Bridging atomistic simulations and thermodynamic hydration models of aqueous electrolyte solutions.

Chemical thermodynamic models of solvent and solute activities predict the equilibrium behavior of aqueous solutions. However, these models are semi-empirical. They represent micro-scale ion and solvent behaviors controlling the macroscopic properties using small numbers of parameters whose values are obtained by fitting to activities and other partial derivatives of the Gibbs energy measured for the bulk solutions. We have conducted atomistic simulations of aqueous electrolyte solutions (MgCl2 and CaCl2) to determine the parameters of thermodynamic hydration models. We have implemented a cooperative hydration model to categorize the water molecules in electrolyte solutions into different subpopulations. The value of the electrolyte-specific parameter, k, was determined from the ion-affected subpopulation with the lowest absolute value of the free energy of removing the water molecule. The other equilibrium constant parameter, K1, associated with the first degree of hydration, was computed from the free energy of hydration of hydrated clusters. The hydration number, h, was determined from a reorientation dynamic analysis of the water subpopulations compared to bulk-like behavior. The reparameterized models [R. H. Stokes and R. H. Robinson, J. Solution Chem. 2, 173 (1973) and Balomenos et al., Fluid Phase Equilib. 243, 29 (2006)] using the computed values of the parameters lead to the osmotic coefficients of MgCl2 solutions that are consistent with measurements. Such an approach removes the dependence on the availability of experimental data and could lead to aqueous thermodynamic models capable of estimating the values of solute and solvent activities as well as thermal and volumetric properties for a wide range of compositions and concentrations.

Hydrogen-Bond Structure and Low-Frequency Dynamics of Electrolyte Solutions: Hydration Numbers from ab Initio Water Reorientation Dynamics and Dielectric Relaxation Spectroscopy.

We present an atomistic simulation scheme for the determination of the hydration number (h) of aqueous electrolyte solutions based on the calculation of the water dipole reorientation dynamics. In this methodology, the time evolution of an aqueous electrolyte solution generated from ab initio molecular dynamics simulations is used to compute the reorientation time of different water subpopulations. The value of h is determined by considering whether the reorientation time of the water subpopulations is retarded with respect to bulk-like behavior. The application of this computational protocol to magnesium chloride (MgCl2 ) solutions at different concentrations (0.6-2.8 mol kg-1 ) gives h values in excellent agreement with experimental hydration numbers obtained using GHz-to-THz dielectric relaxation spectroscopy. This methodology is attractive because it is based on a well-defined criterion for the definition of hydration number and provides a link with the molecular-level processes responsible for affecting bulk solution behavior. Analysis of the ab initio molecular dynamics trajectories using radial distribution functions, hydrogen bonding statistics, vibrational density of states, water-water hydrogen bonding lifetimes, and water dipole reorientation reveals that MgCl2 has a considerable influence on the hydrogen bond network compared with bulk water. These effects have been assigned to the specific strong Mg-water interaction rather than the Cl-water interaction.

Density functional theory based molecular dynamics study of solution composition effects on the solvation shell of metal ions.

We present an ab initio molecular dynamics study of the alkali metal ions Li+, Na+, K+ and Cs+, and of the alkaline earth metal ions Mg2+ and Ca2+ in both pure water and electrolyte solutions containing the counterions Cl- and SO42-. Simulations were conducted using different density functional theory methods (PBE, BLYP and revPBE), with and without the inclusion of dispersion interactions (-D3). Analysis of the ion-water structure and interaction strength, water exchange between the first and second hydration shell, and hydrogen bond network and low-frequency reorientation dynamics around the metal ions have been used to characterise the influence of solution composition on the ionic solvation shell. Counterions affect the properties of the hydration shell not only when they are directly coordinated to the metal ion, but also when they are at the second coordination shell. Chloride ions reduce the sodium hydration shell and expand the calcium hydration shell by stabilizing under-coordinated hydrated Na(H2O)5+ complexes and over-coordinated Ca(H2O)72+. The same behaviour is observed in CaSO4(aq), where Ca2+ and SO42- form almost exclusively solvent-shared ion pairs. Water exchange between the first and second hydration shell around Ca2+ in CaSO4(aq) is drastically decelerated compared with the simulations of the hydrated metal ion (single Ca2+, no counterions). Velocity autocorrelation function analysis, used to probe the strength of the local ion-water interaction, shows a smoother decay of Mg2+ in MgCl2(aq), which is a clear indication of a looser inter-hexahedral vibration in the presence of chloride ions located in the second coordination shell of Mg2+. The hydrogen bond statistics and orientational dynamics in the ionic solvation shell show that the influence on the water-water network cannot only be ascribed to the specific cation-water interaction, but also to the subtle interplay between the level of hydration of the ions, and the interactions between ions, especially those of opposite charge. As many reactive processes involving solvated metal ions occur in environments that are far from pure water but rich in ions, this computational study shows how the solution composition can result in significant differences in behaviour and function of the ionic solvation shell.

