Evaporation of sulfate aerosols at low relative humidity

Evaporation of sulfuric acid from particles can be important in the atmospheres of Earth and Venus. However, the equilibrium constant for the dissociation of H2SO4 to bisulfate ions, which is the one of the fundamental parameters controlling the evaporation of sulfur particles, is not well constrained. In this study we explore the volatility of sulfate particles at very low relative humidity. We measured the evaporation of sulfur particles versus temperature and relative humidity in the CLOUD chamber at CERN. We modelled the observed sulfur particle shrinkage with the ADCHAM model. Based on our model results, we conclude that the sulfur particle shrinkage is mainly governed by H2SO4 and potentially to some extent by SO3 evaporation. We found that the equilibrium constants for the dissociation of H2SO4 to HSO−4 (KH2SO4) and the dehydration of H2SO4 to SO3 (KSO3) areKH2SO4 = 2–4×10 9 mol kg−1 and KSO3 ≥ 1.4× 10 10 at 288.8± 5 K.


Introduction
Suspended particulate matter in the atmosphere plays a key role in Earth's climate. Atmospheric aerosol particles affect the amount of solar radiation absorbed by the Earth system. This is accomplished either when atmospheric aerosol particles directly 30 absorb or scatter incoming solar energy (causing warming or cooling), or when particles act as cloud condensation or ice nuclei (leading to an increase in cloud albedo, which causes cooling). A substantial fraction of particle number and mass across a wide range of environmental conditions arises from sulphur emissions (Clarke et al., 1998a;Turco et al., 1982).
Sulphur in Earth's atmosphere in turn originates from natural phenomena like volcanic eruptions and biota decomposition. Violent volcanic eruptions can loft sulphur dioxide (SO2) to the stratosphere, which can then form sulphur aerosol particles. Those sulphur aerosols can remain suspended in the stratosphere for ~1-2y before falling into the troposphere 5 (Wilson et al., 1993;Deshler, 2008). The three main natural agents for sulphate aerosol formation in troposphere are dimethyl sulphide (DMS), which arises from marine phytoplankton decomposition (Charlson et al., 1987;Kiene, 1999;Simó and Pedrós-Alió, 1999), SO2, which occurs naturally as a decay product of plant and animal matter (Grädel and Crutzen, 1994;Hübert, 1999;Capaldo et al., 1999), and carbonyl sulphide (OCS), which is emitted from anaerobic biological activity and provides the main non-volcanic flux of sulphur into the stratosphere (Galloway and Rodhe, 1991;Rhode, 1999). 10 The atmospheric sulphate burden is substantially perturbed by sulphur emissions associated with anthropogenic activities. The largest anthropogenic source of sulphur is fossil-fuel combustion; coal is the predominant source, but also heavy fuel oil is important (Öm et al., 1996;Smith et al., 2001). Fossil-fuel combustion constitutes ~⅔ of the total global sulphur flux to the atmosphere (Rhode, 1999;Wen and Carignan, 2007), and dominates emissions in most populated regions. Other anthropogenic factors also affect the sulphuric acid (H2SO4) budget, notably sulphur aerosol formation in aircraft plumes 15 (Fahey et al., 1995;Curtius et al., 1998), and extensive sulphur use in industry with a direct environmental impact on local scale. However, on a regional to global scale the acidification of fresh water and forest ecosystems is mainly caused by wet and dry deposition of SO2 and sulphate particles (Simpson et al., 2006).
Sulphur is also a crucial constituent in Venus' atmosphere, an environment with very low relative humidity (RH) (Moroz et al., 1979;Hoffman et al., 1980a), forming the main cloud layer in the form of sulphuric acid droplets (Donahue et 20 al., 1982), which are maintained in an intricate photochemical cycle (photooxidation of OCS, Prinn 1973). Sulphuric acid's reaction paths remain a subject of investigation (Zhang et al., 2010), which makes the study of the sulphur cycle (including the sulphur species SO, SO2, SO3, H2SO4) an important endeavour for understanding both the chemistry and climate of Venus (Mills et al., 2007;Hashimoto and Abe, 2000).
H2SO4 serves as an effective nucleating species and, thus, strongly influences atmospheric new-particle formation 25 (Laaksonen and Kulmala, 1991;Weber et al., 1999;Kulmala et al., 2000;Yu and Turco, 2001;Fiedler et al., 2005;Kuang et al., 2008). The nucleation rate, which is the formation rate (cm -3 •s -1 ) of new particles at the critical size, strongly depends upon the saturation ratio of H2SO4. Uncertainty in this ratio results in an uncertainty of several orders of magnitude in the calculated nucleation rate (Roedel, 1979). Τo model the excess H2SO4 responsible for the gas-to-particle conversion it is necessary to know the vapour pressure of H2SO4 over sulphuric acid and/or neutralized solutions. 30 The sulphuric acid vapour pressure appears through the free-energy term in the exponent of the new-particle formation rate (Volmer and Weber, 1926;Stauffer, 1976). Quantitative theoretical predictions of nucleation rates are highly uncertain because the pure H2SO4 equilibrium vapour pressure is not well known (Gmitro and Vermeulen, 1964;Doyle, 1961;Kiang and Stauffer, 1973). However, accurate calculations of the H2SO4 vapour pressure require accurate equilibrium rate constant values to constrain the reactions of formation and dissociation of H2SO4 in aqueous solutions.
While H2SO4 is often presumed to be practically non-volatile, this is not always the case. There are several circumstances on Earth and Venus where the vapour pressure of H2SO4 matters; specifically, at very low RH, high temperature (T), when there is a deficit of stabilizing bases, and when particles are very small. A very important region of Earth's 5 environment is the upper stratosphere where these conditions prevail (Vaida et al. 2003). Under these conditions H2SO4 can evaporate from particles. This can either inhibit growth of nanoparticles or lead them to shrink.
Furthermore, molecular H2SO4 is never the dominant constituent in sulphuric acid solutions. It will completely dehydrate to sulphur trioxide (SO3, which is extremely volatile) in a truly dry system and yet almost entirely dissociate into bisulphate ion (HSO4 -) and hydronium cation (H3O + ) in the presence of even trace water (H2O) (Clegg and Brimblecombe, 10 1995). This is why H2SO4 is such a powerful desiccant. Also, bases such as ammonia (NH3) will enhance chemical stabilization and form sulphate salts. The thermodynamics of the H2SO4-H2O system at low RH are uncertain, so we seek to improve our understanding of this part of the phase diagram. To accomplish this, we measured the shrinkage of nearly pure H2SO4 particles in the CLOUD chamber at CERN at very low RH and then simulated these experiments with an aerosol dynamics model coupled with a thermodynamics model to constrain the equilibrium constants, for the dissociation 2 4 and the dehydration 15 x 3 , of H2SO4 coupling HSO4 -, H2SO4, and SO3. These new values can be used in models that simulate the evolution of sulphate aerosol particles in the atmospheres of Venus and Earth. H2SO4 partially dissociates to form HSO4via reaction 1 (R1). 2 4 represents the equilibrium constant for R1. HSO4can then undergo a second dissociation reaction (R2) to form a sulphate ion (SO4 2-). In above reactions, sulphur's oxidation number is 6 (S(VI)). 25 For dilute aqueous solutions, R1 is considered to be complete. However, when the mole fraction of S(VI) exceeds ~0.5, H2SO4 can be detected in the solution (Walrafen et al., 2000;Margarella et al., 2013). When H2SO4 is present in the solution, dehydration of H2SO4 to form SO3 (R3) can also be important (Wang et al., 2006;Que et al., 2011). x 3 represents the equilibrium constant for R3 on a mole fraction basis. NH3, which mainly originates from anthropogenic agriculture emissions, is the most abundant base in atmospheric secondary aerosol particles. NH3 neutralises sulphuric acid particles by reacting with H + and forming an ammonium ion (NH4 + ) Even in the cleanest environments, such as the stratosphere, NH3 is present at low concentrations and NH3(g) will be dissolved 5 in the acidic sulphate particles.

