Magnetization of magnetoactive elastomers under the assumption of breakable adhesion at the particle/matrix interface.

In this work we study the magnetization of magnetoactive elastomers (MAE) in which the interface between the matrix and magnetic particles is unstable and allows for slipping of the particles against the wall of their elastomer cavities. The estimate of the maximal angle at which each particle can decline its axis from the initial position is made based on cyclic measurement of several consecutive hysteresis loops at different maximal magnetic fields. A model of magnetization of magnetically hard multigrain particles in an elastic environment with allowance for their possible slipping is proposed. Results of modelling is in fair agreement with the experimental data obtained on MAEs whose polymeric matrix is made of polydimethylsiloxane and the magnetic filler is NdFeB spherical particles.

Magneto-elastic coupling as a key to microstructural response of magnetic elastomers with flake-like particles.

Using the combination of experiment and molecular dynamics simulations, we investigate structural transformations in magnetic elastomers with NdFeB flake-like particles, caused by applied moderate magnetic fields. We explain why and how those transformations depend on whether or not the samples are initially cured by a short-time exposure to a strong field. We find that in a cured sample, a moderate magnetic field leads mainly to in-place flake rotations that are fully reversed once the applied field is switched off. In contrast, in an initially non-cured sample the flakes perform both translation and rotations under the influence of a moderate applied field that lead to the formation of chain-like structures that remain such even if the field is switched off.

Scale-dependent particle diffusivity and apparent viscosity in polymer solutions as probed by dynamic magnetic nanorheology.

In several upcoming rheological approaches, including methods of micro- and nanorheology, the measurement geometry is of critical impact on the interpretation of the results. The relative size of the probe objects employed (as compared to the intrinsic length scales of the sample to be investigated) becomes of crucial importance, and there is increasing interest to investigate the dynamic processes and mobility in nanostructured materials. A combination of different rheological approaches based on the rotation of magnetically blocked nanoprobes is used to systematically investigate the size-dependent diffusion behavior in aqueous poly(ethylene glycol) (PEG) solutions with special attention paid to the relation of probe size to characteristic length scales within the polymer solutions. We employ two types of probe particles: nickel rods of hydrodynamic length Lh between 200 nm and 650 nm, and cobalt ferrite spheres with diameter dh between 13 nm and 23 nm, and examine the influence of particle size and shape on the nanorheological information obtained in model polymer solutions based on two related, dynamic-magnetic approaches. The results confirm that as long as the investigated solutions are not entangled, and the particles are much larger than the macromolecular correlation length, a good accordance between macroscopic and nanoscopic results, whereas a strong size-dependent response is observed in cases where the particles are of similar size or smaller than the radius of gyration Rg or the correlation length ξ of the polymer solution.

Modeling the magnetomechanical behavior of a multigrain magnetic particle in an elastic environment.

The Stoner-Wohlfarth model of a single-domain grain is applied to a complex situation: magnetization of a solid multigrain particle embedded in an elastic medium. In this situation, application of a magnetic field establishes a specific magnetomechanical process: polarization and switching of individual grains change the net energy of the particle and, as a result, make it rotate as a whole relative to the matrix. Because of that coupling, the magnetic hysteresis loop of a particle composed of highly coercive grains progressively shrinks with the increase of the matrix compliance. The effect is studied theoretically by numerical simulations on a particle comprising several hundred magnetically uniaxial grains with randomly oriented easy axes. The results of the model are discussed with regard to magnetic measurements performed on dispersions of spherical NdFeB microparticles in PDMS matrices of varied stiffness.

Non-ergodic tube structures in magnetic gels and suspensions.

We present results of a study of internal structures, which can appear in magnetic suspensions and gels filling a flat gap under the influence of a magnetic field applied perpendicular to the gap walls. The considered system consists of magnetizable microparticles with a mean diameter of ∼35 µm. Experimental observation demonstrates that the particles can form stable tube shaped structures elongated along the field direction. These structures have internal cavities. The theoretical analysis, performed in this study, shows that the tubes do not correspond to a thermodynamic equilibrium state of the system and rather present transitive non-ergodic structures. These structures are stacked in a state of local energetic minima because of the relatively large size of the particles and negligible Brownian effects. Our theoretical model is suggested to explain the physical reason of the appearance of tube-like structures.

