Orientational transitions in symmetric diblock copolymers on rough   surfaces
  We present a model addressing the orientation transition of symmetric block copolymers such as PS/PMMA on smooth and rough surfaces. The distortion free energy of parallel and perpendicular lamellar phases in contact with a rough solid surface is calculated as function of the surface roughness amplitude and wavelength, as well as the polymer lamellar periodicity (molecular weight). We find an analytical expression for the orientation transition. This expression is compared and agrees well with recent experiments done with six different polymer molecular weights and surface preparations. 
Yoav Tsori, Easan Sivaniah, David Andelman, Takeji Hashimoto