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Infrared Optical Constants of Crystalline Sodium Chloride Dihydrate: Application To Study the Crystallization of Aqueous Sodium Chloride Solution Droplets at Low Temperatures Robert Wagner,* Ottmar Möhler, and Martin Schnaiter Karlsruhe Institute of Technology (KIT), Institute for Meteorology and Climate Research (IMK-AAF), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany S Supporting Information *

ABSTRACT: Complex refractive indices of sodium chloride dihydrate, NaCl·2H2O, have been retrieved in the 6000−800 cm−1 wavenumber regime from the infrared extinction spectra of crystallized aqueous NaCl solution droplets. The data set is valid in the temperature range from 235 to 216 K and was inferred from crystallization experiments with airborne particles performed in the large coolable aerosol and cloud chamber AIDA at the Karlsruhe Institute of Technology. The retrieval concept was based on the Kramers− Kronig relationship for a complex function of the optical constants n and k whose imaginary part is proportional to the optical depth of a small particle absorption spectrum in the Rayleigh approximation. The appropriate proportionality factor was inferred from a fitting algorithm applied to the extinction spectra of about 1 μm sized particles, which, apart from absorption, also featured a pronounced scattering contribution. NaCl·2H2O is the thermodynamically stable crystalline solid in the sodium chloride−water system below the peritectic at 273.3 K; above 273.3 K, the anhydrous NaCl is more stable. In contrast to anhydrous NaCl crystals, the dihydrate particles reveal prominent absorption signatures at midinfrared wavelengths due to the hydration water molecules. Formation of NaCl·2H2O was only detected at temperatures clearly below the peritectic and was first evidenced in a crystallization experiment conducted at 235 K. We have employed the retrieved refractive indices of NaCl·2H2O to quantify the temperature dependent partitioning between anhydrous and dihydrate NaCl particles upon crystallization of aqueous NaCl solution droplets. It was found that the temperature range from 235 to 216 K represents the transition regime where the composition of the crystallized particle ensemble changes from almost only NaCl to almost only NaCl·2H2O particles. Compared to the findings on the NaCl/NaCl·2H2O partitioning from a recent study conducted with micron-sized NaCl particles deposited onto a surface, the transition regime from NaCl to NaCl·2H2O is shifted by about 13 K to lower temperatures in our study. This is obviously related to the different experimental conditions of the two studies. The partitioning between the two solid phases of NaCl is essential for predicting the deliquescence and ice nucleation behavior of a crystalline aerosol population which is subjected to an increasing relative humidity. 3000 cm−1 that can clearly be differentiated from the broad, structure-less feature of liquid water.6,8,15,16 In addition to the qualitative identification of different chemical compounds, infrared extinction spectra of an ensemble of aerosol particles can quantitatively be analyzed for the aerosol number size distribution and volume concentration using Mie theory for spheres or applying the T-matrix approach17 and the discrete dipole approximation (DDA)18 for nonspherical particle shapes. This, however, requires knowledge of the particles’ wavelength-dependent complex refractive indices (optical constants).19 Many studies in our own and other aerosol laboratories have aimed to improve and complete the database of infrared optical constants for atmospheric compounds over the past decade.20−30 In this work, we address a further species for which,

1. INTRODUCTION Vibrational spectroscopic techniques like infrared extinction and vibrational Raman spectroscopy are valuable tools to identify the phase of aerosol particles.1−11 Whether aerosol particles are prevalent as crystalline solids or aqueous solution droplets affects their ability to catalyze heterogeneous processes, to absorb and scatter radiation, and to act as nuclei in cloud formation.12 Research on phase transitions of atmospherically relevant aerosol particles is therefore of continuous interest and has recently also included amorphous solid and semisolid phases.13,14 For aqueous species like ammonium sulfate forming an anhydrous phase, crystallization is readily evidenced in vibrational spectra by the disappearance of the broad liquid water vibrational band at around 3300 cm−1 associated with the O−H stretching mode.2 For compounds where hydrated crystals like sodium chloride dihydrate and oxalic acid dihydrate are partly or exclusively formed upon efflorescence, the molecules of hydration water usually give rise to a sharp, well-structured spectral habitus between 3600 and © 2012 American Chemical Society

