Morphology of Block Copolymer Droplets on a Flat Substrate

Abstract

We study the equilibrium morphology of a droplet of symmetric AB diblock copolymer on a flat substrate. A previous experiment [A. B. Croll et al. Phys. Rev. Lett., 97, 204502 (2006)] has reported conical-shaped droplets with a terraced surface. Using self-consistent field theory (SCFT), we provide the first predictions for the equilibrium droplet shape and its internal structure. When the substrate affinity for the A component, ηA, is small, the droplet adopts a nearly spherical shape much like that of simple fluids. Inside the spherical droplet, however, the block copolymer molecules acquire an ordered morphology consisting of concentric circular lamellar layers stacked on top of each other; hence the thickness of the droplet is effectively quantized by a half-integer or integer number of layers. At larger ηA and smaller contact angle, the area of the upper-most layer becomes relatively large resulting in a nearly flat, faceted top surface, followed by a semi-spherical slope. This geometry is remarkably reminiscent of the droplet shapes observed for smectic liquid crystals.