Fast oxidation of sulfur dioxide by hydrogen peroxide in deliquesced aerosol particles.

Atmospheric sulfate aerosols have important impacts on air quality, climate, and human and ecosystem health. However, current air-quality models generally underestimate the rate of conversion of sulfur dioxide (SO2) to sulfate during severe haze pollution events, indicating that our understanding of sulfate formation chemistry is incomplete. This may arise because the air-quality models rely upon kinetics studies of SO2 oxidation conducted in dilute aqueous solutions, and not at the high solute strengths of atmospheric aerosol particles. Here, we utilize an aerosol flow reactor to perform direct investigation on the kinetics of aqueous oxidation of dissolved SO2 by hydrogen peroxide (H2O2) using pH-buffered, submicrometer, deliquesced aerosol particles at relative humidity of 73 to 90%. We find that the high solute strength of the aerosol particles significantly enhances the sulfate formation rate for the H2O2 oxidation pathway compared to the dilute solution. By taking these effects into account, our results indicate that the oxidation of SO2 by H2O2 in the liquid water present in atmospheric aerosol particles can contribute to the missing sulfate source during severe haze episodes.

The Acidity of Atmospheric Particles and Clouds.

Acidity, defined as pH, is a central component of aqueous chemistry. In the atmosphere, the acidity of condensed phases (aerosol particles, cloud water, and fog droplets) governs the phase partitioning of semi-volatile gases such as HNO3, NH3, HCl, and organic acids and bases as well as chemical reaction rates. It has implications for the atmospheric lifetime of pollutants, deposition, and human health. Despite its fundamental role in atmospheric processes, only recently has this field seen a growth in the number of studies on particle acidity. Even with this growth, many fine particle pH estimates must be based on thermodynamic model calculations since no operational techniques exist for direct measurements. Current information indicates acidic fine particles are ubiquitous, but observationally-constrained pH estimates are limited in spatial and temporal coverage. Clouds and fogs are also generally acidic, but to a lesser degree than particles, and have a range of pH that is quite sensitive to anthropogenic emissions of sulfur and nitrogen oxides, as well as ambient ammonia. Historical measurements indicate that cloud and fog droplet pH has changed in recent decades in response to controls on anthropogenic emissions, while the limited trend data for aerosol particles indicates acidity may be relatively constant due to the semi-volatile nature of the key acids and bases and buffering in particles. This paper reviews and synthesizes the current state of knowledge on the acidity of atmospheric condensed phases, specifically particles and cloud droplets. It includes recommendations for estimating acidity and pH, standard nomenclature, a synthesis of current pH estimates based on observations, and new model calculations on the local and global scale.

Accurate Measurements of Aerosol Hygroscopic Growth over a Wide Range in Relative Humidity.

Using a comparative evaporation kinetics approach, we describe a new and accurate method for determining the equilibrium hygroscopic growth of aerosol droplets. The time-evolving size of an aqueous droplet, as it evaporates to a steady size and composition that is in equilibrium with the gas phase relative humidity, is used to determine the time-dependent mass flux of water, yielding information on the vapor pressure of water above the droplet surface at every instant in time. Accurate characterization of the gas phase relative humidity is provided from a control measurement of the evaporation profile of a droplet of know equilibrium properties, either a pure water droplet or a sodium chloride droplet. In combination, and by comparison with simulations that account for both the heat and mass transport governing the droplet evaporation kinetics, these measurements allow accurate retrieval of the equilibrium properties of the solution droplet (i.e., the variations with water activity in the mass fraction of solute, diameter growth factor, osmotic coefficient or number of water molecules per solute molecule). Hygroscopicity measurements can be made over a wide range in water activity (from >0.99 to, in principle, <0.05) on time scales of <10 s for droplets containing involatile or volatile solutes. The approach is benchmarked for binary and ternary inorganic solution aerosols with typical uncertainties in water activity of <±0.2% at water activities >0.9 and ∼±1% below 80% RH, and maximum uncertainties in diameter growth factor of ±0.7%. For all of the inorganic systems examined, the time-dependent data are consistent with large values of the mass accommodation (or evaporation) coefficient (>0.1).

