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

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.

Figure S1: A schematic depicting the angle (θ jik ) used in defining the relative neighbor orientation.For a reference particle i, having two nearest neighbors j and k, located at the distances ⃗ r ij and ⃗ r ik respectively, θ jik gives the relative arrangement of the particles j and k with respect to the particle i.

Figure S2 :
Figure S2: Data for the dumbbell (DB) system at T * = 0.2 (panels A, B, and C) and T * = 0.8 (panels D, E, and F).Shown are the distributions of the probability of the lobes of a particular size for forming a specific number of bonds (N lobe b ) at three different values of standard deviation (σ G = 0.1, 0.3, and 0.5).

Figure S3 :
Figure S3: Data for the DB system at T * = 0.4.Shown are the traces from the quantitative analyses for all values of σ G : (A) RDF, (B) P(θ jik ), (C) P(N lobe b ), and (D-F) the lobe-size and bond distributions for three different values of standard deviation (σ G = 0.1, 0.3, and 0.5).

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Figure S4: (A-F) Data similar to Figure S3 are shown for the DB system at T * = 0.6.

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Figure S5: (A-F) Data similar to Figure S3 are shown for the DB system at T * = 1.0.

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Figure S7: A comparison of results between multiple runs of the DB system at T * = 0.2 and ϕ = 0.1.Shown are the RDF traces for (A) run1, (B) run2, and P(N lobe b ) traces for (C) run1, (D) run2.

Figure S8 :
Figure S8: Self-assembly of the TP particles at T * = 0.2.Shown are the snapshots of the interconnected networks observed for different conditions of σ G : (A) σ G = 0.1, and (B) σ G = 0.5.

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Figure S9: (A-F) Data similar to Figure S3 are shown for the TP system at T * = 0.2.

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Figure S10: (A-C) Data similar to Figure S2 are shown for the TP system at T * = 0.4.

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Figure S11: (A-F) Data similar to Figure S3 are shown for the TP system at T * = 0.6.

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Figure S12: (A-F) Data similar to Figure S3 are shown for the TP system at T * = 0.8.

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Figure S13: (A-F) Data similar to Figure S3 are shown for the TP system at T * = 1.0.

Figure S14 :
Figure S14: Self-assembly of the TH particles at T * = 0.2.Shown are the snapshots of the interconnected networks observed for different conditions of σ G : (A) σ G = 0.1, and (B) σ G = 0.5.

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Figure S15: (A-F) Data similar to Figure S3 are shown for the TH system at T * = 0.2.

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Figure S16: (A-F) Data similar to Figure S3 are shown for the TH system at T * = 0.4.

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Figure S17: (A-F) Data similar to Figure S3 are shown for the TH system at T * = 0.6.

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Figure S18: (A-F) Data similar to Figure S3 are shown for the TH system at T * = 0.8.

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Figure S19: (A-C) Data similar to Figure S2 are shown for the TH system at T * = 1.0.

Figure S20 :
Figure S20: Shown are data on the pore size distributions for three lobed particle systems at different conditions of T * : (A) DB at T * = 0.6, (B) TP at T * = 0.8, and (C) TH at T * = 1.0.