SSP Project Summary:

Computer simulation of thermotropic liquid crystals

The simulation of thermotropic liquid crystals is probably one of the hottest topics amongst computer modellers of condensed matters. This interest is largely motivated by the widening of areas in which liquid crystals offer revolutionary alternatives to conventional materials, the most famous example being that of the new generation LC displays.

But what exactly is a liquid crystal? A liquid crystalline phase is a phase ...in which long-range orientational order persists but molecular centres of mass are (to some extent) disordered and translationally mobile [Allen and Tildesley 1987]. By opposition to lyotropic LC (those found in detergents), thermotropic LC can be formed solely by a variation in thermal energy and do not require any interaction with a solvent. The simplest LC phase is known as the nematic phase in which the molecules centre of mass are translationally disordered but their axis are distributed along a preferred direction called the director.

The first attempts to simulate the formation of such systems were undertaken in the early 70's. The molecules were then represented as hard spherocylinders or hard ellipsoids of revolution. Although some evidence of the formation of a metastable orientationally ordered liquid phase were obtained, those simulations suffered from serious limitations.

Since then, the models were continuously refined to overcome those limitations. The most noticeable improvement is the use of soft orientation-dependent potentials such as the Gay-Bern potential described by its characteristic shape parameter:

(Hard to reproduce maths omitted!)

Indeed, he use of such potentials allows to gain a better understanding of the mechanisms involved in the formation of nematic LC phases by introducing anisotropic repulsive and attractive dispersion forces. An extensive series of simulations [Frenkel and Mulder 1985] allowed to obtain a complete phase diagram for hard ellipsoids of different length-to-width ratio. Current simulations produce results much closer to experimental data. The project consists in carrying out simple isothermal-isobaric NPT Monte Carlo simulations of a system of 512 hard ellipsoids of length-to-width ratio a/b = 5 interacting by a Gay-Berne potential. Observables such as the pair distribution function, g(r), the translational rho(k) and orientational order parameters P_2 can be monitored throughout the simulation to identify the occurrence of a phase transition. The project will be organised as two different stages:

• The first 3 weeks will be spent building the simulation code (partly from existing subroutines) and getting a basic understanding of the simulation techniques.
• The remaining time will be used to carry out a series of simulations, process the data and visualise the different phases using AVS.

Expertise Required

Resources Required

Resources Supplied

References

Gerbrand van der Zouw worked on this project.

Compressed PostScript of the project's final report is available here (395 bytes) .

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