Organic component vapor pressures and hygroscopicities of aqueous aerosol measured by optical tweezers.

Measurements of the hygroscopic response of aerosol and the particle-to-gas partitioning of semivolatile organic compounds are crucial for providing more accurate descriptions of the compositional and size distributions of atmospheric aerosol. Concurrent measurements of particle size and composition (inferred from refractive index) are reported here using optical tweezers to isolate and probe individual aerosol droplets over extended timeframes. The measurements are shown to allow accurate retrievals of component vapor pressures and hygroscopic response through examining correlated variations in size and composition for binary droplets containing water and a single organic component. Measurements are reported for a homologous series of dicarboxylic acids, maleic acid, citric acid, glycerol, or 1,2,6-hexanetriol. An assessment of the inherent uncertainties in such measurements when measuring only particle size is provided to confirm the value of such a correlational approach. We also show that the method of molar refraction provides an accurate characterization of the compositional dependence of the refractive index of the solutions. In this method, the density of the pure liquid solute is the largest uncertainty and must be either known or inferred from subsaturated measurements with an error of <±2.5% to discriminate between different thermodynamic treatments.

Hydration of atmospherically relevant molecular clusters: computational chemistry and classical thermodynamics.

Formation of new particles through clustering of molecules from condensable vapors is a significant source for atmospheric aerosols. The smallest clusters formed in the very first steps of the condensation process are, however, not directly observable by experimental means. We present here a comprehensive series of electronic structure calculations on the hydrates of clusters formed by up to four molecules of sulfuric acid, and up to two molecules of ammonia or dimethylamine. Though clusters containing ammonia, and certainly dimethylamine, generally exhibit lower average hydration than the pure acid clusters, populations of individual hydrates vary widely. Furthermore, we explore the predictions obtained using a thermodynamic model for the description of these hydrates. The similar magnitude and trends of hydrate formation predicted by both methods illustrate the potential of combining them to obtain more comprehensive models. The stabilization of some clusters relative to others due to their hydration is highly likely to have significant effects on the overall processes that lead to formation of new particles in the atmosphere.

An isotherm-based thermodynamic model of multicomponent aqueous solutions, applicable over the entire concentration range.

In previous studies (Dutcher et al. J. Phys. Chem. C 2011, 115, 16474-16487; 2012, 116, 1850-1864), we derived equations for the Gibbs energy, solvent and solute activities, and solute concentrations in multicomponent liquid mixtures, based upon expressions for adsorption isotherms that include arbitrary numbers of hydration layers on each solute. In this work, the long-range electrostatic interactions that dominate in dilute solutions are added to the Gibbs energy expression, thus extending the range of concentrations for which the model can be used from pure liquid solute(s) to infinite dilution in the solvent, water. An equation for the conversion of the reference state for solute activity coefficients to infinite dilution in water has been derived. A number of simplifications are identified, notably the equivalence of the sorption site parameters r and the stoichiometric coefficients of the solutes, resulting in a reduction in the number of model parameters. Solute concentrations in mixtures conform to a modified Zdanovskii-Stokes-Robinson mixing rule, and solute activity coefficients to a modified McKay-Perring relation, when the effects of the long-range (Debye-Hückel) term in the equations are taken into account. Practical applications of the equations to osmotic and activity coefficients of pure aqueous electrolyte solutions and mixtures show both satisfactory accuracy from low to high concentrations, together with a thermodynamically reasonable extrapolation (beyond the range of measurements) to extreme concentration and to the pure liquid solute(s).

Surface tensions of inorganic multicomponent aqueous electrolyte solutions and melts.

