A major challenge in modeling liquid crystals at the molecular level is the need to employ very large system sizes, necessitated by their intrinsic long range order. One solution to this problem is to use computationally tractable potentials while still retaining the essential physics of the molecular interactions responsible for the formation of liquid crystals.

Although not working in the field, Corner [1] proposed a seminal solution to the formulation of the pair potentials for anisotropic molecules. He argued that the interaction between such molecules should have the same distance dependence as that between atoms but now the parameters in the potential, for example the contact distance and the well depth, should depend on the orientations of the two molecules and the vector joining them.

The most famous example of such a single-site potential is that developed by Gay and Berne [2] which we, and others, have shown to be a powerful model for simulations of a wide range of liquid crystal behaviour, involving both rod-like and disc-like molecules [3]. The effective shape of a Gay-Berne particle is ellipsoidal and this shape is not altered by varying the parameters in the potential. This is clearly a limitation in modeling the properties of real mesogenic molecules whose shapes are far more complex.

There are several ways to overcome this fundamental difficulty and one, which retains the computational simplicity of the Corner potential, is to write the contact distance and well depth as an expansion in scalar invariants or S-functions [4] of the vectors defining the molecular orientations and that of the intermolecular vector. This approach has been used by Zewdie to model the phase behaviour of rods [5] and discs; it is found to work well allowing significant differences in shape to be included. We have also explored this S-function potential in the simulation of rods and discs which include a sphere at their centres thus introducing a shape quadrupole [6] to the model. The concept has been taken further by Zannoni and his colleagues who has used it to introduce shape polarity [7].

We wish to extend the potentials and at the same time to see how valuable they can be in modeling the behaviour of real mesogens, at least in a generic sense. This would then be expected to provide general guidance as to the essential features a molecule should have to possess a given phase sequence or properties. In particular we will:

	Parameterise the attractive part of the potential by mapping onto atomistic potentials for archetypal molecules [8].
	Use the potential to explore the dependence of phase type on the molecular shape and attractions.
	Determine properties, such as elastic constants and viscosity coefficients, as a function of the molecular shape and attractions.
	Extend the potential to chiral molecules by the introduction of an appropriate invariant in the expansions for the potential parameters.
	Use the potential to explore the dependence of the formation and properties of chiral phases on the shape and attractive chirality.
	Develop the S-function potentials for unlike molecules possibly by mapping onto atomistic models.
	Use the S-functions developed for ulike molecules to model, n a generic sense, the behaviour of liquid crystal mixtures.

[1] J Corner 1948 Proc R Soc, 192,275.

[2] J G Gay and B J Berne 1981 J Chem Phys, 74,3316.

[3] M A Bates and G R Luckhurst 1999 Struct Bond, 94,65.

[4] A J Stone 1978 Mol Phys, 36,241.

[5] H B Zewdie 1998 J Chem Phys, 108,2117.

[6] A H Ghahrai 2002 MPhil Thesis (University of Southampton).

[7] R Berardi, M Ricci and C Zannoni 2001 Chem Phys Chem,2,443.

[8] G R Luckhurst and P J Simmonds 1993 Mol Phys, 80,223.