Buckling of paramagnetic chains in soft gels

Huang, Shilin; Pessot, Giorgio; Cremer, Peet; Weeber, Rudolf; Holm, Christian; Nowak, Johannes; Odenbach, Stefan; Menzel, Andreas M.; Auernhammer, Günter K.

doi:10.1039/c5sm01814e

Cited by 74 publications

(80 citation statements)

References 64 publications

(150 reference statements)

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“…Eq. (22) here contains a term ∼ 1/(1 − 2ν), which would diverge for ν → 0.5. However, it gets canceled by a counter-factor ∼ (1−2ν) in the calculation.…”

mentioning

confidence: 99%

“…(17) into Eq. (22), the expression ∇ · G appears; straightforward calculation of ∇ · G via Eq. (16) leads to a factor ∼ (1 − 2ν).…”

mentioning

confidence: 99%

“…We carefully selected Ni particles of similar sizes (deviation less than 2% within each group) and a roundness > ∼ 0.91 (measured by image analysis [21]). These particles were embedded in the middle plane of a soft elastic polydimethylsiloxanebased [22] gel, see Fig. 3(a).…”

mentioning

confidence: 99%

“…Using a 32-magnet Halbach array to generate a homogeneous magnetic field [22], we applied ∼ 216 mT to the embedded Ni particles, which is close to saturation. Starting from the initial direction, the magnetic field was rotated clockwise for 180 • in 18 steps within the plane containing the Ni particles.…”

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confidence: 99%

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Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions

et al. 2016

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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. planes, vehicles, ships, and propellers [4]. All these processes are described by the Navier-Stokes equations [5] or variants thereof. This set of equations typically poses significant challenges during solution due to a convective nonlinearity reflecting inertial effects. Basically, turbulence is driven by the inertial term. It often renders analytical solutions impossible.The situation changes for small dimensions and velocities or high viscosity. Then, the relative strength of inertial effects, measured by the Reynolds number, is low. The nonlinearity can be neglected. A Green's function in terms of the so-called Oseen matrix is then available, which formally solves the problem analytically [6,7]. In this way, semi-dilute colloidal suspensions, i.e. the dispersion of nano-to micrometer-sized particles in a fluid [7,8], or microswimmer suspensions [9] are described effectively. The explicit role of the fluid is eliminated and replaced by effective hydrodynamic interactions between the suspended particles [6,7].Despite the success of this theoretical approach for colloidal suspensions, hardly any investigations consider a surrounding elastic solid instead of a suspending fluid. This is surprising, since, as we show below, the formalism can be adapted straightforwardly to linearly elastic matrices and is confirmed by our experiments. Our approach will, for instance, facilitate describing the response of elastic composite materials to external stimuli. Such materials consist of more or less rigid inclusions embedded in an elastic matrix. They are of growing technological interest and may serve, e.g., as soft actuators or sound attenuation devices [10].In previous theoretical studies, the physics of one single rigid or deformable inclusion was addressed [11,12], also under acoustic irradiation [13]. For more than a single inclusion, mainly the so-called load problem was analyzed theoretically for a pair of rigid inclusions: one prescribes displacements of two rigid inclusions in an elastic matrix, and then determines the forces necessary to achieve these given displacements [14].Here, we take the converse point of view, based on the cause-and-effect chain in our experiments: external forces are imposed onto the inclusions, or mutual forces between the inclusions are induced, for example to actuate the material or to tune its properties. In response to the forces, the inclusions are displaced. Since they cannot penetrate through the surrounding elastic ma...

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“…Eq. (22) here contains a term ∼ 1/(1 − 2ν), which would diverge for ν → 0.5. However, it gets canceled by a counter-factor ∼ (1−2ν) in the calculation.…”

mentioning

confidence: 99%

“…(17) into Eq. (22), the expression ∇ · G appears; straightforward calculation of ∇ · G via Eq. (16) leads to a factor ∼ (1 − 2ν).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions

et al. 2016

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“…In order to keep the models simple, we study effective one-dimensional set-ups. Such a situation is realized, for instance, for elongated magnetic particle chains embedded into an elastic matrix [34], but also for magnetic filaments [35] made, e.g., of magnetic colloidal particles connected by DNA polymer strands [36]. We map this system with its particle-distinguishing connectivity onto another one with an effective connectivity and indistinguishable particles [37].…”

Section: Introductionmentioning

confidence: 99%

A density functional approach to ferrogels

Cremer¹,

Heinen²,

Menzel³

et al. 2017

J. Phys.: Condens. Matter

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Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a "pairwise pseudopotential". Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an "external pseudopotential" when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.

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Flexible Magnetic Filaments and their Applications

Cēbers

Ērglis

2016

Adv Funct Materials

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This review of the properties of flexible magnetic filaments covers the problems of their buckling under the action of a magnetic field. The dependence of the buckling on the magnetic properties of the filaments is considered. It is shown that these filaments may be used as artificial analogues of structures with important roles in the living world: cilia, elastic tails of self‐propelling microorganisms etc. The main methods used to study the relevant phenomena are considered: models, numerical simulation algorithms, and the results of linear stability analysis. Special emphasis is placed on the possible uses of the flexible magnetic filaments as model systems to study the dynamics of magnetic fields using magnetometers based on optical detection of the magnetic resonance of NV− centers in diamonds.

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Buckling of paramagnetic chains in soft gels

Cited by 74 publications

References 64 publications

Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions

Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions

A density functional approach to ferrogels

Flexible Magnetic Filaments and their Applications

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