Physical Review E, 69, 061705 (2004)

Abstract

We present a study of the effects of confinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle–wall potential. Using geometrical arguments to calculate the molecular volume absorbed at the substrates, we show that both planar and homeotropic arrangements can be obtained using this model. Monte Carlo simulations are then used to perform a systematic study of the model’s behaviour as a function of the system density and the hard-needle–wall interaction parameter. As well as showing the homeotropic to planar anchoring transition, the anchoring phase diagrams computed from these simulations indicate regions of bistability. This bistable behaviour is examined further through the explicit simulation of field-induced two-way switching between the two arrangements.

  Computer simulation of a liquid-crystal anchoring transition (1.4 MiB)

Introduction

Confinement of a liquid crystal has a symmetry breaking effect; this induces both positional layering and orientational coupling which is transmitted to the bulk alignment through a mechanism called anchoring [1]. While the former effect is a universal consequence of confine- ment [2, 3], the latter is specific to mesogenic systems. For these, three main arrangements for the particles close to the surface can be observed, namely homeotropic, planar and tilted. A range of azimuthal anchoring states are also possible. Upon change of experimental conditions, modification of the surface arrangement can be observed to lead to a change in the bulk alignment; such an event is called an anchoring transition [1].

Experimental studies of confined liquid crystals have reported that anchoring transitions can be achieved by various means such as change in temperature [4–6] or the conformation of the aligning agent [7, 8]. Incident radiation can also induce anchoring transitions by selectively switching the conformations of substrate molecules and, thus, modifying the interfacial interactions [9]. Alternatively, the absorption behaviour of a liquid crystal at a solid substrate, either directly [10, 11], or through the introduction of a second species [12], can lead to anchoring transitions if the density of absorbed particles or the nature of the absorption is changed. One last example is that in which a multistable anchored system which, preferentially adopts one of its possible conformation due to its treatment history [1, 13], is switched into an alternative state by, e.g., an appropriate applied field.

Although a number of mechanisms underlying anchoring transitions have been raised (see [14] for a review) rather few theoretical analyses have been performed. Teixeira and Sluckin [15, 16] used a Landau-de Gennes free energy functional to study the planar to homeotropic anchoring transition in liquid crystal systems confined by different substrates. They found a rich anchoring behaviour which helped in the identification of mechanisms responsible for the anchoring transitions, specifically, the compositions of binary mixtures of liquid crystals and the amount of absorption at the surface. Subsequently Teixeira et al. [17] used a Landau-de Gennes formalism to observe a temperature driven anchoring transition at the interface between a liquid crystal and smooth solid surface, thus confirming the experimental findings. The effect of non-uniform substrates (i.e. microtexture) has also been studied using a Landau-de Gennes formalism [18, 19]. This work found temperature-driven phase transitions between states with different tilt angles.

In the field of molecular simulations, the effects of confinement on liquid crystalline systems has been increasingly well studied, and all of the surface arrangements listed above have been obtained through appropriate choices of particle-surface interaction potential. Using various parameterizations of the Gay-Berne model [20] and taking the particle-wall contact distance to be that between a rod and a sphere, both tilted and planar anchoring states have been observed [21–24]. If, alternatively, the surface is represented using a monolayer of spheres, the particle-substrate interaction can be designed to induce either homeotropic or planar anchoring [25–27]. Using hard ellipsoids confined so that their centres of mass interacted sterically with smooth substrates, Allen [28] observed homeotropic surface arrangement. Subsequently van Roij et al. [29–31] investigated the behaviour of hard spherocylinders at a hard smooth wall and observed surface-induced wetting and planar ordering. These studies also showed that the planar arrangement is the natural state of hard-rod nematic phase in contact with a flat surface. Chrzanowska et al. and Cleaver et al. [32, 33] used the hard Gaussian overlap (HGO) model [34] (i.e. a hard version of the Gay-Berne model) to investigate confined symmetric and hybrid anchored films using the hard-needle–wall (HNW) potential as a surface model. Here, simulations of symmetrically anchored systems showed that, with appropriate tuning, this surface model can induce either homeotropic or planar anchoring, a finding which we expand upon in the current article.

