^{1,a)}

### Abstract

The formation of water clusters on Li^{+}, Na^{+}, K^{+}, Cl^{−}, and I^{−} ions from water vapor at atmospheric conditions have been studied using Monte Carlo simulations. The extended simple point charge model has been employed for water molecules. The polarization of ions in the field of molecules and the polarization of molecules in the field of ions have been considered explicitly in the total Hamiltonian of the molecular system. The cluster formation work and the Gibbs free energy and enthalpy of attachment reactions of one water molecule to the cluster have been calculated via the bicanonical ensemble method. Our results reveal the formation of stable clusters in equilibrium with the moist atmosphere in a wide range of vapor pressure values, with largest clusters are formed around cations. Decreasing the temperature, from 293 K to 253 K, leads to the formation of larger equilibrium clusters, and enhances the stability of systems as whole. According to clusters’ molecular structures, negative ions are expected to be more active in atmospheric processes, including chemical reactions and cloud formation, than positive ones.

We are grateful to Professor Sergei Viktorovich Shevkunov who had amiably accepted to provide us the software (practical implementation of the BCMC) used in this simulation work.

I. INTRODUCTION

II. DETAILS OF THE CALCULATION PROCEDURE

III. THE CLUSTER HAMILTONIAN

IV. STABILITY OF ION–WATER CLUSTERS

V. CONCLUSIONS

### Key Topics

- Atmospheric water
- 20.0
- Gibbs free energy
- 17.0
- Water energy interactions
- 17.0
- Nucleation
- 14.0
- Cluster stability
- 13.0

## Figures

Formation works, *A*(*n,p,T *), of cation–water clusters from the vapor at different pressures as a function of the cluster size : (a) Li^{+}(H_{2}O)_{ n }, (b) Na^{+}(H_{2}O)_{ n }, (c) K^{+}(H_{2}O)_{ n }. *T* = 298 K. φ = 3.15% is the relative humidity value corresponding to *p* = 1.0 mbar.

Formation works, *A*(*n,p,T *), of cation–water clusters from the vapor at different pressures as a function of the cluster size : (a) Li^{+}(H_{2}O)_{ n }, (b) Na^{+}(H_{2}O)_{ n }, (c) K^{+}(H_{2}O)_{ n }. *T* = 298 K. φ = 3.15% is the relative humidity value corresponding to *p* = 1.0 mbar.

Formation works, *A*(*n,p,T *), of anion–water clusters from the vapor at different pressures as a function of the cluster size: (a) Cl^{−}(H_{2}O)_{ n }, (b) I^{−}(H_{2}O)_{ n }. *T* = 298 K. φ = 3.15% is the relative humidity value corresponding to *p* = 1.0 mbar.

Formation works, *A*(*n,p,T *), of anion–water clusters from the vapor at different pressures as a function of the cluster size: (a) Cl^{−}(H_{2}O)_{ n }, (b) I^{−}(H_{2}O)_{ n }. *T* = 298 K. φ = 3.15% is the relative humidity value corresponding to *p* = 1.0 mbar.

Attachment enthalpy; Δ*H*(*n,*T), of water molecule to different *ion*-(H_{2}O)_{ n }-clusters as a function of the cluster size *n*. *T* = 298 K. Dashed line corresponds to Δ*H* _{ vap }.

Attachment enthalpy; Δ*H*(*n,*T), of water molecule to different *ion*-(H_{2}O)_{ n }-clusters as a function of the cluster size *n*. *T* = 298 K. Dashed line corresponds to Δ*H* _{ vap }.

Attachment Gibbs free energy; Δ*G(n,p,T)*, of water molecule to different *ion*-(H_{2}O)_{ n }-clusters as a function of the cluster size *n*. *T* = 298 K. Pressure of surrounding vapor *p* = 1 atm. Dashed line corresponds to Δ*G* _{ vap }.

Attachment Gibbs free energy; Δ*G(n,p,T)*, of water molecule to different *ion*-(H_{2}O)_{ n }-clusters as a function of the cluster size *n*. *T* = 298 K. Pressure of surrounding vapor *p* = 1 atm. Dashed line corresponds to Δ*G* _{ vap }.

