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

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 constan

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

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Temperature-dependent formation of NaCl dihydrate in levitated

NaCl and sea salt aerosol particles

Andreas Peckhaus,1Alexei Kiselev,1, a)Robert Wagner,1Denis Duft,1

and Thomas Leisner1,2

1Atmospheric Aerosol Research Department, Institute for Meteorology and Climate Research, Karlsruhe Institute

of Technology (KIT), Hermann-von-Helmholtz pl 1, Eggenstein-Leopoldshafen 76344, Germany

2Institute of Environmental Physics, Heidelberg University, Im Neuenheimer Feld 229, Heidelberg, Germany

(Received 27 June 2016; accepted 7 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

crys-talline 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 5 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

solu-tion 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

emis-sion 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 5Although SSA has a complex composition,6the 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·2H2O) The latter can serve as an efficient ice

nucle-ating 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,

anhy-drous NaCl is the thermodynamically stable phase formed

upon efflorescence of solution above 273.3 K.9 , 10Below 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

temperatures above 253 K.11A similar observation was made

by Koop et al., who studied the efflorescence and

deliques-cence 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 rel-ative 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.2,13–18Such solid inclusions could facilitate the nucleation of crystalline NaCl

Understanding phase transitions of NaCl under realistic atmospheric conditions is difficult and has only been inves-tigated in 2 experimental studies conducted at low

temper-atures 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 environ-mental 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.

0021-9606/2016/145(24)/244503/12 145, 244503-1 © Author(s) 2016

In contrast, Wagner et al used the AIDA (Aerosol

Inter-action and Dynamics in the Atmosphere) cloud chamber to

investigate the temperature-dependent partitioning between

the two crystalline phases of NaCl and observed no

forma-tion of sodium chloride dihydrate above 235 K.19The 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 1 and 2 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

ade-quately explained in terms of the bulk phase diagram of NaCl

and its mixtures with organic and inorganic species The bulk

of experimental evidence20and previous attempts of atomistic

modelling21 – 24suggest that the efflorescence of NaCl in

micro-scopic 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,

miss-ing 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

supersatu-rated 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

Wise et al and Wagner et al., obtained under different

temper-ature 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 – 29The 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 cryo-stat (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 mea-surements 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, cylin-drical housing) The accommodation of the each droplet to the temperature inside the EDB is completed within about 1 s.30

The size of a suspended droplet is measured continuously by analyzing the two-dimensional angle-resolved scattering pat-tern recorded with a CCD camera installed at a right angle to the beam of the HeNe laser28,29(seesupplementary material

for details) Shadow images of the droplets and residual parti-cles have been recorded with the Raman microscope, providing additional information about the morphology, the phase, and the size of the particles

FIG 1 Schematic representation of the experimental setup.

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 cm1to 4400 cm1 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

ana-logue mixture (Instant Ocean®, Aquarium Systems) was

dis-solved 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

“dis-solved 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.,32a 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

mag-netic stirrer for several hours During the preparation,

indi-vidual 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

alkalin-ity) 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)

determina-tion of crystalline phase partidetermina-tioning as a funcdetermina-tion of

temper-ature 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

(RH) inside the EDB was set between 38% and 44% A typ-ical 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 efflo-rescence takes place The effloefflo-rescence 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 efflo-resced 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 allow-ing for precise determination of droplet diameter (see Figure S2 of thesupplementary material) In total, 612 NaCl solu-tion droplets (resulting in 330 anhydrous NaCl and 282 NaCl dihydrate particles) and 264 sea salt mixture droplets (result-ing in 134 anhydrous NaCl and 130 NaCl dihydrate contain(result-ing SSA particles) have been studied The details of experimen-tal conditions are given in thesupplementary material(Tables S1–S3)

III RESULTS AND DISCUSSION

A Shape of NaCl and NaCl·2H 2 O residual particles

The vast majority of the effloresced anhydrous NaCl par-ticles 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 orien-tations (Fig 2, panel C) The morphology of NaCl particles found in this study was in good agreement with previous mea-surements 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 spheri-cal 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 supersat-urated 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 parti-cle images) was found to be a factor 1.33 larger than that of

FIG 2 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,

pan-els 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 (Figure2, panels J–L) We interpret this

obser-vation 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 (Figure3) Only

lat-tice vibrations in the spectral range from 100 cm1to 390 cm1

FIG 3 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 cm 1and are vertically offset for

clarity.

