Modelling a nematic liquid crystal

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Abstract
The bulk phase liquid crystalline behaviour of a cyclic siloxane with a pentamethylcyclosiloxane core and biphenyl-4-allyloxybenzoate mesogens (BCS) was studied using molecular dynamics (MD) and wide angle X-ray analysis. This material exhibits partial crystallinity at room temperature and liquid crystalline behaviour above 120° C. For the MD simulations an ensemble of 27 molecules with 135 mesogenic units was simulated and a molecular mechanics force field was used to model the structural anisotropy of the siloxane molecules. Simulations were carried out both at room temperature and at an elevated temperature (425 K). Room temperature simulations showed that, contrary to our initial assumptions, the low energy molecular conformations were not cylindrical but splayed in shape. During the simulation a smectic-like, tilted layer structure was found to evolve for the cluster when full atom potentials were used, while no such development was observed when electrostatic interactions were neglected. The presence of a tilted layered structure was also suggested by the X-ray data. These results indicate that long range electrostatic interactions are significant for the molecular system under study. In order to calculate the orientational order parameter, the orientation of the molecular axis had to be determined. This was achieved by describing the mesogen shapes to be ellipsoidal and defining the principal axis of the ellipsoids to be the molecular directors. By sampling over 200 ps of simulation at 425 K, the time averaged order parameter (S) was calculated. The calculated S of 0.36 was comparable to the value of 0.4–0.45 found from the experimental data. Apart from providing insight into the relative importance of the various competing forces in the formation of the liquid crystalline phase, these simulations are also expected to be useful in predicting the mesophase behaviour of liquid crystalline systems.