Orientation of a nanocylinder at a fluid interface

A nanocylinder placed on a fluid interface can assume an end-on or side-on orientation, or it can immerse itself in the surrounding bulk phases. Any of these orientations can satisfy a mechanical force balance when the particle is small enough that gravitational effects are negligible. The orientation is determined by the surface energies of the fluid-solid, fluid-vapor, and vapor-solid surfaces. A comparison of the energy of each state allows phase diagrams to be defined in terms of the scaled aspect ratio x = 2L/πr and the contact angle θ_o, where L and r denote the nanocylinder length and radius, respectively. Line tension can also influence the orientations by changing the equilibrium contact angle 9 and by increasing the energetic cost of the contact line. Phase diagrams accounting for positive line tensions 2 are also constructed. These phase diagrams can be divided into two classes. In the first, over some range of x and ∑, nanocylinders can be driven from side-on to end-on orientations with increasing 2. This transition terminates at a triple point where the side-on, end-on, and immersed energies are the same. In the second class, there is no triple point and, for a range of 2 values, nanocylinders of all aspect ratios x prefer an end-on orientation. In all cases, for high enough 2, line tension drives a wetting transition similar to that already noted in the literature for spherical particles. The zero line tension predictions are compared favorably to experiment, in which functionalized gold nanowires made by template synthesis are spread at aqueous-gas interfaces, immobilized using a gel-fixation technique, and observed by scanning electron microscopy. The small aspect ratio particles (disks) were in an end-on configuration, while the longer nanowires were in a side-on orientation, in agreement with the theory.