Methods
In the CLOUD (Cosmics Leaving OUtdoor Droplets, Kirkby et al. (2011)) chamber at CERN, we measured the H2SO4 aerosol evaporation process under precisely controlled temperature and relative humidity. We designed experiments to accomplish a gradual decrease of RH (from 11.0 to 0.3 %) under atmospherically relevant conditions. To understand the processes governing 10 the measured particle evaporation, we modelled the experiments with the Aerosol Dynamics, gas-and particle-phase chemistry model for laboratory CHAMber studies (ADCHAM, Roldin et al., 2014).

Experimental set up
Details of the CLOUD chamber, the main element of the experimental set up can be found in Kirkby et al. (2011) andDuplissy et al. (2016). For the experiments described here, we formed and grew sulphuric acid particles in the chamber by oxidising 15 SO2 with OH radicals that were generated by photolysing O3 and allowing the resulting O( 1 D) to react with water vapour.
During these experiments we fed the aerosol population to an array of instruments for characterisation of both physical and chemical properties.
We measured the evolution of the aerosol number size distribution with a Scanning Mobility Particle Sizer (SMPS, 25 Wang and Flagan, 1990), which recorded the dry particle mobility diameter in the size range from about 10 to 220 nm. We operated the SMPS system with a recirculating dried sheath flow (RH<14 % controlled by a silicon dryer) with a sheath to aerosol sample flow ratio of 3:0.3 L. We maintained the Differential Mobility Analyser (DMA) and recirculating system at 278-288 K by means of a temperature control rack, while we operated the Condensation Particle Counter (CPC) at room temperature. We corrected the SMPS measurements for charging probability, including the possibility of multiple charges, diffusion losses, and CPC detection efficiency.
We measured aerosol particle chemical composition with an Aerodyne Aerosol Mass Spectrometer (AMS) quantifying sulphate, nitrate, ammonium and organics for particles between 50 and 1000 nm aerodynamic diameter (Jimenez et al., 2003a;Drewnick et al., 2006;Canagaratna et al., 2007). The AMS provided the mass concentration measurements 5 (μg•m -3 ) calculated from the ion signals by using measured air sample flow rate, nitrate ionization efficiency (IE) and relative IE of the other species.

