Rheology of cubic blue phases

The work of a collaboration between the Institute for Condensed Matter and Complex Systems (ICMCS), the Edinburgh Parallel Computing Centre (EPCC) and the Centre for Computational Science, University College London, has been recently highlighted on the cover of the RSC journal 'Soft Matter'. The team of scientists presents first insights into the complex bulk flow behaviour of liquid-crystalline Blue Phases.

Liquid crystals are states of matter with properties between those of a simple Newtonian liquid and a solid crystal. At high temperature or low volume fraction most liquid crystals have an isotropic phase, but undergo an ordering transition to phases with positional and/or orientational order upon cooling or densification. Today, they are wellknown for their technological applications. Nonetheless they play also an important role for living systems as they combine structural with functional properties. Cell membranes for instance are smectic liquid crystals and the chitin in the exoskeleton of anthropods has the structure of a chiral nematic liquid crystal. Blue Phases (BPs) are a particularly fascinating example of liquid-crystalline phases. They occur in chiral nematic liquid crystals and consist of a network of defect lines where for topological reasons the local order is strongly suppressed. The fact that the distance between these defect lines is about the same as the wavelength of visible light gives them unique optical properties and makes them very attractive for applications in photonic materials and optical switch gear.

It seems logical to find out more about these promising materials. However, some of their properties are notoriously difficult to study. This is particularly true for their rheological behaviour. When liquid crystals flow changes in the local order structure induce a flow field which acts back onto the order structure, giving rise to a non-linear coupling mechanism between order structure and flow that is referred to as back-flow. On the other hand the power of modern supercomputers has dramatically increased during the last two decades, enabling us to study problems that were previously inaccessible. This progress has been paralleled by the development of sophisticated models of complex fluids, which allow us to describe their dynamical behaviour. Hence, it appears viable to try to gain understanding and to provide experimental guidance by tapping into these resources.

The highlighted article reports results of detailed computational studies of the bulk flow behaviour of cubic BPI and BPII. The project drew on EPCC’s lattice-Boltzmann application ‘Ludwig’ for simulating complex fluids. It was possible to identify a number of different flow regimes, three in case of BPII and five for BPI, both BPs have some in common. At high flow rates a flow-aligned nematic state emerges, where all molecules orient on average along the main flow direction. At slightly lower flow rates a so-called Grandjean texture is the preferred mode of flow. It features a helical alignment of the molecules with minimal dissipation. At intermediate flow rates a regime with periodically recurring conformations and oscillatory stress patterns is established. Similar rheological response has been observed in experiments. One striking aspect that has not been reported so far is that the whole defect network moves ‘sideways’ in the direction of vorticity and perpendicular to the flow and the flow gradient direction. This phenomenon is related to the order structure of the liquid crystal in which the BPs form as the sense of motion of the network depends on the handedness of the chiral nematic liquid crystal.

BPI has a generally more complex flow behaviour than BPII owing to topological differences in its network structure. Contrary to BPII the defect lines of a quiescent BPI are well separated and do not intersect. But the shear flow squeezes the defect lines more and more together and creates a situation which is incommensurable with the topology of this phase. Ultimately, at very low flow rates, this leads to dissolution of the defect network and formation of an amorphous defect network that has the constant yield stress of a solid undergoing plastic deformation. At shear rates where neither elastic forces nor viscous forces clearly dominate, the BPI network is also more prone to dissolution, and another amorphous network forms.

The practical implications of these findings are numerous and reach from manufacturing and processing aspects to micro- and optofluidic applications based on BPs and other liquid-crystalline materials. Although direct experimental evidence to support these results is currently not available, the ability to predict and understand the structure and dynamical behaviour of complex liquid-crystalline system by means of careful computer simulation has been already demonstrated in the past. The team hopes that such experiments will be inspired by this work.

http://pubs.rsc.org/en/content/articlelanding/2013/sm/c3sm50228g Soft Matter, 2013, 9, 10243-10256, DOI: 10.1039/C3SM50228G