The process of forming liquid crystal mixtures with a set of required material properties is a black art rather than a science. All liquid crystal materials used in current displays are mixtures, in many instances using more than 20 components. Despite this the desired final properties are rarely achieved. If the same material properties could be created systematically using a mixture of only a few, tailor-made components, the impact on the chemical synthesis and display industry would be enormous.

To achieve this, one needs a good fundamental understanding of the relation between bulk and molecular properties. Important equilibrium bulk properties include the range of temperatures over which the phase is stable, the elastic constants, the dielectric constant and the flexo-electric coefficients. Important dynamical properties are the shear viscosities and, most crucially, the rotational viscosity. The aim of this project is to study how these properties depend on molecular characteristics, such as molecular shape, size and polarity. The output will be predictive tools which focus synthetic effort on molecules with a high
probability of leading to useful materials.

To achieve this end we will focus on fairly simple molecular models, using a mixture of computer simulation and statistical mechanical theory. A key element to the determination of phase stability by simulation is the accurate calculation of free energies. The standard approaches [1] are continually being improved and the most efficient calculations, particularly for ordered phases rather than simple liquids, require a thorough knowledge of statistical mechanics [2-4]. To avoid expensive exploration of the entire multi-component phase diagram, modern methods focus on tracing out phase coexistence boundaries, or on studying whole families of molecules at once. Accurate force fields have been developed for liquid crystals [5] and realistic simulations relating observed structures to molecular properties are within reach [6], although such brute-force simulations are expensive.

To efficiently obtain materials properties of a range of structures, thermodynamic perturbation theory and molecular mutation techniques will be used, based on an underlying simplified model reflecting the common 'hard core' molecular shape, plus softened potentials for the variety of functional units. Recent reviews explain the methodologies that we intend to employ, namely semi-grand Monte Carlo simulation, Gibbs-Duhem integration, Gibbs ensemble simulation, expanded ensembles, tempering and histogram reweighting [7,8]. Efficient methods exist for determining three-phase coexistence [9] azeotropes [10], and eutectics [11].

Determination of dynamical properties of liquid crystals and other complex fluid mixtures is currently feasible, but again a thorough knowledge of time-dependent statistical mechanics is essential for the maximum efficiency [12,13]. Recent
studies have demonstrated the feasibility of determining transport coefficients of molecular mixtures with good accuracy [14,15].

The references above give the impression that the translation of modern simulation techniques into practical materials modelling tools is entirely conducting outside the UK, with groups in the USA being especially prominent. UK simulation groups established a strong international position in liquid crystal simulation over the last 15 years, with several of the present applicants involved in a High-Performance Computing consortium. Examples of successes, which established new methods for calculating liquid crystal properties, include the first calculation of Frank elastic constants [16] and helical twisting power [17] of a liquid crystal; first mapping of phase diagram of rod-plate mixtures [18,19]; first calculation of surface tension of equilibrium nematic-isotropic interface [20]. Masters and Allen already have an excellent record of collaboration - the combination of simulation and theoretical expertise has proved very fruitful and has resulted in several joint publications [21-26].

The aim of the project is to restore the UK's lead in liquid crystal simulation of materials properties. Even for simple models, however, accurate simulations are very computationally intensive. What are also needed are less fundamental but reliable approximate methods which can rapidly scan the properties of a wide range of molecular shapes and properties. Two approaches are proposed. The first of these is to make use of integral equation theory (based on the hypernetted chain and Percus-Yevick equations) for one-component and two component mixtures. These yield equilibrium properties, including the two-particle distribution function. The latter can be used in Enskog theory to provide an estimate of the viscosity coefficients. A second theoretical approach is to make use of the virial expansion. Renormalised second and third virial coefficient theories have proved remarkably successful in predicting the properties of models of the nematic and smectic phases and we have a track record in calculating these virials in Manchester.

These calculations can again lead to equilibrium properties and, via Enskog theory, to estimates of transport coefficients. These theoretical predictions will be validated against the simulation results and then compared with available experimental results on existing mixtures. Given a methodology for predicting the behaviour of liquid crysalline materials in terms of the molecular components, we will be in a position to instigate the synthesis of new molecules to produce new materials with optimised properties.

[1] D. Frenkel and B. Smit. Understanding molecular simulation : from algorithms to applications. Academic Press, San Diego, 2nd edition, 2002.

[2] N. D. Lu and D. A. Kofke. Accuracy of free-energy perturbation calculations in molecular simulation. I. Modeling. J. Chem. Phys., 114:7303-7311, 2001.

[3] N. D. Lu and D. A. Kofke. Accuracy of free-energy perturbation calculations in molecular simulation. II. Heuristics. J. Chem. Phys., 115:6866-6875, 2001.

