# Difference between revisions of "Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry"

Original Entry: Aaron Goldfain, AP 225, Fall 2012

(UNDER CONSTRUCTION)

## General Information

Author: Vinothan N. Manoharan

Publication: Vinothan Manoharan. Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry. Solid State Communications (2006) vol. 139 (11-12) pp. 557-561

Keywords: diffusion, colloids, emulsion, interface, self-assembly

## Summary

Figure 1, taken from [1].
Figure 1, taken from [1].

This paper describes the self-assembly of colloidal aggregates within water and oil emulsions. It summarizes and categorizes the experiments performed by others. In general, for the experiments discussed, micrometer sized colloids are dispersed in emulsions composed of spherical droplets of controlled sizes, ranging from a few micrometers to a millimeter in diameter. Different preparation methods and droplets sizes were shown to produce three types of structures; colloidosomes (Pickering Emulsions), colloidal clusters, and supraparticles.

The interactions between the colloids and the oil-water interface, interactions between colloids, and the thermal energy of the system determine what structures are formed. The energy of colloid-interface interaction is described by a 3 phase contact line between the colloid, oil, and water. Using different types of colloids, colloid functionaliziations, and surfactants in the liquids enables the experimenters to tune this interaction energy to range from $10^4kT$ to $<<kT$. The interactions between colloids depend on the colloids themselves. Such interactions can be short ranged steric if the colloids are coated in polymer chains, or long ranged if the colloids are coated in charged group. The strength of these interactions can be readily tuned by changing how the colloids are functionalized and what salts and surfactants are in the water and oil. However, the functional form of the energy of colloid groups is not well established.

Colloidalsomes are formed when the colloids bind to the spherical interfaces in the emulsion. Accordingly, the colloids form structures where each colloid is on the surface of a sphere. These structures are formed when the binding energy to the interface is much larger than $kT$. At high colloid concentrations, the colloids close-pack around the interface in configurations independent of the inter-colloid interaction form. The colloids form a hexagonal lattice, but with defects due to the curvature of the droplets. At low concentrations, when the area of colloids in the sphere is small compared to the sphere's surface area, the equilibrium configuration depends on the functional form of the inter-colloid interaction energy. Since this potential is not well characterized, precise configurations cannot be predicted. The 12 particle, icosahedron configuration shown in Figure 1, however can be described by an $r^{-p}$ potential where $r$ is the distance between two colloids and $p$ is either $1$ or $\infty$.

Colloidal clusters are formed by removing the liquid from the inside of a low density colloidalsome. The liquid can either be removed by evaporating the inner liquid or having it diffuse out to a lower pressure container. As the colloidalsome shrinks, the colloids remain adsorbed to the interface until they are in contact and become bound by Van der Waals forces. Geometrical arguments dictate that clusters with fewer than 19 colloids are unique, and clusters of greater numbers can be simulated using a linear interaction force. Clusters with fewer than 15 colloids have been experimentally examined and agree with the geometrical arguments, but larger colloidal clusters have not been tested. Some interesting images of clusters are shown in Figure 2.

Supraparticles

Discussion here

## References

[1] Vinothan Manoharan. Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry. Solid State Communications (2006) vol. 139 (11-12) pp. 557-561