Methods Nucleation and Growth

According to Gibbs [4] and Vohner [5], the free energy of formation of a spherical nucleus, AG, is given by the sum of two contributions (i) a positive surface energy term AGg which increases with increase in the radius of the nucleus r and (ii) a negative contribution due to the appearance of a new phase, which also increases with increases in r. 

In the initial stages of nucleation, AGg increases faster with increases in r when compared to AG., and AG remains positive, reaching a maximum at a critical radius r, after which it decreases and eventually becomes negative. This occurs because 

It is clear from Equations (9.1) to (9.4) that the free energy of formation of a nucleus and the critical radius r, above which the cluster formation grows spontaneously, depend on two main parameters, namely a and (S/S ), both of which are influenced by the presence of surfactants, a is influenced in a direct way by the adsorption of surfactant onto the surface of the nucleus this adsorption lowers y and this in turn reduces r and AG in other words, spontaneous cluster formation will occur at a smaller critical radius. In addition, surfactant adsorption stabilises the nuclei against any flocculation. The presence of micelles in solution also affects the processes ofnucleation and growth, both directly and indirectly. For example, the micelles can act as nuclei on which growth may occur, and may also solubilize the molecules of the material this can affect the relative supersaturation and, in turn, may have an effect on nucleation and growth. 

Wetting is a fundamental process in which one fluid phase is displaced completely or partially by another fluid phase from the surface of a solid. One useful parameter to describe wetting is the contact angle 0 of a liquid drop on a solid substrate 

Ysv Asv + Ysl sl + Ylv lv should be a minimum at equilibrium, and this leads to the well-known Young s equation  

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Low-temperature synthesis. Due to the homogeneity of the dried powder/gel product and the smaller particle size when compared to grind-and-fire methods, nucleation and growth of crystalline phases can occur at lower temperatures. This also allows the synthesis of metastable phases and the inclusion of organic or other compounds with low thermal stability into the final product. Volatile materials are no longer lost and amorphous phases can be formed. Lower temperatures avoid the effects of particle sintering. 

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