  We characterize the elastic contribution to the surface free energy of a
nematic in presence of a sawtooth substrate. Our findings are based on
numerical minimization of the Landau-de Gennes model and analytical
calculations on the Frank-Oseen theory. The nucleation of disclination lines
(characterized by non-half-integer winding numbers) in the wedges and apexes of
the substrate induces a leading order proportional to qlnq to the elastic
contribution to the surface free energy density, q being the wavenumber
associated with the substrate periodicity.
