Classical nucleation theory balances the positive surface free energy of a droplet against its negative bulk free-energy gain. In three dimensions,has critical radius and barrier .
In the spherical capillarity approximation, the nonzero maximum of lies at when . Smaller nuclei tend to shrink and larger ones tend to grow. Surface anisotropy and molecular-scale structure limit the approximation.
The maximum free-energy cost along a nucleation pathway, at its critical nucleus. A pathway with fixed shape is a constraint and need not coincide with an unconstrained saddle point.
A cylindrical model nucleus of diameter and height . Its free energy is , where is the signed bulk free-energy change per volume.
A critical nucleus is the unstable droplet at the maximum of the nucleation free energy. Smaller droplets shrink, while larger droplets lower their free energy by growing.
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Classical Nucleation Theory (CNT) is a theoretical framework used to describe the formation of new phase domains, such as droplets or crystals, in a system. This process, called nucleation, is essential in areas like materials science, atmospheric science, and the study of phase transitions. Here are the key components of Classical Nucleation Theory: 1. **Nucleation Basics**: Nucleation occurs when a new phase (e.g.