Wetting transition of a nematic liquid crystal on a periodic wedge-structured substrate

Abstract

In this article, we generalize Wenzel law, which assigns an effective contact angle for a droplet on a rough substrate, when the wetting layer has an ordered phase, like a nematic. We estimate the conditions for which the wetting behavior of an ordered fluid can be qualitatively different from the one usually found in a simple fluid. To particularize our general considerations, we will use the Landau-de Gennes mean field approach to investigate theoretically and numerically the complete wetting transition between a nematic liquid crystal and a saw-shaped structured substrate.PACS numbers: 61.30. Hn, 61.30.Dk It is known that the wetting behavior of a fluid is deeply altered in the presence of rough or structured substrates. Leaves for instance have often developed a patterned texture, with micro reliefs, in order to adapt themselves to a particular humid environment [1]. Recently, technological advances allowed the controlled manufacturing of artificial micro structured substrates, which were used to show spectacular results concerning waterrepellency, switchable wettability, and other practical applications [2].In this article, we will investigate the wetting behavior of an ordered fluid (a nematic liquid crystal), on a rough substrate. We will first review some simple considerations about isotropic fluids and rough substrates, and then we will generalize these ideas for the case of ordered fluids. We will particularize our study by considering the complete wetting of a nematic on a saw-shaped substrate. Quantitative results will be obtained by solving analytically and numerically the Landau-de Gennes free energy.Consider two isotropic phases at coexistence (let us call them A and B phases), their bulk free energy densities being the same f A = f B = 0. Suppose now the B-phase is the one preferred in the far field, and our system is in the presence of a flat substrate or wall. The substrate interacts with the fluid through a local surface energy with strength w, which favors the A-phase. In this situation, an A-phase layer may appear close to the wall, because the decrease we have in the surface energy is already sufficient to compensate the creation of an interface between the two phases. Let us define the wettability function g(w) as g(w) = σ BW − σ AW where σ αβ is the surface tension associated to a flat α-β interface. For fixed bulk coexistence conditions, the wettability coefficient will depend on the strength of the surface energy, and usually is an increasing function of w. The Young equation yields g(w) = σ AB cos θ π where θ π is the contact angle of the sessile drop. Thus, as w increases, the contact angle θ π decreases. Eventually, θ π = 0 at the wetting transition, when the A-B interface unbinds from the substrate. In this case g(w = w t π ) = σ AB , where w t π is the transition value. For larger values of w, the interface remains unbounded as a thick A-phase layer is formed between the substrate and the bulk B-phase (complete wetting). The specific effective interactions between the wall and t...

Filling and wetting transitions of nematic liquid crystals on sinusoidal substrates

“…(8)]. A similar behavior was observed for the wetting transition of the sawtoothed substrate [7,11]. However, there are quantitative discrepancies even for the largest system considered.…”

“…On the other hand, the cutoff length is given by the size of the defects, which scales with the correlation length ξ . The dry-to-nematic wet transition may be derived from the generalized Wenzel law [7]:…”

“…These laws extend Young's law [6] for planar substrates, including new substrate geometrical parameters. If these laws are justified in some situations [7], they may also fail in general theoretical or experimental conditions [8]. In addition to the usual wetting transition, simple fluids at bulk coexistence may present other surface transitions as the filling transition [9,10].…”

“…(12)] for very general smooth structured substrates [7]. We calculated numerically the wetting phase diagram for a periodic triangular (or sawtoothed) substrate and explained how the nucleation of defects, with noninteger topological * patricio@cii.fc.ul.pt charges, near the singular points of the triangular substrate, leads to logarithmic contributions to the elastic part of the nematic free energies [7,13].…”

“…(12)] for very general smooth structured substrates [7]. We calculated numerically the wetting phase diagram for a periodic triangular (or sawtoothed) substrate and explained how the nucleation of defects, with noninteger topological * patricio@cii.fc.ul.pt charges, near the singular points of the triangular substrate, leads to logarithmic contributions to the elastic part of the nematic free energies [7,13]. More recently, we reviewed and highlighted the differences and similarities of the wetting transitions of simple and nematic fluids for different types of periodic substrates, and reported some preliminary results for wetting of sinusoidal and rectangular substrates [11].…”