were observed with one prominent maximum located at

235 cm1.41 The spectral features characteristic for NaCl dihydrate particles are located in the three regions of the Raman spectrum (see Figure3, panels (a)–(c)) In the high-frequency region (from 3000 cm1to 3800 cm1), two main peaks at 3424 cm1 with a shoulder at the low-frequency side (at ∼3410 cm1) and a weaker peak at 3545 cm1have been observed These peaks have been identified as the symmetric and asymmetric OH-stretching vibrations of water.16Two Raman bands with

a significant lower intensity could be identified at 3299 cm1 and 3320 cm1(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 cm1 and

1664 cm1, in agreement with previous studies.5,42,43 Wise

et al also reported both the OH-stretching and OH-bending

regions of NaCl · 2H2O at 244 K but the Raman peaks in the OH-stretching region were not resolved in great detail In addi-tion 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 cm1 to 800

cm1) These modes correspond to the rotational oscillations

of H2O molecules restricted in their motion by the interaction with neighboring lattice atoms, but are often hidden by numer-ous Raman bands of the matrix or substrate.16A pronounced librational mode was observed at 390 cm1

The Raman spectra representative of SSA solution and effloresced SSA particles are shown in Figure 4 The main spectral features used for the identification of crystalline phase

of NaCl in effloresced particles were the two sharp peaks cor-responding to the stretching vibrations of water at 3424 cm1 and 3545 cm1, and the librational mode at 390 cm1(the red line in Figure4, panels (a) and (c)) These features are unique for NaCl·2H2O, and, if present, always dominate the Raman spectrum in this region due to the prevalence of NaCl in the solution.5,16The hydrated salts other than NaCl could be iden-tified on the basis of their own characteristic H2O stretching and bending modes For example, the spectrum shown in black

in Figure4is a characteristic for carnallite (KMgCl3·6H2O), found previously in SSA particles.17 , 44

The Raman spectrum of carnallite exhibits a sharp band at

3430 cm1with a small shoulder at 3260 cm1, which can be

FIG 4 Raman spectra of the suspended SSA solution droplet (green), SSA

residual particles containing NaCl·2H 2 O (red), the residual particle containing

NaCl in the presence of precipitated carnallite KMgCl3·6H 2 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 cm 1and 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 cm1 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 cm1 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 (Figure4, the blue spectrum in

panel (a))

Additionally, all Raman spectra of SSA particles

con-tained the ν1(SO2−4 ) stretching mode peak at 984 cm1 and

an additional minor feature at 1008 cm1indicating the

pres-ence of aqueous SO2−4 ions in the environment of Ca2+ and

Mg2+ions, similarly to what have been reported by Zhang and

Chan.45The Raman spectra clearly show that even after

efflo-rescence a significant amount of hydration water is present

in the SSA residual particles.13 More discussion of Raman

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 chemi-cal composition SSA particles contained clearly recognizable cubic crystals of anhydrous NaCl embedded into the crust of other inorganic components (see Figure S5 of the supplemen-tary 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 (CaSO4·2H2O, gypsum) or hemihydrate (CaSO4·0.5H2O), which can be part of a gypsum formation pathway.46,47This finding is in general agreement with the picture of SSA con-taining a solid NaCl core and a mixture of hydrated Mg-rich and Ca-rich material.14,17,36,44,48 Both gypsum and hemihy-drate 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 do 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 (Figure5(a)) The tran-sition 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.,2and Wise et al.,5no 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 5 (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 SectionIII 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.

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% min1)

have been used in the study of Wise et al.

Using the FTIR extinction spectra as a method for the

par-ticle phase detection, Wagner et al.19have 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 6 h (green open diamonds in Figures5(a)and5(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

Figure5(b)shows the thermodynamic conditions of the

efflorescence experiments (i.e., the temperature and

humid-ity where the efflorescence has been observed) plotted on the

phase diagram of NaCl aqueous solution, adapted from the

work of Koop et al.2The 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

dif-ference in the droplet size and induction time when comparing

these experiments In Secs.III D–III G, we show that

exper-imental 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

coeffi-cients of NaCl and NaCl·2H2O, we have analyzed the

efflo-rescence 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,

P k (t)=(wt) k

k! e

where ω is the average number of crystallized droplets per

unit time (efflorescence rate) From that, the probability of N liq

droplets to remain liquid (k = 0) after time t can be calculated

as

P0(t) = exp (−ωt) ' N liq (t)

which is also asymptotically equal to the fraction of liquid

droplets observed at time t: f liq (t) = N liq (t)/N0 The probability

of observing exactly one efflorescence event (k = 1) can be related to experimental data by the following equation:52

P1(t) = ωt · exp (−ωt) ' N liq (t)

N0 ln N0

N liq (t)

! (2b)

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 Figure6) At the same time, the Poisson statistics provides a way of calculating the

statis-tic 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 w low or below the upper fiducial limit, w up.53,54The 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 thesupplementary material) Figure6gives 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

solu-tion droplets require time t ind(induction time) to adjust to the humidity inside the trap and thus reach the efflorescence

con-centration, the time t in Equations(1)–(2b)has to be replaced

with t t ind.55,56The induction time becomes a fitting param-eter 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 thesupplementary 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 neces-sary to calculate homogeneous nucleation rate coefficients

FIG 6 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 P0(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.

