Although virtually all of our experiments are supported by physical models and theoretical arguments, we are also interested in several areas of fundamental importance where theory is the primary focus and experiments play only a supporting role. First is our exploration of nanoionics where "macroscopic" interactions, such as electrostatics and van der Waals forces, compete with "molecular" interactions, such as hydrogen bonding and solvation forces. Here, we combine continuum models, such as the Poisson-Boltzmann equation and the Lifshitz theory of van der Waals forces, with discrete models, such Monte Carlo methods and Molecular Dynamics simulations, to identify the unique characteristics of self-assembly at the nanoscale (Nano Lett. 2007, much more to come soon).
At the macroscale, our theoretical team (Kyle, Siowling, Nicolas, Konstantin and Paul) is attacking the fundamental ??and outstanding -- question of dynamic self-assembly (DySA, J. Phys. Chem. B 2006), in which components organize and function spontaneously far from thermodynamic equilibrium (that is, only when they are "fed" external energy). In recent years, we have pioneered rational design of experimental systems belonging to this category and have been developing them for novel engineering applications (e.g., self-assembling micromachines, Appl. Phys. Lett. 2004, microfluidic devices, Proc. Roy. Soc. 2004, as well as adaptive and reconfigurable nanomaterials, PNAS, to appear soon). Our theoretical work on DySA work builds on the foundations of nonequilibrium thermodynamics and we seek to develop a set of universal variational principles governing DySA across all length scales. Our theoretical research often involves elements of fluid dynamics (calculation of flows fields and dissipation spectra in fluidic systems), dynamic systems theory (phase-space portraits, Lyapunov exponents) and lattice-gas simulations.