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Concept
Classical nucleation theory
Résumé
Classical nucleation theory (CNT) is the most common theoretical model used to quantitatively study the kinetics of nucleation.
Nucleation is the first step in the spontaneous formation of a new thermodynamic phase or a new structure, starting from a state of metastability. The kinetics of formation of the new phase is frequently dominated by nucleation, such that the time to nucleate determines how long it will take for the new phase to appear. The time to nucleate can vary by orders of magnitude, from negligible to exceedingly large, far beyond reach of experimental timescales. One of the key achievements of classical nucleation theory is to explain and quantify this immense variation.
The central result of classical nucleation theory is a prediction for the rate of nucleation , in units of (number of events)/(volume·time). For instance, a rate in a supersaturated vapor would correspond to an average of 1000 droplets nucleating in a volume of 1 cubic meter in 1 second.
The CNT prediction for is
where
is the free energy cost of the nucleus at the top of the nucleation barrier, and is the average thermal energy with the absolute temperature and the Boltzmann constant.
is the number of nucleation sites.
is the rate at which molecules attach to the nucleus.
is the Zeldovich factor, (named after Yakov Zeldovich) which gives the probability that a nucleus at the top of the barrier will go on to form the new phase, rather than dissolve.
This expression for the rate can be thought of as a product of two factors: the first, , is the number of nucleation sites multiplied by the probability that a nucleus of critical size has grown around it. It can be interpreted as the average, instantaneous number of nuclei at the top of the nucleation barrier. Free energies and probabilities are closely related by definition. The probability of a nucleus forming at a site is proportional to . So if is large and positive the probability of forming a nucleus is very low and nucleation will be slow. Then the average number will be much less than one, i.
Source officielle
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