Liquid crystal adsorption has also been studied using simulations of all-atom models, investigating, for example, the behaviour of 8CB on various substrates [35–37]. These studies gave results which were largely consistent with scanning tunneling microscopy investigations with respect to the structure of the observed planar arrangements. A more systematic series of simulation was performed subsequently by Binger and Hanna [38–40] who simulated the adsorption of several liquid crystals (e.g. 5CB, 8CB, MBF). Systems ranging from single molecules up to two monolayers anchored on different polymeric substrates (e.g. PE, PVE, Nylon 6) were investigated. From this, the authors found that, for most substrates, the liquid crystals adopted planar arrangements with some specific conformations being favoured; conversely, Doerr and Taylor [41, 42] reported preferential homeotropic anchoring from their simulations of 5CB on amorphous PE.

Comparatively, the literature on computer simulations of anchoring transitions is extremely scarce. Using HGO and HNW potentials for, respectively, intermolecular and surface interactions, Cleaver and Teixeira [33] have found a density-driven homeotropic to planar anchoring transition at one wall of a model cell with hybridly-set boundaries. Also, more recently, Lange and Schmid [43–45] have observed an anchoring transition in a system of ellipsoidal Gay-Berne particles confined by grafted poly- mer chains. Here, the transition between tilted and homeotropic arrangements was induced by changes in the grafting density.

In this paper, we use Monte Carlo simulations to study the effects of confinement on a system of model mesogenic particles and so gain a microscopic understanding of their anchoring transition. This paper is organised as follows: the models used for this study are described in Section II. The model’s surface induced structural changes are studied in Section III through observation of typical profiles obtained from the simulations and the dependence of these profiles on the surface potential and the system density. From this, in Section IV, we obtain a comprehensive mapping of the model’s anchoring behaviour, including the identification and localisation of its planar to homeotropic anchoring transition. This Section also contains an explicit study of the anchoring bistability found to be associated with this transition. The conclusions drawn from this work and a description of future studies are given in Section V.

Conclusions

In this paper we have studied the behaviour of liquid crystalline systems confined in slab geometry between symmetric walls. For the simple HNW potential used here, we have shown that the preferred anchoring direction is controlled by the particle-substrate interaction needle length, k_S. At nematic densities, all of the systems simulated have exhibited a homeotropic to planar anchoring transition on increase in k_S. As well as having orthogonal bulk alignments, the homeotropic and planar states have been shown to involve distinct surface arrangements, with little configurational overlap.

The anchoring transition observed here appears to be first order, because of both the associated discontinuity in the anchoring orientation and the configurational hysteresis (or bistability) observed. This bistability has been found over a relatively narrow parameter window, but has proved highly reproducible with both states being very long lived. Presumably, this longevity is related to the configurational distinctiveness of the two surface states and the anchoring-orientation-conserving effect of the overlying nematic fluid. It should be possible to characterize this bistability more quantitatively by using reweighting techniques to determine the form of free-energy barrier separating the stable states; the height of this ρ^*-dependent barrier height sets the time-scale of any spontaneous switching between the states and, so, knowledge of it would enable some sort of comparison to be made with bistable experimental systems.

Rather surprisingly, the anchoring behaviour of this system has shown very little dependence on the system density; the limits of the bistability regions are, essentially, isochores. One consequence of this has been that the approximate transition needle lengths, k_S^T, calculated in the high packing limit, have proved reasonably accurate for all nematic densities. Put another way, this suggests that even at ρ_NI^*, this system was aware of the two states’ particle-volume absorption efficiencies in the high packing limit. This counterintuitive result is presumably a consequence of the simplicity of the HNW model used here: we will revisit this issue, and the routes it offers for manipulation of the bistability region, in future work employing models with less idealized particle-substrate interactions [52]. Specifically, focus will be brought to bear on the influence of the particle-surface contact function on the surface anchoring behaviour and the size and shape of the bistability region.

References

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