Received: June 25, 2012 Revised: July 30, 2012 Published: August 2, 2012 8557

dx.doi.org/10.1021/jp306240s | J. Phys. Chem. A 2012, 116, 8557−8571

The Journal of Physical Chemistry A

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experiments even at 235 K, i.e., at a temperature where Wise et al.6 have exclusively detected the precipitation of NaCl·2H2O. In order to get a complete picture of this system and to better compare our results to those from Wise et al.,6 we have performed an additional series of crystallization experiments between 235 and 216 K using airborne NaCl particles with median diameters between 0.06 and 1.1 μm whose results are discussed in this article. At temperatures below 235 K, we did no longer observe the exclusive formation of only anhydrous NaCl crystals in the AIDA experiments. Instead, a fraction of the aqueous NaCl solution droplets then also crystallized as NaCl·2H2O, as again sensitively detected by infrared extinction spectroscopy. As mentioned above, the quantitative analysis with respect to the relative number and volume fraction of anhydrous NaCl and NaCl·2H2O particles requires accurate optical constants for the latter species, whose derivation will therefore be a central subject of this article that is organized as follows. After presenting the experimental setup of our crystallization studies in section 2, section 3 addresses our approach to retrieve the optical constants of NaCl·2H2O from the particles’ infrared extinction spectra. The key idea is to record the spectra of two differently sized particle ensembles, one population with particle sizes much smaller than the wavelength of the incident light where the contribution of light scattering is negligible and light absorption can be described by Rayleigh theory,19 and another population with median sizes of at least about 1 μm where scattering also becomes important. The retrieved data set of the wavelength dependent complex refractive index for NaCl·2H2O in the spectral regime between 6000 and 800 cm−1 is then presented in section 4, including a thorough discussion of the uncertainties that are associated with our retrieval approach. In section 5, we apply the new data set to quantify the low-temperature crystallization behavior of aqueous NaCl solution droplets with respect to the partitioning between anhydrous and dihydrate crystals. A summary in section 6 concludes our article. Note that, similar to Wise et al.,6 we have also probed the heterogeneous ice nucleation ability of the crystallized particles. The results from these expansion cooling experiments will be summarized in a separate article.

to the best of our knowledge, infrared optical constants are not yet available, namely, crystalline sodium chloride dihydrate. Sodium chloride (NaCl) is one of the most important inorganic species of tropospheric aerosol particles and the primary constituent of sea salt aerosol particles.31 Several previous studies therefore have investigated the phase transitions in the binary sodium chloride−water system down to low temperatures.3,6,32 Its bulk phase diagram reveals the existence of two solid phases: anhydrous NaCl and sodium chloride dihydrate, NaCl·2H2O. The peritectic at 273.3 K defines the transition for the two different solid phases to be in thermodynamic equilibrium with a saturated brine solution: above 273.3 K, it is anhydrous NaCl, and below 273.3 K, NaCl·2H2O is the stable crystalline solid.33 In contrast to the predictions by the bulk phase diagram, aerosol flow tube experiments by Cziczo and Abbatt3 did not indicate the formation of NaCl·2H2O upon crystallization of aqueous NaCl solution droplets down to a temperature of 253 K. In their study, the aerosol flow was probed by infrared extinction spectroscopy. The infrared spectra of the effloresced NaCl aerosol particles only retained a minor, spectrally broad background signal in the regime of the O−H stretching mode, presumably due to physically trapped water, but did not reveal the prominent triplet signature of NaCl·2H2O at 3413, 3471, and 3559 cm−1. This signature was first recorded by Mutter et al.34 and erroneously interpreted as a new form of ice.16 In agreement with Cziczo and Abbatt,3 flow cell microscopy experiments by Koop et al.32 also showed that NaCl instead of NaCl·2H2O was formed upon efflorescence down to 249 K because the measured value of the deliquescence relative humidity (DRH) of the crystallized particles (∼75% RH) agreed with that of anhydrous NaCl but not with that expected for NaCl·2H2O particles (∼81% RH at 252 K). Recently, Wise et al.6 have examined NaCl deliquescence and efflorescence down to even lower temperatures, probing 1−10 μm sized NaCl particles deposited onto a hydrophobic quartz disk with a combination of optical microscopy and Raman spectroscopy. They observed that, above 252 K, only anhydrous NaCl particles crystallized. In a transition regime between 252 and 236 K, a mixture of anhydrous and dihydrate crystals was formed, whereas below 236 K, only NaCl·2H2O crystallized. The formation of thermodynamically stable NaCl·2H2O seems to be favored in the case of heterogeneous crystallization on available surfaces. In freezing experiments with bulk and emulsion samples of aqueous NaCl, Koop et al.32 have detected that ice nucleation can immediately trigger the precipitation of NaCl·2H2O, presumably induced by heterogeneous crystallization on the ice crystal surface. In AIDA cloud chamber experiments, probing an ensemble of airborne particles of different composition at 244 K,35 we have recently shown that oxalic acid crystals embedded in aqueous NaCl solution droplets provoke the precipitation of NaCl·2H2O in a subset of the particle ensemble, whereas only anhydrous NaCl particles crystallized from pure aqueous NaCl solution droplets without solid inclusions at the same temperature. The dihydrate formation was evidenced by in situ infrared extinction spectroscopy and by the appearance of a second deliquescence step at 82% RH due to NaCl·2H2O that was additionally observed after the deliquescence step due to anhydrous NaCl at about 75% RH. This deliquescence behavior was probed by in situ laser light scattering and depolarization measurements. Interestingly, dihydrate formation upon crystallization of pure aqueous NaCl solution droplets was absent in our former

