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.

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.

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.

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.

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.

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.

Magnetoviscosity of a Magnetic Fluid Based on Barium Hexaferrite Nanoplates.

This paper presents the results of an experimental study of the influence of an external magnetic field on the shear flow behaviour of a magnetic fluid based on barium hexaferrite nanoplates. With the use of rheometry, the magnetoviscosity and field-dependent yield-stress in the fluid are evaluated. The observed fluid behaviour is compared to that of ferrofluids with magnetic nanoparticles having high dipole interaction. The results obtained supplement the so-far poorly studied topic of the influence of magnetic nanoparticles' shape on magnetoviscous effects. It is concluded that the parameter determining the observed magnetoviscous effects in the fluid under study is the ratio V2/l3, where V is the volume of the nanoparticle and l is the size of the nanoparticle in the direction corresponding to its orientation in the externally applied magnetic field.

Bioprinting of Magnetically Deformable Scaffolds.

Mechanical stimulation of cells embedded in scaffolds is known to increase the cellular performance toward osteogenic or chondrogenic differentiation and tissue development. Three-dimensional bioplotting of magnetically deformable scaffolds enables the spatially defined distribution of magnetically inducible scaffold regions. In this study, a magnetic bioink based on alginate (alg, 3%) and methylcellulose (MC, 9%) with incorporated magnetite microparticles (25% w/w) was developed and characterized. The size and shape of particles were monitored via scanning electron microscopy and X-ray micro-computed tomography. Shear-thinning properties of the algMC ink were maintained after the addition of different concentrations of magnetite microparticles to the ink. Its viscosity proportionally increased with the added amount of magnetite, and so did the level of saturation magnetization as determined via vibrating sample magnetometry. The printability and shape fidelity of various shapes were evaluated, so that the final composition of algMC + 25% w/w magnetite was chosen. With application of this ink, cytocompatibility was proven in indirect cell culture and bioplotting experiments using a human mesenchymal stem cell line. Toward the deformation of cell-laden scaffolds to support cell differentiation in the future, radiography allowed the real-time monitoring of magnetically induced deformation of scaffolds of different pore architectures and scaffold orientations inside the magnetic field. Varying the strand distance and scaffold design will allow fine-tuning the degree of deformation in stimulatory experiments.

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.

Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations.

Three-dimensional calculations of the meniscus of a magnetic fluid placed around a current carrying vertical and cylindrical wire are presented. Based on the material properties of experimentally used magnetic fluids, the numerically determined menisci are compared with the experimentally measured ones reported by May. The comparison is made for a linear law of magnetisation as well as for the experimentally measured nonlinear magnetisation curve. Up to moderate strengths of the applied current ( I < = 45 A), i.e., up to moderate strengths of the magnetic field close to the wire, the calculated profiles agree satisfyingly with the experimentally measured ones for a linear as well as for a nonlinear law of magnetisation. At a great strength of the applied current ( I = 70 A), i.e., at a large strength of the magnetic field close to the wire, the agreement is less good than in the range up to moderate strengths. Our analysis revealed that the numerically assumed isothermal conditions are not present in the experiment, particularly at the great strength of the applied current. A control of the temperature in the experiment and the implementation of a coupled thermal model in the numerics are considered the most relevant future steps for an improved agreement.

Experimental Investigations on the Effect of Axial Homogenous Magnetic Fields on Propagating Vortex Flow in the Taylor-Couette System.

Experimental investigations of propagating vortex flow states (pV states) in a short Taylor-Couette system with asymmetric boundary conditions are presented. The flow state was established in a ferrofluid showing no magneto-viscous effect and was exposed to axial magnetic fields. It was found that the magnetic field led to a change in the spatial and temporal behavior of the pV state, indicating complex interactions between the flow field and magnetic field. A stepwise applied axial magnetic field destabilized the pV state, leading to an intermittent flow state. Gradually increasing the axial magnetic fields changed the temporal behavior of the regime. Up to magnetic field strengths of 20 kA/m, the orbital frequency, as a measure for the temporal periodicity, was increased with field strength.

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.

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.

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.

Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling.

