Evaporation-Driven Assembly of Colloidal Particles

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Wiki entry by Emily Gehrels, Fall 2012

Based on the article: Lauga, E., Brenner, M.P. (2004). Evaporation-Driven Assembly of Colloidal Particles. Physical Review Letters, 93, 238301.

Background

Vinny Manoharan wrote a paper describing how clusters of small (d=844nm) polystyrene spheres could be formed in reproducible configurations by dispersing them in a toluene-water emulsion and then preferentially evaporating the toluene. The geometries that formed minimized the second moment of the cluster as defined by <math>\mathcal{M}=\sum_{i}||r_i-r_o||^2</math>. This paper examines the theoretical basis for these findings.

Theories and Simulations

For a droplet with particles attached to the surface, the particles arrange themselves in such a way to minimize the total surface energy between the particles and the drop, the drop and the surrounding medium and the particle and the surrounding medium. A program (Brakke's Surface Evolver) was used to simulate the equilibrium positions of particles in a droplet. The system was initialized with a certain number of particles positioned randomly on the droplet and then the volume of the drop was slowly decreased in steps. At each step the particles were moved to the positions that minimized the energy. The final packings (when the dop volume went to zero) in the simulation agreed with the experimentally observed results as seen in the figure below.

Wiki4 Figure2.jpg

Results and Conclusions