Generalized van der Waals theory for phase behavior of two-dimensional nematic liquid crystals: Phase ordering and the equation of state

Generalized van der Waals theory for phase behavior of two-dimensional nematic liquid crystals. II. Phase coexistence and adsorption

Adsorption of asymmetric particles or molecules into monolayers is important for many biological and technologically relevant physical systems. In-plane ordering can drastically affect adsorption and phase behavior. In this work, a generalized van der Waals theory previously developed [M. V. Zonta and E. R. Soulé, Phys. Rev. E 100, 062703 (2019)10.1103/PhysRevE.100.062703] is used to calculated phase behavior and adsorption isotherms in a system of hard-core rodlike particles with in-plane nematic order, as a function of the model parameters (aspect ratio L/B, isotropic and anisotropic interaction parameters χ and ν, and adsorption constant K_{ads}). For small L/B, isotropic-nematic and/or (depending on χ) isotropic liquid-gas coexistence is observed; as L/B increases, coexistence between two different nematic phases appears at low temperature, and liquid-gas equilibrium ceases to be observed for large enough L/B; this is understood considering that as aspect ratio increases, the range of stability of the nematic phase becomes larger. Adsorption isotherms are found to significantly deviate from Langmuir behavior, and are strongly affected by ordering and interactions (surface density in the adsorbed layer increases as interaction parameters and ordering increase). Phase coexistence is observed as discontinuous transitions in adsorption isotherms, where adsorption-desorption hysteresis cycles are possible.

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

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 isotropic-nematic phase transition, driven by orientational interactions between surface deposited rods. This interaction is mediated by the deformation of the underlying elastic substrate and is quantified by the Boussinesq solution adapted to the case of slender, 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)system context.