Formation works, *A*(*n,p,T *), of different ions-water clusters from the vapor at *p* = 0.5 mbar as a function of the cluster size *n*. *T* = 298 K.

Formation works, *A*(*n,p,T *), of different ions-water clusters from the vapor at *p* = 0.5 mbar as a function of the cluster size *n*. *T* = 298 K.

Selected molecular configurations of some equilibrium size clusters. *T* = 298 K and *p* = 7 mbar: (a) Li^{+}, (b) K^{+}, and (c) Cl^{−}.

Selected molecular configurations of some equilibrium size clusters. *T* = 298 K and *p* = 7 mbar: (a) Li^{+}, (b) K^{+}, and (c) Cl^{−}.

Formation works, *A*(*n,p,T *), of ion–water clusters from the vapor at different pressures as a function of the cluster size: (a) Na^{ + } (H_{2}O)_{ n } and (b) Cl^{ − }(H_{2}O)_{ n }. *T* = 253 K.

Formation works, *A*(*n,p,T *), of ion–water clusters from the vapor at different pressures as a function of the cluster size: (a) Na^{ + } (H_{2}O)_{ n } and (b) Cl^{ − }(H_{2}O)_{ n }. *T* = 253 K.

Selected molecular configurations of different ion-(H_{2}O)_{ n } clusters at *n* _{eq}. *T* = 253 K and *p* = 0.5 mbar: (a) Na^{+} and (b) Cl^{−}.

Selected molecular configurations of different ion-(H_{2}O)_{ n } clusters at *n* _{eq}. *T* = 253 K and *p* = 0.5 mbar: (a) Na^{+} and (b) Cl^{−}.

The radial density distributions of water molecules around ions. *p* = 0.5 mbar: (a) *ρ* _{Na} ^{+} _{O} and (b) *ρ* _{I} ^{−} _{O}.

The radial density distributions of water molecules around ions. *p* = 0.5 mbar: (a) *ρ* _{Na} ^{+} _{O} and (b) *ρ* _{I} ^{−} _{O}.

## Tables

Potential parameters of SPC/E water model; *r* _{OH} is the O–H bond length, ∠ HOH is the H–O–H bond angle, *ɛ* _{OO} and *σ* _{OO} are the potential well depth and the interaction radius of the LJ potential, *q* _{O} and *q* _{H} are the charges of negative and positive sites.^{22}

Potential parameters of SPC/E water model; *r* _{OH} is the O–H bond length, ∠ HOH is the H–O–H bond angle, *ɛ* _{OO} and *σ* _{OO} are the potential well depth and the interaction radius of the LJ potential, *q* _{O} and *q* _{H} are the charges of negative and positive sites.^{22}

LJ parameters of ion–water interaction.

LJ parameters of ion–water interaction.

Comparison between the Gibbs free energy Δ*G*, the enthalpy Δ*H*, of the successive association reactions ion(H_{2}O)_{ n } _{−1} + H_{2}O = ion(H_{2}O)_{ n } at the temperature *T* = 298 K and pressure *p* = 1 atm, as obtained by the experiment and by using the Monte Carlo simulation method. Also, the ion–oxygen water RDF first peak positions R_{ion–water} are reported.

Comparison between the Gibbs free energy Δ*G*, the enthalpy Δ*H*, of the successive association reactions ion(H_{2}O)_{ n } _{−1} + H_{2}O = ion(H_{2}O)_{ n } at the temperature *T* = 298 K and pressure *p* = 1 atm, as obtained by the experiment and by using the Monte Carlo simulation method. Also, the ion–oxygen water RDF first peak positions R_{ion–water} are reported.

Cluster size in equilibrium with vapor, *n* _{eq}, and formation work at this point A_{eq} = A(*n* _{eq},0.5,*T *) for different studied ions. Vapor pressure is 0.5 mbar.

Cluster size in equilibrium with vapor, *n* _{eq}, and formation work at this point A_{eq} = A(*n* _{eq},0.5,*T *) for different studied ions. Vapor pressure is 0.5 mbar.

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