Ordering of adsorbed rigid rods mediated by the Boussinesq interaction on a soft substrate

Abstract

Orientational ordering driven by mechanical distortion of soft substrates plays a major role in material transformation processes such as elastocapillarity and surface anchoring. We present a theoretical model of the orientational response of anisotropic rods deposited onto a surface of a soft, elastic substrate of finite thickness. We show that anisotropic rods exhibit a continuous {\sl isotropic-nematic phase transition}, driven by rod-rod interactions mediated by the deformation of the underlying elastic substrate, and quantified by the Boussinesq solution adapted to the case of surface deposited rods. From the microscopic rod-rod interactions we derive the appropriate Maier-Saupe mean-field description, which includes the Boussinesq elastic free-energy contribution due to the substrate elasticity, derive the conditions for the existence of a continuous orientational ordering transition and discuss the implication of results in the soft (bio) systems context.