A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory.

A unifying identity is derived relating the reversible work of cluster formation (W) and its molecular number content (n) and surface work (Φ) components, each ratioed to the corresponding values for a spherical capillary drop of critical size in classical nucleation theory. The result is a relationship that connects these ratios: fW = -2fN + 3fS, where fW = W/W*CNT, fN = n/n*CNT, and fS = Φ/Φ*CNT. Shown to generalize two early thermodynamic relationships of Gibbs, the new result is demonstrated here for Fletcher's model of heterogeneous nucleation, resulting in a unified treatment of condensation on flat and curved substrates and smooth passage to the homogeneous limit. Additional applications are made to clusters of non-critical as well as critical size and to a molecular-based extension of classical nucleation theory based on the Kelvin relation. The new identity serves as a consistency check on complicated theoretical expressions and numerical calculations and can be used to guide the construction of theory and interpretation of measurements.

Temperature Dependence in Heterogeneous Nucleation with Application to the Direct Determination of Cluster Energy on Nearly Molecular Scale.

A re-examination of measurements of heterogeneous nucleation of water vapor on silver nanoparticles is presented here using a model-free framework that derives the energy of critical cluster formation directly from measurements of nucleation probability. Temperature dependence is correlated with cluster stabilization by the nanoparticle seed and previously found cases of unusual increasing nucleation onset saturation ratio with increasing temperature are explained. A necessary condition for the unusual positive temperature dependence is identified, namely that the critical cluster be more stable, on a per molecule basis, than the bulk liquid to exhibit the effect. Temperature dependence is next examined in the classical Fletcher model, modified here to make the energy of cluster formation explicit in the model.  The contact angle used in the Fletcher model is identified as the microscopic contact angle, which can be directly obtained from heterogeneous nucleation experimental data by a recently developed analysis method. Here an equivalent condition, increasing contact angle with temperature, is found necessary for occurrence of unusual temperature dependence. Our findings have immediate applications to atmospheric particle formation and nanoparticle detection in condensation particle counters (CPCs).

Reversible uptake of water on NaCl nanoparticles at relative humidity below deliquescence point observed by noncontact environmental atomic force microscopy.

The behavior of NaCl nanoparticles as a function of relative humidity (RH) has been characterized using non-contact environmental atomic force microscopy (e-AFM) to measure the heights of particles deposited on a prepared hydrophobic surface. Cubic NaCl nanoparticles with sides of 35 and 80 nm were found to take up water reversibly with increasing RH well below the bulk deliquescence relative humidity (DRH) of 75% at 23(∘)C, and to form a liquid-like surface layer of thickness 2 to 5 nm, with measurable uptake (>2 nm increase in particle height) beginning at 70% RH. The maximum thickness of the layer increased with increasing RH and increasing particle size over the range studied. The liquid-like behavior of the layer was indicated by a reversible rounding at the upper surface of the particles, fit to a parabolic cross-section, where the ratio of particle height to maximum radius of curvature increases from zero (flat top) at 68% RH to 0.7 ± 0.3 at 74% RH. These observations, which are consistent with a reorganization of mass on the solid NaCl nanocrystal at RH below the DRH, suggest that the deliquescence of NaCl nanoparticles is more complex than an abrupt first-order phase transition. The height measurements are consistent with a phenomenological model that assumes favorable contributions to the free energy of formation of a liquid layer on solid NaCl due both to van der Waals interactions, which depend partly upon the Hamaker constant, A(film), of the interaction between the thin liquid film and the solid NaCl, and to a longer-range electrostatic interaction over a characteristic length of persistence, ξ; the best fit to the data corresponded to A(film)= 1 kT and ξ = 2.33 nm.

Formation of nanoparticles of blue haze enhanced by anthropogenic pollution.

The molecular processes leading to formation of nanoparticles of blue haze over forested areas are highly complex and not fully understood. We show that the interaction between biogenic organic acids and sulfuric acid enhances nucleation and initial growth of those nanoparticles. With one cis-pinonic acid and three to five sulfuric acid molecules in the critical nucleus, the hydrophobic organic acid part enhances the stability and growth on the hydrophilic sulfuric acid counterpart. Dimers or heterodimers of biogenic organic acids alone are unfavorable for new particle formation and growth because of their hydrophobicity. Condensation of low-volatility organic acids is hindered on nano-sized particles, whereas ammonia contributes negligibly to particle growth in the size range of 3-30 nm. The results suggest that initial growth from the critical nucleus to the detectable size of 2-3 nm most likely occurs by condensation of sulfuric acid and water, implying that anthropogenic sulfur emissions (mainly from power plants) strongly influence formation of terrestrial biogenic particles and exert larger direct and indirect climate forcing than previously recognized.