Structure formation in low concentration magnetoactive polymers

Magnetoactive elastomers (MAE) are composite materials comprising micrometer sized ferromagnetic particles distributed within a soft, nonmagnetic elastomer matrix.¹ Their mechanical^2,3 and electrical^4,5 properties have been extensively investigated.

There is considerable interest in the engineering of such materials to have deliberate structure, though most research has dealt with surface, rather than internal, structuring.⁶ Recent developments in 3D printing technology have extended the conventional 3 degrees of freedom to 6 by including particulate orientation and gradient distribution.⁷ However, the precise positioning of micro-structures within a MAP is still difficult using conventional fabrication technology.

In this work, a large range of samples was prepared using soft carbonyl iron powder (CIP) of average grain diameter 4.2 μm.⁸ CIP content ranged from 1% to 5% by weight. The polymer matrix comprised Polydimethylsiloxane (PDMS) as addition-curing RTV-2 silicone rubber. The addition-curing RTV-2 silicone rubber was realized by mixing two components: silicone base and silicone catalyst in exactly the prescribed ratio by weight. After mixing the two appropriately proportioned silicone components, the CIP particles were added and the samples completed by chaotic mixing at room temperature (22°C). Subsequently, the removal of cavities in the uncured polymer mixture was achieved by degassing under adequate vacuum (10 mBar). Sheets of 2 mm thickness were then produced from the resulting mixture and left to cure for two hours. The magnetic moments of individual samples were measured using a SQUID magnetometer (Quantum Design MPMS XL), as shown in Figure 1.

The vacuum removal of cavities usually takes several minutes before the MAP is void free. During this time bubbles rise to the surface before being dissipated. With such sparse concentrations, particles tend to gather on the boundary layers of the bubbles while they ascend. A similar effect, previously intended for the attachment of much lighter talc particles⁹ and the self-assembly of particles in ring structures in two-phase fluids¹⁰ have been documented.

The hydrodynamic interaction of the higher viscosity polymer tends to hinder the ascent of the heavier particles under the influence of gravitational acceleration causing them to lag behind the basic flow field.¹¹ Rather than a homogeneous distribution of particles over the spherical surface, a circumferential collection and eventual ring (Torus) formation is created, as shown in Figure 2.

The break point of the CIP ring around the rising bubble depends on the ascent rate. The diameter of the toroid, which is a function of the bubble dimensions, depends on the gas used, the surface tension of the polymer, the mixing strategy and the degree of cross-linking at the point of evacuation. As can be seen in Figure 1, average diameters of 80-90μm were achieved for 1% wt samples.

The Reynolds factor depends on the flow rate of an object of diameter L through a medium having density ρ and dynamic viscosity μ (1).

For an 80 μm diameter bubble rising at a velocity of 0.1 m/s through a medium with a dynamic viscosity of μ = 1500 mPa.s at 23° (polymer prior to curing), then expression (1) yields a Reynolds factor much lower than 1 thus ensuring laminar flow.

The volume of the torus formed is given by expression (2)

where R is the radius of the torus and α the radius of the tubular section of the torus. However, cavities do not always rise vertically but also obliquely as shown in Figure 3.

Assuming the bubbles are so spaced that they do not come into contact with one another, then depending on the flow regime the rising bubble will collect particles in a volume represented by an oblique cylinder with radius R and height h, the volume for which is given in (3).

Dividing (2) by (3) gives the volume fraction ϕ in expression (4)

By use of the Hough transform, it is possible to determine geometrical parameters, including the identification of partial and full circles, within an image.¹² Measurements made on X-ray tomographic images revealed a distribution in the toroidal size with a median diameter of about 80 μm for PDMS samples with 1%wt CIP.

Taking the mean toroidal radius of R = 40 μm, with a cylinder height h = 100 μm, for particles of average radius α = 2.5 μm and placing these in (4) reveals a volume fraction for a torus comprising a ring of single particles of 2.45%.

However, the density of iron is 7.86 kg/m³ and that of silicone around 0.96 kg/m³. Consequently, the mass fraction is 8.2 times lower or 0.3%. This represents the absolute minimum particle mass faction required before torus production can commence and assumes that the rising bubble gathers all free particles within V_C. At the other end of the scale, it is logical to assume that there must be a maximum mass concentration, above which toroid production is no longer possible.

As the CIP concentration increases toward 2%, the diameter of the toroids grows until the ring structures can no longer stand alone and contigation takes place as shown in Figure 4 b). At this point, the ring diameters measure around 130 μm. This can easily be explained by the fact that the bubbles expand slightly as the weight of the collected particles are shed toward the interface between two connecting rings.

This results in the onset of capillary doublet formation at approximately 1.5wt% CIP which reaches a fully developed condition between 2wt% and 3%wt.

These structures then disappear with higher concentrations of CIP (>3%) resulting in the usual random CIP distribution of agglomerated particles within the polymer matrix shown in Figure 5. The absence of any visible structure is typical for usual MAP, in which an arbitrary distribution of CIP particles in spatially separated aggregates prevails.

There are also measurable differences in the transmission of light in the visible spectrum as shown in Figure 6. The toroidal particles in a 1% wt CIP sample tend to arrange themselves in layers as can be observed from Figure 3.

The application of an external magnetic field producing a flux density of 250 mT results in a small increase in transmission at wavelwngths longer than 500 nm. On the other hand, the disordered distribution of the particles at CIP concentrations of 3% wt or higher, results in a corresponding reduction in magnetic field dependent transmission.

Although the changes in magnetic field induced transmission are small, they represent a phenomenon not present with higher, isotropic CIP concentration.

For the first time, investigations have been conducted into low CIP concentration MAP. At CIP concentrations in a range of 1% wt to 3% wt, the development of internal toroidal micro-structures, completely absent with higher concentrations, have been demonstrated. These toroidal structures have been confirmed and their physical dimensions measured with the assistance of X-Ray tomography. Potential applications include micro-MAP elements for electrical, acoustic and optical purposes, where the closed structure forms an electrically conductive ring having a minute inductance embedded within a dielectric. The integration of self-organizing structures within the silicone matrix also introduces potential for intrinsic LC resonant circuits in the higher GHz and THz regions.

The authors would like to express their thanks to the German Research Federation (DFG) for financial support within the SPP1681 (MO 2196/2-2) research program and for the Microcomputertomograph according to the DFG grant award INST 102/11-1 FUGG.