Kinetics of nucleation at increasing supersaturation

The kinetics of homogeneous nucleation-growth processes under increasing su persaturation is investigated, The increase of the supersaturation is hereb y caused by an appropriate variation of external parameters such as pressur e and temperature. Analytic expressions are formulated for the dependence o f the number of supercritical clusters both on the rate of change of the su persaturation and on time. In generalization of previous studies, both ther mal and athermal nucleation are taken into consideration. It turns out that in dependence on the rate of change of the external parameters, either the rmal (for moderate rates) or athermal (for higher rates) nucleation, domina tes the process. It is shown further that, in the range where thermal nucle ation dominates, the onset of nucleation-growth processes, i.e., the minimu m value of the supersaturation required for intensive nucleation, depends w eakly (logarithmically) on the rate of increase of the supersaturation. Cri teria are formulated under which conditions the commonly employed assumptio n-independence of the nucleation-growth process on the way the initial unst able state is established-is applicable. As shown, quite generally these cr iteria are not fulfilled. In a further step of the analysis, simultaneously to external variations of the thermodynamic parameters, internally generat ed changes of the state of the system (depletion effects) are accounted for , For segregation processes in solutions (bubble formation), which are anal yzed here as an example, such effects result from a decrease of the supersa turation due to the consumption of solute particles by the clusters of the newly formed phase. Basic characteristics of the nucleation-growth process, such as the maximum number of dusters formed in the system, are determined in dependence on both externally (rate of change of the external parameter s) and internally (depletion effects) induced changes of the thermodynamic state of the system. It is shown, in particular, that the interplay of both factors is, in general, of comparable importance for the outcome of the nu cleation-growth process. (C) 1999 Academic Press.