Importance of matrix inelastic deformations in the initial response of magnetic elastomers.

Being able to predict and understand the behaviour of soft magnetic materials paves the way to their technological applications. In this study we analyse the magnetic response of soft magnetic elastomers (SMEs) with magnetically hard particles. We present experimental evidence of a difference between the first and next magnetisation loops exhibited by these SMEs, which depends non-monotonically on the interplay between the rigidity of the polymer matrix, its mechanical coupling with the particles, and the magnetic interactions in the system. In order to explain the microstructural mechanism behind this behaviour, we used a minimal computer simulation model whose results evidence the importance of irreversible matrix deformations due to both translations and rotations of the particles. To confirm the simulation findings, computed tomography (CT) was used. We conclude that the initial exposure to the field triggers the inelastic matrix relaxation in the SMEs, as particles attempt to reorient. However, once the necessary degree of freedom is achieved, both the rotations and the magnetisation behaviour become stationary. We expect this scenario not only to be limited to the materials studied here, but also to apply to a broader class of hybrid SMEs.

Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix.

Soft elastic composite materials containing particulate rigid inclusions in a soft elastic matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft elastic polymeric gel matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify our experimental results by different theoretical tools, i.e., explicit analytical calculations in the framework of linear elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.

Microgels at the Water/Oil Interface: In Situ Observation of Structural Aging and Two-Dimensional Magnetic Bead Microrheology.

Stimuli-responsive microgels can be used as stabilizers for emulsions. However, the details of structure and the viscoelastic property of the microgel-laden interface are still not well-known. We synthesized fluorescently labeled microgels and used confocal microscopy to observe their arrangement at the water/oil interface. The microgels aggregated spontaneously at the interface, and the aggregated structure reorganized due to thermal motion. The structure of the interfacial layer formed by microgels depended on the microgel concentration at the interface. We suggest that the structure was controlled by the aggregation and adsorption of microgels at the interface. The interparticle separation between microgels at the interface decreased over time, implying a slow aging process of the microgels at the interface. Magnetic beads were introduced at the interface and used to trigger deformation of the microgel layer. Under compression and shear the microgels in the aggregated structure rearranged, leading to plastic deformation, and some elastic responses were also observed.

Buckling of paramagnetic chains in soft gels.

We study the magneto-elastic coupling behavior of paramagnetic chains in soft polymer gels exposed to external magnetic fields. To this end, a laser scanning confocal microscope is used to observe the morphology of the paramagnetic chains together with the deformation field of the surrounding gel network. The paramagnetic chains in soft polymer gels show rich morphological shape changes under oblique magnetic fields, in particular a pronounced buckling deformation. The details of the resulting morphological shapes depend on the length of the chain, the strength of the external magnetic field, and the modulus of the gel. Based on the observation that the magnetic chains are strongly coupled to the surrounding polymer network, a simplified model is developed to describe their buckling behavior. A coarse-grained molecular dynamics simulation model featuring an increased matrix stiffness on the surfaces of the particles leads to morphologies in agreement with the experimentally observed buckling effects.

Dynamics of Single Hydrogen Bubbles at a Platinum Microelectrode.

Bubble dynamics, including the formation, growth, and detachment, of single H2 bubbles was studied at a platinum microelectrode during the electrolysis of 1 M H2SO4 electrolyte. The bubbles were visualized through a microscope by a high-speed camera. Electrochemical measurements were conducted in parallel to measure the transient current. The periodic current oscillations, resulting from the periodic formation and detachment of single bubbles, allow the bubble lifetime and size to be predicted from the transient current. A comparison of the bubble volume calculated from the current and from the recorded bubble image shows a gas evolution efficiency increasing continuously with the growth of the bubble until it reaches 100%. Two different substrates, glass and epoxy, were used to embed the Pt wire. While nearly no difference was found with respect to the growth law for the bubble radius, the contact angle differs strongly for the two types of cell. Data provided for the contact point evolution further complete the image of single hydrogen bubble growth. Finally, the velocity field driven by the detached bubble was measured by means of PIV, and the effects of the convection on the subsequent bubble were evaluated.

