Homogeneous nucleation is often described by the classical nucleation theory (CNT). According to CNT, the free energy change associated with the formation of a new phase includes a volume term (related to the bulk properties) and a surface term (related to the interfacial energy). The theory predicts the formation of a critical nucleus size, beyond which the nucleus will grow spontaneously. The nucleation rate can be expressed as:
\[ J = A \exp \left( -\frac{\Delta G^*}{k_BT} \right) \]
where \( J \) is the nucleation rate, \( A \) is a pre-exponential factor, \( \Delta G^* \) is the Gibbs free energy barrier for nucleation, \( k_B \) is the Boltzmann constant, and \( T \) is the temperature.
