Phase transitions are the change of matter from one state to another following a change in a thermodynamic parameter (such as temperature pressure and volume). The study of phase transitions goes back to classical thermodynamics, where it is defined in terms of chemical potential.
In general, two phases will coexist if they are in thermal, mechanical and chemical equilibrium:
\[\mu_1 (p, T) = \mu_2 (p, T) \\ T_1 = T_2 \\ p_1 = p_2\]
Q: This defines the p(T) equation of state, however, how do you calculate chemical potential in molecular simulation – theoretically?
While this gives a very clear picture on how the bulk (infinite) phases are related, that is not enough to describe how things work at finite scale and at an atomistic level. The problem faced are related to surface tension, in general the system will have difficulty of forming a new interface.
For example, in a liquid-solid phase transition, it is necessary to under-cool the system before triggering the phase transition. The system can be in a meta-stable state, trapped in a free energy local minimum.
TODO: definition of meta-stablility...
Metastable systems are at the core of many physical and biological processes. Organisms in cold environments developed strategies to prevent freezing thorugh the use of anti-freeze protein that inhibit nucleation. Another striking example is cloud formation.
KEYWORD: Symmetry breaking
Despite its importance, the description of nucleation processes, especially during their first stages has proven hard to do experimentally because the process happens at nanoscopic scale, both in terms of size and lifetime of the nuclei.
Molecular simulation is an excellent tool in this case because it is able to describe the process at atomistic level of detail, and also enables to change the physics of the problem allowing us to understand how the mechanism works and how it is affected. The data is very rich and we are able to abstract from the various “continuum” approximations.