# Summary of Research Accomplishments

September, 2008.My research career started in the spring of 2000 when I began working with Professor Hans Andersen at Stanford University. Motivated by the desire to understand supercooled liquids and the glass transition, my thesis work involved the kinetic theory of liquids. For a stochastic lattice model of the near equilibrium dynamics of a liquid, we formulated a diagrammatic kinetic theory which expressed the time correlation function of density fluctuations in terms of an infinite series of diagrams. The simplicity of the lattice model facilitated developing approximate kinetic theories which we quantitatively compared with simulation results. Due to the similarity of this formalism with a diagrammatic formalism for a classical atomic liquid, this work suggests how to develop approximate kinetic theories for more realistic models of supercooled liquids. Moreover, these ideas provide a foundation for understanding the dynamics of wide variety of complex fluids such as a dense colloidal dispersion or an entangled solution of rod-like polymers.

My postdoctoral work with Professor Glenn Fredrickson at the UC Santa Barbara focused on supramolecular polymer systems in which reversible intermolecular bonding affects the inhomogeneous phase behavior. These systems have enormous technological potential since temperature controls the number of intermolecular bonds and hence the physical properties of the material. Treating the reversible bonding as a chemical reaction, we worked out the combinatorics in formulating a field-theoretic model in the grand canonical ensemble. The theory is natural in this ensemble since the bonding reaction implies an equality between the chemical potentials of the reactant and product species. While we applied this theory to equilibrium polymers and supramolecular diblock copolymers in which two homopolymers can form a diblock, the general principles apply to any polymer systems with reversible bonding. Mean-field results for the supramolecular diblock copolymers revealed re-entrant phase behavior in which the system transitioned from an inhomogeneous lamellar phase to a disordered phase back to a lamellar phase with decreasing temperature. Moreover, the length scale of the lamellae can change drastically as a function of temperature, suggesting the application of supramolecular polymers to technological applications that require precise control over domain spacing.

My interests as a Miller Fellow at UC Berkeley shifted to statistical mechanics far from equilibrium. With Dr. Gavin Crooks at Lawrence Berkeley National Laboratory, we are using work fluctuation relations to understand single molecule biophysical experiments. Our key result is a relationship between far from equilibrium work measurements and an equilibrium quantity called the thermodynamic length. Applying this result to RNA pulling experiments provides an optimal method for extracting a free energy profile from work measurements as well as a means to experimentally measure the thermodynamic length. Entropy man gives an introduction to the principles behind this research.