arXiv subjects

Andreas M. Menzel

Publications and source records attributed to Andreas M. Menzel.

At least 73 records · Page 4Linked to original sources

arXiv2018

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

Ferrogels are smart soft materials, consisting of a polymeric network and embedded magnetic particles. Novel phenomena, such as the variation of the overall mechanical properties by external magnetic fields, emerge consequently. However, the dynamic behavior of ferrogels remains largely unveiled. In this paper, we consider a one-dimensional chain consisting of magnetic dipoles and elastic springs between them as a simple model for ferrogels. The model is evaluated by corresponding simulations. To probe the dynamics theoretically, we investigate a continuum limit of the energy governing the system and the corresponding equation of motion. We provide general classification scenarios for the dynamics, elucidating the touching/detachment dynamics of the magnetic particles along the chain. In particular, it is verified in certain cases that the long-time relaxation corresponds to solutions of shock-wave propagation, while formations of particle pairs underlie the initial stage of the dynamics. We expect that these results will provide insight into the understanding of the dynamics of more realistic models with randomness in parameters and time-dependent magnetic fields.

cond-mat.soft↗

arXiv2017

Tunable dynamic moduli of magnetic elastomers: from X-$μ$CT characterization to mesoscopic modeling

Ferrogels and magnetoelastomers 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 large magnetostriction as well as significant increase of the elastic moduli in the presence of external magnetic fields. By means of X-ray micro-computed tomography, 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 magnetostriction, 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, their overall distortions, 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, resulting in significant overall deformations. 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 show 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.

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arXiv2017

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.

cond-mat.soft↗

arXiv2017

Force-induced elastic matrix-mediated interactions in the presence of a rigid wall

We consider an elastic composite material containing particulate inclusions in a soft elastic matrix that is bounded by a rigid wall, e.g., the substrate. If such a composite serves as a soft actuator, forces are imposed on or induced between the embedded particles. We investigate how the presence of the rigid wall affects the interactions between the inclusions in the elastic matrix. For no-slip boundary conditions, we transfer Blake's derivation of a corresponding Green's function from low-Reynolds-number hydrodynamics to the linearly elastic case. Results for no-slip and free-slip surface conditions are compared to each other and to the bulk behavior. Our results suggest that walls with free-slip surface conditions are preferred when they serve as substrates for soft actuators made from elastic composite materials. As we further demonstrate, the presence of a rigid wall can qualitatively change the interactions between the inclusions. In effect, it can switch attractive interactions into repulsive ones (and vice versa). It should be straightforward to observe the effects in future experiments and to combine our results, e.g., with the modeling of biological cells and tissue on rigid surfaces.

cond-mat.soft↗

arXiv2017

Forces on rigid inclusions in elastic media and resulting matrix-mediated interactions

To describe many-particle systems suspended in incompressible low-Reynolds-number fluids, effective hydrodynamic interactions can be introduced. Here, we consider particles embedded in elastic media. The effective elastic interactions between spherical particles are calculated analytically, inspired by the approach in the fluid case. Our experiments on interacting magnetic particles confirm the theory. In view of the huge success of the method in hydrodynamics, we similarly expect many future applications in the elastic case, e.g. for elastic composite materials.

cond-mat.soft↗

arXiv2016

Superelastic stress-strain behavior in ferrogels of different types of magneto-elastic coupling

Colloidal magnetic particles embedded in an elastic polymer matrix constitute a smart material called ferrogel. It responds to an applied external magnetic field by changes in elastic properties, which can be exploited for various applications like dampers, vibration absorbers, or actuators. Under appropriate conditions, the stress-strain behavior of a ferrogel can display a fascinating feature: superelasticity, the capability to reversibly deform by a huge amount while barely altering the applied load. In a previous work, using numerical simulations, we investigated this behavior assuming that the magnetic moments carried by the embedded particles can freely reorient to minimize their magnetic interaction energy. Here, we extend the analysis to ferrogels where restoring torques by the surrounding matrix hinder rotations towards a magnetically favored configuration. For example, the particles can be chemically cross-linked into the polymer matrix and the magnetic moments can be fixed to the particle axes. We demonstrate that these systems still feature a superelastic regime. As before, the nonlinear stress-strain behavior can be reversibly tailored during operation by external magnetic fields. Yet, the different coupling of the magnetic moments causes different types of response to external stimuli. For instance, an external magnetic field applied parallel to the stretching axis hardly affects the superelastic regime but stiffens the system beyond it. Other smart materials featuring superelasticity, e.g. metallic shape-memory alloys, have already found widespread applications. Our soft polymer systems offer many additional advantages like a typically higher deformability and enhanced biocompatibility combined with high tunability.

