Orientational Transitions: from Liquid Crystals to Viral Capsids
Lars Onsager proposed in 1948 a new type of phase transition in which a liquid loses its rotational symmetry but retains its translational symmetry. This unlike the freezing transition where a liquid loses both symmetries. He proposed that this is what happens when nematic liquid crystals form, materials that now are used extensively in displays. By the 1980's, when more complex forms of liquid-crystallinity had been discovered, it became evident that there was a deep connection between liquid crystals, the mathematics of the spherical harmonics and the theory of representations of groups. More recently, it was proposed, by Lorman and Rochal, that the formation of viruses should be viewed as belonging to the class of orientational phase transitions. In the colloquium I will review the proposal of Lorman and Rochal, the critical questions that were raised, and how these questions may be resolved.