Tangential Flow Ultrafiltration Allows Purification and Concentration of Lauric Acid-/Albumin-Coated Particles for Improved Magnetic Treatment.

Superparamagnetic iron oxide nanoparticles (SPIONs) are frequently used for drug targeting, hyperthermia and other biomedical purposes. Recently, we have reported the synthesis of lauric acid-/albumin-coated iron oxide nanoparticles SEON(LA-BSA), which were synthesized using excess albumin. For optimization of magnetic treatment applications, SPION suspensions need to be purified of excess surfactant and concentrated. Conventional methods for the purification and concentration of such ferrofluids often involve high shear stress and low purification rates for macromolecules, like albumin. In this work, removal of albumin by low shear stress tangential ultrafiltration and its influence on SEON(LA-BSA) particles was studied. Hydrodynamic size, surface properties and, consequently, colloidal stability of the nanoparticles remained unchanged by filtration or concentration up to four-fold (v/v). Thereby, the saturation magnetization of the suspension can be increased from 446.5 A/m up to 1667.9 A/m. In vitro analysis revealed that cellular uptake of SEON(LA-BSA) changed only marginally. The specific absorption rate (SAR) was not greatly affected by concentration. In contrast, the maximum temperature Tmax in magnetic hyperthermia is greatly enhanced from 44.4 °C up to 64.9 °C by the concentration of the particles up to 16.9 mg/mL total iron. Taken together, tangential ultrafiltration is feasible for purifying and concentrating complex hybrid coated SPION suspensions without negatively influencing specific particle characteristics. This enhances their potential for magnetic treatment.

Different storage conditions influence biocompatibility and physicochemical properties of iron oxide nanoparticles.

Superparamagnetic iron oxide nanoparticles (SPIONs) have attracted increasing attention in many biomedical fields. In magnetic drug targeting SPIONs are injected into a tumour supplying artery and accumulated inside the tumour with a magnet. The effectiveness of this therapy is thus dependent on magnetic properties, stability and biocompatibility of the particles. A good knowledge of the effect of storage conditions on those parameters is of utmost importance for the translation of the therapy concept into the clinic and for reproducibility in preclinical studies. Here, core shell SPIONs with a hybrid coating consisting of lauric acid and albumin were stored at different temperatures from 4 to 45 °C over twelve weeks and periodically tested for their physicochemical properties over time. Surprisingly, even at the highest storage temperature we did not observe denaturation of the protein or colloidal instability. However, the saturation magnetisation decreased by maximally 28.8% with clear correlation to time and storage temperature. Furthermore, the biocompatibility was clearly affected, as cellular uptake of the SPIONs into human T-lymphoma cells was crucially dependent on the storage conditions. Taken together, the results show that the particle properties undergo significant changes over time depending on the way they are stored.

Treatment Efficiency of Free and Nanoparticle-Loaded Mitoxantrone for Magnetic Drug Targeting in Multicellular Tumor Spheroids.

Major problems of cancer treatment using systemic chemotherapy are severe side effects. Magnetic drug targeting (MDT) employing superparamagnetic iron oxide nanoparticles (SPION) loaded with chemotherapeutic agents may overcome this dilemma by increasing drug accumulation in the tumor and reducing toxic side effects in the healthy tissue. For translation of nanomedicine from bench to bedside, nanoparticle-mediated effects have to be studied carefully. In this study, we compare the effect of SPION, unloaded or loaded with the cytotoxic drug mitoxantrone (MTO) with the effect of free MTO, on the viability and proliferation of HT-29 cells within three-dimensional multicellular tumor spheroids. Fluorescence microscopy and flow cytometry showed that both free MTO, as well as SPION-loaded MTO (SPION(MTO)) are able to penetrate into tumor spheroids and thereby kill tumor cells, whereas unloaded SPION did not affect cellular viability. Since SPION(MTO) has herewith proven its effectivity also in complex multicellular tumor structures with its surrounding microenvironment, we conclude that it is a promising candidate for further use in magnetic drug targeting in vivo.

Structural control of elastic moduli in ferrogels and the importance of non-affine deformations.

