A DOUBLE-PARABOLA MODEL FOR THE NONCLASSICAL CAHN-HILLIARD THEORY OF HOMOGENEOUS NUCLEATION

A double-parabola model is used to calculate various properties of the critical droplet in homogeneous nucleation using the Cahn-Hilliard non-classical theory, and the results are compared with those predicted from the classical theory due to Becker and Doring. The calculation can be performed mostly analytically, and various quantities can be characterized by two parameters: the supersaturation which measures difference in chemical potential from two-phase coexistence, and the asymmetry of thermodynamic properties of the liquid and the vapour phase. The predictions of the non-classical theory do not differ much from those of the classical theory in liquid-vapour nucleation (liquid droplet formation), but the difference is significant in vapour-liquid nucleation (gas bubble formation). In particular, the non-classical nucleation rate of bubble formation is found to be significantly faster, typically 18 orders of magnitude, than the classical nucleation rate. The deviations of the non-classical results from classical data increase as the asymmetry becomes more pronounced.