1. How are Liquid Crystals like Superconductors? Charles Rosenblatt, Case Western Reserve University, DMR 0345109 Many seemingly different phase transitions actually can be quite similar in global behavior. If two systems have the same symmetry and can be described by similar free energy functionals, then particular aspects of one phase transition may map onto another phase transition. In this work we examined the similarities between the nematic to smectic-A liquid crystal phase transition in liquid crystals and the normal to superconducting phase transition. In particular, it is well known that a magnetic field applied to a type-I superconductor will be expelled (This is the “Meissner Effect”). But if the field is sufficiently large, a transition to the higher temperature normal phase takes place. Similarly, the smectic-A liquid crystal phase prohibits bend distortion. In this work we showed that for a sufficiently large bend distortion, the region of bend melts into the higher temperature nematic phase, and we determined the spatial extent of the melted phase vs. temperature. The results were then compared to our theoretical model, based upon a DeGennes free energy that is nearly identical to that for a superconductor. [Phys. Rev. Lett. 97, 167802 (2006)] Polarized micrograph of a thin layer of smectic liquid crystal deposited on a herringbone-patterned substrate designed to provide a large bend distortion across the light-dark interface between horizontal stripes. The enlargement of the interface (at the right) shows a smooth variation of intensity across the interface, which corresponds to the region that has melted into the nematic phase. This is analogous to the breakdown of the superconducting Meissner Effect. The figure at the right shows the width of the melted region L vs. temperature (below the transition). The solid lines show our theoretical model for several different “anchoring strength” parameters W.

2. How are Liquid Crystals like Superconductors? Charles Rosenblatt, Case Western Reserve University, DMR-0345109 Broader Impact:  A deeper understanding of the “universality” of seemingly different phase transitions.  Connection linking the soft condensed matter community with the more traditional solid state community.  Presentation of results at several international venues.  Formalized university-to-university international collaboration with the Liquid Crystal National Laboratory, University of Calabria (Italy) Education: Two graduate students (Ruiting Wang and Ishtiaque Syed) and one postdoc (Giovanni Carbone) were involved in this project, and presented the work at the 2006 International Liquid Crystal Meeting in Colorado and the 2007 Gordon Research Conference on Liquid Crystals in New Hampshire. The PI recently presented this work to academic audiences in Hong Kong, Italy, France, and the United States. Syed is now a faculty member at University of Dhaka (Bangladesh) and Carbone is a faculty member at University of Calabria (Italy)