One of the central appealing properties of magnetic gels and elastomers is that their elastic moduli can reversibly be adjusted from outside by applying magnetic fields. The impact of the internal magnetic particle distribution on this effect has been outlined and analyzed theoretically. In most cases, however, affine sample deformations are studied and often regular particle arrangements are considered. Here we challenge these two major simplifications by a systematic approach using a minimal dipole-spring model. Starting from different regular lattices, we take into account increasingly randomized structures, until we finally investigate an irregular texture taken from a real experimental sample. On the one hand, we find that the elastic tunability qualitatively depends on the structural properties, here in two spatial dimensions. On the other hand, we demonstrate that the assumption of affine deformations leads to increasingly erroneous results the more realistic the particle distribution becomes. Understanding the consequences of the assumptions made in the modeling process is important on our way to support an improved design of these fascinating materials.

Empirical Law for the Magnetorheological Effect of Nanocomposite Hydrogels with Magnetite Microparticles.

Hydrogels are functional smart materials which can be tailored by modifying their chemical composition. Further functionalization can be achieved by incorporating magnetic particles into the gel matrix. In this study, a hydrogel with magnetite micro-particles is synthesized and characterized by rheological measurements. Inorganic clay is used as the crosslinking agent, which additionally prevents the sedimentation of the micro-particles during the synthesis of the gel. The mass fractions for the magnetite particles in the synthesized gels range from 10% to 60% in the initial state. Rheological measurements are performed in different degrees of swelling using temperature as a stimulus. The influence of a homogeneous magnetic field is analyzed by a step-wise activation and deactivation during dynamic mechanical analysis. For the evaluation of the magnetorheological effect in the steady states a procedure is developed, which takes occurring drift effects into account. Using the magnetic flux density, the particle volume fraction and the storage modulus as independent parameters, a general product approach is deployed for a regression analysis of the dataset. In the end, an empirical law for the magnetorheological effect in nanocomposite hydrogels can be found.

Mechanism for the Magnetorheological Effect of Nanocomposite Hydrogels with Magnetite Microparticles.

In a previous study, we presented an empirical law for the magnetorheological effect of nanocomposite hydrogels with magnetite microparticles derived from rheological data. In order to understand the underlying processes, we employ computed tomography for structure analysis. This allows the evaluation of the translational and rotational movement of the magnetic particles. Gels with 10% and 3.0% magnetic particle mass content are investigated at three degrees of swelling and at different magnetic flux densities in steady states by means of computed tomography. Since a temperature-controlled sample-chamber is difficult to implement in a tomographic setup, salt is used to deswell the gels instead. Based on the findings of the particle movement, we propose a mechanism using an energy-based approach. This leads to a theoretical law that shows the same scaling behavior as the previously found empirical law.

Fabrication and Actuation of Magnetic Shape-Memory Materials.

Soft actuators are deformable materials that change their dimensions or shape in response to external stimuli. Among the various stimuli, remote magnetic fields are one of the most attractive forms of actuation, due to their ease of use, fast response, and safety in biological systems. Composites of magnetic particles with polymer matrices are the most common materials for magnetic soft actuators. In this paper, we demonstrate the fabrication and actuation of magnetic shape-memory materials based on hydrogels containing field-structured magnetic particles. These actuators are formed by placing the pregel dispersion into a mold of the desired on-field shape and exposing it to a homogeneous magnetic field until the gel point is reached. At this point, the material may be removed from the mold and fully gelled in the desired off-field shape. The resultant magnetic shape-memory material then transitions between these two shapes when it is subjected to successive cycles of a homogeneous magnetic field, acting as a large deformation actuator. For actuators that are planar in the off-field state, this can result in significant bending to return to the on-field state. In addition, it is possible to make shape-memory materials that twist under the application of a magnetic field. For these torsional actuators, both experimental and theoretical results are given.

Combined beam hardening artifact correction and quantitative microanalysis of colloidal depositions in deep bed filtration experiments investigated by 3D X-ray computed microtomography.