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

super-saturation 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 N0identical droplets of volume V dinto

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 liqof liquid droplets, the number

of effloresced droplets N eff , and the number N i of droplets

effloresced into state i,

dN liq

dt = −(J A + J B )V d N liq, (3a)

dN eff

dt = (J A + J B )V d N liq, (3b)

dN i

dt = J i V d N liq, (3c)

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

liq-uid decay curve The system can be solved by integrating

Equation(3a) and substituting the result into the successive

Equations(3b)and(3c)leading to

N liq = N0exp [−(J A + J B )V d t] , (4a)

N eff = N0



1 − N liq



N i= J i

J A + J B

Equation(4a)can be rearranged to yield the time dependence

of the number of liquid droplets,

lnN liq

N0 = −(J A + J B )V d t = −JV d t, (5)

which is identical to Equation (2) As it follows from

rela-tions(4a)–(4c), the volume specific nucleation rates J ican be

determined from the effloresced fractions f i = N i /N eff = J i /J

at any time, e.g., also when all droplets are effloresced, i.e.,

N eff = N0,

J i= N i

Additionally, as the effloresced fractions are time independent,

they can be identified as the probabilities p ito arrive in final

state A or B in a single event by setting N eff = 1,

p i= J i

Equations(5)and(6)can be used to determine the volume

nucleation rate J for the single state i by measuring the fraction

f i and the total nucleation rate ω = J · V d, which are both experimentally accessible in our experiments,

J i= N i

N0

ω

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 homo-geneous nucleation rate for NaCl dihydrate has been deter-mined from the data shown in Figure6 The results are shown in Figure7 It shows that the homogeneous nucleation rate coeffi-cient 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 parameteriza-tion of our efflorescence nucleaparameteriza-tion rate of NaCl dihydrate which is then extended into the range of experimental

condi-tions 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

coef-ficient of water DH2O(T ) in supersaturated NaCl solution at

very high concentrations and low temperatures and (b) the interfacial energy of NaCl dihydrate crystal σsl (T ) in

super-saturated 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

vol-ume specific homogeneous nucleation rate J hom (T ) can be

expressed as follows:

J hom (T )=kT

h n vexp −∆F diff (T )

kT

! exp −∆G(T )

kT

! , (9)

where ∆G(T ) is the energy of formation of a critical nucleus

in the aqueous solution, ∆F diff (T ) is the diffusion activation energy, n v is the molecular concentration in the crystalline NaCl nucleus (∼6.1 · 1021 cm−3), and k and h are the

Boltz-mann and the Plank constants The diffusion activation energy

is given by

∆F diff (T ) = kT2 ∂

∂T ln DH2O(T )
(10)

FIG 7 Volume specific nucleation rates obtained from NaCl dihydrate efflorescence experiments of type B.

The temperature and concentration dependence of the

diffu-sion coefficient of water DH2O(c, T ) can be parameterized with

the Vogel-Fulcher-Tammann (VFT) equation,58 – 60

DH2O(c, T ) = D0(c) · exp − B(c)

T − T0(c)

! , (11)

where D0(c), B(c), and T0(c) are concentration dependent

parameters We use the linear parameterization of D0(c)

= (38.6 × c + 40) × 10−9m2s−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 1 to 5 mol/l and temperature

range from 300 K to 230 K For T0(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 Figure8(a)) not only reproduces the

experimental data of Garbacz and Price but also follows the

power law (PL) parameterization of Koop and Murray,60which

was shown to provide the most physically consistent

descrip-tion of nucleadescrip-tion 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 Figure8(a))

With this constraint, we use Equation(11) to calculate

the DH2O(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 DH2O are poorly known below 230 K, as shown

by a strong deviation between the VFT and PL

parameter-izations as T approaches 220 K (green and blue lines in

Figure8) For concentrated NaCl solution, no direct

measure-ments exist that could be used to constrain the parameterization

of DH2O(c, T ) at this low temperature and high concentration of

NaCl Therefore, the parameterization of DH2O(c, T ) described

above should be treated with caution

The energy of critical nucleus formation is defined as

∆G(T )= 16πσsl (T )3υ2

3kT ln(S*(T ))2, (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= 4.5·1023cm3)

or NaCl dihydrate (υ= 9.6 · 1023cm3), and S*is the supersat-uration of the solute

