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Welcome to the Computational Soft Matter Group in the Department of Chemical and Environmental Engineering at Yale. The main focus of our group is to develop and utilize theoretical and computational tools and techniques rooted in thermodynamics and statistical mechanics to understand phase transitions in soft matter systems.
The most interesting- and yet the most difficult to study and characterize- of such phase transitions are those that involve crossing a free energy barrier. If the corresponding barrier is much larger than the thermal energy, kT, the characteristic time needed for the occurrence of the transition will be orders of magnitude larger than the characteristic structural relaxation times in the system. Under such circumstances, the phase transition will be a rare event. As an example consider the crystallization of Argon. At 36 K, the barrier for the formation of a large enough crystalline nucelus within the supercooled liquid is rather small. Therefore multiple crystallites spontaneously emerge within the liquid, and the crystallization process is a rather slow and steady process:
At 53 K, however, the nucleation barrier is large. So the liquid has to spend a rather large time in the supercooled state until the right type of fluctuation pushes the system on top of the barrier. This takes at around 2:10 of the following video.
Studying rare events with conventional sampling techniques is inefficient at best as one needs to spend an unnecessarily long time in the metastable basin. Sometimes barriers are so large that observing a single transition is impossible even on the best existing supercomputers on the planet. Due to these challenges, a variety of advanced sampling techniques have been developed for studying rare events in molecular simulations. These techniques work by preferentially sampling the right type of fluctuations that take the system from the metastable basin to the equilibrium basin.
Development and utilization of advanced sampling techniques is a major focus of research in our group at Yale. We use those techniques to study phenomena as wide as ice nucleation, self-assembly and protein folding and denaturation.