School of Chemistry, **Machine** VP

University of Sydney

**Co-Investigators** Alison Casey

School of Chemistry, University of Sydney

**The Role of Molecular Flexibility in Stabilising Translational Order in
Liquid Crystals**

The aim of this project is to study the effect of flexible polymer groups incorporated in a realistic model of a liquid crystal forming molecule on the nature of the structural phase transitions. Of particular interest is the manner in which chain length and flexibility influences the stability of the smectic phase. The problem combines two major computational challenges: the Monte Carlo simulation of anisotropic molecules undergoing phase transitions, and the accurate counting of polymer configurations.

**What are the basic questions addressed?**

Despite the importance of liquid crystals in a wide variety of technologies, very few explicit models which form liquid crystals have been studied using computer simulations. Of those which have, most involve simple convex shapes (ellipsoids, spherocylinders, etc.) which bear little resemblance to actual molecular types found to produce liquid crystals. In this project we consider specific structural features common to large classes of liquid crystal-forming molecules and, using computer simulations, try to understand the part they play in structural phase transitions. What role do flexible end groups have in stabilising or destabilising various ordered phases? What influence does molecular biaxiality have in structural phase transitions, in particular those not directly associated with global biaxial symmetry.

**What are the results to date and the future of the work?**

We began this project with simulations of the rigid core of our model molecules, modelled as hard parallelepipeds. These calculations, intended as simply providing a comparison to the results of core+chain, produced some surprising results. Instead of the expected isotropic-nematic transition, these lattice based simulations produced a first order isotropic-layered transition. The layering is unusual with the long molecular axes lying on the layer rather than normal to it (as it is in smectic A, for example). Further more, as the molecular shape was varied from rod to plate, we observed the appearance of a columnar phase, similar to that seen in off-lattice simulations of spherocylinders. We have carried out extensive studies of these new phases which include testing their stability with respect to lattice pacing, system size and orientational constraints.

The immediate future of this work lies in incorporating the flexible end groups. Calculations are currently underway to determine the phase behaviour of a rod+chain system. These studies will include examining the effect of chain stiffness and chain-chain interactions.

**What computational techniques are used and why is a supercomputer
required?**

The computational problem can be broken down into two parts. The first involves the complete evaluation of the number of polymer chain configurations available for each configuration of the molecular cores. The second consists of Monte Carlo sampling of core configurations. If done as a scalar problem, each such chain evaluation would involve an enormous amount of CPU time. Note that this calculation has to be repeated many times as the program samples various core arrangements. Time on the VP2200 has allowed us to use a new algorithm which carries out an exact count of chain configurations in an arbitrary confinement. This routine is 100% vectorized.

**Publications**

*Monte Carlo simulations of a layering transition in hard
parallelepipeds*, A Casey and P Harrowell, Phys.Rev.Lett. (1994),
submitted.