The smallest nanodrop describable via macroscopic interfacial concepts: Testing classical heterogeneous nucleation theory with perfect wetting down to 3 nm

Hypothesis: The smallest nanodrop tractable with macroscopic notions such as the interfacial energy could be determined by comparing heterogeneous nucleation observations and capillary theory predictions at decreasing drop diameters d(p). Analysis: This is done here for the condensation of n-butanol vapors on polyethylene glycol nano-globules (3 nm <= d(p) <= 9 nm). We use published activation probability measurements P(w,d(p)), where w is the accurately controlled saturation ratio of n-butanol vapor in a gas stream exiting a saturator. The maximal saturation ratio achieved in the nucleation region by cooling this gas-vapor stream in the apparatus of Gallar et al. satisfies S-max = Cw. The key unknown constant C and the preexponential term K governing the nucleation rate are determined by assuming that classical theory applies to the largest particles used. This yields P(S-max,d(p)) data, directly comparable with capillary theory with perfect wetting. Findings: Excellent agreement is found above 5 nm for the critical dependence S-max(d(p)) resulting from the constraint P(S-max,d(p)) = 0.5. The entire P(S-max,d(p)) curves also agree closely between 5 and 7 nm. Smaller particles depart only slightly from theory, even at d(p) = 3 nm. Capillary theory hence describes accurately the heterogeneous nucleation process above 3-5 nm, provides a reliable method to determine S-max, and yields experimentally the nucleation rate constant K.