## Thursday, January 29, 2015

### What are liquid crystals?

Once you accept the idea that the simple, microscopic interactions between bits of matter can lead to the emergence of dramatic collective properties when large numbers of particles are concerned, it's not surprising to realize that there are many different ways that large ensembles of particles end up organizing.  As mentioned previously, a true liquid is a system where the average distance between the particles is comparable to the particle size, but the particles are in constant motion and there is no particular long-range order to the way the particles are arranged.

New possibilities present themselves if the particles have some kind of "internal degree of freedom".  For example, think of the particles not as little featureless billiard balls, but as elongated objects.  Now we can consider having the orientation of all the particles have some long-range correlation.  A liquid crystal is an emergent phase when the particles are close together and there is not 3d spatial order in the arrangement of particle positions, but there is order in the orientations of the particles.  In nematic liquid crystals, the centers of mass of the particles are completely spatially disordered, but there is long-range order in their orientation. For example, they could all be pointing the same direction, indicated by the not-so-cleverly-named vector, the directorCholesteric liquid crystals have some twist or chirality to the particle orientation.  In smectic liquid crystals, the particle centers of mass are actually spatially ordered in one direction, but not in the other two (i.e., you can think of stacks of layers of particles, with particles free to move within each layer).  The wiki page about liquid crystals gets into the history of these systems, and here is a nice webpage that classifies them.  Liquid crystals are very useful because their directed nature gives them anisotropic optical properties, and if the objects in question are polar molecules, it is possible to reorient them electrically.  This combination enables many technologies, almost certainly including the display device you're using to read this.

There was a time when I was somehow skeptical that all these phases were "real" thermodynamic phases.  I was used to solids, liquids, and gases, and I'd learned about "hard" condensed matter phases like ferromagnets and superconductors that dealt with emergent properties of the electron gas.  Somehow these liquid crystal things didn't seem like the same sort of thing to me.  Then I read the really great book by Chaikin and Lubensky, and saw things like the figure at right (from G. S. Iannacchione and D. Finotello, Phys. Rev. E 50, 4780 (1994)).  The figure shows the specific heat of a liquid crystal (in some nanopores) as it goes through a thermally driven transition between the nematic and isotropic phases, as a function of scaled temperature, $t \equiv (T/T_{\mathrm{c}})-1$.  This kind of sharp, divergent feature and scaling as a function of temperature are hallmarks that show these phases and their transitions are every bit as real as any other thermodynamic phase, even though the materials are squishy.