Liquid crystals

Most solids melt straight into a liquid. Some compounds stop halfway: on heating, the crystal first becomes a cloudy fluid, and only at a second, higher temperature does it clear into an isotropic liquid. That intermediate fluid is a liquid crystal. The first one noticed was cholesteryl benzoate in 1888, which seemed to have two melting points.

The molecules (mesogens) need an awkward shape. A typical rod-like mesogen has a rigid core of linked benzene rings, a flexible alkyl tail at one end and often a polar group such as -\mathrm{C{\equiv}N} at the other. The rigid core keeps neighbours lined up; the tail stops them packing into a crystal.

The main phases differ in how much order survives:

• Nematic: molecules point in a common direction but their centres are scattered at random.
• Smectic: molecules also sit in layers, like a stack of books on a shelf.
• Cholesteric (chiral nematic): the common direction twists steadily from one slice to the next, forming a helix. Its pitch changes with temperature, so the reflected colour changes too, which is how strip thermometers work.

These are thermotropic liquid crystals, controlled by temperature. Lyotropic ones form when molecules such as soaps are mixed with a solvent and depend on concentration.

In a display, a thin film of nematic sits between two crossed polarising filters. Applying a voltage realigns the molecules, which switches each pixel between letting light through and blocking it.

Describing order

The average molecular direction in a region is the director, a unit vector \hat{n} with no sense (\hat{n} and -\hat{n} are equivalent). How well molecules follow it is measured by the orientational order parameter

where \theta is the angle between a molecule's long axis and \hat{n}. Perfect alignment (\theta = 0) gives S = 1; a random distribution gives \langle\cos^2\theta\rangle = 1/3 and so S = 0. Real nematics sit between about 0.3 and 0.8, falling as temperature rises, and drop discontinuously to zero at the nematic–isotropic transition, which is first order. Maier–Saupe mean-field theory, which treats each molecule in an averaged anisotropic attraction from its neighbours, predicts S \approx 0.43 just below the clearing point. Order parameters are measured by NMR (quadrupolar splittings of deuterated mesogens), by birefringence, or by polarised IR and Raman.

Phases and textures

Adding positional order gives smectics: smectic A has layers with the director along the layer normal; in smectic C the director tilts. A chiral centre turns a nematic into a cholesteric with pitch p; when p approaches the wavelength of visible light the phase acts as a one-dimensional photonic crystal, selectively reflecting light of wavelength \lambda \approx \bar{n}p and one handedness. Disc-shaped mesogens such as hexa-alkoxytriphenylenes form columnar phases. Under a polarising microscope each phase has a characteristic texture (schlieren for nematics, focal conic fans for smectic A), which remains the quickest identification method alongside DSC.

Switching a display

Anisotropic molecules have different permittivities along and across the long axis. With positive dielectric anisotropy, \Delta\varepsilon = \varepsilon_\parallel - \varepsilon_\perp > 0, as in cyanobiphenyls, the director rotates towards an applied field. The torque must overcome elastic resistance to splay, twist and bend, so reorientation only starts above a threshold voltage (the Fréedericksz transition). In a twisted nematic cell the surfaces are rubbed at 90°, the director twists through the film and guides polarised light round into the second, crossed polariser: the pixel is bright. A few volts untwist the director, the guiding stops and the pixel goes dark.

Liquid crystal research has moved well beyond displays. Commercial screens now mostly use in-plane switching or vertically aligned cells with negative-\Delta\varepsilon mixtures, tuned for viewing angle and response time, and the mixtures contain a dozen or more components chosen to widen the nematic range.

New phases keep appearing. The twist–bend nematic, found around 2011 in bent dimers such as CB7CB, has a heliconical structure with a pitch of only about ten nanometres, giving chirality from achiral molecules. The ferroelectric nematic, identified from 2017 onward in strongly polar mesogens such as RM734 and DIO, has a spontaneous polarisation in a fluid and has prompted work on nonlinear optics and electromechanical devices. Blue phases, cubic lattices of defect lines, have been stabilised by polymer networks over tens of kelvin and switch in well under a millisecond.

Liquid crystal elastomers, lightly crosslinked networks of mesogens, contract by tens of percent when heated through the clearing point and are studied as soft actuators and artificial muscles. Lyotropic phases of chromonic dyes, DNA and cellulose nanocrystals give templates for ordered materials, and nematic droplets act as sensors because adsorbed molecules at the interface flip the director field. Active nematics, made from microtubule bundles driven by motor proteins, are a test bed for physics far from equilibrium.

Open problems include predicting mesophase type and transition temperatures from molecular structure. Atomistic simulations still struggle to reproduce clearing points within a few kelvin, so coarse-grained models and synthesis remain closely coupled.