The supersaturation of the solute has been calculated fol-lowing the method of Richardson and Snyder.61In this method,

the ratio of the mole fraction of water x wto the mole fraction

of solute x sis 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

lnS* =

 a w,del

a w,eff

xw

x s d ln (a w) (13)

Using the water activity value at efflorescence a w,eff = 0.47

as the lower integration limit and the water activity at

del-iquescence a w,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 dihy-drate shows a strong temperature dependence due to the tem-perature 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 quan-tity has to be estimated from the measurements of nucle-ation rate That was done by substituting Equnucle-ation(10)into Equation(9), which was then rearranged for σsl (T ) The

inter-facial energy was estimated by using the parametrization of

FIG 8 (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 0 to 5 mol/l Solid lines are VFT parameterization with c = 0 (pure water) used in this work (red), VFT adapted from Koop and Murray60(green), and power law (PL) parameterization of D H2O(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 a w = 0.47 (c = 10.1 mol/l), together with Huang-Bartell fit extrapolated into low temperature range.

DH2O(c, T ), the supersaturation S* with respect to NaCl

dihy-drate, and the measured volume specific homogeneous

nucle-ation rate J hom (T ) for NaCl dihydrate To calculate σ sl (T ) for

temperature outside of the experimental range, the

parameter-ization proposed by Huang and Bartell63has been used,

σsl (T )= σ0

T

T0

!n

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

mea-sured 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 (Figure8(b))

The values of σsl (T ) derived from the measured

nucle-ation 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 σ sl= 38 mJ/m2

at room temperature has been reported before.64–66

Surpris-ingly, 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

anhy-drate 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 Shchekin23have derived the solid/liquid

inter-facial energy of anhydrous NaCl from the measurements of

ERH and DRH of nanometer-sized NaCl particles reported in

the work of Biskos et al.67The interfacial energy was shown to

increase from σsl = 86.6 mJ/m2at NaCl concentration of 15.2

mol/kg to σsl = 89.4 mJ/m2at NaCl concentration of 15.95

mol/kg.23Interestingly, these values are close to the value of

σsl= 89 mJ/m2for NaCl crystal in its own melt.68

Although the values of σsl for anhydrous NaCl

can-not be directly compared to our values for NaCl dihydrate,

they could be useful to understand the concentration

depen-dence 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(σ sl) ∼ 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 1 mol/l

was reportedly associated with 5% increase of crystal/liquid

interfacial energy.23We use this estimation in the following

analysis

The fraction of NaCl dihydrate as a function of

tempera-ture for a given droplet volume V d and observation time t can

be calculated as

fNaCl·2H2O(T ) = 1 − exp (−J hom (T ) · V d·t). (15)

Figure 5(a) (the red solid line) shows the fraction of

NaCl dihydrate calculated with Eq.(15)for our experimental

conditions (a w = 0.47, d d = 30 µm, t = 60 s) with the

nucle-ation 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.5could be reproduced with the same parameterization and initial average droplet diameter

of 10 µm, as shown in Figure5(a) Assuming average ERH of 45% (see phase diagram, Figure5(b)), the average

supersatura-tion was found to be S* = 7.1 at 245 K Since the drying rate was

not reported, we have estimated the induction time by

divid-ing the range between DRH and ERH (∆RH ≈ 30% ) by the

slowest (1% min1) and fastest (10% min1) reported drying rate, resulting in the range of times between 180 s and 1800 s The measured fractions of NaCl dihydrate falls into the mid-dle of the range predicted with these limiting induction times (the blue shaded area in Figure5(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

frac-tions 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 a w,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 depen-dence, as mentioned previously in this section To do so, we project the concentration dependence of σsl (T , c) reported in

the work of Hellmuth and Shchekin23into the range of con-centrations 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 4 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

(Figure5(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.2observed initiation of NaCl

crys-tallization 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.69There, the crystallization of NaCl dihy-drate was facilitated by the presence of oxalic acid crystals Recently, the CaSO4 was identified by means of EDX analy-sis of the sea salt particles collected in the field.37Following 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 Figure9 A minor fraction of NaCl dihydrate was observed already at 257 K Nearly all SSA solution droplets effloresced

G Temperature- dependent formation of NaCl dihydrate in SSA particles< /b>... 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