# Difference between revisions of "Phase Behavior and Structure of a New Colloidal Model System of Bowl-Shaped Particles"

Entry by Pichet Adstamongkonkul, AP 225, Fall 2011

Work in progress

Reference:

Title: Phase Behavior and Structure of a New Colloidal Model System of Bowl-Shaped Particles

Authors: Matthieu Marechal, Rob J. Kortschot, Ahmet Faik Demirors, Arnout Imhof, and Marjolein Dijkstra

Journal: Nano Letters, 2010, Vol. 10, No. 5

## Summary

This paper investigated the structural organization of the bowl-shaped particles, which may have many possible applications such as nanocontainers, coatings due to the aggregation behavior of the particles, and perhaps in the field of sensors and shape-memory materials. The bowl-shaped particles appear to form stacks in the wormlike phase or columnar and other ordered structures, depending on many factors, including the particle dimensions, densities, sedimentation, free energy of crystal structures, and packing fraction. In addition, the authors also tried to capture the important features of the phase behaviors of the particles by implementing a computer simulation model, which was shown to support the experimental observations that these particles have a strong tendency to form bent, non-aligned stacks. The calculations also suggested that the wormlike phase is not the equilibrium state of the system and the columnar phase is more thermodynamically stable for deep nanobowls and at high densities. Lastly, this study also proposed a phase diagram, in which the phase behavior changes depending on the dimensions and the packing fractions of these particles, which may have some benefits in designing the particles of this kind for other applications.

## Methodology

The first step in the synthesis of these bowl-shaped particles is the preparation of uniform oil-in-water emulsion droplets of silicone via the hydrolysis and polymerization of the precursor, dimethyldiethoxysilane. The droplets are then coated with a solid shell of tunable thickness of tetraethoxysilane. The silicone inside is then dissolved by ethanol. During the drying step in air, the shells collapse inside, resulting in hemispherical double-walled bowls.

The model used in the computer simulation viewed a particle as the solid of revolution of a crescent. The shape parameter was defined by a reduced thickness, $D/\sigma$, when D is the thickness of the bowl measured from the bottom of the bowl to the top, and $\sigma$ is the diameter of the bowl. This can be easily visualized, as this quantity equals to 0 in the infinitely thin hemispherical surfaces, and it equals to 0.5 in solid hemispheres. This model then captured the continuous range of shapes of the particles.

The colloidal particles were then suspended in an index-matched mixture of dimethylsulfoxide and ethanol and the suspension were allowed to sediment, and their macroscopic structures were studied and implemented by the computer simulation.

## Results and Discussion

From the experiment, the authors found that, after the particles underwent sedimentation, they slowly compacted and formed stacks throughout the sample. The formed stacks were found to be up to 10 particles lining up in random directions. The stacks were not straight, however, but rather were bent and bifurcated by forming Y-shaped junctions. The process slowed down as the density at the bottom of the sample increased significantly from the sedimentation. This prevented further ordering of the particles in order to get to thermodynamic stability. The computer simulation also suggested that density increases smoothly with pressure during the stack formation corresponding to a continuous transition from a low-density fluid with few stacks to a high-density fluid with wormlike stacks whose lengths increases with the pressure. The authors also found that the average stack length increases significantly as the reduced thickness quantity decreases. This makes sense because the deeper bowls will be able to stack and form longer wormlike structure than the shallower ones. This agreed with the experimental data.

At certain values of the reduced thickness, the system transforms into a columnar phase, according to the simulation. This follows the fact that isotropic-to-columnar transition occurs at lower packing fractions for deeper bowls, whose shape normally facilitates the stack formation. By simulating a system of 2-6 particles using Monte Carlo algorithm, final configuration could be obtained and used as the unit cell of a potential crystal structure. The resulting four different stable crystal phases were found and represented in a phase diagram as the packing fraction $\phi$ and the reduced thickness were being varied.

Each crystal phase are described below:

• Invert crystal (IX)
• Particles are stacked in columns, with half of columns flipped upside down and the rims of the bowls interdigitate.
• Columns are all aligned
• Inverted braid-like crystal (IB)
• Particles are stacked in columns, with half of columns flipped upside down and the rims of the bowls interdigitate.
• Columns are like braids with alternating, tilted particles within each column.
• Solid hemispheres - two stable crystal structures
• (IX')
• Sheared version of IX, with alternating orientation of particles, not organized in columns
• Paired face-centered-cubic ($fcc^2$)
• Pairs of hemispheres join together, completing the spheres, which can rotate freely on the lattice positions.
• The coexistence between fluid and $fcc^2$ packing fractions is very similar to that between fluid and fcc packing fractions of the hard spheres, clearly indicating the similarity of the resulting crystals.

It was also found that the columnar phase of particles pointing in the same direction is more stable than that of particles with half of the columns flipped. Nonetheless, the polar ordering is not expected to occur spontaneously, due to the small free energy difference between the two phases, which is in the order of $0.01k_BT$.