Phase Diagram and Orientational Order in a Biaxial Lattice Model: A Monte Carlo Study

Abstract

We have determined the phase diagram for a lattice system of biaxial particles interacting with a second rank anisotropic potential using Monte Carlo simulations for a number of values of the molecular biaxiality. We find increasing differences from mean field theory as the biaxiality increases. We have also calculated for the first time the full set of second rank biaxial and uniaxial order parameters and their temperature dependence, and on this basis we comment on the difficulties of measuring phase biaxiality by NMR.

Molecular simulation of liquid crystals: progress towards a better understanding of bulk structure and the prediction of material properties

“…It shows a first order phase transition between ordered and disordered states as a function of temperature, has a small enthalpy change associated with the phase transition (as with real liquid crystals) and with suitable boundary conditions, can be adopted to simulate a liquid crystal display. 4 Lattice models are highly configurable, and by careful choice of the inter-site potential it has been possible to adapt the basic model of Lebwohl and Lasher to make it suitable for the simulation of biaxial liquid crystals, 5 liquid crystal mixtures, a cubatic phase, liquid crystal dimers, chiral liquid crystals and for studying liquid crystal ordering in aerogels.…”

Liquid Crystal Observables: Static and Dynamic Properties

“…However, the idea, outlined above, of introducing suitable molecular observables and determining their average in the laboratory system as in a virtual experiment is quite helpful and has been used to determine the biaxial and uniaxial order parameters [19]. The minimum set of order parameters required to describe biaxial molecules in a biaxial phase is [20,21,12 …”

“…= 6 different systems corresponding to the eigenvalue permutations. In [19] we have chosen the eigenvalue permutation which satisfies the following conditions: a) P 2 > 0; b) the same order parameters must have the same values in all the ways they are computed (here, e.g., P 2 and R 2 20 are computed in two different ways); c) for each configuration at one temperature the order parameters must be as close as possible to the mean value of the order parameters of the previous temperature (the sum of the differences is minimized). The above procedure effectively assigns the X and Y axes when the phase is biaxial.…”

“…In fig. 5 we show a set of order parameters obtained from MC simulation of the simple second rank attractive pair potential [19,22]:…”

Biaxial Nematic Droplets and their Optical Textures: A Lattice Model Computer Simulation Study

“…Our model biaxial and uniaxial nematics are obtained from a discretized version of the orientational biaxial potential put forward many years ago by Luckhurst et al [12,13] and whose phase diagram has already been studied in detail by us through extensive computer simulations of bulk systems [14]. This lattice model reproduces the rich phase diagram of a biaxial nematic system with isotropic, uniaxial and biaxial phases and it reduces to the well known Lebwohl-Lasher (LL) uniaxial one [1] for nematics when the molecular biaxiality vanishes.…”