# Self-Organization of a Mesoscale Bristle into Ordered, Hierarchical Helical Assemblies

## Contents

## Short Overview

The authors report self-assembling upright micro-scale pillars into twisted clusters and spirals using the capillary force to bring the pillars to within a proximity where they could spontaneously adhere to one another.

## Materials Used

### Bristles

The bristles (upright pillar array) are made of epoxy. The arrays were fabricated using soft-lithographic techniques described by the authors in a previous paper:

- B. Pokroy, A. Epstein, M. C. M. Persson Gulda, J. Aizenberg, Adv. Mater., published online 18 November 2008; 10.1002/adma.200801432.

A silicon master of the bristle was created via an unspecified process. A soft mold of this master was created using PDMS ((poly)dimethylsiloxane) to avoid damaging the delicate silicon master when the were seperated. The mold was filled with epoxy and after drying the PDMS was pulled away to reveal an epoxy bristle.

__Accompanying description of brisle fabricatio (also taken from paper)__- Figure 1. Two-step soft-lithography process for creating replicas of nanostructured surfaces with high-aspect-ratio features. A) SEM image of an exemplary original nanostructured surface-a silicon master bearing a square array of posts 8mmlong with the diameter 250nmand pitch 2mm. The oblique view is used to best visualize the structure. The insert is an EDS spectrum. B) Liquid PDMS precursor is poured onto the master, treated with an antisticking agent, and cured. C) The curedPDMSis peeled off from the master.D) The negativePDMSmold, which contains an array of high-aspect-ratio wells corresponding to the posts of the positive master, is surface-treated with an antisticking agent. E)SEMimage of thePDMSmold, revealing the high-aspect-ratio wells. F) Liquid precursor (polymer, liquid metal) is poured onto the negativePDMSmold and cured. G) ThePDMS mold is peeled from the cured positive replica. H) SEM image of an exemplary nanostructured replica fabricated from epoxy resin. The insert is an EDS spectrum. The replicated structure is geometrically indistinguishable from the master shown in A).

It is assumed that substrate is also made of epoxy.

### Wetting Liquids

The authors report experimenting with the following liquids:

- Ethanol
- IPA
- Toluene
- Acetone
- Ethanol-water mixtures

All were reported as anhydrous except the mixture.

## Model

### Critical Length

The critical length, <math>L_c</math> is the minimum pillar height in order to bring the two pillars into contact via the capillary. To do this the capillary force is balanced with the force required to buckle the pillars: <math> \gamma r \approx (Er^4)\frac{d}{L} \rightarrow L_c\approx \left(\frac{Ed}{\gamma}\right)r</math>

- Where:
- r - pillar radius
- <math>\gamma</math> - surface tension
- E - Young’s modulus
- L - pillar length
- d – interpillar distance
- J – adhesive energy per area

- Where:

### Wrapping

Once the pillars are in close contact, Van der Waals forces (we presume take over), adhering the pillars. Once again, there is minimum length associated with this interaction that comes from balancing with force needed to cause buckling. <math>L_a\approx \left(\frac{Ed}{J}\right)^\frac{1}{3}r</math> There are three general regimes here:

- <math>L_a>L>L_c</math>: Pillars approach during evaporation, but separate after all liquid is gone.
- <math>L>L_a</math> and <math>L>L_c</math> Clustering in small groups; doubles, quartets etc.
- <math>L>>L_a</math> Pillars wrap around one another and cluster into spirals on a large scale.

### Energy

Given that two pillars wind around one another with pitch, p, and radius, r, the energy associated with a pair of winding pillars is just the sum of the adhesive energy and energy of deformation. <math>U\approx JaL\sqrt{1+\left(\frac{2\pi R}{p}\right)^2} + \frac{BL}{R^2}\left(1+\left(\frac{p}{2\pi R}\right)^2\right)^2</math> At the minimum, <math>\frac{B}{JaR^s}\approx \frac{\sqrt{1+\left(\frac{2\pi R}{p}\right)^2}}{\left(1+\left(\frac{p}{2\pi R}\right)^2\right)^2}</math>

If the bristles are hard, then this ratio is larger than one. The minimum then occurs as <math>p\rightarrow \infty</math>, which sends ratio towards unity. This corresponds with upright bristles, which comports with intuition.

On the other hand, for soft pillars, the ratio is already less than. The minimum here is achieved by having <math>R\rightarrow r</math>. This is physically achieved by two pillars wrapping around one another, or in the case of a cluster, spiraling.

## Results

The authors have shown here the schematic of the clustering of pillars in a helical shape. For this they used pillars that varied in length; L = 4 to 9 <math>\mu m</math> and of stiffness E = 0.1 to 2 GPa.

