Abstract
The minimization principle of the second moment of the mass distribution () is responsible for the unique structure of three-dimensional clusters by using emulsion droplet evaporation. Herein we study the structure of two-dimensional clusters of colloidal particles bound at the interface of liquid droplets in the plane. We found that, differently from the three-dimensional system, the two-dimensional clusters have multiple degenerate configurations (isomers). An interesting feature of such two-dimensional clusters is that they have the same packings as those belonging to a class of geometric figures known as polyiamonds. In particular, except for the six-particle cluster, many higher order clusters of polyiamond have not been reported previously. Using a simple geometrical approach, based on the number of ways to generate a packing, we calculated the occupation probabilities of distinct isomeric clusters. The level of agreement with the results of metropolis Monte Carlo simulations was good for clusters containing up to nine particles, suggesting that our two-dimensional cluster structures are not a result of the minimization of the second moment. In addition, the structure of these clusters is somewhat insensitive to the range and depth of the interparticle potential, in good agreement with the results in the literature.
Highlights
The formation dynamics and structures of colloidal clusters have been extensively studied because of their important role in a variety of applications, such as sensors, plasmonics and photonic crystals [1,2,3]
Manoharan et al [6] developed an assembling route based on the use of emulsion droplets as a three-dimensional (3D) template to obtain identical colloidal clusters with high yields
We suggest that the known ground state clusters for systems of particles interacting through the weak depletion interaction [20] are relevant to colloidal clusters assisted by evaporating emulsion droplets
Summary
The formation dynamics and structures of colloidal clusters have been extensively studied because of their important role in a variety of applications, such as sensors, plasmonics and photonic crystals [1,2,3]. Manoharan et al [6] developed an assembling route based on the use of emulsion droplets as a three-dimensional (3D) template to obtain identical colloidal clusters with high yields. Following the pioneering work of Manoharan and coworkers [6], numerous studies based on emulsion droplet evaporation have been performed Some of these focused on different types of materials/solvents [7,8,9,10], others on submicron-sized particles [11,12,13] and others still on clusters with large sizes [14,15]. The structures and occurrence probabilities of small clusters of colloidal particles assembled in the spherical confinement of emulsion droplets are analyzed.
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