Nucleation free Gibbs energy change

J is the number of nuclei formed per unit time per unit volume, No is the number of molecules of the crystallizing phase in a unit volume, v is the frequency of atomic or molecular transport at the nucleus-liquid interface, and AG is the maximum in the Gibbs free energy change for the formation of clusters at a certain critical size, 1. The nucleation rate was initially derived for condensation in vapors, where the preexponential factor is related to the gas kinetic collision frequency. In the case of nucleation from condensed phases, the frequency factor is related to the diffusion process. The value of 1 can be obtained by minimizing the free energy function with respect to the characteristic length. 

Scheme 2 Gibbs free energy change of the formation of differently sized nanocrystals (nucleation)...

Following the classical theory of nucleation, the Gibbs free energy change (AG) of crystals nucleated from a homogeneous solution can be expressed as (Wu and Nancollas, 1999) ... 

The following treatment of nucleation in classical nucleation theory (CNT) provides a glimpse of the methods and reasoning of classical theories. A supersaturated solution is assumed to contain spherical nuclei of radius R and with ric particles, and the Gibbs free energy change on formation of these nuclei includes a term in the difference between the free energies of the solid and the liquid, Ap, and a term that represents... 

Initially, crystallization is a two-step process viz. nucleation and crystal growth requiring a change of free energy (Gibbs, 1928), as shown schematically in Figure 5.1. 

Gibbs considered the change of free energy during homogeneous nucleation, which leads to the classical nucleation theory and to the Gibbs-Tliompson relationship (Mullin, 2001). 

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