2. EXPERIMENTAL SECTION 2.1. Instrumentation. The experiments were conducted in the 84 m3 sized aerosol and cloud chamber AIDA at the Karlsruhe Institute of Technology (Figure 1).36 The cylindrical aluminum vessel is mounted inside an isolating containment and its temperature can be controlled from ambient down to 183 K, as monitored by ensembles of horizontally and vertically arranged temperature sensors. The temperature variability is typically below ± 0.3 K throughout the chamber volume, as ensured by continuously operating a mixing fan mounted at the bottom of the vessel, which also maintains homogeneous conditions in terms of the aerosol number concentration in the chamber interior. The aerosol vessel can be efficiently cleaned by evacuation down to a pressure of about 0.1 hPa and performing several flushing cycles with particle-free synthetic air before refilling the chamber to ambient pressure. In the preparation of each crystallization experiment, the inner chamber walls were coated by a thin ice layer. This ice layer was the prerequisite to establish ice supersaturated conditions inside the vessel in subsequent expansion cooling cycles, which, as mentioned above, were additionally performed to probe the heterogeneous ice nucleation ability of the crystallized particles. 8558



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Figure 1. Schematic view of the AIDA aerosol chamber facility, featuring the relevant instrumentation for the NaCl crystallization experiments.

The AIDA instrumentation has been detailed in several recent publications, and we will therefore only briefly summarize the key components for aerosol generation and characterization used in the present experiments.35,37 Aerosol particles were prepared from dilute aqueous solutions of 1−5 wt % NaCl, generated by dissolving sodium chloride (Merck, >99.5%) in purified water. After filtration with a submicron syringe filter, the solutions were injected into the AIDA chamber either with a compressed-air atomizer (TSI, model 3076) or an ultrasonic nebulizer (GA2400, Sinaptec) with initial number concentrations between 2 × 103 and 5 × 104 cm−3, as measured with two condensation particle counters (CPC3010 and 3775, TSI). The size distributions were measured with a combination of a scanning mobility particle sizer (SMPS, TSI, mobility diameter range from 0.014 to 0.82 μm) and an aerodynamic particle spectrometer (APS, TSI, aerodynamic diameter range from 0.523 to 19.81 μm), which both operated at ambient temperature (∼298 K) outside the isolating housing and sampled the aerosol particles through stainless steel tubes connected to the chamber. Aqueous NaCl solution droplets crystallized as NaCl·2H2O at temperatures below 235 K in the chamber will most presumably lose their hydration water upon warming and be detected as anhydrous NaCl crystals in the size distribution measurements. We therefore used the particle density, ρ, of anhydrous NaCl (2.165 g cm−3) and a dynamic shape factor, χ, of 1.08 as representative for cubes to convert the aerodynamic diameter of the APS into a volume-equivalent sphere diameter, dp.38 The same value for χ was assumed to translate the mobility-equivalent diameter of the SMPS into dp. Figure 2 shows the size distribution measurements for two different ensembles of completely crystallized NaCl particles to illustrate the particle size range covered by the present experiments. The smallest crystals, having a count median diameter of only 0.06 μm, were obtained after crystallization of

