Entropy-Mediated Patterning of Surfactant-Coated Nanoparticles and Surfaces

We perform atomistic and mesoscale simulations to explain the origin of experimentally observed stripelike patterns formed by immiscible ligands coadsorbed on the surfaces of gold and silver nanoparticles. We show that when the conformational entropy gained via this morphology is sufficient, microphase-separated stripelike patterns form. When the entropic gain is not sufficient, we instead predict bulk phase-separated Janus particles. We also show corroborating experimental results that confirm our simulational predictions that stripes form on flat surfaces as well as on curved nanoparticle surfaces.

Figure 1

(a),(b) $\mathrm{C}4:\mathrm{C}6$ surfactant mixture of SAMs from atomistic simulations and experiments (STM images), respectively. The tail end-groups are identical, but the lengths differ. (c),(d) Dodecanethiol/Mercaptoundecanoic acid ($\mathrm{C}11:\mathrm{C}12$) surfactant mixture of SAMs from atomistic simulations and experiment (STM images), respectively. Here the tail end-groups differ somewhat in size and the tail lengths are nearly identical. (e) Atomistic simulation of mixture of equal-length ($\mathrm{C}3:\mathrm{C}3$) surfactants, with different tail end-groups. For atomistic snapshots, dark (blue) and light (yellow) beads are head groups of surfactants that are short (or contain -COOH) and long (or contain $\mathrm{\text{−}}{\mathrm{CH}}_3$), respectively. In all cases, the head groups (-SH) are identical. (f) Variation of stripe width with the length of long surfactant in number of carbon atoms. The same trend is seen when stripe width is plotted against short surfactant length. The atomistic simulation data points are for equal-length surfactants.

Figure 2

(a),(b) Schematic two-dimensional representation of shared free volume (conical shaded area) available to surfactant tails when they are surrounded by other surfactants on curved surfaces, for equal-length and unequal-length surfactants, respectively. Extension of these diagrams to 3D and to flat surfaces is trivial. The free volume available to surfactant tails on flat surfaces in both cases (same length and different length) is less than that available on curved surfaces due to geometry. (c) Cross sectional view of DPD simulation of equal-length surfactants showing that a surfactant tail has the same available free volume (indicated by dashed lines) when it is placed next to a similar or different surfactant. This snapshot is for surfactants of length $4$ each on a sphere of radius $5\sigma$. (d) Cross sectional view of DPD simulation of unequal-length surfactants (lengths $4$ and $8$) on a sphere of radius $5\sigma$ showing how the longer tails (lighter/yellow) fill the extra available free volume by bending over shorter ones (darker/red). The wedgelike structures thus formed are shown by dashed lines. (e) Radius of gyration, $R_g$, vs length difference, $\Delta l$, with length of longer surfactant fixed at $9$.

Figure 3

Equilibrium structures obtained by mesoscale simulations of self-assembly of binary mixtures of surfactants with varying length difference or bulkiness difference on a sphere of radius $5\sigma$. Dark (red) beads and light (yellow) beads represent head groups of the two species of surfactants (tails not shown). (a) Length ratio $4:4$, equal bulkiness. (b) Length ratio $6:6$ with one surfactant (yellow heads) having a bulkier tail group. (c)–(e) Length ratios $4:6$, $4:7$ and $4:13$, respectively, with equal bulkiness.

Figure 4

(a)–(d) Equilibrium structures obtained by mesoscale simulations of self-assembly of a binary mixture of surfactants of length ratio $4:7$ on surfaces with varying degrees of curvature. Dark (red) beads and light (yellow) beads represent head groups of shorter and longer surfactants, respectively (tails not shown). Sphere radius: (a) $3\sigma$, (b) $5\sigma$, (c) $10\sigma$, (d) infinite. Sphere radii not drawn to scale. (e) Atomistic simulation of $\mathrm{C}4:\mathrm{C}6$ (both having $\mathrm{\text{−}}{\mathrm{CH}}_3$ tail end-group) mixed monolayer showing stripelike domains. Dark (blue) and light (yellow) beads are the head groups of the short and long surfactant, respectively. (f) STM height images of $\mathrm{C}4:\mathrm{C}6$ mixed monolayer showing stripelike morphology with a domain width of 5 nm.