Temperature dependent formation of nacl dihydrate in levitated nacl and sea salt aerosol particles

Temperature-dependent formation of NaCl dihydrate in levitated NaCl and sea salt aerosol particles Andreas Peckhaus, Alexei Kiselev, Robert Wagner, Denis Duft, and Thomas Leisner Citation: J Chem Phys 145, 244503 (2016); doi: 10.1063/1.4972589 View online: http://dx.doi.org/10.1063/1.4972589 View Table of Contents: http://aip.scitation.org/toc/jcp/145/24 Published by the American Institute of Physics Articles you may be interested in Acoustic metasurface-based perfect absorber with deep subwavelength thickness J Chem Phys 108, 063502063502 (2016); 10.1063/1.4941338 Wireless power transfer based on magnetic quadrupole coupling in dielectric resonators J Chem Phys 108, 023902023902 (2016); 10.1063/1.4939789 Evolution of planar defects during homoepitaxial growth of β-Ga2O3 layers on (100) substrates—A quantitative model J Chem Phys 120, 225308225308 (2016); 10.1063/1.4971957 Effective scheme for partitioning covalent bonds in density-functional embedding theory: From molecules to extended covalent systems J Chem Phys 145, 244103244103 (2016); 10.1063/1.4972012 THE JOURNAL OF CHEMICAL PHYSICS 145, 244503 (2016) Temperature-dependent formation of NaCl dihydrate in levitated NaCl and sea salt aerosol particles Andreas Peckhaus,1 Alexei Kiselev,1,a) Robert Wagner,1 Denis Duft,1 and Thomas Leisner1,2 Atmospheric Aerosol Research Department, Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz pl 1, Eggenstein-Leopoldshafen 76344, Germany Institute of Environmental Physics, Heidelberg University, Im Neuenheimer Feld 229, Heidelberg, Germany (Received 27 June 2016; accepted December 2016; published online 27 December 2016) Recent laboratory studies indicate that the hydrated form of crystalline NaCl is potentially important for atmospheric processes involving depositional ice nucleation on NaCl dihydrate particles under cirrus cloud conditions However, recent experimental studies reported a strong discrepancy between the temperature intervals where the efflorescence of NaCl dihydrate has been observed Here we report the measurements of the volume specific nucleation rate of crystalline NaCl in the aqueous solution droplets of pure NaCl suspended in an electrodynamic balance at constant temperature and humidity in the range from 250 K to 241 K Based on these measurements, we derive the interfacial energy of crystalline NaCl dihydrate in a supersaturated NaCl solution and determined its temperature dependence Taking into account both temperature and concentration dependence of nucleation rate coefficients, we explain the difference in the observed fractions of NaCl dihydrate reported in the previous studies Applying the heterogeneous classical nucleation theory model, we have been able to reproduce the K shift of the NaCl dihydrate efflorescence curve observed for the sea salt aerosol particles, assuming the presence of super-micron solid inclusions (hypothetically gypsum or hemihydrate of CaSO4 ) These results support the notion that the phase transitions in microscopic droplets of supersaturated solution should be interpreted by accounting for the stochastic nature of homogeneous and heterogeneous nucleation and cannot be understood on the ground of bulk phase diagrams alone © 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4972589] I INTRODUCTION Seawater spray is the dominant source of atmospheric aerosol over oceans and in coastal areas With its global emission of 1733 Tg/y, the see spray aerosol (SSA) compares only with mineral dust.1 The phase state of sea spray particles controls their physical and chemical properties, for example, in interaction with ozone2 or in heterogeneous nucleation of ice.3–5 Although SSA has a complex composition,6 the phase transition of NaCl can play an important role in the final state and morphology of ambient aerosol particles NaCl aerosol can exist either as aqueous solution droplets or in one of the two crystalline forms: anhydrous NaCl and NaCl dihydrate (NaCl·2H2 O) The latter can serve as an efficient ice nucleating particle and might be essential for the microphysics of high altitude marine clouds.4,5,7,8 According to the bulk phase diagram of NaCl/water, anhydrous NaCl is the thermodynamically stable phase formed upon efflorescence of solution above 273.3 K.9,10 Below this peritectic temperature, the dihydrate form is more stable However, measurements performed with submicron droplets have shown that sodium chloride dihydrate does not form at Note: This article was intended as part of the Special Topic on Nucleation: New Concepts and Discoveries in Issue 21 of Volume 145 of J Chem Phys a) Author to whom correspondence should be addressed Electronic mail: alexei.kiselev@kit.edu 0021-9606/2016/145(24)/244503/12 temperatures above 253 K.11 A similar observation was made by Koop et al., who studied the efflorescence and deliquescence behavior of micron-sized droplets of NaCl solution and found that NaCl dihydrate was only formed via heterogeneous nucleation on available surfaces of ice.2 Moreover, the relative humidity at which the efflorescence occurs (ERH) has been found to increase with droplet size.9,12 The nucleation of NaCl dihydrate in sea spray aerosol may be further influenced by the presence of inorganic (CaSO4 , MgCl2 , MgSO4 , KMgCl3 ) and organic substances Some of these salts (e.g., gypsum) have lower solubility than NaCl and therefore would precipitate at humidity values higher than the ERH for micron size pure NaCl solution droplets.2,13–18 Such solid inclusions could facilitate the nucleation of crystalline NaCl Understanding phase transitions of NaCl under realistic atmospheric conditions is difficult and has only been investigated in experimental studies conducted at low temperatures Wise et al.5 probed the efflorescence of micron size (1 µm−10 µm) droplets of NaCl solution deposited onto a hydrophobic quartz substrate in a setup combining an environmental cell and a Raman microscope The authors observed a partitioning between crystallized anhydrous NaCl and NaCl dihydrate in the temperature range from 236 K to 252 K, with no dihydrate forming above 252 K In this temperature regime, a linear relationship between the fraction of NaCl dihydrate and temperature was proposed by Wise et al 145, 244503-1 © Author(s) 2016 244503-2 Peckhaus et al In contrast, Wagner et al used the AIDA (Aerosol Interaction and Dynamics in the Atmosphere) cloud chamber to investigate the temperature-dependent partitioning between the two crystalline phases of NaCl and observed no formation of sodium chloride dihydrate above 235 K.19 The strong increase in dihydrate formation was found at the temperature 13 K lower than in the study of Wise et al., which was attributed to the smaller size of the solute droplets (between and µm in diameter), and to a possible influence of a heterogeneous surface aiding the nucleation of NaCl dihydrate The difference in the experimental conditions of the two studies (efflorescence relative humidity (ERH), solution droplets size, unknown induction time, presence of substrate, and possible contamination) makes intuitive comparison of the results very difficult The experimental data cannot be adequately explained in terms of the bulk phase diagram of NaCl and its mixtures with organic and inorganic species The bulk of experimental evidence20 and previous attempts of atomistic modelling21–24 suggest that the efflorescence of NaCl in microscopic