Ion-mediated nucleation

The nucleation of critical clusters is highly promoted in presence of electric charges (ions or charged nano-particles), since the Gibbs free energy barrier is lowered as compared to neutral clusters. The homogeneous nucleation of a vapor on ions was first experimentally investigated, at the turn of 20^th century, by Wilson [39] in a cloud chamber, where he adiabatically expanded a vapor causing condensation on ions generated by alpha particles, fast electrons, gamma and X rays. Alternatively, an upward thermal diffusion cloud chamber can be used to create a well defined narrow supersaturation region, and ions are generated by resonant absorption of

2.4 Heterogeneous nucleation

UV light by molecules added to the nucleating substance. Such devices was used, for instance, by Katz et al. [88].

In the cited publication, they pointed out that, owing to the self-repulsion between identically charged ions and to the low ion density typical of a cloud chamber nucleation experiment (10⁵−10⁸ cm³), almost all clusters contain only one ion.

It would be extremely difficult to assess the nucleation efficiency of charged clus-ters if the ion specific chemical properties strongly affected the nucleation process, since one can not prevent potential charge transfer from the resonant molecules to other acceptors or donor that may be present in the chamber. However, at the nucleation rates typically attained in diffusion chambers, a critical cluster contains a number of molecules in the order of 100. Therefore an ion buried near its center has little influence on its surface properties other than those due to its charge, i.e.

the generation of a central force field which hinders the evaporation of molecules from the cluster. Indeed, while the distance between a molecule at the surface of a cluster and the embedded ion is∼1 nm, the free vapor molecules in the outer volume are at least 10 times farther. This results in a decrease of the evaporation rate of nucleating monomers, hence a reduction of the cluster critical size and of the critical supersaturation.

J.J.Thomson [89] first attempted to quantify such effect, by considering the elec-trostatic potential energy of the charged cluster, treated as a single ion buried in a bulk liquid; its calculations showed a reduction of the Gibbs energy barrier depending on ∼q², q being the ion charge. He derived the so-called classical Kelvin-Thomson equation(CKT), which provides an estimation of the supersatu-rationSfor the formation of a critical cluster of radiusr:

k_BTlnS= M where M, ρ and σ are, respectively, the molecular weight, density and surface tension of the bulk liquid,N_Ais the Avogadro constant,ε₀is the vacuum dielectric constant and the(1−ε_l⁻¹)term is a correction factor later introduced by Thomfor and Volmer [90] to account for the dielectric properties of the bulk liquid, repre-sented by its relative permittivityε_l.

The total Gibbs free energy change to form a chargedi-mer from the core ion of radiusr₀is: Eq. (2.21) and (2.22) constituted the fundamental equations driving the classi-cal ion-induced nucleation theory. According to the original formulation of CKT theory, the ion-induced nucleation appears to be independent upon the sign ofq,

photo-induced processes since it neglects the dipole interaction of condensing ligands with the ions. This is a good approximation when such molecules are non-polar, but fails in the opposite case. For instance, recent observations showed a sign preference of the nucleation rate of polar molecules on ions [91], which could not be predicted by the Thom-son equation.

Therefore, it appeared necessary to consider the polarizability of condensing molecules when modelling the charge-assisted nucleation. Motivated by these arguments, several researchers proposed different methods to account for such effect.

Kusaka et al. [92] suggested a density functional theory accounting for the asym-metric microscopic structure of pre-nucleating clusters due to the presence of elec-tric dipoles; such asymmetry is responsible for the sign-dependence of the free energy change and thus of the nucleation rate. Yu developed a modified Kelvin-Thomson equation (MKT, Eq.(22) in Ref. [93]), which explicitly considers the kinetic energy change of condensing polar molecules when approaching the ions, or the extra energy needed for such molecules to move away for the charged clus-ter. When used to predict the enthalpy changes for small (less than 10 molecules) ion-clustering reactions involving protonated clusters, this extended formulation of the CKT proved to offer a much better agreement with experimental data as compared to the classical Thomson equation [93].

However, even considering the corrections for the ion-dipole interactions, the crit-ical supersaturation required for the ion-induced nucleation of water vapor lies in a range which is atmospherically irrelevant (e.g. S∼3.3 in the experimental data of Ref. [94]).The situation dramatically changes when considering a mixture of typical atmospheric vapor species, such as sulfuric acid, nitric acid, ammonia, as well as volatile organics. Owing to the efficient stabilization effect yielded by these substances to the nucleating molecules, the nucleation on natural ions con-stitutes an important source of atmospheric aerosols. Yu and Turco [77] developed a kinetic model for the heteromolecular homogeneous nucleation of water and sul-furic acid, referred to asion-mediated nucleation(IMN).

The dominant source of ambient ionization in the boundary layer is represented by galactic cosmic rays (GCRs), yielding a ion generation rate spanning from

∼2 ion−pairs cm³ s⁻¹⁶ at ground level up to∼20−30 cm³ s⁻¹ in the upper troposphere [95]. Ions can alternatively be generated by other localized sources such as soil radioactivity, lightning and corona discharges, or combustion.

According to the mechanism proposed by Yu and Turco, such primary ions quickly react with common air constituents to form more stable ions, such as H₂SO^–₄, around which H₂SO₄, H₂O or NH₃vapor ligands can accumulate and grow to ul-trafine particles if the vapor is supersaturated with respect to its condensed phase.

6For simplicity, the notation ion−pairs cm³s⁻¹will be abbreviated to cm³s⁻¹in the case of ion nucleation rate.

2.4 Heterogeneous nucleation

On the other hand, charged ions concentration can be counteracted by ion-ion recombination, leading to the neutralization of the cluster. The buildup of molec-ular clusters by binary or ternary nucleation is also kinetically limited, since it depends on the collision rate and thermal stability. Based on typical small ions ambient concentrations of∼1000cm⁻³and H₂SO₄abundance, Yu and Turco es-timated that the ion-mediated homogeneous nucleation of sulfuric acid is largely favoured with respect to the ion-cluster neutralization or the classical homoge-neous nucleation on a neutral cluster. Indeed, the time needed for an ion to ag-gregate an H₂SO₄ molecule is∼50 s, one order of magnitude less than for the other competing processes. Furthermore, H₂SO₄ is present in sufficiently large concentration to allow for some of the larger ion clusters to evolve and generate cloud condensation nuclei. The presence of ammonia vapor, as well as common organic atmospheric compounds, can further enhance the nucleation and growth of ion-aerosols.

The ion-mediated nucleation theory, applied to the study of major nucleation events at a remote continental site [77] and in the marine boundary layer [96]

under the action of GCRs, can support the observed nucleation rates, which on the contrary can not be predicted by the classical binary or ternary homogeneous nucleation.

Generally speaking, IMN is expected to be relevant in the ionosphere as well as in the troposphere and in the boundary layer, where it also competes with het-erogeneous nucleation for the particle formation. Furthermore, it is of high in-terest in the context of laser-induced particle generation, since multi-photon ion-ization of air molecules is a typical phenomenon that accompanies the propaga-tion of infrared filaments in the atmosphere, yielding a free-electron density of

∼10¹⁵−10¹⁷ cm⁻³ [38]. Therefore, we can expect that charge-assisted nucle-ation and growth may play an important role in the complex dynamics of laser-induced effects.