Activated nucleation relative supersaturation

The higher the relative supersaturation, the more likely nucleation becomes, and the faster crystal growth proceeds. Molecules or ions will remain dissolved provided that the conditions are energetically favorable. However, all molecules above a certain threshold solution activity will remain in, or become part of, the solid phase. Molecules are in equilibrium between the solid state and the dissolved state. The extent to which the equilibrium balance favors the dissolved phase indicates the degree of solubility. 

The equation = 3.67 G x is only valid when all MSMPR assumptions are fulfilled (besides other no attrition and no agglomeration). However, in the case a < 0.1 the mean crystal size L q and especially the maximum ciystal size with max 2 Z50 is controlled by attrition, see Fig. 8.5-1 below. On the other hand, agglomeration can be the dominant process parameter for a > 10. Nanocrystals can only be produced if the relative supersaturation is high with the result of high rates of activated nucleation and by the avoidance of agglomeration. Aggregates which are formed under low or zero supersaturation do not possess crystalline bridges and can be redispersed. 

Membrane surfaces act as a promoter of crystallization by lowering the activation barrier to the nucleation stage, thus allowing molecules to aggregate in conditions of supersaturation that would not be adequate for the spontaneous nucleation. The relatively small elapsed time for the appearance of biomolecular crystals demonstrates the existence of the molecule-membrane interactions that favorably affect the mechanisms of nucleation. A short list of biomolecnles tested by the authors is reported in Figure 10.7. 

If, within the diffusion zone, there is no active vacancy source or sink, then no drift of lattice planes could occur and the difference in the diffusion fluxes of substitutional chemical species would result in vacancy supersaturation and build-up of local stress states within the diffusion zone. Return to local equilibrium in a stress-free state could be achieved by the nucleation of pores leading to the well-known Kirkendall porosity (Fig. 2.2d). All intermediate situations are possible depending on local stress states and the density, distribution and efficiency of vacancy sources or sinks. However, it should be emphasized that complete Kirkendall shift would occur only in stress-free systems in local equihbrium. Therefore, all obstacles to the free relative displacement of lattice planes would lead to local non-equilibrium. Such a situation corresponds to the build-up of stress states that modify the conditions of local equilibrium and the action of vacancy sources or sinks these stress states must therefore be taken into account to define and analyse these local conditions and their spatial and temporal evolutions. 

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