[4] N. D. Lu, C. D. Barnes, and D. A. Kofke. Free-energy calculations for fluid and solid phases by molecular simulation. Fluid Phase Equilibria, 194:219-226, 2002.

[5] E. Garcia, M. A. Glaser, N. A. Clark, and D. M. Walba. HFF: a force field for liquid crystal molecules. J. Molec. Struc. - THEOCHEM, 464:39-48, 1999.

[6] Y. Lansac, M. A. Glaser, and N. A. Clark. Microscopic structure and dynamics of a partial bilayer smectic liquid crystal. Phys. Rev. E, 64:051703, 2001.

[7] D. A. Kofke. Semigrand canonical Monte Carlo simulation; integration along coexistence lines. Adv. Chem. Phys., 105:405-441, 1999.

[8] J. J. Depablo, Q. L. Yan, and F. A. Escobedo. Simulation of phase transitions in fluids. Ann. Rev. Phys. Chem., 50:377-411, 1999.

[9] R. Agrawal, M. Mehta, and D. A. Kofke. Efficient evaluation of 3-phase coexistence lines. Int. J. Thermophys., 15:1073-1083, 1994.

[10] S. P. Pandit and D. A. Kofke. Evaluation of a locus of azeotropes by molecular simulation. AICHE J., 45:2237-2244, 1999.

[11] M. R. Hitchcock and C. K. Hall. Solid-liquid phase equilibrium for binary Lennard-Jones mixtures. J. Chem. Phys., 110:11433-11444, 1999.

[12] J. L. McWhirter and G. N. Patey. Molecular dynamics simulations of a ferroelectric nematic liquid under shear flow. J. Chem. Phys., 117:8551-8564, 2002.

[13] C. McCabe, C. W. Manke, and P. T. Cummings. Predicting the newtonian viscosity of complex fluids from high strain rate molecular simulations. J. Chem. Phys., 116:3339-3342, 2002.

[14] D. K. Dysthe, A. H. Fuchs, and B. Rousseau. Fluid transport properties by equilibrium molecular dynamics. I. Methodology at extreme fluid states. J. Chem. Phys., 110:4047-4059, 1999.

[15] D. K. Dysthe, A. H. Fuchs, B. Rousseau, and M. Durandeau. Fluid transport properties by equilibrium molecular dynamics. II. Multicomponent systems. J. Chem. Phys., 110:4060-4067, 1999.

[16] Michael P. Allen and Daan Frenkel. Calculation of liquid crystal Frank constants by computer simulation. Phys. Rev. A, 37:1813-1816, 1988.

[17] Michael P. Allen. Calculating the helical twisting power of dopants in a liquid crystal by computer simulation. Phys. Rev. E, 47:4611-4614, 1993.

[18] Philip J. Camp and Michael P. Allen. Hard ellipsoid rod-plate mixtures: Onsager theory and computer simulations. Physica A, 229:410-427, 1996.

[19] Philip J. Camp, Michael P. Allen, Peter G. Bolhuis, and Daan Frenkel. Demixing in hard ellipsoid rod-plate mixtures. J. Chem. Phys., 106:9270-9275, 1997.

[20] Andrew J. McDonald, Michael P. Allen, and Friederike Schmid. Surface tension of the isotropicnematic interface. Phys. Rev. E, 63:010701(R)/1-4, 2000.

[21] Michael P. Allen and Andrew J. Masters. Computer simulation of a twisted nematic liquid crystal. Molec. Phys., 79:277-289, 1993.

[22] Michael P. Allen, D. Brown, and A. J. Masters. Use of the McQuarrie equation for the computation of shear viscosity via equilibrium molecular dynamics - comment. Phys. Rev. E, 49:2488-2492, 1994.

[23] Michael P. Allen, Philip J. Camp, Carl P. Mason, Glenn T. Evans, and Andrew J. Masters. Viscosity of isotropic hard particle fluids. J. Chem. Phys., 105:11175-11182, 1996.

[24] P. J. Camp, Michael P. Allen, and A. J. Masters. Theory and computer simulation of bent-core molecules. J. Chem. Phys., 111:9871-9881, 1999.

[25] Guido Germano, Michael P. Allen, and Andrew J. Masters. Simultaneous calculation of the helical pitch and the twist elastic constant in chiral liquid crystals from intermolecular torques. J. Chem. Phys., 116:9422-9430, 2002.

[26] Michael P. Allen and Andrew J. Masters. Molecular simulation and theory of liquid crystals: chiral parameters, flexoelectric coefflcients, and elastic constants. J. Mater. Chem., 11:2678-2689, 2001.