Kamien

Kamien Group

Department of Physics and Astronomy
209 South 33rd Street
University of Pennsylvania
Philadelphia, PA 19104-6396

Theoretical Condensed Matter Physics

Our research interests center on problems in condensed matter theory. We are currently exploring problems in liquid crystals, foams, soft self-assembly, and biological physics.

Crystal Structure

Great advances in synthetic chemistry have produced a new class of monodisperse, yet highly complex, molecules. These molecules self-assemble into a variety of crystalline lattices with lattice constants on the order of 10nm. Unlike colloidal crystals, these materials form lattices that are not close-packed such as the face-centered-cubic (FCC) lattice. Instead the body-centered-cubic (BCC) lattice as well as the more exotic beta-Tungsten lattice form. While detailed modeling can lead to precise intermolecular potentials, progress has been made on a generic approach to crystal formation based on the mathematics of minimal surfaces By considering the interface between the Voronoi cells that contain each molecule, one can argue that the complex molecular coats favor a minimum area. This leads to the BCC lattice among others.

Liquid Crystals

The theory of liquid crystals and liquid crystalline polymers runs the gamut from the rheology of complex fluids to the esoterica of homotopy and topological defects. All aspects of theory are intimately influenced and connected with experiment. This places liquid crystal physics in an exciting position: it is driven by both theory and experiment and by both the abstract and the applied. Specifically, chiral molecules are ubiquitous in nature and exhibit many liquid crystal phases. They are extensively studied by biologists, chemists and biophysicists. There is still much theoretical work to be done on the wealth of experimental data. Smectic liquid crystals as well as columnar liquid crystals have the analogue of the Meissner phase in superconductors, in which chirality is excluded from the bulk (just as the magnetic field is expelled in a superconductor). The constraints imposed by topology and geometry can screen out chirality as well. We are studying the nonlinear elasticity of these phases through exact solutions and geometric principles.

Minimal Surfaces, Smectics, and Foams

Minimal surfaces have a long history of lying in the interface between Physics and Mathematics. Their use has had somewhat of a revival due to the ever increasing complexity of lyotropic phases of matter. Block copolymers and amphiphiles form structures that resemble doubly- and triply-periodic minimal surfaces. This is no surprise: because physics problems can be posed as extremal problems and because the mean curvature is the lowest-degree, rotationally-invariant scalar, minimal surfaces arise as solutions. However, nonlinearities should play an important role as the lengthscales of the structures become comparable to molecular sizes. Generalizing to constant curvature structures, we are working closely with the Durian group to study the properties of random foams using a mean-field model for the polyhedral cells.

Packing

Hard sphere systems are pure: their physics is governed solely by entropic depletion interaction with the only adjustable parameter being the volume fraction. Despite their simplicity, many details of the freezing transition are not understood. We are interested in the rigorous viability of the so-called random-close-packed state. Through geometric methods we are probing this state via analytic and numerical approaches. We study the equation of state via modifications to the virial expansion. We are also interested in the packing of long, stiff and semi-stiff polymers in the presence of entropic depletors.

This work is supported, in part, through the ACS Petroleum Research Fund and the National Science Foundation Through Grants DMR97-32963, INT99-10017, DMR01-02459, DMR01-29804, DMR05-20020, and DMR05-47230.