Ferrogels and magnetorheological elastomers are composite materials obtained by embedding magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They combine the reversible elastic deformability of polymeric materials with the high responsivity of ferrofluids to external magnetic fields. These materials stand out, for example, for significant magnetostriction as well as a pronounced increase of the elastic moduli in the presence of external magnetic fields. By means of x-ray micro-computed tomography, the position and size of each magnetic particle can be measured with a high degree of accuracy. We here use data extracted from real magnetoelastic samples as input for coarse-grained dipole-spring modeling and calculations to investigate internal restructuring, stiffening, and changes in the normal modes spectrum. More precisely, we assign to each particle a dipole moment proportional to its volume and set a randomized network of springs between them that mimics the behavior of the polymeric elastic matrix. Extending our previously developed methods, we compute the resulting structural changes in the systems as well as the frequency-dependent elastic moduli when magnetic interactions are turned on. Particularly, with increasing magnetization, we observe the formation of chain-like aggregates. Interestingly, the static elastic moduli can first show a slight decrease with growing amplitude of the magnetic interactions, before a pronounced increase appears upon the chain formation. The change of the dynamic moduli with increasing magnetization depends on the frequency and can even feature nonmonotonic behavior. Overall, we demonstrate how theory and experiments can complement each other to learn more about the dynamic behavior of this interesting class of materials.

Adapted MR velocimetry of slow liquid flow in porous media.

MR velocimetry of liquid flow in opaque porous filters may play an important role in better understanding the mechanisms of deep bed filtration. With this knowledge, the efficiency of separating the suspended solid particles from the vertically flowing liquid can be improved, and thus a wide range of industrial applications such as wastewater treatment and desalination can be optimized. However, MR velocimetry is challenging for such studies due to the low velocities, the severe B0 inhomogeneity in porous structures, and the demand for high spatial resolution and an appropriate total measurement time during which the particle deposition will change velocities only marginally. In this work, a modified RARE-based MR velocimetry method is proposed to address these issues for velocity mapping on a deep bed filtration cell. A dedicated RF coil with a high filling factor is constructed considering the limited space available for the vertical cell in a horizontal MR magnet. Several means are applied to optimize the phase contrast RARE MRI pulse sequence for accurately measuring the phase contrast in a long echo train, even in the case of a low B1 homogeneity. Two means are of particular importance. One uses data acquired with zero flow to correct the phase contrast offsets from gradient imperfections, and the other combines the phase contrast from signals of both odd and even echoes. Results obtained on a 7T preclinical MR scanner indicate that the low velocities in the heterogeneous system can be correctly quantified with high spatial resolution and an adequate total measurement time, enabling future studies on flow during the filtration process.

Smart hydrogels as storage elements with dispensing functionality in discontinuous microfluidic systems.

Smart hydrogels are useful elements in microfluidic systems because they respond to environmental stimuli and are capable of storing reagents. We present here a concept of using hydrogels (poly(N-isopropylacrylamide)) as an interface between continuous and discontinuous microfluidics. Their swelling and shrinking capabilities allow them to act as storage elements for reagents absorbed in the swelling process. When the swollen hydrogel collapses in an oil-filled channel, the incorporated water and molecules are expelled from the hydrogel and form a water reservoir. Water-in-oil droplets can be released from the reservoir generating different sized droplets depending on the flow regime at various oil flow rates (dispensing functionality). Different hydrogel sizes and microfluidic structures are discussed in terms of their storage and droplet formation capabilities. The time behaviour of the hydrogel element is investigated by dynamic swelling experiments and computational fluid dynamics simulations. By precise temperature control, the device acts as an active droplet generator and converts continuous to discontinuous flows.

Multi-loaded ceramic beads/matrix scaffolds obtained by combining ionotropic and freeze gelation for sustained and tuneable vancomycin release.

For a targeted release against bacteria-associated bone diseases (osteomyelitis) ceramic beads with a high drug loading capacity, loaded with vancomycin as model antibiotic, are synthesized as drug carrier and successfully incorporated in an open porous hydroxyapatite matrix scaffold via freeze gelation to prevent bead migration at the implantation site and to extend drug release. We demonstrate that the quantity of loaded drug by the hydroxyapatite and ß-tricalcium phosphate beads, produced by ionotropic gelation, as well as drug release can be tuned and controlled by the selected calcium phosphate powder, sintering temperature, and high initial vancomycin concentrations (100mg/ml) used for loading. Bead pore volume up to 68mm(3)/g, with sufficiently large open pores (pore size of up to 650nm with open porosity of 72%) and high surface area (91m(2)/g) account likewise for a maximum drug loading of 236mg/g beads or 26mg/sample. Multi-drug loading of the beads/matrix composite can further increase the maximum loadable amount of vancomycin to 37mg/sample and prolong release and antibacterial activity on Bacillus subtilis up to 5days. The results confirmed that our approach to incorporate ceramic beads as drug carrier for highly increased drug load in freeze-gelated matrix scaffolds is feasible and may lead to a sustained drug release and antibacterial activity.