The experimental procedure
To study aerosol particle evaporation, the formation of sulphuric acid particles preceded. At the lowest H2O levels (RH<11 %) and in the presence of O3, controlled UV photo-excitation reactions initiated the oxidation of SO2 to H2SO4. Sulphuric acid 10 particles nucleated and grew to a size of ~220 nm by condensation of H2SO4(g) at a quasi-constant gas phase concentration (~1•10 9 cm -3 with an uncertainty of >20 %). The H2SO4 formation and particle growth ended when we closed the shutters in the front of the UV light source. Afterwards, we induced particle shrinkage by decreasing the RH. We decreased the RH in two separate ways; either by minimizing the influx of water vapour to the chamber, or by increasing the temperature. This separation in experimental procedures gave the ability to achieve and control extremely low RH values (Table 1). 15 After the end of the particle formation period and during the initial steps of evaporation, before the RH started to decrease, the aerosol size distribution remained nearly constant. Subsequently, the RH decreased gradually initiating the particle evaporation. When the RH reached a certain low value (RH≤1.5 % for T=288.8 K) the particles shrank rapidly, as revealed by the SMPS measurements, and the [H2SO4(g)] increased until it reached a peak value (see Supplement, Fig. S1).
The [H2SO4]peak was significantly higher than the background concentration before the onset of evaporation (Table 1). After 20 reaching a maximum in gas-phase concentration, the sulphuric acid decreased again, though the size distribution remained stable (e.g., ~50 (±10) nm for experiments 1 and 2, see Sect. 4.3) depending on the RH and T conditions. This behaviour revealed that the remaining aerosol could not be pure sulphuric acid, but rather consisted of a more stable chemical mixture that inhibited further evaporation.
Similarly, the AMS recorded the evaporation of particles (see Supplement, Fig. S1). The AMS measurements showed 25 that the particles were composed almost exclusively of sulphuric acid (but not pure H2SO4). Based on AMS data, calculations of the kappa value (κ), which is defined as a parameter that describes the aerosols water uptake and cloud condensation nucleus activity (CCN activity), (Petters and Kreidenweis, 2007) of the mixed particles as a function of time during particle evaporation (see Supplement, Fig. S2) yield a value close to the κ for pure sulphuric acid particles (Sullivan et al., 2010). A κ value is indicative of the solubility of aerosol particles, with κ=0 referring to an insoluble particle and κ=0.7 to pure sulphuric acid (1) when the critical diameter Dd and critical saturation Sc (or supersaturation, sc, when referring to CCN activity) are known. The term Α can be calculated from the water properties.

The model framework
In the present work we use ADCHAM (Roldin et al., 2014(Roldin et al., , 2015 to study the evolution of the particle number size distribution and particle chemical composition. Instead of simulating the new-particle formation in the CLOUD chamber, we use the 5 measured particle number size distribution before the UV-lights are turned off as well as time sequences of RH, T and [H2SO4(g)] as inputs to the model (Fig. 1). In order to capture the evolution of the particle number size distribution we consider Brownian coagulation, particle wall deposition, condensation and evaporation of H2SO4, SO3 and H2O from the particles.

The activity coefficients
Within an aqueous electrolyte solution, such as the H2SO4-SO3-H2O system, cations, anions and molecular species all disrupt 10 ideality. Here, we consider interactions between ions (HSO4 -, SO4 2-, NH4 + , H + ) and molecules (H2SO4, SO3, H2O) in the particle-phase chemistry model. To calculate the molality based activity coefficients for the inorganic ions (γi) and the mole fraction based activity coefficient for water ( 2 ) we apply the Aerosol Inorganic Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model (validated at room temperatures, Zuend et al., 2008 and. The reference state for ions and water in the model is an infinitely dilute aqueous solution ( ( 2 → 1)=1 and 2 ( 2 → 1)=1. 15 For relatively dilute H2SO4(aq) solutions (low solute concentration), typical for most atmospheric conditions, it is reasonable to assume that the dissociation of H2SO4 to HSO4 -(R1) is complete (Clegg et al., 1998, Zuend et al., 2008. However, in this work we demonstrate that this assumption fails at low RH and also for small particles with a large Kelvin term. Furthermore, at a very low water activity (aw) (less than ~0.01) a non-negligible fraction of the H2SO4 could potentially decompose to SO3 (R3); if this is the case, the thermodynamic model need to consider not only R1 but R3 as well ( Fig. 1). 20 Since AIOMFAC does not consider inorganic non-electrolyte compounds like H2SO4 and SO3 we implement additionally to this the symmetric electrolyte-NonRandom Two-Liquid (eNRTL) activity coefficient model (Bollas et al., 2008, Song andChen, 2009) which is optimized for the H2SO4-H2O-SO3 systems by Que et al., (2011). In this work we use the regressed eNRTL binary interaction parameters from Que et al., 2011. Following the convention of the eNRTL model (Chen et al., 1982), we set the unknown binary parameters for NH4 + -molecule, molecule-NH4 + and NH4 + -ions to -4, 8 and 25 0, respectively.

