Deformation free energy and elastic description of a self-assembled system

A continuum model is proposed to describe orientational states of a self-assembled system formed by rodlike molecules, in contact with an isotropic solid substrate. The total free energy is determined by taking into account the interactions between the molecules forming the film and between the molecules and the substrate. A phase diagram is presented, demonstrating that a critical surface molecular density exists, depending on the the ratio between the surface and the bulk free energy, separating homeotropic from tilted phases. The behavior of the elastic constants is investigated as a function of the surface molecular density. The elastic description leads to the presence of a linear term in the free energy, which accounts for the existence of possible spontaneous elastic distortions induced in the system.