3D assembly of Janus spheres: potentials, dynamics, and experiments

Figures & data

Figure 1. Point potentials used in JP assembly studies, detailed in supplementary material, table S1. (a) Typical geometric definitions for point potentials. Reproduced with permission from [81], conveyed through Copyright Clearance Center, Inc. (b) Radial variation of contributions to potentials. (c) Angular variation of contributions to potentials. Calculations use specific values from corresponding KF [82] (potential form $\mathit{Vf}({\theta }_i)\mathit{f}({\theta }_j)$, λ = 1.5, $\mathit{\beta }={90}^{\circ }$), LJ [83] ($V_R+V_A{f}_A({\theta }_i)f_A({\theta }_j)$, ${\theta }_{\mathit{tail}}={10}^{\circ }$, $\mathit{\beta }={90}^{\circ }$), Yukawa [77] ($V_R+V_A{f}_A({\theta }_i,{\theta }_j)$, $C_1=\mathit{ϵ}$, λ = 3, ${\theta }_j=0$) and DLVO [84] ($V_R{f}_R({\theta }_i)f_R({\theta }_j)+V_A{f}_A({\theta }_i)f_A({\theta }_j)$, $C_2=\mathit{ϵ}$, ${\lambda }_D=\mathit{\sigma }/100$, λ = 1.05, ρ₁ = 1, ${\rho }_2=-1$) studies. Values for C₁ and C₂ are defined here arbitrarily, and for Hong et al.’s model [84] note that $f_R(\mathit{\theta })=0$ when $\mathit{r}>\mathit{\lambda \sigma }$ and hydrophobic sides are facing.

Figure 2. (a) Examples of JP clusters simulated using a LJ point potential. From left to right with increasing β: small micelles (4–13 particles), branched worm-like aggregates, and fluid amorphous aggregates. Reproduced with permission from [83], copyright (2009) by the American Physical Society. (b) Examples of n-particle clusters simulated using a Yukawa-like potential. Reproduced with permission from [77], AIP Publishing. (c) Staged assembly strategies using triblock patchy particles, simulated using a hydrophobic/charged point potential. Reproduced with permission from [50], copyright (2018) by the American Chemical Society.

Figure 3. (a) Rings and strings formed by 60-site coulombic JPs. Reproduced with permission from [106], conveyed through Copyright Clearance Center, Inc. (b) Multi-site LJ JPs in MD simulations of a dimer, showing (left to right) the geometric setup, the probability distribution for polar angles with examples of specific configurations labelled (i)–(iii), and comparison between MD and numerical integration (NI) occurrence probability results. Reproduced with permission from [107], copyright (2021) by the American Physical Society. (c) A 72-vertex multi-site JP structure, reproduced with permission from [108], with the permission of AIP Publishing. (d) Multi-site JP with radius 3σ and $\mathit{\beta }={90}^{\circ }$. Reproduced with permission from [109], copyright (2020) American Chemical Society. (e) Geometry (left) and potential landscape (right) for calculations of Coulombic interactions between JPs with 12,002 sites. Reproduced with permission from [110], copyright (2006) American Chemical Society.

Figure 4. (a) Diagrams of floppy bonds for triblock JPs in 2D. Any ‘bond angle’ is allowed if patches are in contact (top). The hexagonal close packed (middle) and the open Kagome lattice (bottom) structures are isoenergetic, and both have 120^∘ bond angles. Reproduced with permission from [138]. (b) Critical shear rate required to break up a single cluster for three interactions strength values C, and for an isotropic hydrophobic case, $C_{\mathit{iso}}=4$. Reproduced with permission from [102], conveyed through Copyright Clearance Center, Inc. (c) Kinked Janus clusters with different chirality emerge in a shear flow. Adapted with permission from [97], copyright (2016) American Chemical Society. (d) Simulated JP structures projected onto the plane of a shear gradient, with colouring indicating the size of each cluster. The shear increases with Peclet number (Pe) from left to right. Reproduced with permission from [98], conveyed through Copyright Clearance Center, Inc.

Figure 5. (a) Suggested transitions between isomers consisting of 7 fluorescent amphiphilic 1 µm polystyrene JPs (above), consistent with MC-simulated structures (below). Reproduced with permission from [84], copyright (2008) American Chemical Society. (b) Three types of bonding geometries identified between small clusters of 1 µm triblock JPs, along with the measured occurrence probability (P${}_{\mathit{i},\mathit{N}}$) of these geometries for 4-particle clusters. Adapted with permission from [121], copyright (2012) American Chemical Society. (c) Histogram of kink angles (left) obtained from images of polystyrene ~ 2 µm bipolar JPs (right), scale bar 20 µm. Reproduced with permission from [103], conveyed through Copyright Clearance Center, Inc. (d) Optical images of DNA-patch JPs at two different temperatures (scale bar 10 µm), and the corresponding cluster size distributions where ϵ is the depth of the attractive potential in simulations giving closest agreement. Adapted with permission from [99]. (e) ‘Rafts’ of DNA patches on polymer colloid surfaces selectively bind to their conjugate, allowing chains of alternating colloids to form. Reproduced with permission from [150], copyright 2018 National Academy of Sciences.

Figure 6. Experimental visualisations of JP orientations. (a) Clusters formed via a drying process from 3 µm silica JPs with Au-coated thiolated hemispheres (scale bar 10 µm) along with statistics for the out-of-plane angle θ. Reproduced with permission from [162], conveyed through Copyright Clearance Center, Inc. (b) 2D visualisation of 1.5 µm silica JPs, with scale bars 10 µm (main image) and 2 µm (inset). Reproduced with permission from [163], conveyed through Copyright Clearance Center, Inc. (c) Time sequence showing changes in orientation for two approaching Ni-coated 3 µm silica JPs in a precessing magnetic field, with scale bar 2 µm. Reproduced with permission from [164]. (d) Au-coated 20 µm fluorescent latex JPs in an electric field, with scale bar 2 µm. The field polarity is reversed between the top and bottom images. Reproduced with permission from [165], copyright (1997) American Chemical Society.

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