The particle phase composition
If ammonium cation (NH4 + ) is present in the sulphuric acid particles, then solid ammonium bisulfate (NH4HSO4(s)) may form when the S(VI) and H2O start to evaporate from the particles. However, the particles may also stay as highly supersaturated droplets with respect to the crystalline phase (Zuend et al., 2011). The particle number size distribution measurements in our 10 experiments did not indicate a sudden drop in particle size during evaporation, which would be expected if the particles crystalized and all particle water was suddenly removed. Thus, in the present work we do not consider formation of any solid salts. We further neglect the influence of any mass-transfer limitations in the particle phase, and assume that the particle ionmolecule equilibrium composition (R1-R3) and water content can be modelled as equilibrium processes (because they are established rapidly compared to the composition change induced by the evaporation of H2SO4 and SO3). We use the 15 thermodynamic model to update the particle equilibrium water content, mole fractions and activity coefficients of all species.
Then the model considers the gas-particle partitioning of H2SO4 and SO3 with a condensation algorithm in the aerosol dynamics model (Sect. 3.3.5). The time step set in the model is 1s.
The thermodynamic model uses an iterative approach to calculate the particle equilibrium mole fractions of H2O, H2SO4, SO3, HSO4 -, SO4 2-, NH3, NH4 + and H + , based on the current time step, known RH, and absolute number of moles of 20 S(VI) and N(-III) for each particle size bin. The modelled particle-phase mole fraction of N(-III) during the evaporation experiments is always substantially lower than that of S(VI) (N:S<0.7). For these particles the saturation vapour pressure of NH3 is always less than 10 -10 Pa, within the experimental water activity range 0-0.11 and 3 ≥0.1. Thus, it is reasonable to assume that during the experiments NH3 does not evaporate from the particles.
Based on the particle diameters from the previous time step (which depend on the particle water content), the 25 thermodynamic model starts by calculating aw for each particle size, considering the Kelvin effect. Given aw, the model estimates the particle water mole fraction. Then the model calculates the H + molality in the aqueous phase via a 4 th order polynomial, derived from the ion balance equation, Eq. (2) in combination with the thermodynamic equilibrium constant equations, Eq. (3-6), and the S(VI) and N(-III) mole balance equations, Eq. (7-8 The thermodynamic equilibrium coefficients for H2SO4 and HSO4dissociations and NH3 protonation (Eq. 3, 4 and 6) are given in a molality based form while the equilibrium coefficient in Eq. (5), which involves the equilibration between the different solvents (H2O, SO3 and H2SO4), is given in a mole fraction based form. The Eq. (5) is given in a mole fraction based form for the following reasons: a) the eNRTL provides mole fraction based activity coefficients, and b) if Eq. (5) would be 10 applied for aw that are even lower than considered in this work, the assumption of using molalities, i.e. where water is considered to be the only solvent, will not be acceptable. The model calculates 4 − and 3 (mol•kg -1 ) with Eq. (9) and Eq. (10) (Jacobson, 2005a). We treat 2 4 and x 3 as unknown model fitting parameters. Once [H + ] is determined, all other ion and molecule concentrations can be derived from Eq. (2-8). Based on the new estimated particle-phase ion and molecule mole fractions, the thermodynamic model uses AIOMFAC and eNRTL to update the ion and molecule activity coefficients. The model then repeats the whole procedure iteratively until the relative change in the concentration and activity coefficients for each compound is less than 10 -9 between successive iteration steps. To stabilize convergence, the model estimates activity coefficients used in the proceeding iteration as a weighted average of the values 20 from the previous and present iteration time steps.

H2SO4 and SO3 in the gas-phase
In the gas phase only a fraction of H2SO4 is in the form of pure sulphuric acid molecules while the rest of the H2SO4 is in a hydrated form. In this work we use the parameterization from Hanson and Eisele (2000), who measured the diffusion loss rate of H2SO4 to flow-tube walls at different RH, to estimate the RH-dependent effective diffusion coefficient of H2SO4(g).
In the gas phase, SO3 reacts rapidly with H2O to form H2SO4. Based on the measured loss rate of SO3, which shows 5 a second-order dependence on the water vapour concentration (Jayne et al., 1997), we estimate that SO3(g) is converted to H2SO4(g) in less than 1s during the CLOUD chamber experiments, even at the lowest RH. Because of this rapid conversion to H2SO4 and the high vapour pressure of SO3 (Eq. 12), it is reasonable to assume that the gas-phase concentration of SO3 (vapour pressure, ∞, 3 ( ) ) is negligibly low.

