Quantitative Characterization of Critical Nanoclusters Nucleated on Large Single Molecules

First order phase transitions involve nucleation, formation of nanoscale regions of a new phase within a metastable parent phase. Using the heterogeneous nucleation theorem we show how clusters formed by nucleation on single molecules evolve from the gas phase and determine the critical size beyond which condensation starts to form aerosol particles. Our experiments reveal the activation of molecules into droplets to happen via formation of critical clusters substantially larger than the seed molecule. The nanosized critical clusters were found to be well predicted by the Kelvin-Thomson relation pointing directly to the key step in the phase transition.

Figure 1

Size distributions of ${\mathrm{THA}}^{+}\mathrm{Br}$ (solid) and ${\mathrm{TDDA}}^{+}\mathrm{Br}$ (dashed) ions as well as $\mathrm{THA}\mathrm{Br}_2^{-}$ (dotted) as determined with the nano-DMPS.

Figure 2

Heterogeneous nucleation probability $P$ vs vapor saturation ratio for nucleation of $n$-propanol on ${\mathrm{THA}}^{+}\mathrm{Br}$ ions at 273 K (red) and 263 K (blue). Open squares refer to the dimer with mobility diameter 1.78 nm and full squares to the monomer with 1.47 nm. Lines are fitted to the data according to physically consistent heterogeneous nucleation probability functions. Corresponding onset saturation ratios ($P=0.5$) are indicated by vertical dotted lines.

Figure 3

Formation free energies for homogeneous nucleation (solid line) and ion-induced nucleation of $n$-propanol ($S=3.0$, $T=273.15\mathrm{K}$) at two different ion sizes (dashed line is calculated for ion radius 0.9 nm, dotted line for ion radius 0.1 nm). Prenucleation clusters are expected to form only when the energy curves go through a minimum as is the case for an ion with radius 0.1 nm.

Figure 4

Experimental onset saturation ratios measured at 273 K (red) and 263 K (blue) as function of seed particle mobility diameter for ions (open symbols) together with the diameter of the corresponding critical cluster (full symbols). Circles refer to ${\mathrm{THA}}^{+}$ monomer, squares to $\mathrm{THA}_2{}^{+}\mathrm{Br}$ dimer, triangles to ${\mathrm{TDDA}}^{+}$ and stars to $\mathrm{THA}\mathrm{Br}_2{}^{-}$ dimer. Solid lines indicate the prediction of the Kelvin-Thomson equation at 273 K (red) and 263 K (blue). Horizontal error bars were obtained by means of variation analysis and indicate the possible range of critical clusters. Vertical error bars show experimental uncertainty in saturation ratio (typically below 2% of absolute value). For comparison the agreement of homogeneous nucleation data and Kelvin equation is shown for 265 K (cyan).