F. Barmes1 and D.J. Cleaver2
Physical Review E, 71, 021705 (2005)
1Centre Européen de Calcul Atomique et Moléculaire, 46, Allée d’Italie, 69007 Lyon, France
2Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield, S1 1WB, United Kingdom
Abstract
We use Monte Carlo simulations of hard Gaussian overlap (HGO) particles symmetrically confined in slab geometry to investigate the role of particle-substrate interactions on liquid crystalline anchoring. Despite the restriction here to purely steric interactions and smooth substrates, a range of behaviours are captured, including tilted anchoring and homeotropic-planar bistability. These macroscopic behaviours are all achieved through appropriate tuning of the microscopics of the HGO-substrate interaction, based upon non-additive descriptions for the HGO-substrate shape parameter.
Using particle shape to induce tilted and bistable liquid crystal anchoring (1,004.4 KiB)
Introduction
The term surface anchoring refers to the means by which a preferred orientation (or set of orientations) is imposed on a liquid crystal by a confining substrate [1]. The mechanisms underlying surface anchoring are fundamental to the operation of virtually all liquid crystal display cells, since the field-off states utilised in such devices are usually surface-aligned [2, 3]. Indeed, surface anchoring is particularly important in the latest generation of bistable devices [4–6] in which the display cells possess two optically distinct surface-stabilised arrangements. Experimental studies of liquid crystal anchoring (see Jérôme [1] for a review) have identified three classes of alignment characterised by α, the angle between the average director tilt and the substrate normal. These alignments are homeotropic, tilted and planar with, respectively, α = 0, 0 < α < π∕2 and α = π∕2. The anchoring properties of adsorbed liquid crystalline systems have also been the subject of several theoretical investigations performed, in the main, using mean field [7, 8] and density functional [9–11] approaches. Despite this range of previous studies, molecular-level understanding of the mechanisms driving anchoring remains limited and the methods used to control surface anchoring in current devices are largely empirical. For instance, it has long been known that rubbed substrates can be used to create planar surface alignment [12], but the mechanisms underlying this result have been the subject of an extended debate [13]. If the surface is a polymer film, soft rubbing has the effect of aligning the polymer chains in the rubbing direction. This, in turn, aligns the liquid crystal molecules thus highlighting a chemical mechanism coupling the nematic director in the interfacial region with the polymer chain orientation [14, 15]. If, however, the substrate is scratched by the rubbing, creating a grooved surface, it has been argued that a steric mechanism can generate the same effect [16]. While treatments such as substrate rubbing offer surface pretilt and azimuthal control over the anchoring direction, they do not represent the only routes to controllable liquid crystal alignment. This has been illustrated by a series of computer simulation studies performed over the last decade, which have given direct insight into the relationship between molecular adsorption and liquid crystal anchoring. The most common arrangement found in such studies is planar anchoring; this has been found at flat substrates for hard-particle [17–20], Gay-Berne [21] and all-atom [22] models (though note that planar alignment of the adsorbed molecules does not always result in planar anchoring [23]). Homeotropic anchoring has been achieved using hard-particle systems employing non-additive wall-particle interactions at perfectly flat walls [11, 19, 20, 24, 25] and full interactions at walls with tethered flexible chains [25–27] and rigid rods [28]. While homeotropic anchoring has been seen in simulations of Gay-Berne particles confined by smooth substrates [21], and could certainly be forced using the well-depth anisotropy tuning approach employed in [29], the majority of such systems have yielded tilted alignments [30–33]. Up to now, the tilt observed in these systems has been ascribed to competition between the particle-particle and particle-wall attractive interactions. However, by investigating the equivalent hard-particle system, we show here that this tilt actually has an entropic origin. Tilted anchoring in hard-particle systems has previously been seen only when the substrates have been made rough through the tethering of chains [25–27] or rods [28]. Indeed, entropy-driven tilt of cylindrically symmetric particles at smooth walls has not, to our knowledge, been seen or even considered in any previous simulation or theoretical study. In this study we extend previous work [20] on the anchoring behaviour of generic hard-particle liquid crystal models by studying the effect of changing the particle-substrate contact function. Specifically, we use Monte Carlo simulations to study the anchoring behaviour of hard Gaussian overlap (HGO) particles confined in a slab geometry using two particle-surface potentials – the HGO-sphere and HGO-surface potentials. As well as investigating the intrinsic anchoring properties of these two surfaces, we study their behaviours for varying degrees of substrate penetrability, in order to identify the conditions under which the stable anchoring condition changes. This is done with the aim of developing and characterising a surface potential capable of exhibiting both homeotropic and planar anchoring alignments, i.e. bistable anchoring. A narrow region of bistability was identified in our previous work based on the simple hard needle-wall (HNW) surface potential [20] and found to be explained by the non-additive nature of this potential. The remainder of this paper is organised as follows: in Section II we describe the HGO-sphere potential and its induced phase behaviour. Following this, in Section III we show equivalent work performed with the HGO-surface model. Finally, in Section IV, we present a discussion and the conclusions deduced from this work and propose some directions for future work.
