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Self-assembly of colloidal particles is emerging as a promising approach for producing novel materials. These colloidal particles can be synthesized with protrusions (lobes) on their surfaces that allow the formation of porous structures with a wide range of applications. Using Langevin dynamics simulations, we studied self-assembly in the binary mixtures of lobed colloidal particles with variations in their lobe sizes to investigate the feasibility of using dumbbell particles (with two lobes) as cross-linkers to increase the porosity in self-assembled morphologies. Each binary system was formed by mixing the dumbbell particles with one of the following types of particles: trigonal planar (three lobes), tetrahedral (four lobes), trigonal bipyramidal (five lobes), and octahedral (six lobes). We observed that the lobe size on each particle can be tuned to favor the formation of random aggregates and spherical aggregates when the lobes are larger and well-ordered crystalline structures when the lobes are smaller. We also observed that these polydisperse systems form self-assembled structures characterized by porosities higher than those of the structures formed by the monodisperse systems. These results indicate that the lobe size is an important design feature that can be optimized to achieve desired structures with distinct morphologies and porosities, and the dumbbell particles are effective cross-linking agents to enhance the porosity in self-assembled structures. 

Colloids with lobed architectures have been shown to self-assemble into promising porous structures with potential biomedical applications. The synthesis of these colloids via experiments can be tuned to vary the number and the position of the lobes. However, the polydispersity involving the numbers, sizes, and the dispositions of lobes, that is often observed in particle designs, can significantly affect their self-assembled structures. In this work, we go beyond the uniform lobe size conditions commonly considered in molecular simulations, and probe the effect of polydispersity due to non-uniform lobe sizes by studying self-assembly in three experimentally observable designs of lobed particles (dumbbell, two lobes; trigonal planar, three lobes; and tetrahedral, four lobes), using coarse-grained Langevin dynamics simulations in the NVT ensemble. With increasing polydispersity, we observed the formation of a crystalline structure from a disordered state for the dumbbell system, and a loss of order in the crystalline structures for the trigonal planar system. The tetrahedral system retained a crystalline structure with only a minor loss in compactness. We observed that the effect of polydispersity on the self-assembled morphology of a given system can be minimized by increasing the number of lobes. The polydispersity in the lobe size may also be useful in tuning self-assemblies toward desired structures. 

We report coarse-grained Langevin dynamics simulations of homogeneous mixtures of lobed colloidal particles with opposite charges. We show that dumbbell, trigonal planar, tetrahedral, square planar, trigonal bipyramidal, and octahedral shaped particles form distinct self-assemblies including chains, sheets, crystalline, and spherical structures. The dumbbell and square planar particles predominantly form chains and sheets while other particles form network-like self-assembled morphologies. At higher temperatures and lower charges, non-planar particles form three-dimensional aggregates. We further report on packing arrangements of particles which lead to differences in porosities within self-assembled morphologies. Our results show that the trigonal planar particles form larger porous structures. The self-assembled structures that we report are potentially useful in designing porous biomaterials for biomedical applications. 

Colloidal particles fabricated with anisotropic interactions have emerged as building blocks for designing materials with various nanotechnological applications. We used coarse-grained Langevin dynamics simulations to probe the morphologies of self-assembled structures formed by lobed particles decorated with functional groups. We tuned the interactions between the functional groups to investigate their effect on the porosity of self-assembled structures formed by lobed particles with different shapes (snowman, dumbbell, trigonal planar, tetrahedral, square planar, trigonal bipyramidal, and octahedral) at different temperatures. The dumbbell, trigonal planar, and square planar shaped particles, with planar geometries, form self-assembled structures including elongated chains, honeycomb sheets, and square sheets, respectively. The particles with non-planar geometries (tetrahedral, trigonal bipyramidal, and octahedral) self-assemble into random aggregate morphologies. The structures formed by trigonal bipyramidal and octahedral particles exhibit smaller and homogeneous pores compared to the structures formed by trigonal planar and square planar particles. The porosity in self-assembled structures is substantially enhanced by the functionalization of particles. 

Entropy plays a key role in the self-assembly of colloidal particles. Specifically, in the case of hard particles, which do not interact or overlap with each other during the process of self-assembly, the free energy is minimized due to an increase in the entropy of the system. Understanding the contribution of entropy and engineering it is increasingly becoming central to modern colloidal self-assembly research, because the entropy serves as a guide to design a wide variety of self-assembled structures for many technological and biomedical applications. In this work, we highlight the importance of entropy in different theoretical and experimental self-assembly studies. We discuss the role of shape entropy and depletion interactions in colloidal self-assembly. We also highlight the effect of entropy in the formation of open and closed crystalline structures, as well as describe recent advances in engineering entropy to achieve targeted self-assembled structures.