PDF《liquid crystals》

3 tilted layer arrangements represents further evidence that surface mobility is a crucial factor: Kralj and Sluckin have argued, using Landau-de Gennes the- ory, that the chevron structure formed by smectic A LCs is always metastable with respect to the tilted layer arrangement, but persists because the lat- ter can only form following layer slippage at the LC-substrate interface [8]. Note, however, that a subsequent paper from the same group showed that the chevron is thermodynamically stable if formed by a smectic C LC [9]. Shalaginov et al. [10, 11] have also considered the presence of ?uid ?ow dur- ing the formation of chevron structures and have estimated the time scale for molecular permeation between layers to be of the order of

106 seconds. Continuum theory has also been used to describe the tip region of various chevron structures. The earliest treatment of this situation, due to Clark and Rieker, assumed a discontinuity in the layer tilt angle at the chevron tip [12]. Subsequent models removed this constraint, allowing, instead, quantities such as the azimuthal angle, cone angle and layer dilatation to vary through the interface as well as the layer tilt [13, 14]. More recently, these approaches have been used to treat the e?ects of shear on the structure and stability of the chevron [15]. Here we present the results of parallel molecular dynamics simulations performed with the aim of determining the microscopic structure of the chevron tip. We also examine the surface conditions required to achieve the

4 formation and stabilisation of this structure. In the next Section, we present the particle-surface interaction potential used for this study and list other simulation details. This is followed by a Results Section and a Discussion.

2 Simulation Model and Details Throughout, the Gay-Berne (GB) potential was used for the particle-particle interactions [16], using the standard parameterisation for which the phase diagram was originally determined by de Miguel et al. [17] (κ = 3, κ′ = 5, ? = 2, ν = 1). This parameterisation gives a length-to-breadth ratio of 3:1 and a well-depth in the side-side con?guration which is

5 times that found in the end-end con?guration. We do not detail the GB model here. The particle-substrate potential used was US?P(θi, φi, xi, |zi ? z0|) = ?S?P(θi, φi, xi) ? ?

2 15 σ0 |zi ? z0| + σ0 ? σS?P(θi)

9 ? σ0 |zi ? z0| + σ0 ? σS?P(θi)

3 ? ? (1) where the particle orientation is written in terms of the usual Euler angles, ? ui = (cos φi sin θi, sin φi sin θi, cos θi), the shape parameter σS?P(θi) = σ0 √

1 ? χ cos2 θi , (2) and χ = (κ2 ? 1)/(κ2 + 1) and σ0 is the particle breadth. In the absence of azimuthal coupling, this wall-particle interaction has been shown to induce

5 tilted surface layers and, on cooling, tilted mesophases [18, 19]. Additionally, the introduction of an azimuthal term, used by analogy with the experimental approach of anti-parallel substrate rubbing, has been shown to yield matching pretilt orientations at a pair of opposing substrates [20]. In the simulations described in this paper, azimuthal particle-substrate coupling terms have been used again but this time with equal and antago- nistic surface pretilts, in analogy with the parallel substrate rubbing used in the generation of pi-cells [21]. Also, a spatial modulation has been applied to the particle-substrate well-depth term in order to introduce a degree of surface friction into the model;

this was shown to be an e?ective approach in a recent paper by Binger and Hanna [22]. Thus the complete well-depth anisotropy term took the form ?S?P(θi, φi, xi) = 2?0 (1 ? χ′ cos2 ψi)? + χ′′ (1 ? cos2 θi) cos2 φi + A(1 + sin kxi) (3) where ?0 scales the well depth, χ′ = (κ′1/? ? 1)/(κ′1/? + 1), χ′′ = 0.2, and cos ψi = ? ui ・ ? psurf is the component of ? ui along the surface bias vector ? psurf. This approach was adopted to enable the surface pretilt ........