Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate

José Manuel Romero-Enrique , Chi Tuong Pham (1, 2) , Pedro Patrício

1 Université Paris-Saclay
2 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the 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, with q being the wave number associated with the substrate periodicity. © 2010 The American Physical Society.

Keywords: wave numbers; elastic contribution; winding number; surface free energy; defects; leading orders; analytical calculation; films; alignment; orientation; disclination lines; landau-de-gennes model; numerical minimization; layer; phase-transitions; samples

Domains: Mathematics [math]; Physics [physics]

José Manuel Romero-Enrique, Chi Tuong Pham, Pedro Patrício. Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate. Physical Review E , 2010, ⟨10.1103/PhysRevE.82.011707⟩. ⟨hal-03863938⟩