Assembly of open clusters of colloidal dumbbells via droplet evaporation

We investigate the behavior of a mixture of asymmetric colloidal dumbbells and emulsion droplets by means of kinetic Monte Carlo simulations. The evaporation of the droplets and the competition between droplet-colloid attraction and colloid-colloid interactions lead to the formation of clusters built up of colloid aggregates with both closed and open structures. We find that stable packings and hence complex colloidal structures can be obtained by changing the relative size of the colloidal spheres and/or their interfacial tension with the droplets.

Figure 1

Sketch of the model of colloidal dumbbells (bright yellow and dark red spheres) and droplets (white spheres). Shown are the diameters of colloidal species 1, ${\sigma }_1$, colloidal species 2, ${\sigma }_2$, and droplet ${\sigma }_d$. (a) In the initial stages the droplet captures the colloidal dumbbells. (b) The droplet has shrunk and has pulled the dumbbells into a cluster. The competition between Yukawa repulsion and surface adsorption energies can lead to open cluster structures.

Figure 2

Sketch of the pair interactions: (a) potentials between two colloidal particles with ${\epsilon }_{\mathrm{SW}}=9k_{\mathrm{B}}T, \mathrm{\Delta }=0.09{\sigma }_2, {\epsilon }_{\mathrm{Y}}=24.6k_{\mathrm{B}}T$ and (b) colloid-droplet potential at ${\sigma }_d\left(t\right)=4{\sigma }_2$, with ${\sigma }_1=1.2{\sigma }_2$.

Figure 3

Snapshots of the simulation for colloidal dumbbells with symmetric sizes and droplets at the energy ratio $k=0.1$. Results are shown at two different stages of the time evolution: (a) after $2.5\times {10}^5$ MC cycles several colloidal dumbbells (bright yellow and dark red spheres) are trapped at the surface of the droplets (gray spheres); and (b) after ${10}^6$ MC cycles the stable clusters that are formed due to the droplets are composed of different colored colloids, that is, blue and green spheres represent colloidal species 1 and colloidal species 2, respectively. Open cluster structures with a compact core by colloid 1 and protruding arms by colloid 2 can be observed.

Figure 4

Radial distribution functions, $g_{i\mathrm{d}}\left(r\right)$ ($i=1,2$), for colloid 1–droplet (solid lines) and colloid 2–droplet (dashed lines) as a function of the scaled distance $r/\sigma$ at energy ratio $k=0.1$. Shown are results at different stages of the computer simulation. (See the notation in Table 1.)

Figure 5

Colloid 1–droplet (a) and colloid 2–droplet (b) radial distribution functions, $g_{1\mathrm{d}}\left(r\right)$ and $g_{2\mathrm{d}}\left(r\right)$, respectively, as a function of the scaled distance $r/\sigma$ after $t=t_6$ ($4.0\times {10}^5$ MC cycles). Results are shown for different energy ratios $k$. An asterisk is used as a guide to the eyes to trace the shift of the second peak. Curves are shifted upwards by 40 units for clarity.

Figure 6

Typical cluster structures found in simulations for (a) $k=0.1$, (b) $k=0.5$, and (c) $k=1$ at the final stage of the simulations. The red- and yellow-colored spheres represent colloid-1 and colloid-2 spheres in each dumbbell, respectively. For each cluster with the same number of constituent colloids the bond number $n_b$ is used to distinguish whether a cluster is an open or closed structure. The wire frame connecting the colloid centers represents the bond skeleton.

Figure 7

Distribution of the number of clusters $N_{n_c}$ as a function of the number of colloids $n_c$ in the cluster in the final stage of simulation. Results are shown for different energy ratios (a) $k=0.1$, (b) $k=0.5$, and (c) $k=1$ at ${\sigma }_1={\sigma }_2\equiv \sigma$ and ${\gamma }_1=100k_{\mathrm{B}}T/{\sigma }^2$. The colored region is labeled with the bond number $n_b$.

Figure 8

Distribution of the number of clusters $N_{n_c}$ as a function of the number of colloids $n_c$ in the cluster in the final stage of simulation. Results are for different interfacial tensions as indicated (a), (d) $\gamma =10k_{B}T/{\sigma }_2^2$; (b), (e) $\gamma =40k_{B}T/{\sigma }_2^2$; and (c), (f) $\gamma =100k_{B}T/{\sigma }_2^2$ at ${\sigma }_1=1.5{\sigma }_2$ and ${\sigma }_1=2.0{\sigma }_2$, respectively. The numerical label in differently colored regions indicates the bond number $n_b$.