Computer simulation of bistable switching in a nematic device containing pear-shaped particles

We study the microscopic basis of bistable switching of a confined liquid crystal via Monte Carlo simulations of hard pear-shaped particles. Using both dielectric and dipolar field couplings to this intrinsically flexoelectric fluid, it is shown that pulsed fields of opposing polarity can be used to switch between the vertical and hybrid aligned states. Further, it is shown that the field-susceptibility of the surface polarisation, rather than the bulk flexoelectricity, is the main driver of this switching behaviour. Flexoelectricity is an effect by which an applied bulk field can induce polar director field gradients in a mesophase such as a nematic liquid crystal (LC) [1]. Essentially, it provides a mechanism by which to impose splay and bend distortions of a given polarity on a mesophase which is otherwise centrosymmetric. Microscopically, this phase polarisation arises due to a combination of the action of the field on molecular dipoles and some steric or electrostatic asymmetry in the molecule-molecule interactions [2–4]. Interest in flexoelectricity, particularly its microscopic origins, has been reignited recently due to the development of liquid crystal displays (LCD’s) which exploit bistable surface anchoring of the nematic phase [5,6]. Several switching mechanisms have been proposed for these devices such as the use of competing dielectric and flexoelectric couplings to the applied field [7], the inclusion of electrochiral ions [8] or self-assembled hydrogen-bonded fibers [9] or, finally, the use of field-induced surface defects [10] whose density can even be used to achieve a grey-scale device. ∗ Corresponding author : F. Barmes ([email protected]) Preprint submitted to Elsevier Science 13 March 2006 Following the lead of Barberi and co-workers [7,10], Davidson and Mottram recently showed that a flexoelectric nematic subject to directional field pulses can execute two-way switching in an LC cell with one monostable homeotropic substrate and one bistable planar/homeotropic substrate [11]. Specifically, by considering both dielectric and flexoelectric couplings to homogeneous applied fields, within an Ericksen-Leslie theory approximation, they identified a narrow parameter window for two-way switching between vertical (V) and hybrid aligned nematic (HAN) states. However, the model used in this study was somewhat simplified when one considers the full range of polar contributions present in real systems: the flexoelectric polarisation can itself be resolved into director-gradient and order parameter gradient terms (the latter being termed the ‘order electric’ polarisation); ion migration effects are known to be significant for the LC mixtures and substrate materials used in prototype devices [12]; and molecular polarisation (or ferroelectric order) in the substrate region is known to be present in many confined LC systems [13,14]. The simplification associated with Davidson and Mottram’s approach is echoed in the recent debate on how best to partition between these different polar terms when using HAN cells to measure flexoelectric coefficients. For HAN cells subject to applied fields, measured director profile distortions are poorly described by director flexoelectricity alone [15]; strong cases have been made to compensate for this with either surface polarisation [16] or ion-distribution terms [17], whereas LatticeBoltzmann simulations indicate significant near-surface order electricity [18]. In practice, then, there is evidence to suggest that a combination of all three of these effects commonly operates in concert with director flexoelectricity. Here, we consider the microscopic basis of directional-pulsed-field switching in such systems using Monte Carlo simulations of hard pear-shaped particles confined in slab geometry. This particle shape is used since, following the original arguments of Meyer [2], its mesophases exhibit splay flexoelectricity. The interparticle interactions are implemented using the parametric hard gaussian overlap (PHGO) approach introduced in [19]; we use the parameterisation with elongation k = 5 shown, in Ref. [19], to possess both nematic and smectic A2 phases, the latter being a bilayer smectic phase with layers formed perpendicular to the director. Being based on a purely steric single-site interaction, this is a particularly efficient model for use here, though similar behaviour can be expected for any of the generic flexoelectric particle models introduced in recent years [20–22]. Investigation of two-way HAN-V switching also requires a bistable particle-substrate interaction potential and a particle-field coupling which induces competition between the dielectric and flexoelectric terms. The latter is achieved here by taking each pear to interact with an applied field through both dielectric and dipolar terms. Thus U i = − 1 2 ∆χ (E · ûi) 2 − μ (E · ûi) (1)