Large Scale lattice-boltzmann simulation of liquid crystals

This project studied by large scale Lattice Boltzmann computer simulations the dynamical and steady state behaviour of liquid crystal blue phases and smectics, especially under the influence of an applied flow or electric field.

Liquid crystals include many high tech materials used in laptop displays, flat-screen TVs, and other devices. In many of these devices, the flow of the material (for example in response to an electric field) is part of what makes the device work or not work. Many of these devices use 'nematic' liquid crystals in which rod-shaped molecules are lined up in the same direction but are not on a lattice; others involve 'cholesteric' or (potentially) 'blue phase' liquid crystals whose structure is more complex.
For both scientific and technological reasons it is very important to understand properly the flow of liquid crystals in response to stresses and/or electric and magnetic fields. This is a very difficult task for two reasons. Firstly, there is the complicated, partially ordered structure to consider. Secondly, this structure is made even more complex in real materials by the presence of so-called 'defects'. These defects are of quite specific types, different in each type of liquid crystal. For nematics the defects are string-like structures. (In fact, the name 'nematic' comes from the greek word for a worm.) In the simplest cases it is possible to solve using pen and paper the equations that describe the flow of pure liquid crystals, but when defects are present this is almost always impossible.
The aim of the project was to develop and use methods for solving the relevant equations on very large computers. Only the biggest computers can provide the high resolution studies needed to address the problem of defects, since these are extended objects, large compared to the molecular scale.

The outcome of our project has been a breakthrough in the understanding of a number of important aspects of blue phase dynamics. One of our main results have been the identification, by large scale computer simulations, of a candidate structure for blue phase III, the third of the experimentally observed blue phases, also known as the blue fog. This has been experimentally observed routinely at least since the 80s, yet no definitive theory existed on its concrete structure before our work. Our research recently published in Physical Review Letters combines data from very large scale simulations on the thermodynamics, kinetics and electric field response of blue phases, and strongly suggests that this elusive structure is an amorphous lattice of disclinations, or lines of defects. Another major outcome of our research grant has been the discovery that the domain growth in blue phases is surprisingly complex. Again by simulations on supercomputers, we put a nucleus of an ordered phase inside a supercooled cholesteric phase. We expected this to slowly grow in an orderly fashion: what we instead found is that there is a rapid disorderly growth of a metastable amorphous defect network. During this process, the original nucleus is destroyed; reemergence of the stable phase may therefore require a second nucleation step. This result is relevant technologically and likely key to the correct modelling of blue phase devices, as often switching between the on and off states in devices requires domain growth. Our results, recently published in the prestigious PNAS journal, suggest that for novel blue phase based devices ordering may occur hierarchically rather than in a two-step process.
Parallel to this groundbreaking simulations on blue phase III and on blue phase domain growth, we have carried out some important work on the characterisation of blue phases under an electric field, and of the rheology of blue phases and of smectics. Some of these works have already been published in mainstream physics journal, including Soft Matter and Physical Review E, and we are currently preparing for publication a further two papers, on the shear response of blue phases and smectics.