Filling and wetting transitions of nematic liquid crystals on sinusoidal substrates

Meniscus osculation and adsorption on geometrically structured walls

We study the adsorption of simple fluids at smoothly structured, completely wet walls and show that a meniscus osculation transition occurs when the Laplace and geometrical radii of curvature of locally parabolic regions coincide. Macroscopically, the osculation transition is of fractional, 7/2, order and separates regimes in which the adsorption is microscopic, containing only a thin wetting layer, and mesoscopic, in which a meniscus exists. We develop a scaling theory for the rounding of the transition due to thin wetting layers and derive critical exponent relations that determine how the interfacial height scales with the geometrical radius of curvature. Connection with the general geometric construction proposed by Rascón and Parry is made. Our predictions are supported by a microscopic model density functional theory for drying at a sinusoidally shaped hard wall where we confirm the order of the transition and also an exact sum rule for the generalized contact theorem due to Upton. We show that as bulk coexistence is approached the adsorption isotherm separates into three regimes: A preosculation regime where it is microscopic, containing only a thin wetting layer; a mesoscopic regime, in which a meniscus sits within the troughs; and finally another microscopic regime where the liquid-gas interface unbinds from the crests of the substrate.

Filling, depinning, unbinding: Three adsorption regimes for nanocorrugated substrates

We study adsorption at periodically corrugated substrates formed by scoring rectangular grooves into a planar solid wall which interacts with the fluid via long-range (dispersion) forces. The grooves are assumed to be macroscopically long but their depth, width, and separations can all be molecularly small. We show that the entire adsorption process can be divided into three parts consisting of (i) filling the grooves by a capillary liquid; (ii) depinning of the liquid-gas interface from the wall edges; and (iii) unbinding of the interface from the top of the wall, which is accompanied by a rapid but continuous flattening of its shape. Using a nonlocal density functional theory and mesoscopic interfacial models all the regimes are discussed in some detail to reveal the complexity of the entire process and subtle aspects that affect its behavior. In particular, it is shown that the nature of the depinning phenomenon is governed by the width of the wall pillars (separating grooves), while the width of the grooves only controls the location of the depinning first-order transition, if present.

Wetting of Nematic Liquid Crystals on Crenellated Substrates: A Frank–Oseen Approach

We revisit the wetting of nematic liquid crystals in contact with crenellated substrates, studied previously using the Landau–de Gennes formalism. However, due to computational limitations, the characteristic length scales of the substrate relief considered in that study limited to less than 100 nematic correlation lengths. The current work uses an extended Frank–Oseen formalism, which includes not only the free-energy contribution due to the elastic deformations but also the surface tension contributions and, if disclinations or other orientational field singularities are present, their core contributions. Within this framework, which was successfully applied to the anchoring transitions of a nematic liquid crystal in contact with structured substrates, we extended the study to much larger length scales including the macroscopic scale. In particular, we analyzed the interfacial states and the transitions between them at the nematic–isotropic coexistence.

Pattern-induced anchoring transitions in nematic liquid crystals

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross-section sculpted on a chemically homogeneous substrate which favours local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal cases, we observe a homeotropic to planar anchoring transition as the substrate roughness increases. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.

Nematic liquid crystals on sinusoidal channels: the zigzag instability

Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau-de Gennes free energy to investigate the texture of nematics in sinusoidal channels with parallel anchoring bounded by nematic-air interfaces that favour perpendicular (hometropic) anchoring. In micron size channels 5CB was observed to exhibit a non-trivial texture characterized by a disclination line, within the channel, which is broken into a zigzag pattern. Our calculations reveal that when the elastic anisotropy of the nematic does not favour twist distortions the defect is a straight disclination line that runs along the channel, which breaks into a zigzag pattern with a characteristic period, when the twist elastic constant becomes sufficiently small when compared to the splay and bend constants. The transition occurs through a twist instability that drives the defect line to rotate from its original position. The interplay between the energetically favourable twist distortions that induce the defect rotation and the liquid crystal anchoring at the surfaces leads to the zigzag pattern. We investigate in detail the dependence of the periodicity of the zigzag pattern on the geometrical parameters of the sinusoidal channels, which in line with the experimental results is found to be non-linear.

Wetting of cholesteric liquid crystals

We investigate theoretically the wetting properties of cholesteric liquid crystals at a planar substrate. If the properties of substrate and of the interface are such that the cholesteric layers are not distorted, the wetting properties are similar to those of a nematic liquid crystal. If, on the other hand, the anchoring conditions force the distortion of the liquid crystal layers the wetting properties are altered, the free cholesteric-isotropic interface is non-planar and there is a layer of topological defects close to the substrate. These deformations can either promote or hinder the wetting of the substrate by a cholesteric, depending on the properties of the cholesteric liquid crystal.

Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model

We study the interfacial phenomenology of a fluid in contact with a one-dimensional array of infinitely long grooves of sinusoidal section, characterized by the periodicity length L and amplitude A. The system is modelled by the Landau-Ginzburg-Wilson functional, with fluid-substrate couplings which control the wettability of the substrate. We investigate the filling and wetting phenomena within the mean-field approximation, and compare with the predictions of the macroscopic and interfacial Hamiltonian theories. For large values of L and under bulk coexistence conditions, we observe first-order filling transitions between dry (D) and partially filled (F) interfacial states, and wetting transitions between partially filled F and completely wet (W) interfacial states of the same order as for the flat substrate. Depending on the order of the wetting transition, the transition temperature is either shifted towards lower temperatures for first-order wetting or it coincides with the wetting temperature on the flat substrate for continuous wetting. On the other hand, if the groove height is of order of the correlation length, only wetting transitions between D and W states are observed under bulk coexistence conditions. For this case, the transition temperature shift obeys approximately Wenzel's phenomenological law if the substrate favors first-order wetting, but it remains unshifted for continuous wetting. The borderline between the small and large L regimes correspond to a D - F - W triple point if wetting is first-order, and a D - F critical point for continuous wetting. Beyond bulk coexistence conditions, filling and first-order wetting transitions continue into off-coexistence filling and prewetting lines, which end up at critical points. Our findings show that the macroscopic theory only describes accurately the filling transition close to bulk coexistence and large L, while microscopic structure of the fluid is essential to understand wetting and filling away from bulk coexistence.

Interfacial motion in flexo- and order-electric switching between nematic filled states

We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterized by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynamical response of the system to an externally-applied electric field, with the aim of identifying switching transitions between these filled states. We find that order-electric coupling between the fluid and the field provides a means of switching between states where the plateaux between grooves are dry and states where they are wetted by a nematic layer, without affecting the configuration of the nematic within the groove. We find that flexoelectric coupling may change the nematic texture in the groove, provided that the flexoelectric coupling differentiates between the types of distortion at the corners of the substrate. We identify intermediate stages of the transitions, and the role played by the motion of the nematic-isotropic interface. We determine quantitatively the field magnitudes and orientations required to effect each type of transition.

Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favors homeotropic anchoring as a function of the wave number of the surface structure q, the tilt angle α, and the surface anchoring strength w. In addition to the previously reported nonanalytic contribution proportional to -q ln q, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to q for a given substrate roughness, in agreement with Berreman's predictions. We characterize this term, finding that it has two contributions: the deviations of the nematic director field with respect to a reference field corresponding to the isolated disclination lines and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit wL>1, when strong anchoring conditions are effectively achieved.

Nematic wetting and filling of crenellated surfaces

We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau-de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observed.