__Caption accompanying figure (also taken from paper)__- Fig. 2 (Figure 1 in paper). (A) Schematic diagrams and (B) corresponding scanning electron microscopy (SEM) images showing the morphogenesis of helical patterns, from the first-order unclustered nanobristle to the fourth-order coiled bundle. Scale bars, 4 <math>\mu m</math>. Note the hierarchical nature of the assembly reflected in the presence of the lower-order braids in the large clusters braided in a unique structure reminiscent of modern dreadlocks or mythical Medusa.

- Fig. 3 (Figure 2 in paper). Large-area self-organization of the bristle. (A) Schematic diagram showing the mechanism of the formation of the long-range order in the assembled bristle. See text for further details. (B) SEM image showing the assembly into uniform, periodic fourfold clusters of nanopillars over the submillimeter area. Note the different coherent domains that arise from the multiple nucleation sites. Scale bar, 20 <math>\mu m</math>.

The authors demonstrate here, the ability to control this process. Here, they chose pillars with a length appropriate to stop clustering at pairs and groups of four. At this level of clustering, they also following the lattice pattern of the bristle. In the opinion of the reviewer, the domains are reminiscent of a chemical etching process. To do this they used pillars of length <math>L = 5 \mu m</math> and of stiffness E = 1 GPa.

- Fig. 4 (Figure 3 in paper). Fig. 3. Hierarchical assembly into large coiled clusters. (A) SEM showing an array of pillars (L = 8 <math>\mu m</math>) self-organized from the ethanol solution into the level IV and V helical assemblies. (Inset) Magnified view of the coiled core. Scale bars, 3 <math>\mu m</math>. (B) Kinetics of the hierarchical assembly. The growth of one representative cluster is shown. The number of clusters was monitored by analyzing the consecutive images from movie S2. The cluster size is defined as the number of pillars in the bundle. The multistep, sequential coalescence of the small blocks into higher-order structures is apparent. The y axis denotes the number or size of clusters.

The authors show here the clustering on a large scale. The clustering isn't uniform and domains aren't as obvious as before. Also, the graph shows that the transition to large clusters from individual pillars and pairs is quick and dramatic.

## Control and Uses

### Clustering

As indicated by the differences between figures 3 and 4, it is possible to control the level of control by modulating the pillar length. Additionally, by changing the stiffness of the pillars it is also possible to change clustering for a given length.

### Handedness

For large clusters it is possible to change the direction of spiral, or the chirality. Some possible methods for doing this include. One way of changing the chirality is to use ellipsoidal pillars instead of circular pillars to bias the direction of buckling. Another way is pretilt the pillars to once again direct the buckling.

The authors also illustrate a third way of controlling the chirality, using directional evaporation. In Figure 5, the authors show the results of a bristle who evaporation is in a single direction. While this particular bristle didn't fully cluster (for unspecified reasons), the directionality is evident.

- Fig. 5 (Figure 4 in paper). Fig. 4. Controlling handedness and pattern of assembled structures. (A) Top and angled SEM views showing an array of ordered helical pairs with uniform handedness. (Inset) Schematic diagram that illustrates the substrate design. The bristles were first tilted in the direction that forms a small angle <math>\delta</math> with the principal diagonal direction of the underlying square lattice (shown by the red and black lines, respectively) and then allowed to assemble. (B) Evaporation along the surface results in the woven braids assembled parallel to the substrate. Scale bars, 2 <math>\mu m</math>.

### Applications

The authors suggest several applications for this technology and demonstrate some tentative success with one. The authors suggest:

- Biological adhesive
- Many adhesives in organisms are based on chirality. Perhaps this can this can behave similarly to a biological adhesive.

- Attaching arbitrary objects
- Attaching objects to surface is often a game of fitting a round peg in a square hole. This may be a way to manually clamp objects down.

- Mixing and transport
- These helical would like disrupt normal flow, perhaps even engendering vortices and more complicated flow patterns from fairly simple flow. This could be used for mixing and even transport if used correctly.

- Particle capturing/ Capture and release
- A particle in the middle of a group of pillars before clustering would be caught after evaporation. If a method of releasing the captured particles could be developed this could be useful in a host of multi-stage processes and applications. The authors show particle capturing and report that the hold is tight, surviving rigorous sonication.

- Fig. 6 (Figure 5 in paper). Illustration of the adhesive and particle trapping potential of the

helically assembling bristle. (A) Low-magnification SEM showing the capture of the 2.5-<math>\mu m</math> polystyrene spheres (indicated by arrows). Scale bar, 10 <math>\mu m</math>. (B) Magnified view depicting a single sphere trapped through the conformal wrapping of the nanobristle. Scale bar, 2 <math>\mu m</math>. (C) Coiled whirlpools remain after the removal of the spheres. Scale bar, 2 <math>\mu m</math>.

Naveen's comments: This work does seem to have many applications. Does anyone have any ideas how to reverse the process so that particles could be released, etc.?