Filling and wetting transitions of nematic liquid crystals on sinusoidal substrates

Abstract

Close to sinusoidal substrates, simple fluids may undergo a filling transition, in which the fluid passes from a dry to a filled state, where the interface remains unbent but bound to the substrate. Increasing the surface field, the interface unbinds and a wetting transition occurs. We show that this double-transition sequence may be strongly modified in the case of ordered fluids, such as nematic liquid crystals. Depending on the preferred orientation of the nematic molecules at the structured substrate and at the isotropic-nematic interface, the filling transition may not exist, and the fluid passes directly from a dry to a complete-wet state, with the interface far from the substrate. More interestingly, in other situations, the complete wetting transition may be prevented, and the fluid passes from a dry to a filled state, and remains in this configuration, with the interface always attached to the substrate, even for very large surface fields. Both transitions are observed only for a same substrate in a narrow range of amplitudes.

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

“…In a similar way as it was obtained at nematic isotropic coexistence in Ref. [31], the interfacial tension for the LdG model has the expression…”

“…The nematic-substrate coupling Eq. (4) has been used to study the orientational wetting phenomena on flat [33,34] and rough substrates [29][30][31]35].…”

“…Since the seminal work by Berreman [12,13], this problem has been extensively studied and generalized in the literature [4,[14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Wetting and filling transitions by nematic on these grooved surfaces [28][29][30][31] have also been studied. When the substrate presents cusps, topological defects nucleate on them [14][15][16]26,27], and Berreman's expression of the elastic contribution to the freeenergy density, which is proportional to the wave number of the substrate structure q, breaks down because of the emergence of a nonanalytical contribution proportional to −q ln q associated to the nucleated defects [27].…”

“…This result contrasts with the phenomenology observed in smooth substrates, as sinusoidal substrates, in the absence of topological defects. In this situation a suitable generalization of Berreman's model may be applied [24,31].…”

Nematic liquid crystals on sinusoidal channels: the zigzag instability

“…Their influence is also significant in wetting phenomena. We have studied how sinusoidal patterns affect wetting of a substrate by a nematic [22] and shown that the wetting state (with the nematic-isotropic interface far from the substrate) is suppressed at high roughness being replaced by a filled state (with the interface pinned at the top of the channels) to avoid the nucleation of topological defects.…”