Two-dimensional self-assembly in diblock copolymers

Diblock copolymers confined to a two-dimensional surface may produce uniform features of macromolecular dimensions (approximately 10-100 nm). We present a mathematical model for nanoscale pattern formation in such polymers that captures the dynamic evolution of a solution of poly(styrene)-b-poly(ethylene oxide), PS-b-PEO, in solvent at an air-water interface. The model has no fitting parameters and incorporates the effects of surface tension gradients, entanglement or vitrification, and diffusion. The resultant morphologies are quantitatively compared with experimental data.