Nucleation

Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears.

For example, if a volume of water is cooled (at atmospheric pressure) significantly below 0 °C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0 °C often stay completely free of ice for long periods (supercooling).

However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay.

However, the CNT fails in describing experimental results of vapour to liquid nucleation even for model substances like argon by several orders of magnitude.

It correctly predicts that the time you have to wait for nucleation decreases extremely rapidly when supersaturated.

The self-assembly process that forms objects like the amyloid aggregates associated with Alzheimer's disease also starts with nucleation.

[7] Energy consuming self-organising systems such as the microtubules in cells also show nucleation and growth.

This predicts that the nucleation slows exponentially with the height of a free energy barrier ΔG*.

For example, computer simulations of gold nanoparticles show that the crystal phase sometimes nucleates at the liquid-gold surface.

[8] Classical nucleation theory makes a number of assumptions, for example it treats a microscopic nucleus as if it is a macroscopic droplet with a well-defined surface whose free energy is estimated using an equilibrium property: the interfacial tension σ.

For a nucleus that may be only of order ten molecules across it is not always clear that we can treat something so small as a volume plus a surface.

However, modern computers are powerful enough to calculate essentially exact nucleation rates for simple models.

These have been compared with the classical theory, for example for the case of nucleation of the crystal phase in the model of hard spheres.

Phase-transition processes can also be explained in terms of spinodal decomposition, where phase separation is delayed until the system enters the unstable region where a small perturbation in composition leads to a decrease in energy and, thus, spontaneous growth of the perturbation.

In many cases, liquids and solutions can be cooled down or concentrated up to conditions where the liquid or solution is significantly less thermodynamically stable than the crystal, but where no crystals will form for minutes, hours, weeks or longer; this process is called supercooling.

This has consequences, for example cold high altitude clouds may contain large numbers of small liquid water droplets that are far below 0 °C.

It is for the nucleation at constant temperature and hence supersaturation of the crystal phase in small droplets of supercooled liquid tin; this is the work of Pound and La Mer.

The freezing of small water droplets to ice is an important process, particularly in the formation and dynamics of clouds.

For example in metals solid-state nucleation and precipitate growth plays an important role e.g. in modifying mechanical properties like ductility, while in semiconductors it plays an important role e.g. in trapping impurities during integrated circuit manufacture.