Topological Emulsions in Two Dimensions David R. Nelson (Harvard University), DMR 0654191

1. Phase diagram for a 2d liquid coexisting with a phase containing p-fold XY order Topological Emulsions in Two DimensionsDavid R. Nelson (Harvard University), DMR 0654191 • Persistent droplets of “liquid disordered” phase surrounded by “liquid ordered” phase have been found in experiments on ternary mixtures of two lipid types and cholesterol in giant unilamellar vesicles by, e.g., the Webb group at Cornell. It’s difficult to understand this emulsion-like stability with conventional mechanisms such as dipole-dipole interactions, which are weak in lipid bilayers. • A simple model which posits a broken tilt, nematic or hexatic symmetry in the liquid ordered phase leads to the phase diagram at the upper right. There is easy coalescence of droplets above the short solid line at left bounding a phase with p-fold XY order and terminating in a critical end point. However,…. • Below the critical end point, droplets of isotropic phase (see figure at right) exhibit a strong short range repulsion that stabilizes the emulsion. Defects in the XY-like texture outside the droplets lead to a universal droplet-droplet pair potential with a long range attraction and a short range repulsion. (Experiment by T. Baumgart et al., see PNAS 2007, and references therein) Two disks of isotropic phase, stabilized and bound together by topological defects in the liquid ordered phase. Shading indicates phase of the order parameter. K. Korolev and D. R. Nelson, Phys. Rev. E77, 051702 (2008)

2. 2RG Outreach: Polymer Physics and Fractal Dimensions David R. Nelson (Harvard University) DMR 0654191 • In lectures to junior high students touring Harvard from the Cambridge public school system, I tried to communicate the passion my colleagues and I feel for soft condensed matter physics. A similar lecture will be given to the children of scientists attending a workshop at the Aspen Institute of Physics in August, 2008. • After highlighting the role of linear polymers in the world around us (plastic bags, Styrofoam cups, DNA and proteins), I introduce the concept of a non integer “fractal dimension”, which is 5/3 for dilute linear polymers in solution. • I then ask the students to crumple aluminum and paper sheets of various sizes, and measure the diameter of the resulting crumpled objects, with the conclusion that the fractal dimension is neither d = 2 (the dimension of a large flat piece of paper) nor the solid object value d = 3, but is instead somewhere in between, d  2.4 Linear self-avoiding polymer chain in d = 2 dimensions with typical size given by RG, the “radius of gyration.” Crushed triangular lattice, N = 61,816 particles… Computer simulation of Vliegenhart and Gompper, Nature Materials (2005) Crumpled piece of writing paper www.bravenewtraveler.com/images/