Conclusions
We have investigated, by means of Monte Carlo computer simulation, the effect of the particle-substrate shape parameter (or contact function) on the anchoring behaviour of a generic confined liquid crystal model. Essentially, by tuning the degree and sense of the non-additivity of this contact function, we have been able to establish both a tilted anchoring state and a strongly first-order (i.e. bistable) planar to homeotropic anchoring transition. Non-additivity has been incorporated into the systems studied in two different ways. Firstly, as was shown in Section II, the HGO-sphere shape parameter has an intrinsic angle-dependent non-additivity; particles approaching the substrate in either planar or homeotropic alignments ‘see’ the full surface, whereas particles approaching at intermediate angles are allowed to partially absorb. For systems with kS ≈ k, this microscopic effect was found to control both the structure of the fluid in the near-substrate region and the macroscopic anchoring orientation. The second use of non-additivity in this work centred on kS, the (dimensionless) particle length used to determine the particle-substrate interactions. By using kS as a model parameter, we have been able controllably to introduce a homeotropic anchoring state into the simulated systems, and continuously vary its relative stability. Given that particle shape is the main determinant of structure in most liquids, it should not, perhaps, be a great surprise that the contact function used to define particle-substrate interactions has had so dominant an effect here. That said, the utility of this approach does not appear to be widely recognised. Whilst non-additivity has been used here as a convenient device with which to control model systems, we stress that this approach does not represent an abstract concept with no relevance to real systems. Indeed, for molecular systems (in which intramolecular flexibility may be significant) adsorbed at substrates with ‘soft’ coatings, the relevance of a fully-additive generic model is arguable. For the specific models used in this work, an experimental realisation of reducing the parameter kS would be to employ a substrate coating that allows some penetration by the molecular endgroups, but repels the central part of the molecule; for mesogens, which commonly have sub-molecular units with significantly different character, this is perfectly achievable behaviour. We have shown that the anchoring properties of generic model mesogens adsorbed at perfectly flat walls can be controlled by details of the mesogen-substrate interaction. Moreover, we have shown that the nature of the interfacial region can depend markedly on the anchoring state. For example, the depth at which the substrate profile ceases to be apparent in the liquid structure depends strongly on the anchoring orientation; since interfacial region structure underlies mesoscopic descriptors such as anchoring coefficients and surface viscosities, a more detailed understanding of such differences may offer a route to enhanced device control. Similarly, orientational correlations parallel with and perpendicular to the substrate can be expected to depend on the anchoring orientation; the systems determined here therefore represent good candidate systems with which to explore phenomena such as nematic bridging in microconfined and/or colloid-bearing mesogenic systems. Finally, having achieved a microscopic model capable of exhibiting anchoring bistability, we are now in a position to examine the orientational behaviour present in more complex systems. These include other liquid crystal cell configurations, such as the bistable hybrid aligned nematic considered by Davidson and Mottram [6], and more exotic liquid crystal models such the PHGO description of flexoelectric pear-shaped particles [43].
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