NaCl or SSA solution droplets is controlled by kinetic effects and should be treated within the framework of Classical Nucleation Theory (CNT) for homogeneous or heterogeneous nucleation.12,25,26 A reliable CNT-based parameterization is, however, missing due to the absence of experimental data on key parameters such as diffusivities of water and ionic species and interfacial energies for the crystalline phase in contact with supersaturated solute in the low temperature range, i.e., below 240 K To mitigate this problem, we use a humidified electrodynamic balance (EDB) coupled with a Raman microscope to measure the volume specific nucleation rates (also called nucleation rate coefficients) of NaCl and NaCl dihydrate in suspended droplets of aqueous NaCl solution at different temperatures Based on these measurements, we estimate the interfacial energy of NaCl dihydrate in the concentrated NaCl solution We then develop a CNT-based parameterization scheme combining the effect of temperature and humidity within one framework, which is used to reconcile our experimental data and the data of J Chem Phys 145, 244503 (2016) Wise et al and Wagner et al., obtained under different temperature and humidity conditions Finally, we extend this concept to the case of heterogeneous nucleation of NaCl dihydrate in a multicomponent system of inorganic salts, simulating the sea salt aerosol II EXPERIMENTAL PART A The EDB setup The basic setup of the EDB experiment was described previously.27–29 The unique feature of the present experimental setup is that the EDB is coupled to a Raman microscope and is connected to a humidity control system (Fig 1) The temperature of the EDB body is controlled by a cryostat (CryoVac, PK 2001) in the range from 300 K to 220 K with an accuracy of ±0.2 K A commercial humidifier (Ansyco GmbH) is used to generate a humidified nitrogen flow, which is divided between the EDB (∼40 ml/min) and a dew point mirror hygrometer (MBW Calibration, 373L) The dew point temperature of the humidified gas can be measured with an accuracy of ±0.1 K in the temperature range from 293 K to 193 K The accuracy of the temperature and dew point measurements leads to an uncertainty of less than ±2% RH in the investigated temperature range After establishing temperature and humidity equilibrium, individual charged droplets of NaCl solution with diameters ranging from 50 µm to 60 µm were injected into the EDB with a piezoelectric injector (GeSIM model A010-006 SPIP, cylindrical housing) The accommodation of the each droplet to the temperature inside the EDB is completed within about s.30 The size of a suspended droplet is measured continuously by analyzing the two-dimensional angle-resolved scattering pattern recorded with a CCD camera installed at a right angle to the beam of the HeNe laser 28,29 (see supplementary material for details) Shadow images of the droplets and residual particles have been recorded with the Raman microscope, providing additional information about the morphology, the phase, and the size of the particles FIG Schematic representation of the experimental setup 244503-3 Peckhaus et al The visual inspection and spectroscopic characterization of the droplets have been carried out with an inverted confocal microscope (Olympus, IX71) coupled to a dispersive Raman spectrometer (Bruker, Senterra) An Nd:Yag laser (wavelength λ = 532 nm) is used to excite Raman spectra in the spectral range from 80 cm1 to 4400 cm1 During the acquisition of the Raman spectra, the HeNe laser beam was blocked B Sample preparation and experimental procedure For the preparation of a 10 wt % aqueous solution, 2.22 g of NaCl (Merck, ACS reagent, ≥99.5%) or sea salt analogue mixture (Instant Ocean®, Aquarium Systems) was dissolved in 20 ml of deionized water (Barnstead-Thermolyne Corporation, NanoPure InfinityTM Ultrapure water system, 18.2 MΩ) At the beginning of each experiment, the injector was rinsed several times with deionized water to remove any contamination from the previous experiment According to Atkinson and Bingman,31 there are “dissolved organic nutrients” present in Instant Ocean The content of these organics is on the order of a few µmol/kg of sea salt water, whereas major ions are in the range of tens or hundreds of mmol/kg sea salt water In the work of Arnold et al.,32 a mean dissolved organic carbon (DOC) value of less than 0.2 mg/l was reported Recent experiments have shown that organic material (i.e., carboxylic acids) in concentrations of a few ppm can inhibit the nucleation of calcium sulfate dihydrate and lead to the initial formation of calcium sulfate hemihydrate.33 However, the amount of organic material in Instant Ocean is on the order of 0.1 ppm which seems to be too low to have a significant impact on the precipitation of calcium sulfate Therefore, Instant Ocean represents a good proxy for the inorganic constituents of natural sea water Instant Ocean was stored in a desiccator to avoid the uptake of moisture The synthetic sea salt mixture (Instant Ocean) was dissolved in water and then agitated in a magnetic stirrer for several hours During the preparation, individual insoluble particles have been observed in the solution, formed via precipitation of insoluble calcium carbonate or in the mixing process itself (high local concentration or alkalinity) Extreme care has been taken to avoid capturing of these particles into the piezoelectric droplet generator Before each efflorescence experiment a freshly prepared aqueous solution of NaCl or Instant Ocean was used An environmental scanning electron microscope (SEM) (ESEM FEI, Quanta 650 FEG) equipped with the energy dispersive X-ray (EDX) spectrometer (Bruker) was used to record images and chemical maps of individual SSA particles deposited on a silicon wafer The particles used in this analysis were obtained by depositing the droplets of sea salt analogue solution onto a silicon wafer and allowing them to evaporate at room conditions With the pure NaCl solution, efflorescence experiments of the following two types have been performed: (A) determination of crystalline phase partitioning as a function of temperature and (B) measurement of the volume specific nucleation rate of NaCl dihydrate For the SSA solution droplets, only the temperature dependency of crystalline phase partitioning has been measured (experiment type A) The relative humidity J Chem Phys 145, 244503 (2016) (RH) inside the EDB was set between 38% and 44% A typical experiment starts with the injection of a solution droplet into the EDB As long as the droplet is not in equilibrium with the water vapor in the EDB, it is evaporating until the efflorescence takes place The efflorescence of NaCl is associated with a sudden loss of mass and can be detected as a jump in the DC voltage controlling the vertical position of a droplet After the efflorescence, both Raman spectra and optical images were recorded allowing for the detection of particle phase and morphology In the experiments of type A, the phase of the effloresced particle (anhydrate or dihydrate) has been recorded after waiting a time long enough to achieve crystallization Neither efflorescence time nor evolution of the droplet size during evaporation has been recorded, which precluded us from deriving the nucleation rate coefficients from these data but allowed determination of particle phase partitioning as a function of temperature In the type B experiments, the time between injection and efflorescence of NaCl solution droplets