Heterogeneous Nucleation with Finite Activation Energy and Perfect Wetting: Capillary Theory Versus Experiments with Nanometer Particles, and Extrapolations on the Smallest Detectable Nucleus

Abstract

Analytical expressions are provided for charged and uncharged particles in the perfect-wetting limit of Fletcher's classical heterogeneous nucleation theory with finite activation energy G * . A dimensionless logarithm of the critical supersaturation can be represented as a single universal curve versus a dimensionless nucleus radius for neutral particles, while a uniparametric family of curves is required for charged particles. Comparison with experimental critical supersaturations for nanoparticles and molecular ions shows qualitative agreement, with substantial quantitative disagreement. At increasing sizes the predicted critical diameter augmented by a fixed length ∼1 nm approaches the Kelvin limit. Predicted activation probability curves versus size (supersaturation) are steep, whence stringent experimental definitions of the thermodynamic state and the seed particle are required for meaningful comparison with theory. Activation curves for mobility-selected WO x particles are broader than predicted, even with a well-defined supersaturation, while those of mobility-purified molecular ions agree qualitatively with theory, even in a turbulent mixing nucleation chamber. Recent work by Winkler (2009) based on the Vienna expansion chamber and mobility-purified molecular ions has anticipated these conclusions. The theory is combined with similar considerations on the onset of homogeneous nucleation, to draw conclusions on the smallest nucleus size that may be activated by heterogeneous nucleation. Water is predicted to be able to detect uncharged nuclei with diameters as small as 0.6 nm. The associated possibility to develop detectors for relatively small single neutral molecules is enticing.

Soot formation in laminar counterflow flames

“…More recently, a diethyl glycol (DEG)-based condensation nano-enhancer, when used in combination with a second-stage growth booster, has been demonstrated to be capable of detecting particles with sizes down to 1 nm [522]. Through a theoretical investigation, de la Mora [523] anticipated that water at low temperature could even activate particles with diameter as small as 0.6 nm.…”

The First Droplet in a Cloud Chamber Track

“…If there is an ion of charge Q at the center of the droplet, the free energy is supplemented by the term (Kelvin-Thomson model [15])…”

“…[This picture is "philosophical" in quotes] because in principle you could run a huge computer simulation and see for yourself the simulated wavefunctions coalescing, then learning how to think and measure, and finally measuring." So this assumption-that small wavefunction means small physical effect without an explicit wavefunction probability interpretation-seems to be a necessary (15) As | | 2 , condition for accounting for canonical quantum measurement behavior without explicit measurement axioms. I doubt that it could also be sufficient.…”

Effect of the finite width of the temperature transition in diffusive condensation particle counters

“…Another approach is to continuously scan over the saturation ratio S in the CPC, to produce spectra in the form of particle counts versus S, C(S) (Gamero-Castaño and Fernandez de la Mora 2000). The resolution with which C(S) spectra can be turned into size spectra naturally depends on how narrowly defined is S within the CPC (Fernandez de la Mora 2011. The adiabatic expansion method of a flow volume pioneered by Wilson (1927) is ideal to produce a spatially uniform S (Winkler et al 2008, Tauber et al 2018, but is a slow batch process unpractical for particle monitoring.…”