A semiempirical model is presented that predicts surface tensions (σ) of aqueous electrolyte solutions and their mixtures, for concentrations ranging from infinitely dilute solution to molten salt. The model requires, at most, only two temperature-dependent terms to represent surface tensions of either pure aqueous solutions, or aqueous or molten mixtures, over the entire composition range. A relationship was found for the coefficients of the equation σ = c(1) + c(2)T (where T (K) is temperature) for molten salts in terms of ion valency and radius, melting temperature, and salt molar volume. Hypothetical liquid surface tensions can thus be estimated for electrolytes for which there are no data, or which do not exist in molten form. Surface tensions of molten (single) salts, when extrapolated to normal temperatures, were found to be consistent with data for aqueous solutions. This allowed surface tensions of very concentrated, supersaturated, aqueous solutions to be estimated. The model has been applied to the following single electrolytes over the entire concentration range, using data for aqueous solutions over the temperature range 233-523 K, and extrapolated surface tensions of molten salts and pure liquid electrolytes: HCl, HNO(3), H(2)SO(4), NaCl, NaNO(3), Na(2)SO(4), NaHSO(4), Na(2)CO(3), NaHCO(3), NaOH, NH(4)Cl, NH(4)NO(3), (NH(4))(2)SO(4), NH(4)HCO(3), NH(4)OH, KCl, KNO(3), K(2)SO(4), K(2)CO(3), KHCO(3), KOH, CaCl(2), Ca(NO(3))(2), MgCl(2), Mg(NO(3))(2), and MgSO(4). The average absolute percentage error between calculated and experimental surface tensions is 0.80% (for 2389 data points). The model extrapolates smoothly to temperatures as low as 150 K. Also, the model successfully predicts surface tensions of ternary aqueous mixtures; the effect of salt-salt interactions in these calculations was explored.

Studies of single aerosol particles containing malonic acid, glutaric acid, and their mixtures with sodium chloride. II. Liquid-state vapor pressures of the acids.

The vapor pressures of two dicarboxylic acids, malonic acid and glutaric acid, are determined by the measurement of the evaporation rate of the dicarboxylic acids from single levitated particles. Two laboratory methods were used to isolate single particles, an electrodynamic balance and optical tweezers (glutaric acid only). The declining sizes of individual aerosol particles over time were followed using elastic Mie scattering or cavity enhanced Raman scattering. Experiments were conducted over the temperature range of 280-304 K and a range of relative humidities. The subcooled liquid vapor pressures of malonic and glutaric acid at 298.15 K were found to be 6.7(-1.2)(+2.6) x 10(-4) and 11.2(-4.7)(+9.6) x 10(-4) Pa, respectively, and the standard enthalpies of vaporization were respectively 141.9 ± 19.9 and 100.8 ± 23.9 kJ mol(-1). The vapor pressures of both glutaric acid and malonic acid in single particles composed of mixed inorganic/organic composition were found to be independent of salt concentration within the uncertainty of the measurements. Results are compared with previous laboratory determinations and theoretical predictions.

Studies of single aerosol particles containing malonic acid, glutaric acid, and their mixtures with sodium chloride. I. Hygroscopic growth.

We describe a newly constructed electrodynamic balance with which to measure the relative mass of single aerosol particles at varying relative humidity. Measurements of changing mass with respect to the relative humidity allow mass (m) growth factors (m(aqueous)/m(dry)) and diameter (d) growth factors (d(aqueous)/d(dry)) of the aerosol to be determined. Four aerosol types were investigated: malonic acid, glutaric acid, mixtures of malonic acid and sodium chloride, and mixtures of glutaric acid and sodium chloride. The mass growth factors of the malonic acid and glutaric acid aqueous phase aerosols, at 85% relative humidity, were 2.11 +/- 0.08 and 1.73 +/- 0.19, respectively. The mass growth factors of the mixed organic/inorganic aerosols are dependent upon the molar fraction of the individual components. Results are compared with previous laboratory determinations and theoretical predictions.

Comparative thermodynamic studies of aqueous glutaric acid, ammonium sulfate and sodium chloride aerosol at high humidity.

