Nematic transitions inside a film on substrates with stripe patterns of graded homeotropic anchoring

We investigate how a spatial pattern on substrates affects nematic-isotropic transitions inside a film deposited on them. The scales of the surface patterns and the film thickness of our interest are both dozens of nanometers. We considered simplified stripe patterns of graded homeotropic anchoring which induce uniaxial order with homogeneous director vectors. We discuss a naive approximation theory based on the Landau–de Gennes free energy, which provides simple physical pictures on the phase transitions inside the film. The reliability of the approximation are quantitatively confirmed by numerical calculations.