Nucleation stable nuclei

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

Note, however, that a) the size of a stable nucleus depends on the model used (see Sect. 3.5.1), and b) molecular nucleation theory (Sect. 3.8.1) rules out such a mechanism. 

Because of its dependence on a, ae, 51, and AF its size can be expected to vary according to the type of nucleation model employed in analyzing a set of experimental data (see Refs. [106 and [107]). The size of a stable nucleus has consequences as far as, e.g., the number of molecules needed to form it and the minimum required substrate length are concerned. 

Nucleation can occur either homogeneously or heterogeneously. Homogeneous nucleation occurs when random molecular motion in the molten state results in the alignment of a sufficient number of chain segments to form a stable ordered phase, known as a nucleus. The minimum number of unit cells required to form a stable nucleus decreases as the temperature falls. Thus, the rate of nucleation increases as the temperature of the polymer decreases. The rate of homogeneous nucleation also increases as molecular orientation in the molten polymer increases. This is because the entropy difference between the molten and crystalline states diminishes as molecular alignment in the molten state increases. 

Homogeneous Nucleation Homogeneous nucleation is based on accretion of molecules in the liquid phase. Single species (molecules or ions) come together and form dimers. Dimers become trimers by addition of a molecule, and this accumulation process continues until eventually a stable nucleus forms depending on temperature and supers aturation. 

According to the classic nucleation theory, a free-energy barrier must be overcome to form a stable nucleus. The energy needed to form a crystal is proportional to the interfacial tension, y, and the surface area. However, once a nucleus is formed, there is a release of energy (latent heat) associated with the phase change. 

For Nq potential, noninteracting nucleation sites, each of which has the same probability ki per unit time of becoming a stable nucleus, the rate of nucleation is... 

Equation (21) establishes a dependence of AG5 and AG on the radius of a nucleus (Figure 5), The sum of these two terms (i.e., AG) passes through a maximum that defines the critical size of a stable nucleus. The formation of a nucleus of a larger size would result in its spontaneous growth accompanied by a decrease in AG. The maximum value of AG is the energy barrier for the nucleation process, AG. The nucleation rate is commonly expressed in the Arrhenius form ... 

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