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

Abstract

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.

Keywords: Aerosol; Capillary theory; Experimental verification; Gas phase; Heterogeneous nucleation; Kelvin diameter; Nanometer.