Figure 2. Normalized number size distributions recorded after crystallization of aqueous NaCl solution droplets injected into AIDA with either the atomizer (a) or the ultrasonic nebulizer (b) at 220.9 and 225.7 K, respectively.

NaCl solution droplets injected with the atomizer using a 1 wt % aqueous NaCl solution (trace a). In contrast, a count median diameter of about 0.85 μm was typically observed after crystallization of solution droplets injected with the nebulizer using a 5 wt % aqueous NaCl solution (trace b). Supplementing the size distribution measurements, the overall NaCl mass concentrations were determined by ion chromatographic analysis of nylon filter samples (Dionex DX500 ion chromatograph). As shown in Figure 1, the filter holders were also located outside the cold housing. We have typically observed discrepancies from 10 to 25% between the NaCl mass concentrations obtained by integration of the measured volume size distributions (assuming ρ = 2.165 g cm−3) and those determined from the filter sampling technique. These differences reflect the combined uncertainties of both methods, which, regarding the filter sampling technique, include uncertainties with respect to flow measurements, sampling losses, and the chromatographic analysis. For sizing of 8559



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nonspherical particles with SMPS and APS, the appropriate choice of the dynamic shape factor represents the largest uncertainty. Three further in situ optical measurement techniques were employed in the present study.37 The relative humidity inside the AIDA chamber was measured with tunable diode laser (TDL) absorption spectroscopy by selectively scanning a rovibrational transition of water vapor at near-infrared wavelengths. The back-scattering linear depolarization ratio, δ, of the aerosol particles was determined by polarization-resolved measurements of the intensities of laser light of 488 nm wavelength scattered from the particles in the center of the aerosol vessel in 178° backward direction. Finally, a FTIR spectrometer (IFS66v, Bruker) was coupled to an open-path multiple reflection cell inside the AIDA chamber to record the infrared extinction spectra of the aerosol particles from 6000 to 800 cm−1. 2.2. Crystallization Experiments. Crystallization of aqueous NaCl solution droplets in AIDA was studied in static mode experiments at constant temperature and relative humidity over a time scale of up to six hours. The relative humidity inside the chamber at a given temperature was controlled by the saturation water vapor pressure over ice deposited on the chamber walls. In the temperature range from 235.7 to 216.0 K covered by our experiments, this yielded relative humidities with respect to supercooled water, RHw, between 61 and 52%.39 As already discussed in the context of our previous crystallization experiments at 244 and 235 K, efflorescence of the aqueous NaCl solution droplets is detected in AIDA at relative humidities higher than that observed in previous literature studies.40 Our experiments, however, feature much longer observation times. We will address this issue in more detail in section 5. The crystallization of the injected solution droplets was tracked by depolarization and infrared extinction measurements. The top panel of Figure 3 shows the time series of the back-scattering linear depolarization ratio for a crystallization experiment at 225.7 K and 56% RH using the ultrasonic nebulizer for aerosol generation. With the start of aerosol injection, marked by time zero, δ adopts a small background value close to zero, which is typical for spherical solution droplets that do not cause any depolarization. The habitus of the infrared extinction spectrum recorded at the beginning of the injection period (trace a) indeed bears the signatures of liquid NaCl solution droplets, as apparent from the broad, structure-less peaks in the regime of the O−H stretching (∼3300 cm−1) and O−H bending (∼1600 cm−1) modes.3 Already during the injection period as well as in the time period thereafter, the depolarization ratio, however, increases, indicating the formation of nonspherical particles with nonzero depolarization due to ongoing crystallization of the particle ensemble. In the infrared spectrum recorded after about 5000 s (trace b), the sharp spectral bands of the hydration water molecules in crystalline NaCl·2H2O (see traces d1 and d2 in Figure 3 for a reference spectrum of NaCl·2H2O) already clearly protrude from the comparatively broad extinction signatures of liquid water originating from aqueous NaCl solution droplets that have not yet crystallized. After about 20 000 s, the depolarization ratio has reached a constant value of 0.34, indicating that the entire aerosol population has crystallized. The magnitude of δ of the crystallized particle ensemble depends on the particle size and is only about 0.12 for the population of smaller sized crystals obtained when using

