The nucleation process
Structure and stability for Alkali Halides
Nucleation from solution of NaCl nanocrystals
Dissolution of NaCl nanocrystals
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.
Classical Nucleation Theory is the standard treatment for nucleation, and it has been widely used to predict nucleation rates albeit, with order-of-magnitude errors. It manages to transform a kinetic theory into a thermodynamic one by making certain assumption about some microscopic quantitites \(\alpha\), \(\beta\) and \(N(n)\).
In this thesis we develop a data-centered approach to the problem.
Nucleation experiments date back to periods earlier than 1970 with experiments dealing especially with the onset of nucleation, after that other techniques were developed to address the problem of nucleation rates, such as thermal diffusion and expansion cloud chambers. Experimental Challenges (Davey 2013)
Direct experiments are mostly able to observe big molecules, that were shown to behave classicaly, for example the work by Sleutel et al, that performed direct observation of nucleation (in 2 dimensions) of the protein glucose isomerase through atomic force microscopy. (Sleutel 2014)
Another important experiment is the detection of stable prenucleation calcium carbonate clusters. By titrating the amount of free calcium carbonate at costant pH, they were able to detect an unusually high amount of bound caco3 clusters, suggesting the presence of metastable prenucleation clusters.(Gebauer 2008)
NaCl supersaturation was also recently studied experimentally providing good estimates of nucleation rate. (Desarnaud 2014)
Alkali halides are pretty good, determination of critical size for glycine and NaCl was also measured different times (Na 1994)