Directing Colloidal Self-Assembly through Roughness-Controlled Depletion Attractions

The surfaces of colloidal particles resulting from many new fabrication methods are not molecularly smooth, so understanding how surface roughness can affect the depletion attraction between the particles and their assembly is very important. We show that the depletion attraction between custom-shaped microscale platelets can be suppressed when the nanoscale surface asperity heights become larger than the depletion agent. In the opposite limit, the attraction reappears and columnar stacks of platelets are formed. Exploiting this, we selectively increase the site-specific roughness on only one side of the platelets to direct the mass production of a single desired assembly: a pure dimer phase.

Figure 1

Surface roughness-controlled depletion attractions between platelike particles. (a) Atomic force micrographs reveal a distribution of asperities on the flat faces of the pentagons. The height axis has been enlarged twofold to display the surface roughness with greater clarity. (b) Probability distribution of asperity heights $p(h)$ has an average: $h=17\pm 7\mathrm{nm}$. (c) Pentagonal polymer platelets in dilute aqueous solution remain unaggregated when the diameter $d$ of the depletion agent is smaller than the average asperity height $h$ (SDS at 20 mM: $d=4\mathrm{nm}$, ${\varphi }_s=0.35\%$). Bars are $5\mu \mathrm{m}$. (d) Lateral aggregation of platelets occurs when $d/h$ just exceeds unity (PS spheres: $d=20\mathrm{nm}$, ${\varphi }_s=0.067$). (e) Long columnar aggregates are observed for larger $d/h$ and ${\varphi }_s$ (nanoemulsion: $d=130\mathrm{nm}$, ${\varphi }_s=0.15$). (f) Universal aggregation diagram of particles having rough facets at dilute ${\varphi }_l$. No aggregation occurs for $d/h<1$ (region $U_r$), nor below the solid line of constant attractive energy, $U_{\mathrm{ff}}/(k_{B}T)=10$ (region $U_c$) (squares). Lateral aggregates ($L$) are observed for $d/h\approx 1$ (circles). Long columns of platelets ($C$), including side-by-side bundles and T structures of columns, form at higher ${\varphi }_s$ and $d/h$ (triangles). A disordered gel-like structure ($G$) of platelets can occur at even larger ${\varphi }_s$ and $d/h$.

Figure 2

Turning on depletion attractions using temperature $T$ to increase the diameter $d$ of the depletion agent. The depletion agent is a pluronic copolymer (P103 by BASF) at 3.75% by mass (${\varphi }_s\approx 9\%$). Scale bars of optical micrographs are $5\mu \mathrm{m}$. (a) At lower $T=26°\mathrm{C}$, $d=15\mathrm{nm}$ and the pentagons remain unaggregated due to roughness ($d<h$). (b) At higher $T=40°\mathrm{C}$, $d=34\mathrm{nm}$ and the pentagons aggregate face-to-face into columns ($d>h$). (c) Probability $p$ of observing a column comprised of $N$ pentagons at lower $T$ (first bar) and higher $T$ (other bars).

Figure 3

Controlling the structure of depletion aggregates by tailoring site-specific surface roughness. Janus platelets are roughened to a higher degree on only one face by binding silica nanospheres (diameter $D=75\mathrm{nm}$) prior to lift-off from the wafer. Scanning electron micrographs show: (a) The untreated faces have smaller roughness $h\approx 17\mathrm{nm}$. (b) Opposite faces to which silica spheres are bound have greater roughness $D\approx 75\mathrm{nm}$. (c) For $h<d<D$, the silica-modified Janus pentagons form aligned dimers when a depletion agent (PS spheres: $d=40\mathrm{nm}$ at ${\varphi }_s=0.8\%$) is added (optical micrograph). (d) Phase diagram of assembled structures: unaggregated pentagons ($U_r$ and $U_c$—squares), offset lateral dimer aggregates ($L_D$—circles), aligned dimers ($D$—diamonds), long columnar stacks ($C$—triangles), disordered gel ($G$).

Figure 4

Asperities influence the excluded volume (shaded regions—yellow) of the depletion agent (solid circles—blue) between platelets. (a) Particles having asperities with height $h>d$ on the surfaces can greatly reduce the excluded volume between aligned plates, inhibiting aggregation. (b) Thermal rearrangement can still lead to laterally offset face-to-face aggregation in which the largest asperities on one surface avoid contact with the opposite surface. (c) When $d>h$, the excluded volume becomes large, leading to columnar aggregation. (d) In principle, ideally corrugated surfaces, such as a sawtooth pattern, can create larger excluded volumes and stronger depletion attractions than just simple flat surfaces.