Figure 3. Top panel: time series of the back-scattering linear depolarization ratio, δ, after injection of an aqueous 5 wt % NaCl solution into the AIDA chamber at 225.7 K and 56% RH with an ultrasonic nebulizer. The time period of aerosol injection, tinj, starting at time zero, is indicated by the horizontal arrow. The vertical arrows a−c denote time stamps of individual FTIR spectra measurements that are shown in the bottom panel. The bottom panel additionally includes a literature infrared spectrum of NaCl·2H2O in the regimes of the O−H stretching mode (trace d1) and the O−H bending mode (trace d2), obtained by digitizing Figure 1 from Schiffer and Hornig.16 All spectra were normalized and offset to facilitate their comparison.

the atomizer for aerosol generation (Figure 2, trace a). The time period for crystallization of the entire particle ensemble decreases with decreasing temperature and is only about 6000 s for the experiment conducted at 216.0 K and 52% RH. The infrared extinction spectra recorded after the entire aerosol populations had crystallized (e.g., trace c in Figure 3) were then used to deduce the optical constants of NaCl·2H2O as explained in the following section.

3. DERIVATION OF THE OPTICAL CONSTANTS FOR NACL·2H2O 3.1. Basic Approach. The framework of our retrieval approach builds on the application of the Kramers−Kronig relationship to the complex function f(ν̃),41,42 f (ν)̃ = (N 2(ν)̃ − 1)/(N 2(ν)̃ + 2)

(1)

where N(ν̃) = n(ν̃) + ik(ν̃) denotes the wavenumber dependent complex refractive index with its real and imaginary parts n and k, which are called the optical constants. The imaginary part of f, Im{f(ν̃)}, for a given compound is directly accessible from the measurement of its small particle extinction spectrum, provided that the contribution of particle scattering is negligible so that extinction equals absorption. Then, according to the Rayleigh approximation for the absorption of spheres, the recorded optical depth, τ(ν̃), is directly proportional to Im{f}:19,27,43 τ(ν)̃ = 8560

6πνlV ̃ s ⎛ N 2(ν)̃ − 1 ⎞ Im⎜ 2 ⎟ ln 10 ⎝ N (ν)̃ + 2 ⎠

(2)



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experiments at 244 and 235 K.35 At lower temperatures, heterogeneous ice nucleation was observed before reaching the deliquescence RH of anhydrous NaCl particles so that their presence cannot be verified by this technique. Thus, we cannot exclude that a fraction of anhydrous NaCl crystals is still formed in the small particle crystallization experiment at 220.9 K, so that the overall NaCl mass concentration inferred from the size distribution measurement and filter sample analysis cannot be fully attributed to NaCl·2H2O. We therefore employed an iterative technique where the scaling factor Vs is optimized by fitting the recorded infrared extinction spectra of the larger sized NaCl and NaCl·2H2O crystals when the ultrasonic nebulizer was used for aerosol generation (Figure 2, trace b). The basic idea behind this approach, similar to the iterative technique previously adopted by Clapp et al.,47 is illustrated in Figure 4. In the left part, we show the spectra of the optical constants n and k for NaCl·2H2O obtained from the small particle absorption spectrum using eqs 1−3 for three different values of Vs; Vs = 100, 150, and 200 μm3 cm−3. An increase in Vs leads to a decrease of the magnitude of the absorption bands in the k spectrum and concomitantly reduces the amplitude of the associated anomalous dispersion features in the spectrum for n. For particle absorption in the Rayleigh regime, all three different data sets necessarily yield the same spectral habitus. The situation, however, is different regarding extinction spectra of ∼1 μm sized particles where also the scattering contribution becomes important and Mie theory has to be applied to compute the spectra. Here, the differences in the relative scaling between n and k as well as the different amplitudes in the anomalous dispersion features in the three data sets will clearly affect the spectral habitus of the calculated extinction spectra. Hence, with an n and k data set for NaCl·2H2O inferred from an inaccurate scaling factor Vs in eq 2, the extinction spectrum of micron-sized NaCl·2H2O crystals cannot be properly reproduced. This is demonstrated by a test calculation shown in the right panel of Figure 4. The two dashed black lines in the right panel of Figure 4 show the Mie computed extinction spectrum of log-normally distributed NaCl·2H2O particles with a number concentration, N, of 400 cm−3, a mode width, σg, of 1.37, and a count median diameter, CMD, of 1.1 μm, using the optical constants calculated for Vs = 150 μm3 cm−3. These two dashed black traces are identical spectra and are shown with an offset to facilitate the comparison with the red and blue curves, which are discussed below. The σg value was obtained from a lognormal fit to the number size distribution (b) in Figure 2. The count median diameter of 1.1 μm for NaCl·2H2O particles as present in AIDA at low temperatures was estimated by scaling the CMD value for anhydrous NaCl crystals (∼0.85 μm, Figure 2) from the ex situ SMPS/APS measurements at room temperature with the factor

