In addition to determining material contributions to the design of a more responsive actuator, it is important to understand the effect of forces at the micron scale on high aspect
ratio fabricated structures. Rods with high aspect ratios are subject to adhesive forces which act to pull them either to the ground, known as ground collapse, or against their nearest neighbors, known as lateral collapse. The success of these adhesive forces tends to be proportional to a rod’s aspect ratio; higher aspect ratios imply a higher likelihood of collapse. Collapse occurs because the elastic forces which work to keep a rod upright are weaker than the adhesive forces which work to keep a rod in contact with either the ground or another rod. This is particularly a problem with PDMS, the polymer utilized for both composite and core-shell biomimetic cilia, because of its hydrophobic nature and lower affinity for a liquid environment than for itself. PDMS’s surface energy is therefore lower
when it is in contact with itself (Roca-Cusachs et al., 2005; Zhang et al., 2006).
Ground collapse is defined literally as the collapse of rods to the ground and subse- quent adherence due to adhesion forces such as van der Waals forces. Rods are considered collapsed if they do not return to their original upright positions. Roca-Cusachs et al. devel- oped a quantitative model in 2005 to predict the critical aspect ratio above which ground collapse occurs due to these adhesive forces. This critical aspect ratio is(Roca-Cusachs et al., 2005) �L d � g = π5/3 211/331/2 � 1−ν2�−1/6 �Ed W �2/3 (3.33)
where ν is Poisson’s ratio, E is the elastic modulus (EPDMS = 2.5 MPa), and W is the
work of adhesion of the material to itself (Roca-Cusachs et al., 2005). Poisson’s ratio for a material is defined as the negative of the lateral strain over the axial strain, or the decrease in width divided by the increase in length. For PDMS, ν = 0.5. In addition to ground
collapse, there is also lateral collapse, which is the adhesion of one rod to another due to their proximity. The critical aspect ratio for lateral collapse is defined as (Roca-Cusachs et al., 2005) �L d � L = � 33π4 211(1−ν2) �1/12�s d �1/2�Ed W �1/3 (3.34) where sis the spacing between rods, which for our templates is on the order of 7µm. To
calculate the conditions for ground and lateral collapse for biomimetic cilia, approximate values for the work of adhesion of PDMS in air, water, and ethanol were taken from Roca- Cusachs et al.: WA = 44 mN/m, WW = 86 mN/m, and WE = 11 mN/m (Roca-Cusachs
et al., 2005). For rods with a diameter of 0.55µm, the critical aspect ratios for ground and lateral collapse are presented in Table 3.1 for air, water, and ethanol.
Table 3.1: Critical rod aspect ratios for ground and lateral collapse (L/d)g (L/d)L
Air 3.19 11.8 Water 2.04 9.40 Ethanol 8.03 18.7
The values in Table 3.1 indicate that aspect ratios on the order of 10 or larger are un- likely to survive ground or lateral collapse. To have an array of rods which truly mimic biological cilia, I typically fabricate rods which are 10 µm and 0.55 µm in diameter, an
aspect ratio of 18. Thus, it is particularly important to develop materials and a fabrication process which are more robust as rods with this aspect ratio are not considered stable by these models for ground and lateral collapse. Figure 3.11 shows several different examples
of collapsed rods with aspect ratios ranging from 18 to 31.
A
B
C
Figure 3.11: SEM images of rods with aspect ratios ranging from 18-31 exhibiting both ground and lateral collapse. (A) FFPDMS-NH2. (B) FFPDMS. (C) core-shell rods.
Chapter 4
Materials and Fabrication
Designing an actuator by maximizing its bend angle and torque through consideration of flexibility and magnetic permeability is valuable for determining the materials and length scales used in the fabrication process. Different materials may require fabrication at varying
length scales due to differences in responsiveness. Higher elastic moduli may result in a
more rigid actuator at lower aspect ratios; thus, fabrication at higher aspect ratios may be required for a particular application. For flexibility in the fabrication process, we use polycarbonate track-etched filter membranes as a template for our biomimetic cilia. With these filter membranes, we can easily alter the pore diameter to adjust the aspect ratio, creating more or less rigid biomimetic cilia for a given material.
In the first section of this chapter, I discuss the template fabrication process including how pore diameter is altered. This template method is utilized in the remaining sections where I discuss two types of materials from which we fabricate biomimetic cilia: mag- netic nanoparticle composite materials and core-shell materials. The magnetic composite materials utilize either maghemite or magnetite nanoparticles, both of which are superpara- magnetic. The core-shell materials are fabricated with a nickel shell and are ferromagnetic in nature. The synthesis of these materials and the fabrication of biomimetic cilia using
these materials are described in detail throughout this chapter.