Computer simulations of self-assembling particles have provided substantial insight into the ways that ordered states can emerge in time from even simple interactions. Our general understanding of these dynamics, however, still falls well short of that for time-independent equilibrium properties of molecular systems. In particular, the exploration of equilibrium behaviors is greatly facilitated by examining the statistics of fluctuations far from the average values of characteristic order parameters. The tails of such probability distributions can be extremely revealing, for example indicating proximity to coexistence of distinct phases, a key feature of complex systems that may not be at all evident from typical configurations of a single equilibrium state. For the non-equilibrium dynamics of self-assembly, capabilities for exploring rare fluctuations in computer simulations are by contrast sorely lacking. As a result, numerical studies have been limited to computing average behaviors, often just assessing whether typical trajectories achieve a certain ordered state after a given amount of time. The proposed work aims to address this lack, developing new and efficient ways to systematically harvest trajectories that are far from typical. Equipped with these methods, we will map out the space of assembly trajectories for a model system to reveal the ways that such a system can respond to diverse perturbations. Based on the dramatic sensitivities implied by many previous studies, we expect to find a wealth of dynamical behaviors that could be realized by applying appropriate external fields. This accomplishment would reflect in interesting ways on the general statistical mechanics of self-organization, helping to bring its theory closer to the standards established for equilibrium systems.

Research Team:

Christoph Dellago (ESI, U Vienna), Phillip L. Geissler (UC Berkeley and Lawrence Berkeley National Laboratory)