Magnetoelastic filament

Magnetoelastic filaments are one-dimensional composite structures that exhibit both magnetic and elastic properties. Interest in these materials tends to focus on the ability to precisely control mechanical events using an external magnetic field. Like piezoelectricity materials, they can be used as actuators, but do not need to be physically connected to a power source.

Mechanical Behavior

Colloidal Chains

Paramagnetic colloids are small particles with an inducible magnetic moment that are used in a variety of applications, such as imaging and drug delivery. The magnetic force exerted on a particle depends on the strength, direction, and dynamics of the applied magnetic field as well as the position and orientation of local magnetic dipoles. Polymerizing paramagnetic colloids into a chain results in a one-dimensional structure whose extended structure imparts new mechanical behaviors. In general, linking methods involve two steps. Initially the colloids are aligned using a static magnetic field that brings them into physical contact. Next, they are attached, usually by the formation of a covalent bond. Earlier linking attempts used polyacrylic acid (PAA) coatings and relied on physical polymer entanglement. However, these methods do not produce as stable of a link as a chemical bond. Later methods involve tetraethoxysilane condensation, biotinylation or glucose decomposition.

The conformations adopted by magnetoelastic filaments are dictated by the competition between its elastic and magnetic properties. Each contributes to the total energy of the filament. Dynamic magnetic fields allow for the greatest range of control over chain shape. Of principal interest is the force exerted on the ends of the chain as a result of a dynamic field. The effect of Larmor precession with a row of magnetic colloids results in dynamic interactions dependent on the field precession angle. In fact, sweeping through the magic angle flips sign of the dipole-dipole interaction. In a field precessing quickly around the z-axis, the force exerted on the end of the chain is given by

$F_{end}\ {=}\ {\frac {3\mu ^{2}}{\sigma ^{4}}}\sin(2(\omega -{\frac {d\psi }{dt}})t)\mathbf {N} -\gamma {\frac {d\psi }{dt}}\mathbf {N}$

where $\mu$ is the dipole moment, $\sigma$ is the bead diameter, $\omega$ is the angular frequency of the field precession, ${\frac {d\psi }{dt}}$ is the rate of change of the filament path, $\gamma$ is the viscous drag coefficient and $\mathbf {N}$ is the unit vector of the plane perpendicular to the tangent of the filament curve. This produces a periodic magnetic force. However, under fast precession, the second term remains non-zero and scales with$\omega ^{-1}$. At low $\omega$, the magnetic torque dominates and the chain winds around itself. With a high $\omega$, the bending modulus dominates the energetic landscape and filaments form branched gels with a field-dependent bulk modulus.

The applied load on a filament is generally limited by the polymer linking method. The elastic strain regime for a simple covalently linked filament is short and are taken as inextensible under most conditions. If tensile forces become too large, plastic deformation can occur due to bond breaking and polymer disentanglement. These irreversible changes can result in the permanent change in the bending modulus which ultimately effects the filament performance.

Alloy Nanopillars

Using etching techniques such as focused ion beam milling, micro- or nano-sized pillars can be formed in magnetic materials. However, repeated bending of crystal pillars can cause defect formation and fatigue damage. This damage comes from the nucleation of cracks on the pillars surface, even in the elastic regime, due to localized plasticity. Crack propagation during successive compression and tension cycles can lead to pillar fracture. This is similar to what can be seen in cantilever magnetometry when operating under strong fields. Because of this, it is desirable to link smaller magnetic particles together with tougher, elastic materials, such as a polymer, rather than use a continuous alloy filament.

Applications

• Mechanical sensors for testing the elastic moduli of biomolecules and nanostructures.
• Microactuation
• MRI imaging
• Drug delivery
• Responsive coatings

See also

• Superparamagnetism
• Magnetic shape-memory alloy
• Magnetostriction