has been recorded for every efflorescence event Additionally, the shadow images of each NaCl solution droplet have been recorded every second prior to the efflorescence to measure the droplet volume and to derive the actual concentration of NaCl at the moment of efflorescence For every tenth droplet, a series of the Mie scattering patterns have been recorded allowing for precise determination of droplet diameter (see Figure S2 of the supplementary material) In total, 612 NaCl solution droplets (resulting in 330 anhydrous NaCl and 282 NaCl dihydrate particles) and 264 sea salt mixture droplets (resulting in 134 anhydrous NaCl and 130 NaCl dihydrate containing SSA particles) have been studied The details of experimental conditions are given in the supplementary material (Tables S1–S3) III RESULTS AND DISCUSSION A Shape of NaCl and NaCl·2H2 O residual particles The vast majority of the effloresced anhydrous NaCl particles observed in this study had the structure of a single cube (Fig 2, panels A and B) A few particles consisted of two and more intergrown cubes with different crystallographic orientations (Fig 2, panel C) The morphology of NaCl particles found in this study was in good agreement with previous measurements in wind tunnel experiments34 and in a scanning electron microscope (SEM).35–37 Deviations from the ideal cubic shape have been reported in the experiments with rapidly drying polydisperse NaCl droplets.38 All NaCl dihydrate particles exhibited a nearly spherical shape (Fig 2, panels D–F) Some of them showed shape irregularities, probably arising during the efflorescence (Fig 2, panel E) Apparently, the observed morphology of the residual NaCl dihydrate particles does not reflect the monoclinic crystal structure of NaCl dihydrate.39 We suggest that the supersaturated NaCl solution droplets effloresced into polycrystalline NaCl dihydrate particles while maintaining the envelope shape of the droplet (as can be perceived in the shadow image in Fig 2, panel F) The volume equivalent diameter of dihydrate particles (as calculated from the projection area of the particle images) was found to be a factor 1.33 larger than that of 244503-4 Peckhaus et al J Chem Phys 145, 244503 (2016) FIG Shadow images of residual NaCl particles (A-F) and SSA particles (G-L) suspended in the EDB Panels A-C: anhydrous NaCl Panels D-F: NaCl dihydrate Panels G-I: SSA particles containing anhydrous NaCl Panels J-L: SSA particles containing NaCl dihydrate The scale bars are 20 µm long anhydrous NaCl particles This is in good agreement with the difference in bulk densities between the two crystalline forms of NaCl.40 The residual particles of sea salt analogue mixtures were different in morphology The cubic shape characteristic for anhydrous NaCl crystals was never observed (Fig 2, panels G–I) However, the particles containing NaCl dihydrate (Figure 2, panels J–L) had prevalently spherical shape and were less transparent than the particles containing NaCl in its anhydrous form (Figure 2, panels J–L) We interpret this observation in terms of the polycrystalline state of the residual SSA particles B Chemical composition and morphology of NaCl and SSA particles The Raman spectra of the residual particles have been used to identify the phase state of NaCl after efflorescence The Raman spectra of anhydrous NaCl recorded at 253 K in the EDB and at room temperature (powder bulk sample) showed no characteristic spectral features (Figure 3) Only lattice vibrations in the spectral range from 100 cm1 to 390 cm1 FIG Raman spectra of a suspended NaCl solution droplet (green), NaCl dihydrate particle at 233 K (red), an anhydrous NaCl particle at 253 K (blue), and a bulk Raman spectrum of anhydrous NaCl at room temperature (black) The three panels show the regions of OH-stretching (a), OH-bending (b), and libration and lattice modes (c), respectively The spectra are normalized to the lattice vibration of anhydrous NaCl at ∼107 cm1 and are vertically offset for clarity were observed with one prominent maximum located at 235 cm1 41 The spectral features characteristic for NaCl dihydrate particles are located in the three regions of the Raman spectrum (see Figure 3, panels (a)–(c)) In the high-frequency region (from 3000 cm1 to 3800 cm1 ), two main peaks at 3424 cm1 with a shoulder at the low-frequency side (at ∼3410 cm1 ) and a weaker peak at 3545 cm1 have been observed These peaks have been identified as the symmetric and asymmetric OH-stretching vibrations of water.16 Two Raman bands with a significant lower intensity could be identified at 3299 cm1 and 3320 cm1 (not visible) These bands have been reported before,42,43 but their chemical assignment is not clear The OH-bending modes of water are centered at 1644 cm1 and 1664 cm1 , in agreement with previous studies.5,42,43 Wise et al also reported both the OH-stretching and OH-bending regions of NaCl·2H2 O at 244 K but the Raman peaks in the OH-stretching region were not resolved in great detail In addition to the OH-stretching and OH-bending modes reported before, we have observed the librational modes of hydrated NaCl in the low-frequency region (from 200 cm1 to 800 cm1 ) These modes correspond to the rotational oscillations of H2 O molecules restricted in their motion by the interaction with neighboring lattice atoms, but are often hidden by numerous Raman bands of the matrix or substrate.16 A pronounced librational mode was observed at 390 cm1 The Raman spectra representative of SSA solution and effloresced SSA particles are shown in Figure The main spectral features used for the identification of crystalline phase of NaCl in effloresced particles were the two sharp peaks corresponding to the stretching vibrations of water at 3424 cm1 and 3545 cm1 , and the librational mode at 390 cm1 (the red line in Figure 4, panels (a) and (c)) These features are unique for NaCl·2H2 O, and, if present, always dominate the Raman spectrum in this region due to the prevalence of NaCl in the solution.5,16 The hydrated salts other than NaCl could be identified on the basis of their own characteristic H2 O stretching and bending modes For example, the spectrum shown in black in Figure is a characteristic for carnallite (KMgCl3 ·6H2 O), found previously in SSA particles.17,44 The Raman spectrum of carnallite exhibits a sharp band at 3430 cm1 with a small shoulder at 3260 cm1 , which can be 244503-5 Peckhaus et al FIG Raman spectra of the suspended SSA solution droplet (green), SSA residual particles containing NaCl·2H2 O (red), the residual particle containing NaCl in the presence of precipitated carnallite KMgCl3·6H2 O (black), and the residual particle containing precipitated anhydrous NaCl in the presence of dissolved ionic species (blue) The spectra are normalized to the sulfate stretching mode peak at 984 cm1 and are vertically offset for clarity attributed to the OH-stretching vibrations of water molecules confined in the crystal lattice A weak δ(OH)-bending mode is located at 1645 cm1 The nucleation of carnallite is assumed to take place on the preexisting anhydrous NaCl crystals,17 as suggested by the absence of the double peak feature in the high frequency region and librational mode at 390 cm1 In the absence of signals from hydrated salts, water in concentrated ionic solution is responsible for the broad spectral feature in the stretching vibration region (Figure 4, the blue spectrum in panel (a)) Additionally, all Raman spectra of SSA particles con1 and tained the ν1 (SO2− ) stretching