the ion gel possesses formability and processability, it is also advantageous for practical applications. We demonstrate that the gel does work as an engine.

Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

Effect of single-particle magnetostriction on the shear modulus of compliant magnetoactive elastomers

The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al., Phys. Rev. E 93, 062503 (2016)10.1103/PhysRevE.93.062503]. The planar problem of magnetostriction in an MAE with magnetically soft inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain, and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is nonlinearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. The obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Padé approximants, which predicts that both the absolute and relative changes of the magnetic-field-dependent effective shear modulus will significantly increase with the growing concentration of filler particles.

Anisotropic magnetoresistivity in structured elastomer composites: modelling and experiments

A constitutive model for the anisotropic magnetoresistivity in structured elastomer composites (SECs) is proposed. The SECs considered here are oriented pseudo-chains of conductive-magnetic inorganic materials inside an elastomer organic matrix. The pseudo-chains are formed by fillers which are simultaneously conductive and magnetic dispersed in the polymer before curing or solvent evaporation. The SEC is then prepared in the presence of a uniform magnetic field, referred to as Hcuring. This procedure generates the pseudo-chains, which are preferentially aligned in the direction of Hcuring. Electrical conduction is present in that direction only. The constitutive model for the magnetoresistance considers the magnetic pressure, Pmag, induced on the pseudo-chains by an external magnetic field, H, applied in the direction of the pseudo-chains. The relative changes in conductivity as a function of H are calculated by evaluating the relative increase of the electron tunnelling probability with Pmag, a magneto-elastic coupling which produces an increase of conductivity with magnetization. The model is used to adjust experimental results of magnetoresistance in a specific SEC where the polymer is polydimethylsiloxane, PDMS, and fillers are microparticles of magnetite-silver (referred to as Fe3O4[Ag]). Simulations of the expected response for other materials in both superparamagnetic and blocked magnetic states are presented, showing the influence of the Young's modulus of the matrix and filler's saturation magnetization.

Single-particle mechanism of magnetostriction in magnetoactive elastomers

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of magnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient K is much larger than the shear modulus µ of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.