# Mesoscale Self-Assembly of Hexagonal Plates Using Lateral Capillary Forces: Synthesis Using the “Capillary Bond”

## Overview

Reference:

• [1] Bowden, N., Choi, I.S., Grzybowski, B.A., & Whitesides, G.M. J. Am Chem. Soc. 121, 5373-5391 (1999).

Keywords: Self-Assembly, Capillary Forces, Hydrophobic / Hydrophilic, Meniscus, Mesoscale

## Summary

Bowden, Choi, Grzybowski, and Whitesides took advantage of capillary forces to induce mesoscale self-assembly of millimeter-sized hexagons. This example of self-assembly is particularly innovative because most other instances of self-assembly are on the molecular scale.

Bowden et. al. studied hexagonal pieces (1.2 mm by 5.4 mm) of solid PDMS floating on top of perfluorodecalin (PFD) and covered with a layer of water. PDMS has a density between that of PFD and water, so the hexagons stayed at the interface between the two liquids. The researchers chose to use PFD and water in part for their "high" interfacial energy with each other $\left(\gamma=.05 \frac{J}{m^2}\right)$ which led to strong capillary forces. The controlled variable in this experiment was the number of hydrophobic edges on the hexagons. PDMS is naturally hydrophobic, but the researchers oxidized certain edges and one face of each hexagon to make these areas hydrophilic. This study compares all fourteen different ways of combining hydrophilic and hydrophobic edges on hexagons (see figure below).

Shown are all fourteen ways to combine hydrophobic and hydrophilic edges on a hexagon. (thick lines=hydrophobic, thin lines=hydrophilic) The bracketed numbers under each hexagon indicate which of the six faces are hydrophobic. Fig. 2 from [1]

After fabricating a set of matching hexagons, the researchers placed the hexagons at the interface. The scientists then shook the container with an orbital shaker and studied the resulting self-assembled arrangements of hexagons. Here are a couple examples of array patterns they observed:

• Hexagons with six hydrophilic edges or six hydrophobic edges assembled into tightly-packed arrays. Each edge in the interior of an array touches another edge.
• Hexagons with only one hydrophobic edge formed dimers. The hydrophobic edges paired up with each other.
• Hexagons with two adjacent hydrophobic edges assembled into trimers.
• A honeycomb array assembles from hexagons with alternating hydrophobic and hydrophilic edges (see image a below).
Honeycomb arrays formed by hexagons with three hydrophilic edges and three hydrophobic edges. Fig. 12 from [1]

As one can see, modifying the surface properties of the PDMS pieces leads to a variety of different self-assembled arrays. In addition to varying the configuration of surface-modified edges, Bowden et. al. also varied the thickness of the hexagons, the densities of the water and PDMS by adding potassium bromide and iron oxide respectively, and the fraction of an edge that was oxidized. The article also delves into the effect of hexagons which do not float levelly, but rather tip to one side because of asymmetrical capillary forces.

## Soft Matter Details

Mesoscale/Length Scale: The mesoscale is an interesting length scale at which the approaches to soft matter may be particularly applicable. The authors write that "a mesoscopic object is one whose dimensions are comparable to the characteristic length of a phenomenon being examined [1, p. 5374]." In soft matter, we look at length scales to determine the relevancy of competing forces. Finding a situation where an object's length is on the same order of magnitude as a phenomenon's length scale may be a good way to find interesting problems. In the hexagon experiments, using hexagons with dimensions on the scale of the meniscus certainly led to interesting self-assembly behavior.

The authors also state that a mesoscopic object is of "a size qualitatively intermediate between small (molecular) and large (easily manipulated by conventional means) [1, p. 5374]. Because mesoscopic objects are hard to assemble by conventional means, self-assembly is an attractive process to investigate at the mesoscale.

Self-assembly, Energy on order of energy fluctuations: Right in the introduction of the paper, the authors address the analogous energy scales for molecular and mesoscale self-assembly; the forces of non-covalent bonds organizing molecules into self-assembled structures are on the order of forces from collisions due to Brownian motion, while the capillary forces assembling the hexagons are on the same scale as forces from the orbital shaker. The forces from Brownian Motion and from the orbital shaker can help instigate self-assembly by randomly bringing components close to each other, but can also break up aggregates.

Capillary Forces/Capillary Bond: The forces bringing the hexagons together originate from the minimization of the surface area of the PFD/water interface. The liquid interactions with the edges of the hexagons create menisci which increase the surface area. Rearrangement of the hexagons can minimize the additional meniscus surface area. The summary of Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range is a good source for a description of the attractive and repulsive capillary forces between floating objects. For another demonstration of capillary forces at work, one may observe the aggregation of a few Cheerios floating in a bowl of milk (The ‘Cheerios Effect’).