mode peak at 984 cm an additional minor feature at 1008 cm indicating the pres2+ and ence of aqueous SO2− ions in the environment of Ca 2+ Mg ions, similarly to what have been reported by Zhang and Chan.45 The Raman spectra clearly show that even after efflorescence a significant amount of hydration water is present in the SSA residual particles.13 More discussion of Raman J Chem Phys 145, 244503 (2016) spectra of SSA particles is offered in the supplementary material (Section S3 and Figure S3) The ESEM/EDX study of residual SSA particles deposited onto a Si wafer revealed their complex morphology and chemical composition SSA particles contained clearly recognizable cubic crystals of anhydrous NaCl embedded into the crust of other inorganic components (see Figure S5 of the supplementary material) The EDX mapping of this crust allowed for the determination of its chemical composition, which was found to be in general agreement with bulk composition of Instant Ocean Ca, S, and O were co-located in the same regions of the crust suggesting formation of calcium sulfate dihydrate (CaSO4 ·2H2 O, gypsum) or hemihydrate (CaSO4 ·0.5H2 O), which can be part of a gypsum formation pathway.46,47 This finding is in general agreement with the picture of SSA containing a solid NaCl core and a mixture of hydrated Mg-rich and Ca-rich material.14,17,36,44,48 Both gypsum and hemihydrate have solubility values lower than that of NaCl, suggesting that they should precipitate prior to the efflorescence water activity of NaCl dihydrate is reached The weakly soluble salts precipitating before the ERH of NaCl could serve as centers of heterogeneous nucleation of NaCl dihydrate Although we not have direct evidence of such events, the indirect indications for the presence of particulate inclusions prior to nucleation of NaCl dihydrate are quite convincing C Temperature-dependent formation of NaCl dihydrate Our measurements (data of both experiment types A and B) confirmed that the formation of NaCl dihydrate has a strong dependence on temperature (Figure 5(a)) The transition between crystallization of anhydrous NaCl and NaCl dihydrate proceeded in a narrow temperature range from 253 K to 241 K As in the works of Cziczo and Abbatt,11 Koop et al.,2 and Wise et al.,5 no indication for the formation of NaCl dihydrate in the temperature range from 298 K to 253 K has been found Our data are in especially good agreement with the data of Wise et al., although their experimental conditions were FIG (a) Temperature-dependent formation of NaCl dihydrate in the experiments of both types A and B in comparison with previous measurements of Wagner et al and Wise et al Solid lines and shadowed areas are NaCl dihydrate fractions calculated with the CNT-based approach (see Section III G for details) (b) Phase diagram of aqueous solution of NaCl, after Koop et al Data points mark the thermodynamic conditions where the efflorescence has been observed The color symbols are the same as in the panel “(a)” and the filled and open grey squares aligned to the efflorescence line (short dashed line) at about 41% RH are the data of Koop et al and references therein.11,49–51 Solid black lines mark the borders between stable states of the water-NaCl mixture 244503-6 Peckhaus et al quite different: their NaCl droplets were smaller in size (1 µm– 10 µm) and were deposited on a substrate Additionally, longer induction times and variable drying rates (1%–10% min1 ) have been used in the study of Wise et al Using the FTIR extinction spectra as a method for the particle phase detection, Wagner et al.19 have found no evidence for the NaCl dihydrate formation above 244 K In their work, the 1.2 µm droplets of aqueous NaCl solution were suspended in the AIDA chamber at a constant temperature and humidity for up to h (green open diamonds in Figures 5(a) and 5(b)) A small fraction of NaCl dihydrate (7%) was formed at 235.7 K At the lowest investigated temperature of 216 K, a fraction of 0.88 was reported Figure 5(b) shows the thermodynamic conditions of the efflorescence experiments (i.e., the temperature and humidity where the efflorescence has been observed) plotted on the phase diagram of NaCl aqueous solution, adapted from the work of Koop et al.2 The efflorescence of NaCl dihydrate in the AIDA chamber occurred at RH values significantly higher than in this work and in the experiment of Wise et al It is therefore clear that both temperature and humidity effect on the nucleation rate have to be considered in addition to the difference in the droplet size and induction time when comparing these experiments In Secs III D–III G, we show that experimental results of all three studies can be reproduced using a CNT-based framework D Efflorescence nucleation rate of NaCl solution droplets To calculate the homogeneous nucleation rate coefficients of NaCl and NaCl·2H2 O, we have analyzed the efflorescence experiments of type B following Koop et al.52 In this framework, efflorescence of supersaturated NaCl solution droplets follows the Poisson statistics, so that the probability of observing efflorescence of exactly k droplets within time t is described by Poisson distribution, (wt)k −wt e , (1) k! where ω is the average number of crystallized droplets per unit time (efflorescence rate) From that, the probability of N liq Pk (t) = J Chem Phys 145, 244503 (2016) droplets to remain liquid (k = 0) after time t can be calculated as P0 (t) = exp (−ωt) ' Nliq (t) N0 (2a) which is also asymptotically equal to the fraction of liquid droplets observed at time t: fliq (t) = Nliq (t)/N0 The probability of observing exactly one efflorescence event (k = 1) can be related to experimental data by the following equation:52 ! Nliq (t) N0 (2b) ln P1 (t) = ωt · exp (−ωt) ' N0 Nliq (t) Using Equations (2a) and (2b), the value of w can be obtained by fitting the experimental decay curves with P0 (t) and P1 (t) (an example is given in Figure 6) At the same time, the Poisson statistics provides a way of calculating the statistic uncertainties associated with the experimental values of w and N liq on a fixed confidence level (x = 99.9%) Confidence level x is the probability of w being above the lower fiducial limit wlow or below the upper fiducial limit, wup 53,54 The upper and lower fiducial limits have been used here to estimate the uncertainty of experimentally determined nucleation rate (see Fig S6 and Tables S2 and S3 of the supplementary material) Figure gives an example of efflorescence rate experiment performed at 248 K These experimental data have been used to derive the volume specific nucleation rate for both NaCl and NaCl dihydrate as described in Sec III E Because NaCl solution droplets require time t ind (induction time) to adjust to the humidity inside the trap and thus reach the efflorescence concentration, the time t in Equations (1)–(2b) has to be replaced with t t ind 55,56 The induction time becomes a fitting parameter and can be derived from fitting the experimental data The fitting parameters and curves for all temperature settings examined in this study are given in the supplementary material together with the overview of experimental conditions E Derivation of the homogeneous nucleation rate coefficient for NaCl dihydrate In this section, we will derive the basic equations necessary to calculate homogeneous nucleation rate coefficients FIG Efflorescence of levitated NaCl solution droplets at 248 K measured in experiment of type B Panel (a): Probability of the suspended