Saturation vapour pressures, surface tension and particle density 10
We use Eq. (11) and (12) to calculate the temperature dependent sub-cooled pure-liquid saturation vapour pressures for H2SO4 and SO3 (p0,i, where i refers to H2SO4 or SO3 in Pa). Equation (11) is based on the work of Ayers et al. (1980), with corrections for lower temperatures by Kulmala and Laaksonen (1990). We use the (best fit) L parameter value of -11.695 (Noppel et al., 2002, Noppel-Kulmala-Laaksonen, N-K-L parameterisation, see Supplement Fig. S5 (a)). Equation (12) is based on the work of Nickless (1968) (see Supplement Fig. S5 As an alternative to Eq. (11) and (12)  We calculate the saturation vapour pressures of H2SO4 and SO3 for each particle size with Eq. (13), using the mole 20 fractions (χi,j) and mole fraction based activity coefficients (fi,j) of H2SO4 and SO3 (from the thermodynamic model) and the Kelvin term, Ck,i,j Eq. (14) for compound i in particle size bin j.
ai,j is the activity of compound i in size bin j, T is the temperature in Kelvin, R is the universal gas constant (J•mol -1 •K -1 ), Mi is the molar mass (kg•mol -1 ) of compound i, ρp,j is the density (kg•m -3 ) of the liquid particles, σj is the surface tension (N•m -1 ) and Dp,j is the particle diameter (m) of the particles in size bin j.
As an alternative approach we also model the evaporation of H2SO4 using composition dependent H2SO4 activities ( 2 4 , ) derived directly from the tabulated values of the difference in chemical potentials between the sulphuric acid in 5 aqueous solution and that of the pure acid ( 2 4 , − 2 4 0 ). The tabulated values that are valid at 298.15 K are taken from Giauque et al. (1960). The relationship between 2 4 , − 2 4 0 and 2 4 , is given by Eq. (15).
In accordance with Ayers et al. (1980) we neglect any temperature dependence of 2 4 , − 2 4 0 . This empirically based approach is used in several chemistry transport models to simulate the evaporation of pure sulphuric acid particle in the 10 stratosphere (see e.g. Kokkola et al., 2009;English et. al., 2011 andHommel et. al., 2011).
We calculate the surface tension and density of the particles comprising a ternary mixture of water, sulphuric acid and ammonium with parameterisations given by Hyvärinen et al. (2005) that combine surface tension parameterisations for (NH4)2SO4-H2O mixtures (Hämeri et al., 2000, Korhonen et al., 1998b, H2SO4-H2O mixtures  and NH3-H2O mixtures (King et al. 1930). For the range of conditions in our experiment, where the minimum particle diameter
Equation (16) describes the contribution of species i to the mass growth rate of a particle in size bin j, βi,j is the Fuchs-Sutugin correction factor in the transition region (Fuchs and Sutugin, 1971), di ,dj correspond to diameters (m) and Di, Dj to diffusion coefficients (m 2 •s -1 ) of the condensing molecule i and the particles in size bin j, respectively. αi is the massaccommodation coefficient of compounds i and Kni,j is the non-dimensional Knudsen number, Eq.(17). λi,j is the mean free 5 path (m) and νi, νj are the thermal speed (m•s -1 ) of the molecule i and the particles in size bin j, respectively. Equations (16) and (17) take into account that the condensing molecules have a non-negligible size compared to the size of the smallest particles, and that small particles have non-negligible diffusion coefficients (Lehtinen and Kulmala, 2003).
Based on measurements of H2SO4 losses in a flow tube reactor, Pöschl et al., (1998) derived a mass accommodation coefficient of H2SO4(g) on aqueous sulphuric acid, , 2 4 , which was close to unity, with a best fit value of 0.65, a lower 10 limit value of 0.43 and an upper limit of 1.38 (physical limit 1.0). The measured mass accommodation coefficients did not show any dependence on the relative amount of water in the particles (Pöschl et al., 1998). For the model simulations in this work we use unity mass accommodation coefficients. The particle water content is modelled as an equilibrium process with the thermodynamic model (see Sect. 3.3.2).

Particle losses 15
The electric field strength of the stainless-steel CLOUD chamber, in contrast to smog chambers made of Teflon, is very low.
Therefore we can neglect electrostatic deposition enhancements (for details on how ADCHAM treats particle wall deposition losses see Roldin et al., 2014). We simulate the particle size-dependent deposition losses with the model from Lai and Nazaroff (2000). The particle deposition loss depends on the friction velocity (u * ), which we treat as an unknown model fitting parameter. The best possible agreement between the modelled and measured particle number and volume concentration in the 20 chamber is achieved with a friction velocity of ~0.2 m•s -1 . Thus, for all model results we present in this article we use u * =0.2 m•s -1 . Dilution losses due to the purified air injected to the CLOUD chamber are also considered in the model.

Constraining the thermodynamic properties of sulphate aerosol particles
We use ADCHAM to constrain the values of the thermodynamic equilibrium coefficients, 2 4 and x 3 , by treating these coefficients as unknown model fitting parameters. By varying the equilibrium coefficients we search for the best possible 25 agreement (coefficient of determination (R 2 ), see Supplement, Table S1) between the modelled and measured geometric mean diameter (GMD) with respect to particle number. Because experimental results reveal that the sulphate particles did not evaporate completely, they must have been contaminated with a small fraction of effectively non-volatile material (Sect. 3.2).
In the model we address this by assuming that the particles (prior to evaporation) contained either a small fraction of non-volatile organic material (e.g., secondary organic aerosol, SOA) or that the particles contained small amounts of ammonium, which prevented pure H2SO4 particle formation and consequently prevented the evaporation. We calculate the initial SOA and ammonium dry particle volume fraction in particle size bin j (χ ν SOA,j and χ ν NH4 + ,j) with Eq. (18) and (19), respectively. Here dSOA and dNH4 + represent an effective particle diameter of SOA and ammonium if all other particle species are removed. For experiment 1 we use dSOA=60 nm and dNH4 + =26 nm, for experiment 2 dSOA=43 nm and dNH4 + =19 nm and for 5 experiment 3 dSOA=38 nm and dNH4 + =17 nm.

Results and discussion
In order to fit the modelled particle number size distribution evolution to the observations we performed several hundred 10 simulations where we varied 2 4 and x 3 . We summarize these simulations into three main categories (Cases): 1) only H2SO4 and H2O evaporation ( x 3 =∞), (Case 1) 2) combination of H2SO4, H2O and SO3 evaporation, (Case 2) and 3) practically only SO3 and H2O evaporation, (Case 3).
Case 2 is further divided into two subcategories, Case 2a and 2b. In Case 2a the H2SO4 is the dominant evaporating S(VI) 15 species while in Case 2b the SO3 is the dominant evaporating S(VI) species. Figure 2 shows an example of the modelled mole fractions of (a) H2SO4(aq), 2 4 , and (b) SO3(aq), 3 , as a function of the aw and N:S for Case 2a with equilibrium constants 2 4 =2.40•10 9 mol•kg -1 , and x 3 =1.43•10 10 at T=288.8 K. Fig. 2 reveals that the increase of 3 as aw decreases is steeper than for 2 4 . This is because H2SO4(aq) formation precedes SO3 formation 20 (see R3). As expected, the highest values of 2 4 and 3 occur when N:S=0 and aw approaches zero. While N:S increases, 2 4 and 3 decrease gradually and reach lower values when N:S become larger than 0.6.

