Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

Abstract

The square-gradient density-functional model with triple-parabolic free energy is used to study homogeneous bubble nucleation in a stretched liquid to check the scaling rule for the work of formation of the critical bubble as a function of scaled undersaturation $Δμ/Δμ_{\rm spin}$, the difference in chemical potential $Δμ$ between the bulk undersaturated and saturated liquid divided by $Δμ_{\rm spin}$ between the liquid spinodal and saturated liquid. In contrast to our study, a similar density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J. Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation but other various quantities related to the critical bubble show the scaling rule, however, we found virtually no scaling relationships in our model near the coexistence. Although some quantities show almost perfect scaling relations near the spinodal, the work of formation divided by the value deduced from the classical nucleation theory shows no scaling in this model even though it correctly vanishes at the spinodal. Furthermore, the critical bubble does not show any anomaly near the spinodal as predicted many years ago. In particular, our model does not show diverging interfacial width at the spinodal, which is due to the fact that compressibility remains finite until the spinodal is reached in our parabolic models.