NaCl droplet to remain liquid as a function of time Panel (b): Natural logarithm of P (t) as a function of time Panel (c): Probability of observing exactly one efflorescence event for the same experimental data set The blue and red open circles denote the efflorescence times of anhydrous NaCl and NaCl dihydrate particles, respectively Solid lines are fits used to derive the volume specific nucleation rates and induction time Grey shaded areas indicate the region between the lower and upper fiducial limits of the total nucleation rate w 244503-7 Peckhaus et al J Chem Phys 145, 244503 (2016) of anhydrous NaCl and NaCl dihydrate from the measurements of efflorescence rate described in Sec III D As a starting point, we assume that each levitated droplet represents a volume of supersaturated solution and that the efflorescence process follows two independent nucleation paths depending on supersaturation and temperature The nucleation paths A and B are associated with the volume specific nucleation rates J A and J B and refer to the crystallization into the hydrous and anhydrous form of NaCl The nucleation of N identical droplets of volume V d into one of the two possible final states A and B can be described as a system of two parallel irreversible reactions and can be modelled as two competing first order decay processes The two parallel reactions are then described by a set of differential equations for the number N liq of liquid droplets, the number of effloresced droplets N eff , and the number N i of droplets effloresced into state i, dNliq = −(JA + JB )Vd Nliq , dt (3a) dNeff = (JA + JB )Vd Nliq , dt (3b) dNi = Ji Vd Nliq , (3c) dt where i refers to either final state A or B Here, the volume nucleation rates and the droplet volume are considered time independent, which is valid within the linear part of the liquid decay curve The system can be solved by integrating Equation (3a) and substituting the result into the successive Equations (3b) and (3c) leading to Nliq = N0 exp [−(JA + JB )Vd t] , (4a) Neff = N0 − Nliq , (4b) Ni = Ji Neff JA + JB (4c) Equation (4a) can be rearranged to yield the time dependence of the number of liquid droplets, ln Nliq = −(JA + JB )Vd t = −JVd t, N0 (5) f i and the total nucleation rate ω = J · Vd , which are both experimentally accessible in our experiments, Ni ω (8) Ji = N0 Vd The uncertainty of J i is then given by the lower and upper fiducial limits of N i and ω, and variability of droplet size at efflorescence Following this procedure, the total volume specific homogeneous nucleation rate for NaCl dihydrate has been determined from the data shown in Figure The results are shown in Figure It shows that the homogeneous nucleation rate coefficient of NaCl dihydrate increases with decreasing temperature, while the total nucleation rate does not show temperature dependence in the investigated temperature range F CNT-based simulation of experimental results In this section, we construct a CNT-based parameterization of our efflorescence nucleation rate of NaCl dihydrate which is then extended into the range of experimental conditions of Wagner et al with the goal to resolve the apparent inconsistency of experimental results The difficulty of this approach is the necessity to estimate (a) the diffusion coefficient of water DH2 O (T ) in supersaturated NaCl solution at very high concentrations and low temperatures and (b) the interfacial energy of NaCl dihydrate crystal σsl (T ) in supersaturated solution of NaCl To our best knowledge, neither of these quantities has been measured in the temperature and humidity ranges relevant for this study According to the classical nucleation theory,57 the volume specific homogeneous nucleation rate J hom (T ) can be expressed as follows: ! ! −∆Fdiff (T ) −∆G(T ) kT nv exp exp , (9) Jhom (T ) = h kT kT where ∆G(T ) is the energy of formation of a critical nucleus in the aqueous solution, ∆Fdiff (T ) is the diffusion activation energy, nv is the molecular concentration in the crystalline NaCl nucleus (∼6.1 · 1021 cm−3 ), and k and h are the Boltzmann and the Plank constants The diffusion activation energy is given by ∂ ln DH2 O (T ) (10) ∆Fdiff (T ) = kT ∂T which is identical to Equation (2) As it follows from relations (4a)–(4c), the volume specific nucleation rates J i can be determined from the effloresced fractions fi = Ni /Neff = Ji /J at any time, e.g., also when all droplets are effloresced, i.e., Neff = N0 , Ji = Ni J N0 (6) Additionally, as the effloresced fractions are time independent, they can be identified as the probabilities pi to arrive in final state A or B in a single event by setting Neff = 1, Ji (7) J Equations (5) and (6) can be used to determine the volume nucleation rate J i for the single state i by measuring the fraction pi = FIG Volume specific nucleation rates obtained from NaCl dihydrate efflorescence experiments of type B 244503-8 Peckhaus et al J Chem Phys 145, 244503 (2016) The temperature and concentration dependence of the diffusion coefficient of water DH2 O (c, T ) can be parameterized with the Vogel-Fulcher-Tammann (VFT) equation,58–60 ! B(c) , DH2 O (c, T ) = D0 (c) · exp − T − T0 (c) (11) where D0 (c), B(c), and T (c) are concentration dependent parameters We use the linear parameterization of D0 (c) = (38.6 × c + 40) × 10−9 m2 s−1 , B (c) = (94.2 × c + 356.1) K, obtained by Garbacz and Price,58 by fitting the translational diffusion NMR measurements of water in NaCl solution in the concentration range from to mol/l and temperature range from 300 K to 230 K For T (c) we use an exponential decay expression T0 (c) = 114.6+60·exp (−c/2.73)·K instead of quadratic polynomial suggested by Garbacz and Price In this way the self-diffusion coefficient of water calculated with Eq (11) (the red curve in Figure 8(a)) not only reproduces the experimental data of Garbacz and Price but also follows the power law (PL) parameterization of Koop and Murray,60 which was shown to provide the most physically consistent description of nucleation of ice in supercooled water The applicability of this parameterization is limited to the temperature range above 225 K as shown by the deviation of our VFT curve and the PL curve below this temperature (compare red and blue solid lines in Figure 8(a)) With this constraint, we use Equation (11) to calculate the DH2 O (c, T )into the concentration and temperature range relevant for this study (9–10 mol/l and the temperature down to 220 K) It should be noted that even for pure water the values of DH2 O are poorly known below 230 K, as shown by a strong deviation between the VFT and PL parameterizations as T approaches 220 K (green and blue lines in Figure 8) For concentrated NaCl solution, no direct measurements exist that could be used to constrain the parameterization of DH2 O (c, T ) at this low temperature and high concentration of NaCl Therefore, the parameterization of DH2 O (c, T ) described above should be treated with caution The energy of critical nucleus formation is defined as ∆G(T ) = 16πσsl (T )3 υ 2 , kT ln(S * (T )) (12) where σsl (T ) is the interfacial energy between the solid nucleus and the aqueous solution, υ is the specific volume of a single molecule crystal of anhydrous NaCl (υ = 4.5·1023 cm3 ) or NaCl dihydrate (υ = 9.6 · 1023 cm3 ), and S * is the supersaturation of the solute The supersaturation of the solute has been calculated following the method of Richardson and Snyder.61 In this method, the ratio of the mole fraction of water x w to the mole