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arXiv2016

Dynamic Elastic Moduli in Magnetic Gels: Normal Modes and Linear Response

In the perspective of developing smart hybrid materials with customized features, ferrogels and magnetorheological elastomers allow a synergy of elasticity and magnetism. The interplay between elastic and magnetic properties gives rise to a unique reversible control of the material behavior by applying an external magnetic field. Albeit few works have been performed on the time-dependent properties so far, understanding the dynamic behavior is the key to model many practical situations, e.g. applications as vibration absorbers. Here we present a way to calculate the frequency-dependent elastic moduli based on the decomposition of the linear response to an external stress in normal modes. We use a minimal three-dimensional dipole-spring model to theoretically describe the magnetic and elastic interactions on the mesoscopic level. Specifically, the magnetic particles carry permanent magnetic dipole moments and are spatially arranged in a prescribed way, before they are linked by elastic springs. An external magnetic field aligns the magnetic moments. On the one hand, we study regular lattice-like particle arrangements to compare with previous results in the literature. On the other hand, we calculate the dynamic elastic moduli for irregular, more realistic particle distributions. Our approach measures the tunability of the linear dynamic response as a function of the particle arrangement, the system orientation with respect to the external magnetic field, as well as the magnitude of the magnetic interaction between the particles. The strength of the present approach is that it explicitly connects the relaxational modes of the system with the rheological properties as well as with the internal rearrangement of the particles in the sample, providing new insight into the dynamics of these remarkable materials.

cond-mat.soft↗

arXiv2016

Hydrodynamic description of (visco)elastic composite materials and relative strains as a new macroscopic variable

One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a new macroscopic variable: relative strains. We analyze two simplified minimal example geometries as an illustration.

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arXiv2016

Thermophoretically induced large-scale deformations around microscopic heat centers

Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both, thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.

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arXiv2016

Dynamical Density Functional Theory For Microswimmers

Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on the one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state", which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.

cond-mat.stat-mech↗

arXiv2015

Getting drowned in a swirl: deformable bead-spring model microswimmers in external flow fields

Deformability is a central feature of many types of microswimmers, e.g. for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or square-like four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or square-like swimmer remains almost constant, while their orbits become deformed exhibiting an ``egg-like'' shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.

cond-mat.soft↗

arXiv2015

Dynamics of a linear magnetic "microswimmer molecule"

In analogy to nanoscopic molecules that are composed of individual atoms, we consider an active "microswimmer molecule". It is built up from three individual magnetic colloidal microswimmers that are connected by harmonic springs and hydrodynamically interact with each other. In the ground state, they form a linear straight molecule. We analyze the relaxation dynamics for perturbations of this straight configuration. As a central result, with increasing self-propulsion, we observe an oscillatory instability in accord with a subcritical Hopf bifurcation scenario. It is accompanied by a corkscrew-like swimming trajectory of increasing radius. Our results can be tested experimentally, using for instance magnetic self-propelled Janus particles, supposably linked by DNA molecules.

cond-mat.soft↗

arXiv2015

Tailoring superelasticity of soft magnetic materials

Embedding magnetic colloidal particles in an elastic polymer matrix leads to smart soft materials that can reversibly be addressed from outside by external magnetic fields. We discover a pronounced nonlinear superelastic stress-strain behavior of such materials using numerical simulations. This behavior results from a combination of two stress-induced mechanisms: a detachment mechanism of embedded particle aggregates as well as a reorientation mechanism of magnetic moments. The superelastic regime can be reversibly tuned or even be switched on and off by external magnetic fields and thus be tailored during operation. Similarities to the superelastic behavior of shape-memory alloys suggest analogous applications, with the additional benefit of reversible switchability and a higher biocompatibility of soft materials.

cond-mat.soft↗

arXiv2015

Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle velocities; finally, at a maximum of the possible particle speed the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

cond-mat.stat-mech↗

arXiv2015

Towards a scale-bridging description of ferrogels and magnetic elastomers

Ferrogels and magnetic elastomers differentiate themselves from other materials by their unique capability of reversibly changing shape and mechanical properties under the influence of an external magnetic field. A crucial issue in the study of these outstanding materials is the interaction between the mesoscopic magnetic particles and the polymer matrix in which they are embedded. Here we analyze interactions between two such particles connected by a polymer chain, a situation representative for particle-crosslinked magnetic gels. To make a first step towards a scale-bridging description of the materials, effective potentials for mesoscopic configurational changes are specified using microscopic input obtained from simulations. Furthermore, the impact of the presence of magnetic interactions on the probability distributions and thermodynamic quantities of the system is considered. The resulting mesoscopic model potentials can be used to economically model the system on the particle length scales. This first coarse-graining step is important to realize simplified but realistic scale-bridging models for these promising materials.

cond-mat.soft↗

arXiv2015

Focusing by blocking: repeatedly generating central density peaks in self-propelled particle systems by exploiting diffusive processes

Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching on and off the self-propelling drive can generate and afterwards arbitrarily often restore a non-stationary centered peak in their spatial distribution. This corresponds to a partial reversibility of their statistical behavior, in opposition to the above-mentioned long-time diffusive nature. Interestingly, it is a diffusive process that mediates and makes possible this procedure. It should be straightforward to verify our predictions in a real experimental system.

cond-mat.soft↗

arXiv2015

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.

cond-mat.soft↗

arXiv2015

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Phys. Rev. Lett. 112, 218304 (2014)]. Here we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (mobility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the dynamics. We finally discuss results from numerical simulations corroborating the analytical results.

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