Particle number size distribution evolution
In Figure 3 we present the particle number size distribution evolution after the shutter of the UV light is closed and the influx of water vapour to the chamber is interrupted for experiment 2, performed at T=288.8 K, showing (a) the measured and (b)  25 the modelled values for Case 2a with 2 4 =2.40·10 9 mol•kg -1 and x 3 =1.43·10 10 . At the beginning of the evaporation process the particles in the size range from ~60 to ~180 nm in diameter contain approximately 70 mole % H2O; however, this percentage decreases, declining to 15 mole % after 6 h (Fig. 3 (c)). Before H2SO4 and SO3 start to evaporate from the particles the assumed mole fraction of ammonium is very low (Fig. 3 (d)). However, during the evaporation process N:S increases steadily until it reaches a value of ~0.6 after ~6 h. At this point the particles are ~40 nm in diameter and do not shrink further. 5 This model result is in good agreement with the experimental results reported by Marti et al. (1997) and confirms that NH4 + effectively stabilizes sulphur particles against evaporation when N:S≈0.6. Thus, in the stratosphere, even small amounts of a base (such as NH3) can prevent the sulphate particles from shrinking. Figure 4 compares the measured and modelled GMD evolution as a function of (a) time and (b) RH for experiments 1 and 2 10 performed at a temperature of T=288.8 K (Table 1) with NH3 as a particle phase contaminant (see Supplement, Table S1, simulations 1-4 and 13-16 ). The pure liquid saturation vapour pressures of H2SO4 and SO3 are calculated with Eq. (11) and (12). The model results are in good agreement with the measured GMD trend for Case 1 ( 2 4 =2.00·10 9 mol•kg -1 ), Case 2a
With the Aspen Plus Databank pure liquid saturation vapour pressure parameterisations it is also possible to find similarly good agreement between the modelled and observed GMD evolution during experiment 1 and 2 for Cases 1, 2a, 2b and 3 (Fig. S8) with NH3 as the particle phase contaminant, but with somewhat different values of 2 4 and x 3 (see 20 Supplement, Table S1, simulations 8-11 and 20-23).
The model simulations with non-volatile and non-water-soluble organics or dimethylamine (DMA) as the particle phase contaminant give nearly identical results as with NH3, both for experiments 1 and 2 (see Supplement Table S1, simulations 6, 7, 17 and 18). In the case of DMA this occurs because it is also a strong enough base to be completely protonated (all N(-III) is in the form of NH4 + ). In the case of an organic contaminant instead of NH3 the model results mainly differ at a 25 later stage of the particle evaporation phase when the N:S approaches ~0.5. This is because the evaporation rate does not slow down before all S(VI) is lost when the particles do not contain any base (see Fig. S9). Thus, the modelled GMD shrinkage becomes somewhat faster, when assume organic contamination. Without any particle phase contamination (pure sulphuric acid particles) the particles evaporate faster and completely (see Supplement, Fig. S10).
Instead of explicitly calculating the H2SO4 activity with the thermodynamic model we derive it directly from the 30 tabulated values of the H2SO4 chemical potentials as a function of the molality, following Giauque et al. (1960), Eq. (15). With this method we simulate the evaporation of H2SO4 without explicitly calculating the concentration of H2SO4 in the particles. However, since the tabulated chemical potentials from Giauque et al. (1960) are only valid for pure sulphuric acid solutions and temperatures close to 298.15 K it cannot be used if the particle aqueous phase also contains ammonium or other stabilizing molecules.
Based on data from Giauque et al. (1960), Eq. (15) and the pure-liquid saturation vapour pressure parameterization from N-K-L parameterisation Kulmala and Laaksonen, 1990), Eq. (11) the modelled GMD shrinkage is 5 consistent with the observations for experiments 1 and 2, when we consider the Case 1 (H2SO4 as the only evaporating S(VI) species) and particle phase contamination due to non-volatile non-water-soluble organics (see Supplement, Figure S11 and Table S1, simulations 5, 12, 19 and 24). However, when we use the pure-liquid saturation vapour pressure parameterisation from the Aspen Plus Databank, the modelled particles evaporate earlier (at higher RH) than the observed particles. The reason is that the ASPEN compared to N-K-L parameterisation gives higher saturation vapour pressures (see Supplement, Fig. S5). 10