fraction of solute x s is expressed as a function of the negative logarithm of the water activity in the NaCl solution The supersaturation at efflorescence can be calculated as follows:62 aw,del xw d ln (aw ) (13) ln S * = aw,eff xs Using the water activity value at efflorescence aw,eff = 0.47 as the lower integration limit and the water activity at deliquescence aw,del = 0.75 as the upper integration limit, the supersaturation with respect to the anhydrous NaCl and NaCl dihydrate was calculated for the experimental conditions used in this study The supersaturation with respect to NaCl dihydrate shows a strong temperature dependence due to the temperature dependence of the DRH of NaCl dihydrate (see Figure S7b), whereas the supersaturation with respect to anhydrous NaCl is only a weak function of temperature As the interfacial free energy σsl (T ) between the nucleus of NaCl dihydrate and the solution is not known, this quantity has to be estimated from the measurements of nucleation rate That was done by substituting Equation (10) into Equation (9), which was then rearranged for σsl (T ) The interfacial energy was estimated by using the parametrization of FIG (a) Diffusion coefficient of water in supersaturated NaCl solution Grey symbols are experimental data of Garbacz and Price,58 measured by translational diffusion NMR method for the concentration range to mol/l Solid lines are VFT parameterization with c = (pure water) used in this work (red), VFT adapted from Koop and Murray60 (green), and power law (PL) parameterization of DH2 O (T ) adapted from the same work Short dashed and long dashed lines correspond to the diffusion coefficient of water in NaCl solution with c = 9.2 mol/l and 10.1 mol/l, respectively (b) Interfacial energy of NaCl dihydrate nucleus in supersaturated solution derived from the measurements of nucleation rate at water activity aw = 0.47 (c = 10.1 mol/l), together with Huang-Bartell fit extrapolated into low temperature range 244503-9 Peckhaus et al J Chem Phys 145, 244503 (2016) DH2 O (c, T ), the supersaturation S* with respect to NaCl dihydrate, and the measured volume specific homogeneous nucleation rate Jhom (T ) for NaCl dihydrate To calculate σsl (T ) for temperature outside of the experimental range, the parameterization proposed by Huang and Bartell63 has been used, !n T , (14) σsl (T ) = σ0 T0 where T0 = 298 K, and the values of σ0 = 36.9 mJ/m2 and n = 0.49 were obtained from the fit of Equation (9) to the measured values of J hom (T ) According to this parameterization, the solid-liquid interfacial energy is only slightly dependent on temperature within a broad temperature range (Figure 8(b)) The values of σsl (T ) derived from the measured nucleation rates occupy the range from 33.3 mJ/m2 to 33.9 mJ/m2 (Fig 8(b)) We have found no literature data on the interfacial free energy of NaCl dihydrate in solute at low temperatures and relevant concentrations In contrast, the interfacial energy for anhydrous NaCl in equilibrium with solution σsl = 38 mJ/m2 at room temperature has been reported before.64–66 Surprisingly, this value is only slightly higher than what we have derived from the measurements of the nucleation rate of NaCl dihydrate In the recent atomistic simulation of NaCl anhydrate in the concentrated solution (8–12 mol/kg), the values of 41–63 mJ/m2 have been reported,24 hinting at a general increase of the interfacial energy for a higher concentration Hellmuth and Shchekin23 have derived the solid/liquid interfacial energy of anhydrous NaCl from the measurements of ERH and DRH of nanometer-sized NaCl particles reported in the work of Biskos et al.67 The interfacial energy was shown to increase from σsl = 86.6 mJ/m2 at NaCl concentration of 15.2 mol/kg to σsl = 89.4 mJ/m2 at NaCl concentration of 15.95 mol/kg.23 Interestingly, these values are close to the value of σsl = 89 mJ/m2 for NaCl crystal in its own melt.68 Although the values of σsl for anhydrous NaCl cannot be directly compared to our values for NaCl dihydrate, they could be useful to understand the concentration dependence of interfacial energy in supersaturated solutions Even a very weak concentration dependence could strongly affect the prediction of nucleation rate, due to a strong functional relationship between the nucleation rate and interfacial energy J(σsl ) ∼ exp(−σsl3 ), see Eqs (9) and (12) The scarcity of the available data did not allow us to determine the functional form of the relationship between the concentration c and interfacial energy σsl (T , c) However, a simple estimation could be made considering that the increase of solute concentration by mol/l was reportedly associated with 5% increase of crystal/liquid interfacial energy.23 We use this estimation in the following analysis The fraction of NaCl dihydrate as a function of temperature for a given droplet volume V d and observation time t can be calculated as fNaCl·2H2 O (T ) = − exp (−Jhom (T ) · Vd · t) (15) Figure 5(a) (the red solid line) shows the fraction of NaCl dihydrate calculated with Eq (15) for our experimental conditions (aw = 0.47, dd = 30 µm, t = 60 s) with the nucleation rate parameterized as described above Good agreement with experimental data confirms the internal consistency of CNT-based model The temperature dependent fraction of NaCl dihydrate reported in the work of Wise et al.5 could be reproduced with the same parameterization and initial average droplet diameter of 10 µm, as shown in Figure 5(a) Assuming average ERH of 45% (see phase diagram, Figure 5(b)), the average supersaturation was found to be S* = 7.1 at 245 K Since the drying rate was not reported, we have estimated the induction time by dividing the range between DRH and ERH (∆RH ≈ 30% ) by the slowest (1% min1 ) and fastest (10% min1 ) reported drying rate, resulting in the range of times between 180 s and 1800 s The measured fractions of NaCl dihydrate falls into the middle of the range predicted with these limiting induction times (the blue shaded area in Figure 5(a)) Note that the interfacial energy for the NaCl dihydrate nucleus in solution was kept independent of solute concentration due to the similarity to our experimental conditions The same parameterization failed to reproduce the fractions of hydrated NaCl reported in the work of Wagner et al.19 at a lower temperature range The supersaturation S* = 7.8 derived from the water activity aw,eff = 0.52 and concentration c = 9.2 mol/l at efflorescence leads to the values of nucleation rate that are too low to reproduce the measured fractions of NaCl dihydrate This inconsistency could be resolved by taking into account the weak concentration dependence of interfacial energy, in addition to the parameterized temperature dependence, as mentioned previously in this section To so, we project the concentration dependence of σsl (T , c) reported in the work of Hellmuth and Shchekin23 into the range of concentrations relevant to this study Specifically, this would mean a reduction from 32.2 mJ/m2 to 30.6 mJ/m2 at c = 9.2 mol/l and 225 K Such 5% reduction of solid-liquid interfacial energy resulted in almost orders of magnitude higher nucleation rate coefficient The fraction of NaCl dihydrate calculated with this new nucleation rate for experimental conditions of Wagner et al shows a steep increase between 240 K and 230 K (Figure 5(a)), where the efflorescence of NaCl dihydrate was indeed observed.19 Although we could not corroborate such projection of interfacial energy independently, the