Comments on the thermodynamic analysis of nucleation in confined space

Abstract

The effect of depletion of the ambient phase in confined systems on the parameters of the critical clusters in nucleation-growth processes is analyzed by employing the generalized Gibbs' approach. Depletion effects result, in addition to variations of the parameters of the critical clusters (corresponding to a maximum or, in general, saddle point of the thermodynamic potential surface), in the existence of a minimum of the appropriate thermodynamic potential corresponding to a stable state of a cluster in the ambient phase. It is shown that – due to depletion effects – with decreasing volume of the mother phase, the work of formation of both the critical cluster and the stable cluster increases. The results of the analysis of nucleation in confined systems are shown further to allow one to develop a general scenario of first-order phase transitions and to derive, as a particular result, relatively simple equations for the description of the kinetics of competitive growth of the clusters (coarsening or Ostwald ripening) including, in addition to the asymptotic, the initial stages of this process and, as a particularly important special case, the possibility to account for the effect of elastic stresses on coarsening. Experimental examples, where such effects modify the kinetics of coarsening qualitatively, are given here as well as their theoretical interpretation based on thermodynamic considerations as outlined in the present paper.