Molecular monolayers as interacting rolling balls: crystals, liquid and vapor
- When?
- Wednesday 11 January 2012, 16:00 to 17:00
- Where?
- 22AA04
- Open to:
- Staff, Students
- Speaker:
- Vakhtang Putkaradze
Abstract: Molecular monolayers, especially water monolayers, are playing a crucial role in modern science and technology. In order to derive simplified models of monolayer dynamics, we consider the set of rolling self-interacting particles on a plane with an off-set center of mass and a non-isotropic inertia tensor. To connect with water monolayer dynamics, we assume the properties of the particles like mass, inertia tensor and dipole moment to be the same as water molecules. The perfect rolling constraint is considered as a simplified model of a very strong, but rapidly decaying bond with the surface. Since the rolling constraint is non-holonomic, it prevents the application of the standard tools of statistical mechanics: for example the system exhibits two temperatures -- translational and rotational-- for some degrees of freedom, and no temperature can be defined for other degrees of freedom.
In spite of apparent simplicity, the behavior of the system is surprisingly rich. We identify analogies with the regular water by defining crystalline, liquid and gas states, based on the specific energy of a particle. We show the existence and nonlinear stability of ordered lattice states,. We also investigate the effect of rolling on the disturbance propagation through a crystalline lattice, study the chaotic vibrations of the crystalline states and identify an interesting phase transition when the crystal is destroyed. We demonstrate that there are also relatively confined "droplet" states with the center of mass exhibiting seemingly random walk on the surface. Finally, we investigate the dynamics of disordered gas states and show that there is a surprising and robust linear connection between distributions of angular and linear velocity for both lattice and gas states, allowing to define the concept of temperature.
Finally, as a first step towards continuous theory, we develop a Vlasov-like nonholonomic kinetic theory for a gas of rolling balls. Using that framework, we show that the concept of momentum conservation cannot be borrowed from the classical fluids, and derive a set of alternative conservation laws for the system.
Partially supported by NSF
