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

Abstract

HypothesisThe 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 dp. AnalysisThis is done here for the condensation of n-butanol vapors on polyethylene glycol nano-globules (3 nm ≤ dp ≤ 9 nm). We use published activation probability measurements P(w,dp), 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 Smax = 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(Smax,dp) data, directly comparable with capillary theory with perfect wetting. FindingsExcellent agreement is found above 5 nm for the critical dependence Smax(dp) resulting from the constraint P(Smax,dp) = 0.5. The entire P(Smax,dp) curves also agree closely between 5 and 7 nm. Smaller particles depart only slightly from theory, even at dp = 3 nm. Capillary theory hence describes accurately the heterogeneous nucleation process above 3–5 nm, provides a reliable method to determine Smax, and yields experimentally the nucleation rate constant K.