Line Tension of Twist-Free Carbon Nanotube Lyotropic Liquid Crystal Microdroplets on Solid Surfaces

Line tension, the force on a three-phase contact line, has been a subject of extensive research due to its impact on technological applications including nanolithography and nanofluidics. However, there is no consensus on the sign and magnitude of line tension, as it only affects droplets below the length scale dictated by the ratio of line tension to surface tension σ/τ. This ratio is related to the size of molecules in the system, which translates to a nanometer for conventional fluids. This ratio is orders of magnitude larger in lyotropic liquid crystal systems. Such systems form spindle-shaped elongated liquid crystal droplets in coexistence with the isotropic phase, with the droplets flattening when in contact with flat solid surfaces. We propose a method to characterize the line tension by fitting droplet shape to a model that incorporates interfacial forces and elastic deformation of the nematic phase. By fitting droplets of carbon nanotubes in chlorosulfonic acid to this model, we find that σ/τ ∼ −0.84 ± 0.06 μm, which is 2 orders of magnitude larger than what has been reported for conventional fluids, in agreement with theoretical scaling arguments.