In eq 2, l denotes the optical path length and Vs the total particle volume concentration of NaCl·2H2O contributing to the small particle absorption spectrum. The assumption of a spherical particle shape is discussed in detail later in this article. To obtain a small particle absorption spectrum of NaCl·2H2O, we have performed a crystallization experiment at 220.9 K using the atomizer with a 1 wt % NaCl solution for aerosol generation, which yielded the size distribution shown as trace a in Figure 2. The infrared extinction spectrum of the crystallized particles only revealed a slightly slanted baseline at nonabsorbing wavenumbers greater than 4000 cm−1 beyond the strong absorption bands associated with the hydration water molecules in the O−H stretching mode regime. The nonzero baseline is the result of a small scattering contribution. Similar to Norman et al.,44 this scattering part, Isca(ν̃), was subtracted using a Rayleigh-like Isca(ν̃) ∝ ν̃4 behavior to infer the pure absorption contribution. Note that anhydrous NaCl crystals, even if additionally present in the ensemble of crystallized particles, do not reveal any absorption signatures in the mid-IR regime. The spectral features inherent in the recorded small particle absorption spectrum are therefore solely due to NaCl·2H2O. The nontrivial task in this case, however, is to infer the volume concentration of only the dihydrate contribution, i.e., the scaling factor relating Im{f(ν̃)} with the measured τ(ν̃) in eq 2. This issue will be addressed in the following section. Once Im{f(ν̃)} is calculated from τ(ν̃) with a proper estimate for Vs, the real part of the complex function f at a given wavenumber ν̃0, Re{f(ν̃0)}, can be obtained by the Kramers− Kronig transformation. We employed the subtractive Kramers− Kronig integration in the form Re{f (ν0̃ )} = Re{f (νx̃ )} + ×P

∫0

∞

2(ν0̃ 2 − νx̃ 2) π Im{f (ν)} ̃ ν̃

(ν 2̃ − ν0̃ 2)(ν 2̃ − νx̃ 2)

dν ̃ (3)

to minimize the truncation error associated with the unknown frequency behavior of Im{f(ν̃)} beyond the experimentally accessible wavenumber range.45,46 Re{f(ν̃x)} is the so-called anchor point value in the Kramers−Kronig integration. Knowledge of both Im{f(ν̃)} and Re{f(ν̃)} then allows computing the optical constants n and k from eq 1. Technical details regarding the evaluation of eq 3 with respect to the anchor point value and the extension of Im{f(ν̃)} beyond the measurement range are discussed in section 3.4. Before, we turn our attention to the estimation of Vs. 3.2. Specific Adjustments. We encounter the obvious problem that there is no a priori information about the volume concentration of crystallized NaCl·2H2O particles in an ensemble that may also contain a fraction of anhydrous NaCl crystals, which are invisible at mid-IR wavelengths when their scattering contribution is negligible. As outlined in the Introduction, Wise et al.6 have observed the crystallization of only NaCl·2H2O below a threshold temperature of 236 K. Under our experimental conditions, however, we can clearly evidence the formation of a significant amount of anhydrous NaCl crystals at least down to a temperature of 230.7 K. This is shown by the appearance of a pronounced deliquescence step at 72 ± 5% RH due to anhydrous NaCl in the depolarization measurements during the additionally performed ice nucleation experiments, where the relative humidity inside the chamber was raised via expansion cooling, similar to our previous

