Heterogeneous nucleation on convex spherical substrate surfaces:A rigorous thermodynamic formulation of Fletcher's classical modeland the new perspectives derived

摘要

Fletcher's spherical substrate model [J. Chem. Phys. 29, 572 (1958)] is a basic model forunderstanding the heterogeneous nucleation phenomena in nature. However, a rigorous thermodynamic formulation of the model has been missing due to the significant complexitiesinvolved. This has not only left the classical model deficient but also likely obscured its other important features, which would otherwise have helped to better understand and controlheterogeneous nucleation on spherical substrates. This work presents a rigorous thermodynamic formulation of Fletcher's model using a novel analytical approach and discusses the new perspectives derived. In particular, it is shown that the use of an intermediate variable, a selectedgeometrical angle or pseudocontact angle between the embryo and spherical substrate, revealedextraordinary similarities between the first derivatives of the free energy change with respect to embryo radius for nucleation on spherical and flat substrates. Enlightened by the discovery, it wasfound that there exists a local maximum in the difference between the equivalent contact angles for nucleation on spherical and flat substrates due to the existence of a local maximum in the differencebetween the shape factors for nucleation on spherical and flat substrate surfaces. This helps tounderstand the complexity of the heterogeneous nucleation phenomena in a practical system. Also,it was found that the unfavorable size effect occurs primarily when R<5r~*(R:radius of substrate and r~*: critical embryo radius) and diminishes rapidly with increasing value ofR/ r~*beyondR/ r~*=5. This finding provides a baseline for controlling the size effects in heterogeneous nucleation.