Geometric mean diameter shrinkage influenced by relative humidity and temperature
In an attempt to constrain how 2 4 and x 3 depend on the temperature, and the role of H2SO4 and SO3 on the observed particle diameter shrinkage, as a next step we simulate experiment 3, which expands in temperature. For this experiment the temperature increases gradually from 268 K to 293 K while the absolute humidity remains at a constant value, thus allowing the RH to decrease. Equation (20) (20) where i can be either H2SO4 or SO3. With Bi=0 K there is no temperature dependence of Ki.
For other acids like HNO3, HCl and HSO4 -, Ki decreases with increasing T (Bi>0) (Jacobson, 2005a). Que et al. (2011) estimates 2 4 to be 3475 K and 3 to be 14245.7 K. Thus, based on this information we would expect the 20 equilibrium reactions R1 and R3 to shift towards the left (more H2SO4(aq) and SO3 as temperature increases). This would result in a stronger temperature dependence of the H2SO4(aq) and SO3 saturation vapour pressures over aqueous sulphuric acid droplets (Eq. 13) compared to the temperature dependence expected if we only consider the temperature effect of the pure-liquid saturation vapour pressures (Fig. S5). Figure 5 compares the measured and modelled GMD evolution during experiment 3. For the simulations we use either 25 the same temperature dependence as suggested by Que et al. (2011) ( 2 4 =3475 K and 3 =14245.7 K), or no temperature dependence of 2 4 and x 3 ( 2 4 =0 K and 3 =0 K) or weak temperature dependence 2 4 =0 K and 3 = -3000 K. One of these model simulations correspond to Case 1 and the rest to Case 2a (see Supplement, Table S1, simulation 28 and 29, 33, 34 and 36, respectively).
For the Case 1 simulation (see Supplement, Table S1, simulation 28) we use Eq. (15) and the tabulated H2SO4 30 chemical potentials from Giauque et al. (1960) to derive the H2SO4 activity. The particle phase contaminant is assumed to be non-volatile and non-water-soluble organics. In this simulation the modelled particles grow somewhat too much before they start to shrink. For the Case 2a simulation where the temperature dependences of 2 4 and x 3 are described by the 2 4 and 3 values derived by Que et al. (2011) (see Supplement, Table S1, simulation 29) the model cannot capture the observed GMD evolution. For the Case 2a simulations with 2 4 =0 K and 3 =0 K (see Supplement, Table S1, simulations 33 and 34) the particle phase contaminant is assumed to be NH3 or non-volatile and non-water-soluble organics. These model 5 simulations, which agree with the observed GMD, indicate that the temperature dependences of 2 4 and x 3 need to be very weak or insignificant ( 2 4 =0 K and 3 =0 K). If the particles are contaminated with NH3, 3 or 2 4 even needs to be negative for optimum fitting (e.g. 2 4 =0 K and 3 =-3000 K, see Supplement, Table S1, simulations 36). It is also possible to find good agreement between the modelled and measured GMD evolution if one of 2 4 and 3 is negative and the other one is positive ( 2 4 =3475 K and 3 =-10000 K, see Supplement, Table S1, simulation 31). The H2SO4 and SO3 10 pure liquid saturation vapour pressures in these simulations are calculated with Eq. (11) and (12).
If we instead use the pure-liquid saturation vapour pressure parameterizations from the Aspen Plus Databank (which have somewhat weaker temperature dependences than Eq. 11 and 12), the model results captures the observed GMD evolution if both 2 4 and 3 are zero and H2SO4 is the only evaporating (SVI) species (Case 1, see Supplement, Table S1, simulation 50) or the main evaporating S(VI) species (Case 2a, see Supplement, Table S1, simulation 51, see Supplement, Fig.  15 S12).
For Case 2b and 3 simulations in which we assume that SO3 is responsible for most of the S(VI) evaporation, the model can never capture the observed GMD evolution. This is the case regardless of the pure liquid saturation vapour pressure method we use (N-K-L-Nickless or Aspen Plus Databank, see Supplement, Table S1, simulations 42, 48, 52 and 53) .
Based on the simulations of experiment 3 we conclude that most of the S(VI) that evaporated from the particles 20 probably was in the form of H2SO4 (Cases 1 and 2a). The very weak temperature dependences for 2 4 and x 3 needed for the model to capture the GMD evolution during experiment 3 is surprising and calls for further investigation. Part of the explanation to this could be that the AIOMFAC activity coefficient model is developed based on experimental data derived at 298.15 K. The uncertainty arising from the two different pure liquid saturation vapour pressure parameterisations (temperature dependent) also limits our ability to fully constrain the 2 4 and x 3 values. Based on our experiments and model 25 simulations the equilibrium constant 2 4 should be somewhere in the range 2.0-4.0·10 9 mol•kg -1 and the x 3 needs to be larger than 1.4•10 10 at a temperature of 288.8 ± 5 K. The type of contamination of the sulphate particles (NH3, DMA or a nonvolatile non-water-soluble organic compound) does not have a substantial impact on our results and conclusions.
The observed atmospheric daytime range of the [H2SO4(g)] is approximately 10 5 -10 8 molecules cm -3 , and so we shade 10 this range in Figure 6. When 2 4 , * is less than this range (to the upper right in the panel), the particles for most atmospheric daytime conditions will grow by condensation of H2SO4; when 2 4 , * is greater than this (to the lower left in the panel) the particles will for most conditions shrink by evaporation of S(VI); in the shaded range the particles will tend to equilibrate. The larger the mole fraction of bases (NH3) in the aerosol particles the less prone they will be to shrink. When particles are composed only of S(VI) and H2O (N:S=0) and the concentration of H2SO4(g) is 10 7 molecules cm -3 all particles smaller than 15 10 nm will shrink at RH<13.2 %. For the same [H2SO4(g)] and N:S=0.5 all particles smaller than 10 nm shrink at RH<12.1 %.
However, for N:S=0.75 particles smaller than 4 nm shrink at RH<5.5 %, and if N:S=1 only particles smaller than ~1.9 nm shrink, independent of RH except when it is extremely dry (RH≤1.5 %). With the vapour pressure parameterisations from the Aspen Plus Databank and 2 4 =4.00·10 9 and x 3 =4.55·10 10 the results are almost identical. These model results demonstrate that sulphuric acid can evaporate from particles or be unable to contribute to their 20 growth for atmospherically relevant conditions, characterized by low relative humility, relatively high temperatures and weak sources of NH3 and SO2. Such environments can be found in the stratosphere and possibly also in the troposphere over large desert regions.

