On a smooth silicon wafer, gold nanocubes behave like a crowd at an ice rink: at first individual figures slide randomly across the ice, but within a minute they gather into an even carpet. A two-nanometer gap remains between the cubes, roughly the width of a hand between neighbors in a queue. This carpet is no thicker than a single cube, and such an assembly is called a monolayer. But swap the substrate for borosilicate glass, whose roughness is higher by just 0.09 nanometers, less than the diameter of a gold atom, and the picture changes: the cubes begin to pile on top of one another, forming islands four stories tall.
The answer lies in invisible helpers: micelles of a surfactant. These soft spheres, resembling tiny soap bubbles, dart between the cubes and cannot come right up against them. A forbidden zone surrounds each cube, a space the micelles cannot enter. When two cubes approach each other, their forbidden zones overlap, and the micelles, deprived of part of their space, start pushing the cubes together. These are depletion forces: an attraction born from the expulsion of small particles out of narrow gaps.
Why does roughness affect depletion forces so strongly? A smooth surface is like a level floor on which every cube lies snugly, and the forbidden zone between it and the floor is minimal. A rough surface is like a floor strewn with small pebbles: the cube rests on just a few bumps, and gaps remain beneath it where micelles can slip in. This weakens the pushing-out and reduces the attraction to the substrate. As a result, on a smooth floor the cubes spread out into a single layer, while on a stony one they gather into towers, because the attraction between cubes in the upper layers turns out to be stronger than their attraction to the uneven surface.
The difference in roughness between the smooth silicon wafer and borosilicate glass is only 0.09 nm, which is less than the diameter of a gold atom (0.288 nm), yet it is enough to radically change the type of assembly.