Self-Assembly in an Experimentally Realistic Model of Lobed Patchy Colloids

Abstract

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.

Keywords: Langevin dynamics; Self-assembly; lobed colloids; polydispersity; porosity.

Figure 1

(A) A schematic showing three different types (dumbbell, trigonal planar and tetrahedral) of lobed patchy colloids investigated in this work. (B) A schematic of the dumbbell particle showing the minimum (the right-side lobe) and the maximum (the left-side lobe) lobe size spanning six different values of σ_G. (C) The Gaussian distribution used in sampling the lobe size is shown. The distribution is truncated at the minimum and the maximum allowed values.

Figure 2

State diagrams showing the self-assembled phases exhibited by the (A) dumbbell, (B) trigonal planar, and (C) tetrahedral lobed particles at various conditions of reduced temperature (T*) and polydispersity (σ_G).

Figure 3

Self-assembly of the DB particles at T* = 0.2. Shown are snapshots of the interconnected networks at (A) σ_G = 0.1 and (B) σ_G = 0.5. The traces from the quantitative analyses for the DB system at T* = 0.2 and for all values of σ_G are also shown: (C) RDF, (D) P(θ_jik), and (E) P().

Figure 4

Self-assembly of the DB particles at T* = 0.8. (A) Shown is the snapshot of a disordered gaseous state for σ_G = 0.1 and (B) the snapshot of a crystalline structure for σ_G = 0.5, where the inset shows the top view of the crystal structure. For T* = 0.8, the traces of various metrics similar to Figure 3 for all values of σ_G are shown (C) RDF, (D) P(θ_jik), and (E) P().

Figure 5

Self-assembly of the TP particles at T* = 0.4. (A) Shown is a snapshot of the elongated clusters with a local structure of two-dimensional sheets for σ_G = 0.1. The inset shows the microstructure of a typical two-dimensional sheet. The particles forming the hexagonal arrangement around a locus particle are depicted. (B) A snapshot of the elongated clusters for σ_G = 0.5. Shown are the traces of the quantitative metrics computed for the TP system at T* = 0.4, for all values of σ_G: (C) RDF, (D) P(θ_jik), (E) P(), and the lobe-size and bond distributions for (F) σ_G = 0.1 and (G) σ_G = 0.5.

Figure 6

Self-assembly of the TH particles into crystalline structures at T* = 1.0. (A) Shown is a snapshot of the compact three-dimensional crystal for σ_G = 0.1, where the inset shows the ordered structure. (B) Shown is a less compact crystalline structure for σ_G = 0.5, where the inset shows the top view of the crystal. Shown are the traces of the quantitative metrics computed for the TH system at T* = 1.0 for all values of σ_G: (C) RDF, (D) P(θ_jik), and (E) P().