Applied field dependence

To characterize the magnetic properties of core-shell biomimetic cilia, I fabricated sam- ples as described in Figure 4.13, but in this case, the rods remained inside the PCTE mem- brane. The final release step shown in Figure 4.13E was not performed. The arrays (en- cased in the PCTE membrane) were inserted into a straw holder such that the microrods’ long axes were parallel or perpendicular to the applied magnetic field. All magnetization curves were run at 300◦_{K. Initial runs over a large range of applied field determined that the}

In addition, the magnetization of the background was obtained, and all data presented has been background subtracted.

Figure 4.16: The magnetic field was applied both perpendicular (◦) and parallel (•) to the rod axis, and the signal is normalized by the volume of Ni deposited into the PCTE membrane (Fiser et al., 2012).

The microrods’ saturation was the same whether the field was applied parallel or per- pendicular to the rods long axes, and the saturation magnetization was 397±13 emu/cm3,

a value that approaches saturation magnetizations in literature (Ferre et al., 1997; Kisker et al., 1995; Cordente et al., 2001). The ferromagnetic nature of core-shell cilia was con- firmed by the presence of hysteresis in the curves. In addition, I checked for the presence of shape anisotropy which appears as a general shape change in the hysteresis curves when the magnetic field is applied in different orientations. As shown in Figure 4.16, data indi-

cate there may be a subtle anisotropy. When the rods’ long axes are aligned parallel to the applied field, the sample appears to approach saturation more quickly than when the rods’ long axes are aligned perpendicular to the applied field. This phenomenon is expected as

more energy is required to rotate the moment of individual domains away from the long (easy) axis of the rod. Shape anisotropy has been shown in previous magnetization studies of Ni nanorods with packing densities less than 35%. Larger porosities (>35%) have ex-

hibited a reduced anisotropy due to the dipolar coupling between rods, as shown in Figure 4.17 (Encinas-Oropesa et al., 2001). The porosity of rods in Figure 4.17A is 4%, and the porosity of rods in Figure 4.17B is 35-38%. I utilize PCTE membranes with a porosity of 0.31%.

Figure 4.17: Reprinted from Encinas-Oropesa et al. (2009). The magnetic field was applied both perpendicular (open circles) and parallel (filled circles) to the rod axis, and the signal is normalized by the saturation magnetization. The Ni nanowires in (a) have a porosity of 4% and diameter of 56 nm, and in (b), the porosity is 35-38% and the diameter is 250 nm (Encinas-Oropesa et al., 2001).

Chapter 5

Magnetic Actuation

Magnetic forces, such as those generated by permanent magnets or electromagnets, of- fer an appealing solution to driving arrays of biomimetic cilia. The effect of a magnetic field

may be long range, and for permanent magnets, no wires or internal, on-chip power sources are required. Additionally, large actuator displacements may be achieved, and a complex actuator response may be easily orchestrated by manipulating magnet geometries or place- ment. Permanent magnets are therefore a simple and commercially available method for the application of a magnetic field.

Magnetic fields are able to actuate biomimetic cilia through two different mechanisms:

torque and force. The nickel tubes surrounding core-shell biomimetic cilia are ferromag- netic as can be seen in Figure 4.3.3, and are thus capable of retaining a magnetization after the magnetic field has been removed, though the hysteresis is slight. Typically at the microscale objects are superparamagnetic, such as FFPDMS cilia, and dipoles within the material do not remain aligned when a magnetic field is removed.

The torque which is applied to a dipole is (Jackson, 1998)

�

where Bis the applied field and mis the magnetic dipole moment. If a dipole is aligned with the magnetic field, the torque on the dipole will give zero, and when the field and dipole are perpendicular, the torque will be a maximum; thus, the torque acts to align a dipole with the applied field. The force which is applied by the magnetic field to the dipole is (Jackson, 1998)

�

F =∇(m� _·B�), (5.2)

which is dependent on the direction of the greatest increase ofm� _· �B. Thus, the magnetic

field rotates a dipole and the field gradient pulls a dipole closer. In biomimetic cilia, dipoles within the nickel shell interact with one other and the torque and force are both minimized with a head-to-tail alignment along the long (or easy) axis of the cilium. If the long axis of the cilium is not parallel to the applied magnetic field, dipoles within the rod will attempt to align themselves with the field while maintaining their alignment with the cilium’s long axis, causing a torque on the cilium. This torque minimizes the angle between the direction of the applied field and the dipoles. As discussed in Section 3.3.1, the effect of the magnetic

gradient, and thus magnetic force, on the actuator is negligible.

I magnetically actuate biomimetic cilia arrays using rare-earth neodymium-iron-boride permanent magnets (K&J Magnetics) situated from 2-15 mm above the sample. The rect- angular magnet is oriented such that the north and south ends are parallel to the sample plane. This effectively orients the magnet field in a direction perpendicular to the relaxed

orientation of cilia, maximizing the applied torque on the rod. The distance between the magnet and sample controls the strength of the applied magnetic field, as shown in Figure

5.1, where the magnetic field was measured as a function of distance using a gaussmeter (F.W. Bell Teslameter, model 5080G). Each curve in Figure 5.1 represents measurements made with respect to a different location of the magnet.

Figure 5.1: The permanent magnet used in all experiments had dimensions 1.0 in x 0.5 in x 0.25 in. The magnetic field was measured as a function of distance from the center of the 1 in x 0.5 in face of the magnet (solid line) and from the center of the 1.0 in x 0.25 in face of the magnet (dashed-dotted line). In experiments, the magnet is oriented with the 1.0 in x 0.25 in face of the magnet parallel to the sample plane.

In this chapter, I will first compare the responsiveness of composite FFPDMS rods and core-shell rods to an applied magnetic field in various fluids, and follow this by character- izing the abilities of core-shell rods in general. At the low end of the range of magnetic field strength achievable with commercially obtained neodymium magnets (1 in x 0.5 in x 0.25 in),∼5 mT, core-shell cilia achieve bend angles of approximately 20◦_{. Increasing the}

field to a moderate 30−100 mT field strength causes the nickel portion of the cilium to bend a full 90◦_{such that the tip of the cilium contacts the substrate and sticks momentarily. Bend}

angles achieved by FFPDMS cilia, even at the higher applied fields approaching 200 mT, are no larger than 40◦_{. In addition to the responsiveness from a given applied field, I will}

discuss how we utilize various magnetic setups and oscillating fields to engender actuator beat shapes similar to those of biological cilia.