trend in predicted fractions of NaCl dihydrate is encouraging G Temperature-dependent formation of NaCl dihydrate in SSA particles In the past, Koop et al.2 observed initiation of NaCl crystallization initiated on the surface of ice Wagner et al observed a similar effect in crystallization of ternary solution droplets composed of oxalic acid, NaCl, and water in the AIDA cloud chamber at 244 K.69 There, the crystallization of NaCl dihydrate was facilitated by the presence of oxalic acid crystals Recently, the CaSO4 was identified by means of EDX analysis of the sea salt particles collected in the field.37 Following the line of reasoning, solid inclusions precipitating during the efflorescence process could catalyze the nucleation of NaCl dihydrate at low temperatures The temperature-dependent formation of NaCl dihydrate in SSA solution droplets found in our experiments is shown in Figure A minor fraction of NaCl dihydrate was observed already at 257 K Nearly all SSA solution droplets effloresced 244503-10 Peckhaus et al J Chem Phys 145, 244503 (2016) FIG Fractions of NaCl dihydrate in SSA particles and the CNT-based parametrization of heterogeneous nucleation of NaCl dihydrate in SSA droplets (the black curve and the shaded area) Data and the CNT parameterization of homogeneous nucleation of NaCl dihydrate in NaCl solution droplets are given in diamonds and black dashed line, respectively with NaCl dihydrate as a major component below 243 K The formation curve of NaCl dihydrate in SSA solution droplets is shifted to higher temperatures by approximately 5.5 K compared to the pure NaCl case (Figure 9) Although the direct spectroscopic identification of individual solid inclusions was not possible for the levitated residual SSA particles, our ESEM/EDX analysis of SSA residual particles together with the analysis of Raman spectra and solubility considerations strongly suggests the presence of micron-sized solid inclusions precipitating prior to the nucleation of NaCl crystals Based on these observations, we suggest that heterogeneous nucleation of NaCl dihydrate might be responsible for the enhanced formation of NaCl dihydrate in SSA solution droplets In the presence of solid inclusions in SSA droplets, the efflorescence of NaCl dihydrate might be better treated as heterogeneous nucleation facilitated by a presence of a solid surface In this case, the equation for the homogeneous nucleation rate (9) has to be modified with account for the reduced energy of the critical nucleus formation ∆Ghet , ! ! −∆Fdiff (T ) kT −∆Ghet (T ) Jhet (T ) = ns exp exp , (16) h kT kT with ∆Ghet (T ) = ∆G(T )φ(θ) (17) Here ns is the number density of solute NaCl molecules at the nucleus/solution interface (ns ∼ 3.7 · 1014 cm2 ) The correction function φ(θ) describes a reduction of ∆G assuming a spherical nucleus of a new phase on a flat substrate, characterized by a contact angle θ, (2 + cos(θ)) (1 − cos(θ))2 (18) The fraction of NaCl dihydrate forming via heterogeneous nucleation pathway is then estimated analogue to Equation (15), φ(θ) = fhet (T ) = − exp(−Jhet (T ) · sincl · t), (19) where sincl is the surface area of the solid inclusion Note that f het (T ) does not depend on the droplet size but only on the size of inclusion The CNT based model of our data achieved in terms of heterogeneous nucleation is shown as the black solid line in Figure Here, we calculate the fractions of precipitated NaCl dihydrate as a function of temperature assuming the size of an inclusion dincl = µm and contact angle θ = 1.9 rad, but otherwise keeping all experimental parameters as in the case of pure NaCl solution The calculated curve adequately reproduces the measurement data By allowing a variability of inclusion size (3 ± 1) µm, the spread of the experimental data could be covered as well (the grey shaded area in Figure 9) The chosen size of inclusion roughly corresponds to the mass fraction of CaSO4 in the Instant Ocean® sea salt analogue mixture, under an assumption that all CaSO4 in a 30 µm droplet precipitate into a single spherical particle IV SUMMARY We report series of single droplet efflorescence experiments with micron-sized droplets of NaCl and sea salt analogue (Instant Ocean) solutions suspended in the EDB at constant temperature and humidity Our motivation was to establish a relationship between the crystalline phase of the effloresced particle and the thermodynamic and kinetic conditions of a solution droplet The identification of the crystalline phase was performed in situ with the Raman microscope coupled to the EDB The OH stretching vibrations in the high frequency range of the Raman spectra have been used for the identification of NaCl dihydrate in both pure NaCl and SSA residuals The presence of various hydrated inorganic salts CaSO4·2H2 O (gypsum) or CaSO4·0.5H2 O (hemihydrate), KMgCl3·6H2 O (carnallite), or hydrates of MgSO4 have been suggested by the Raman spectra of suspended SSA particles and by ESEM/EDX analysis of the dry residual particles deposited on a silicon substrate Because of lower solubility of hydrated CaSO4 , the particles of hydrated calcium sulfate may crystallize during the evaporation of SSA droplets, thus triggering the heterogeneous nucleation of NaCl dihydrate The temperature-dependent partitioning between anhydrous NaCl and NaCl dihydrate has been observed in the temperature range from 250 K to 241 K, with NaCl dihydrate mostly forming at lower temperatures Our experimental results are in good agreement with the data of Wise et al for NaCl particles deposited on a hydrophobic quartz substrate5 but differ strongly from the observations of Wagner et al where a strong increase in dihydrate formation was observed at temperatures below 235 K In that work, the crystallization of suspended, 1.2 µm large aqueous NaCl solution droplets at lower supersaturation values and longer observation times19 has been probed By measuring the time dependence of individual efflorescence events, we have been able to determine the volume specific nucleation rate of NaCl dihydrate in the temperature range from 241 K to 250 K and average ERH of 47% These measurements allowed us for the first time to derive the interfacial energy of the NaCl dihydrate crystal in the supersaturated NaCl solution as a function of temperature The values (33.5 ± 0.4) mJ/m2 obtained in this study are comparable to previously reported values and 244503-11 Peckhaus et al with the predictions of atomistic simulations of anhydrous NaCl nucleation at room temperature24 but are significantly lower than the interfacial energy of NaCl crystal in own melt By applying the CNT parameterization to the experimental data, the volume specific nucleation rate could be derived lower temperatures and lower solute concentrations To so, we had to develop a parameterization of water diffusivity based on the data published by Garbacz and Price.58 To reduce the level of uncertainty associated with this parameterization, we constrained the parametrization by requiring it to follow the self-diffusivity of pure water recently made available for temperature range down to 220 K.60 Nevertheless, the extrapolation of this parameterization beyond available experimental data should be treated with caution In an attempt to adequately explain the temperature threshold for NaCl dihydrate formation observed in this study and in the work of Wagner et al.,19 we have constructed a CNT model of the NaCl dihydrate efflorescence taking into account the temperature and concentration