3

ρ(NaCl)/ρ(NaCl ·2H 2O) × M(NaCl· 2H 2O)/M(NaCl) (4)

employing values of 2.165 g cm−3 for ρ(NaCl), the density of anhydrous NaCl, 1.63 g cm−3 for ρ(NaCl·2H2O), the density of sodium chloride dihydrate,48 94.47 g mol−1 for M(NaCl·2H2O), the molar mass of sodium chloride dihydrate, and 58.44 g mol−1 for M(NaCl), the molar mass of anhydrous sodium chloride. In our test example, we consider the black traces for Vs = 150 μm3 cm−3 as a reference infrared extinction spectrum of 8561



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Figure 4. Left panels: spectra of the real and imaginary parts of the complex refractive index for NaCl·2H2O deduced from the small particle absorption spectrum using different assumptions for the value of Vs in eq 2. Right panel: Mie calculated infrared extinction spectra for log-normally distributed NaCl·2H2O particles with the n and k data set for Vs = 150 μm3 cm−3 (dashed black lines) in comparison with best fitted spectra for the data sets using Vs = 100 and 200 μm3 cm−3 (red and blue lines, respectively). The two fit examples are offset for clarity. The individual parameters of the log-normal number size distribution are given in the figure panel. See text for details.

further quality assurance for the retrieval result, the deduced number concentration can be compared to that measured with the condensation particle counter as outlined in section 3.3. Having presented the basic principle of how to derive Vs, we must address another issue that adds a further degree of complexity to the retrieval problem. The black, red, and blue spectra shown in Figure 5 were recorded after complete crystallization of the aerosol population following injection at three different temperatures using the ultrasonic nebulizer for aerosol generation. All spectra clearly exhibit the spectral

NaCl·2H2O particles to investigate the influence of different values for Vs in the fitting procedure. The red and blue traces shown in the right panel of Figure 4 are the best fitted spectra when using the optical constant data sets obtained with Vs = 100 and 200 μm3 cm−3 in Mie calculations to reproduce the spectrum computed with the reference Vs value of 150 μm3 cm−3. In those fits, we have constrained CMD to 1.1 μm and have only optimized the values for N and σg. Further computational details are summarized in section 3.4. The best fit using the optical constants with Vs = 100 cm−3 yields a lower particle number concentration of 346 cm−3. It underestimates the scattering contribution in the reference spectrum at wavenumbers greater than 3600 cm−1, reveals spectral mismatches in the regime of the O−H stretching extinction band, and clearly overestimates the intensity of the O−H bending mode. The best fit using the optical constants with Vs = 200 cm−3 yields a higher particle number concentration of 449 cm−3. It overestimates the scattering contribution in the reference spectrum at wavenumbers greater than 3600 cm−1, reveals slight spectral mismatches in the regime of the O−H stretching extinction band, and clearly underestimates the intensity of the O−H bending mode. A different scaling factor in eq 2 thus indeed significantly modifies the spectral signature computed for micron-sized NaCl·2H2O particles. This allows us to use the infrared spectra from the crystallization experiments with the nebulizer to derive Vs just by minimizing the root-mean-square deviations between the measured spectra and those calculated with Mie theory using NNaCl·2H2O, σg, and Vs as the optimization parameter.47 It is favorable to prescribe the CMD value for the NaCl·2H2O particles to that estimated from the size distribution measurements in order to avoid the scenario that a wrong value for Vs could be compensated for by artificially distorting the true number size distribution. As a