Aerosol optical tweezers are used to simultaneously characterize and compare the hygroscopic properties of two aerosol droplets, one containing inorganic and organic solutes and the second, referred to as the control droplet, containing a single inorganic salt. The inorganic solute is either sodium chloride or ammonium sulfate and the organic component is glutaric acid. The time variation in the size of each droplet (3-7 microm in radius) is recorded with 1 s time resolution and with nanometre accuracy. The size of the control droplet is used to estimate the relative humidity with an accuracy of better than +/-0.09%. Thus, the Kohler curve of the multicomponent inorganic/organic droplet, which characterizes the variation in equilibrium droplet size with relative humidity, can be determined directly. The measurements presented here focus on high relative humidities, above 97%, in the limit of dilute solutes. The experimental data are compared with theoretical treatments that, while ignoring the interactions between the inorganic and organic components, are based upon accurate representations of the activity-concentration relationships of aqueous solutions of the individual salts. The organic component is treated by a parametrized fit to experimental data or by the UNIFAC model and the water activity of the equilibrium solution droplet is calculated using the approach suggested by Clegg, Seinfeld and Brimblecombe or the Zdanovskii-Stokes-Robinson approximation. It is shown that such an experimental strategy, comparing directly droplets of different composition, enables highly accurate measurements of the hygroscopic properties, allowing the theoretical treatments to be rigorously tested. Typical deviations of the experimental measurements from theoretical predictions are shown to be around 1% in equilibrium size, comparable to the variation between the theoretical frameworks considered.

Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. 1. The acids as nondissociating components.

Atmospheric aerosols contain a significant fraction of water-soluble organic compounds, including dicarboxylic acids. Water activities at approximately 298.15 K (including data for highly supersaturated solutions) of oxalic, malonic, succinic, glutaric, maleic, malic, and methyl succinic acids are first correlated as a function of concentration, treating the acids as nondissociating components. Methods proposed by Clegg et al. (J. Aerosol. Sci. 2001, 32, 713-738), and by Clegg and Seinfeld (J. Phys. Chem. A 2004, 108, 1008-1017) for estimating water activities and solute activity coefficients in aqueous mixtures containing both electrolytes and uncharged solutes are then evaluated from comparisons with literature data. These data include water activities, solubilities, and determinations of the eutonic points of solutions containing up to five acids, and solutions containing one or more acids and the salts (NH(4))(2)SO(4), NH(4)NO(3), or NaCl. The extended Zdanovskii-Stokes-Robinson approach of Clegg and Seinfeld yields the more accurate predictions for aqueous mixtures containing dicarboxylic acids only, and for aqueous mixtures of the acids and salts (though by a lesser margin). A number of hybrid modeling approaches, which contain elements of both methods, are outlined.

Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. 2. Systems including dissociation equilibria.

Atmospheric aerosols contain a significant fraction of water-soluble organic compounds, including dicarboxylic acids. Pitzer activity coefficient models are developed, using a wide range of data at 298.15 K, for the following systems containing succinic acid (H(2)Succ) and/or succinate salts: [H(+), Li(+), Na(+), K(+), Rb(+), Cs(+)]Cl(-)-H(2)Succ-H(2)O, HNO(3)-H(2)Succ-H(2)O, H(+)-NH(4)(+)-HSucc(-)-Succ(2-)-NH(3)-H(2)Succ-H(2)O, NH(4)Cl-(NH(4))(2)Succ-H(2)O, H(+)-Na(+)-HSucc(-)-Succ(2-)-Cl(-)-H(2)Succ-H(2)O, NH(4)NO(3)-H(2)Succ-H(2)O, and H(2)SO(4)-H(2)Succ-H(2)O. The above compositions are given in terms of ions in the cases where acid dissociation was considered. Pitzer models were also developed for the following systems containing malonic acid (H(2)Malo): H(+)-Na(+)-HMalo(-)-Malo(2-)-Cl(-)-H(2)Malo-H(2)O, and H(2)Malo-H(2)SO(4)-H(2)O. The models are used to evaluate the extended Zdanovskii-Stokes-Robinson (ZSR) model proposed by Clegg and Seinfeld (J. Phys. Chem. A 2004, 108, 1008-1017) for calculating water and solute activities in solutions in which dissociation equilibria occur. The ZSR model yields satisfactory results only for systems that contain moderate to high concentrations of (nondissociating) supporting electrolyte. A practical modeling scheme is proposed for aqueous atmospheric aerosols containing both electrolytes and dissociating (organic) nonelectrolytes.