dependence of the volume specific nucleation rate This model satisfactorily reproduced the data of Wise et al., but failed to deliver the fractions of NaCl dihydrate observed in the experiment of Wagner et al However, a reasonable agreement to all experimental data could be obtained by assuming a weak concentration dependence of solid-liquid interfacial energy Such dependence was suggested in the work of Hellmuth and Shchekin23 and accounts for 5% reduction of interfacial energy when the concentration of solute is reduced by mol/l Independent evidence of such concentration dependence of interfacial energy remains to be delivered Following the concept of heterogeneous nucleation, the CNT model was adjusted to account for the potential presence of solid inclusions capable of catalyzing the nucleation of NaCl dihydrate at lower concentration and/or higher temperatures, or shorter induction times Assuming the presence of such super-micron inclusions, our model was able to adequately predict the K shift of dihydrate efflorescence curve towards higher temperatures observed for the SSA solution droplets Our results support the idea that the phase transitions in microscopic droplets of supersaturated solution should be interpreted with account for the stochastic nature of homogeneous and heterogeneous nucleation and cannot be understood on the ground of phase diagrams for bulk substances alone We conclude with the remark that many thermodynamic quantities (diffusivity of water in highly concentrated solutions, interfacial energy of crystalline phase, etc.) needed for CNT parameterization in a broad range of experimental conditions, are still missing, thus limiting the applicability of the presented approach SUPPLEMENTARY MATERIAL See supplementary material for experimental details, additional discussion of Raman spectra, ESEM/EDX images of residual SSA particles, experiment statistics, Poisson statistics fit parameters, and derivation of solute supersaturation J Chem Phys 145, 244503 (2016) ACKNOWLEDGMENTS This work was supported by the Helmholtz Association under Atmosphere and Climate Research Programme (ATMO) A.P would like to thank the Graduate School of Climate and Environment (GRACE) and the Karlsruhe House of Young Scientists (KHYS) for their support A.K expresses his gratitude to Olaf Hellmuth of the Institute for Tropospheric Research in Leipzig for useful discussion D Koch, G A Schmidt, and C V Field, J Geophys Res 111, D06206, doi: 10.1029/2004JD005550 (2006) Koop et al., J Geophys Res.: Atmos 105, 26393, doi:10.1029/ 2000JD900413 (2000) M D Cohen, R C Flagan, and J H Seinfeld, J Phys Chem 91, 4563 (1987) R Wagner and O Mă ohler, J Geophys Res.: Atmos 118, 4610, doi: 10.1002/jgrd.50325 (2013) M E Wise et al., Atmos Chem Phys 12, 1121 (2012) D B Collins et al., Atmos Meas Tech 7, 3667 (2014) G P Schill and M A Tolbert, J Phys Chem C 118, 29234 (2014) D J Cziczo et al., Science 340, 1320 (2013) U K Krieger, C Marcolli, and J P Reid, Chem Soc Rev 41, 6631 (2012) 10 S T Martin, Chem Rev 100, 3403 (2000) 11 D J Cziczo and J P D Abbatt, J Phys Chem A 104, 2038 (2000) 12 Y G Gao, S B Chen, and L E Yu, Atmos Environ 41, 2019 (2007) 13 I N Tang, A C Tridico, and K H Fung, J Geophys Res.: Atmos 102, 23269, doi:10.1029/97JD01806 (1997) 14 M E Wise et al., J Geophys Res.: Atmos 114, D03201, doi:10.1029/ 2008JD010449 (2009) 15 C.-T Lee and W.-C Hsu, J Aerosol Sci 31, 189 (2000) 16 J Dubessy et al., Chem Geol 37, 137 (1982) 17 H.-S Xiao et al., Environ Sci Technol 42, 8698 (2008) 18 H.-J Tong et al., Acta Phys.-Chim Sin 27, 2521 (2011) 19 R Wagner, O Mă ohler, and M Schnaiter, J Phys Chem A 116, 8557 (2012) 20 Y F Cheng et al., Nat Commun 6, 5923 (2015) 21 H Laksmono et al., J Phys Chem Lett 6, 2826 (2015) 22 J S Kim and A Yethiraj, J Phys Chem B 112, 1729 (2008) 23 O Hellmuth and A K Shchekin, Atmos Chem Phys 15, 3851 (2015) 24 N E R Zimmermann et al., J Am Chem Soc 137, 13352 (2015) 25 M D Cohen, R C Flagan, and J H Seinfeld, J Phys Chem 91, 4583 (1987) 26 Y G Gao, S B Chen, and L E Yu, J Phys Chem A 110, 7602 (2006) 27 D Duft and T Leisner, Atmos Chem Phys 4, 1997 (2004) 28 N Hoffmann et al., Atmos Meas Tech 6, 2373 (2013) 29 D Rzesanke et al., Phys Chem Chem Phys 14, 9359 (2012) 30 P Stă ockel et al., J Phys Chem A 109, 2540 (2005) 31 M J Atkinson and C Bingman, J Aquari Aqua Sci VIII, 39 (1997); available at cmetton.free.fr/Divers/Aqua/35509243.pdf 32 W R Arnold et al., Environ Toxicol Chem 26, 935 (2007) 33 T Rabizadeh, C L Peacock, and L G Benning, Mineral Mag 78, 1465 (2014) 34 S K Mitra, J Brinkmann, and H R Pruppacher, J Aerosol Sci 23, 245 (1992) 35 M Wise et al., Aerosol Sci Technol 39, 849 (2005) 36 M E Wise et al., J Geophys Res.: Atmos 112, D10224, doi:10.1029/ 2006JD007678 (2007) 37 A Laskin et al., J Geophys Res.: Atmos 117, D15302, doi:10.1029/ 2012JD017743 (2012) 38 H R Pruppacher and J D Klett, Microphysics of Clouds and Precipitation, 2nd ed (Kluwer, 1997) 39 B Klewe and B Pedersen, Acta Crystallogr., Sect B: Struct Crystallogr Cryst Chem 30, 2363 (1974) 40 B Light, R E Brandt, and S G Warren, J Geophys Res.: Oceans 114, C07018, doi:10.1029/2008jd011673 (2009) 41 W Mă oller and R Kaiser, Z Naturforsch., A: Phys Sci 25, 1024 (1970) 42 R J Bakker, Can Mineral 42, 1283 (2004) 43 M Baumgartner and R J Bakker, Chem Geol 275, 58 (2010) 44 A P Ault et al., Phys Chem Chem Phys 15, 6206 (2013) 45 Y.-H Zhang and C K Chan, J Phys Chem A 104, 9191 (2000) 46 Y W Wang et al., Chem Commun 48, 504 (2012) 47 Y W Wang and F C Meldrum, J Mater Chem 22, 22055 (2012) 48 A P Ault et al., Environ Sci Technol 47, 5603 (2013) T 244503-12 Peckhaus et al J Chem Phys 145, 244503 (2016) 49 I N Tang, H R Munkelwitz, and J G Davis, J Aerosol Sci 8, 149 (1977) 59 M 50 D 60 T J Cziczo et al., J Geophys Res.: Atmos 102, 18843, doi: 10.1029/97JD01361 (1997) 51 D D Weis and G E Ewing, J Geophys Res.: Atmos 104, 21275, doi:10.1029/1999JD900286 (1999) 52 T Koop et al., J Phys Chem A 101, 1117 (1997) 53 R A Fisher, Econometrica 3, 353 (1935) 54 V H Regener, Phys Rev 84, 161 (1951) 55 C Brandel and J H ter Horst, Faraday Discuss 179, 199 (2015) 56 N S Trasi et al., CrystEngComm 17, 1242 (2015) 57 B Zobrist et al., J Phys Chem C 111, 2149 (2007) 58 P Garbacz and W S Price, J Phys Chem A 118, 3307 (2014) P Longinotti et al., J Chem Phys 134, 244510 (2011) Koop and B J Murray, J Chem Phys 145, 211915 (2016) 61 C B Richardson and T D Snyder, Langmuir 10, 2462 (1994) 62 T B Onasch, R McGraw, and D Imre, J Phys Chem A 104, 10797 (2000) 63 J Huang and L S Bartell, J Phys Chem 99, 3924 (1995) 64 P Bennema and O Sohnel, J Cryst Growth 102, 547 (1990) 65 A Mersmann, J Cryst Growth 102, 841 (1990) 66 K Sangwal, J Cryst Growth 97, 393 (1989) 67 G Biskos et al., Atmos Chem Phys 6, 4633 (2006) 68 J Benet, L G MacDowell, and E Sanz, J Chem Phys 142, 134706 (2015) 69 R Wagner et al., Atmos Chem Phys 11, 2083 (2011) ... droplets (resulting in 330 anhydrous NaCl and 282 NaCl dihydrate particles) and 264 sea salt mixture droplets (resulting in 134 anhydrous NaCl and 130 NaCl dihydrate containing SSA particles) have... projection of interfacial energy independently, the trend in predicted fractions of NaCl dihydrate is encouraging G Temperature- dependent formation of NaCl dihydrate in SSA particles In the past,...THE JOURNAL OF CHEMICAL PHYSICS 145, 244503 (2016) Temperature- dependent formation of NaCl dihydrate in levitated NaCl and sea salt aerosol particles Andreas Peckhaus,1 Alexei Kiselev,1,a)

Định dạng
Số trang	13
Dung lượng	3,43 MB