Summary and conclusions
This study demonstrates, both experimentally and theoretically, the importance of H2SO4 evaporation from aerosol particles 25 at atmospheric relevant conditions. We measured the sulphate aerosol particle shrinkage below a certain low relative humidity (e.x. RH≲1.5% for T=288.8 K and RH≲0.7% for T=268.0 K) in the CLOUD chamber at CERN. We modelled the sulphur evaporation with ADCHAM. Our model simulation show that: i. the dissociation of H2SO4(aq) is not complete, and evaporation of H2SO4 and H2O can explain the observed particle shrinkage. However, we cannot dismiss the possibility that some of the shrinkage is due to evaporating SO3, which 30 is formed when H2SO4(aq) is dehydrated. ii.
iii. the equilibrium coefficient for the dehydration of H2SO4 ( x 3 ) must at least be larger than 1.4•10 10 . The main factors limiting our estimation of 2 4 are uncertainties in the pure liquid saturation vapour pressure of H2SO4 and the relative contribution of SO3 to the observed particle evaporation. Other potential sources of error are the uncertainties 5 in the derived activity coefficients, the mass accommodation coefficient of H2SO4 and solid salt formation during the particle evaporation phase. The model simulations of an experiment where the temperature was gradually increased from 268 to 293 K, indicates that the temperature dependencies of 2 4 and x 3 need to be weak. Future studies should focus on constraining the pure liquid saturation vapour pressures of H2SO4 and SO3 and the temperature dependence of 2 4 and x 3 . 10 In order to be able to make an accurate prediction of the sulphate particles influence on global climate, their thermodynamic properties need to be properly described in global climate models. Thus, our constraints on the dissociation, 2 4 and dehydration, x 3 of H2SO4 are important contributions to the global aerosol-climate model community. The outcome of this study implies that atmospheric modelling studies, especially those dedicated to new particle formation, should not by default assume that sulphate particles are non-volatile. Models that exclude the evaporation process provide faster 15 particle formation rates which has a misleading effect on the impact of aerosols on climate.
Our results are especially meaningful for high-altitude new particle formation (e.g. in the upper troposphere and stratosphere). It has been previously reported the particle formation (Brock et al., 1995) and ion induced nucleation (Lee et al., 2003;English et al., 2011) as a source of new particles in high altitudes. In the upper troposphere and stratosphere general circulation models coupled with aerosol dynamics models use aerosol evaporation as a source of [H2SO4(g)] (English et al., 20 2011). The concentration of H2SO4(g) drastically affects new particle formation rates. The equilibrium constants for the dissociation and dehydration of H2SO4 reported in this study are needed to accurately model the sulphate aerosol particle evaporation and concentration of H2SO4(g). They may also be important to evaluate particle formation schemes (homogeneous, ion-induced) for stratospheric conditions. These schemes are generally constrained based on tropospheric conditions (English et al., 2011) but applied for stratosphere simulations. Moreover, vapour-phase H2SO4 in the atmosphere appears to be 25 ubiquitous, even in the absence of photochemistry (Mauldin et al. 2003;Wang et al., 2013); this may partly be due to evaporation of H2SO4 from aerosol particles.
In a changing climate it will become even more important to understand the thermodynamic properties of the sulphur aerosol particles involved in the development of polar stratospheric clouds and how sulphate aerosols influence the stratospheric O3 layer. Experiments simulating stratospheric conditions (T≈200-265 K, p≈10 -1 -10 -3 atm, RH≥1.0 % and 30 [H2SO4]≤10 8 molec.•cm -3 ), are of great importance. Our results may also assist in explaining the atmospheric sulphur cycle of Venus. The Venusian clouds made up largely of sulphuric acid droplets cover an extended temperature range from 260 K (upper clouds) to 310 K (middle clouds) and even higher (lower clouds). The scientific understanding of the upper tropospheric and stratospheric sulphate aerosol is of great importance for the global climate and requires further investigation. D., F. S. contributed to scientific interpretation and editing of manuscript. All authors contributed to the development of the 5 CLOUD facility and analysis instruments, and commented on the manuscript.

Data availability
Requests for underlying material should be addressed to the corresponding author G.T (george.tsagkogeorgas@tropos.de).

Acknowledgements
We would like to thank CERN for supporting CLOUD with important technical and financial resources, and for providing a 10 particle beam from the CERN Proton Synchrotron. We also thank P. Carrie, L. coefficients for organic-inorganic mixtures containing carboxyl, hydroxyl, carbonyl, ether, ester, alkenyl, alkyl, and aromatic functional groups, Atmos. Chem. Phys., 11, 9155-9206, 2011.  Table 1. Summary of the experimental conditions: temperature (T), relative humidity (RH), and gaseous sulphuric acid concentration ([H2SO4](g)), which is also given as saturation vapour pressure (psat,H2SO4) for each experiment.