In this study we present quantitative X-ray computed microtomography measurements (µCT) of retained sub-micron-sized particles in open porous media carried out in a laboratory µCT setup. Due to the polychromatic spectrum of the used X-rays, the tomograms are affected by various non-linear artifacts, which belong to the class of beam hardening artifacts. These artifacts become more dominant, when the amount of retained particles increases and can affect wide areas of the images, making a qualitative and quantitative analysis barely possible. Furthermore, the colloidal depositions show an inhomogeneous distribution inside the filter, making a reliable material discrimination between filter and particle material challenging. We introduce a calibration method, which is capable to sufficiently remove the majority of the artifacts by linearization of the projection data and thus enabling the precise material quantification of the retained colloids in the reconstructed tomograms. While most beam hardening correction routines are only applicable to homogeneous materials, our algorithm takes into account inhomogeneous material distributions and is adapted to multi-material systems. Moreover, the method includes a material discrimination of the colloids and the filter in the raw data domain. Thus, erroneous segmentations at the interfaces between different material fractions are avoided. As a result we present quantitative concentration maps of the particle distribution inside the porous media with a resolution of < 10µm. A series of validation samples was prepared, covering a wide range of different, representative filter loading stages. The accuracy of the particle quantification was evaluated from these samples and the relative deviation of the overall contained particle mass was less than 10% in all cases, partially even less than 1%. The overall image quality due to the artifact removal was significantly improved. The local variation of the particle concentration could be well assessed from the obtained concentration maps.

CyMAD bioreactor: A cyclic magnetic actuation device for magnetically mediated mechanical stimulation of 3D bioprinted hydrogel scaffolds.

Mechanical stimulation of bioprinted constructs can enhance the differentiation of cells within these scaffolds, such as driving chondrocytes towards cartilage tissue substitutes. In this study, a holistic approach is presented for designing and engineering a material-specific device based on a magnetic field setup using the Maxwell configuration for a touchless cyclic magnetic stimulation of (bioprinted) hydrogel scaffolds containing magnetic microparticles. We describe the entire development process, from the design of the magnetic field to the construction of the bioreactor and provide an evaluation of the calculation. Finally, an analysis of the distribution and orientation of the particles within the hydrogels and a cytocompatibility test after applying the intended stimulation regime were conducted. As a proof-of-principle, a model system in the shape of a cylindrical bending beam consisting of the established magnetisable bioink based on alginate, methylcellulose and magnetite microparticles (algMC + mag), was used instead of 3D printed, macroporous scaffolds of this material. Requirements for the dimensioning of the force, such as the Young's modulus, were determined experimentally. The magnetic field was calculated using the software Finite Element Method Magnetics (FEMM). The cyclic stimulation of the samples was performed over 14 days with a duration of 3 h per day. The aim was to achieve an elongation of up to 10%. The homogeneous particle distribution in stimulated and non-stimulated samples was proven via µCT and digital image processing (DIP). Even after applying a static magnetic field over 30 min, no structure formation such as chains or agglomeration of the magnetic particles were observed. The deformation behaviour defined as a shifted position of the neutral fibre (centre line of an object) during stimulation was measured via µCT and analysed using DIP. From these data, an elongation of approx. 9% was calculated for day 14. This elongation was achieved for both the stimulated samples and the control group without stimulation, which corresponds to the theoretically calculated value. The cytocompatibility of the bioink, scaffold environment and stimulation approach was demonstrated for bioprinted scaffolds with embedded human mesenchymal stem cells and chondrocytes. These findings proved the suitability and versatility of the bioreactor and the presented approach for stimulation experiments.

Visualization of superparamagnetic nanoparticles in vascular tissue using XµCT and histology.

In order to increase the dose of antineoplastic agents in the tumor area, the concept of magnetic drug targeting (MDT) has been developed. Magnetic nanoparticles consisting of iron oxide and a biocompatible cover layer suspended in an aqueous solution (ferrofluid) serve as carriers for chemotherapeutics being enriched by an external magnetic field after intra-arterial application in desired body compartments (i.e., tumor). We established an ex vivo model to simulate in vivo conditions in a circulating system consisting of magnetic iron oxide nanoparticles passing an intact bovine artery and being focused by an external magnetic field to study their distribution in the vessel. Micro-computed X-ray tomography (XµCT) and histology can elucidate the arrangement of these particles after application. XµCT-analysis has been performed on arterial sections after MDT in order to determine the distribution of the nanoparticles. These measurements have been carried out with a cone X-ray source and corresponding histological sections were stained with Prussian blue. It could be shown that combining XµCT and histology offers the opportunity for a better understanding of the mechanisms of nanoparticle deposition in the vascular system after MDT.