Figure 5. Solid lines: infrared extinction spectra of the crystallized aerosol population for crystallization experiments at different temperatures with using the ultrasonic nebulizer for aerosol generation. In all experiments, the nebulizer was operated with identical settings and was filled from a reservoir of the same 5 wt % NaCl solution. To facilitate the comparison of the spectral habitus of the black, red, and blue spectra, the intensity of the latter two spectra was scaled to that of the black spectrum at 3400 cm−1. The dashed green line represents a baseline fit to the measured spectrum. See text for details. 8562



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signatures due to NaCl·2H2O. To enable a closer intercomparison of their spectral habitus, the red and blue spectra were scaled to match the intensity of the black spectrum at 3400 cm−1, corresponding to the extinction peak in the O−H stretching mode regime. In each experiment, the nebulizer was filled with a portion of the same 5 wt % NaCl solution and was operated with identical settings. The crystallized NaCl·2H2O particles should therefore have a similar size and should feature a comparable spectral habitus. With increasing temperature, however, the recorded spectra reveal a larger scattering contribution at nonabsorbing wavenumbers, in particular above 3600 cm−1 and, regarding the black spectrum monitored at 230.7 K, also in the regime between 3000 and 2000 cm−1. This is due to an increasing fraction of anhydrous NaCl in the ensemble of crystallized particles with increasing temperature. These anhydrous crystals do not specifically contribute to extinction in the O−H stretching mode regime but reveal a spectrally smooth scattering contribution over the complete wavenumber range. Variations in the partitioning between anhydrous NaCl and NaCl·2H2O particles thereby changes the overall spectral habitus of the crystallized aerosol population. When using the large particle infrared spectra to infer Vs, we must therefore also consider the spectral contribution due to light scattering by anhydrous NaCl crystals, which was not necessary in the case of the small particle absorption spectrum. The spectral habitus of this scattering contribution can be inferred from another crystallization experiment at 235.7 K (Figure 5, solid green line) where only a very small extinction signature due to NaCl·2H2O was observed. After subtracting this minor dihydrate contribution, we thus obtain the infrared scattering signature due to anhydrous NaCl particles (dashed green line), which can be normalized with respect to their number concentration, NNaCl, as simultaneously measured with the condensation particle counter. We assume that the spectral habitus of the scattering contribution due to anhydrous NaCl particles is identical in the crystallization experiments at lower temperatures and can be simply scaled by tuning NNaCl because the size of the crystallized NaCl particles should be similar. NNaCl is thus incorporated as the forth optimization parameter besides NNaCl·2H2O, σg, and Vs in our retrieval scheme in order to consider that the large particle spectra are a superposition of extinction due to NaCl·2H2O and scattering due to anhydrous NaCl. Concluding this section, let us briefly summarize our retrieval approach with the four optimization parameters NNaCl·2H2O, σg, Vs, and NNaCl: • On the basis of the choice for Vs, the optical constants n and k for NaCl·2H2O are calculated from a small particle absorption spectrum in the Rayleigh approximation using the Kramers−Kronig relationship for the complex function f(ν̃) = (N2(ν̃) − 1)/(N2(ν̃) + 2). • The recorded infrared spectra from the crystallization experiments with the ultrasonic nebulizer are described as a superposition of extinction due to NaCl·2H2O and scattering due to anhydrous NaCl particles. Extinction due to NaCl·2H2O is computed in a Mie calculation with the optical constants from above for log-normally distributed particles with a fixed CMD of 1.1 μm, as derived from the size distribution measurements, and using NNaCl·2H2O as well as σg as the variable parameters. Scattering due to anhydrous NaCl particles is computed

by multiplying the normalized infrared spectral habitus from the crystallization experiment at 235.7 K with NNaCl. • All four variables are simultaneously optimized by minimizing the root-mean-square deviations between the computed and measured infrared extinction spectra for the crystallization experiments with the ultrasonic nebulizer. • The procedure is applied to three different measured spectra from crystallization experiments at 230.7, 225.7, and 216.0 K featuring different number fractions of NaCl·2H2O and anhydrous NaCl particles as already apparent from the differences in the spectral habitus shown in Figure 5. As an indication for the robustness of our method, the optimized values for Vs differed by at most 7% for the three different experiments. This underlines that the approach yields a unique retrieval result for Vs and thus the optical constants for NaCl·2H2O. It also shows that the intensity of the vibrational bands of NaCl·2H2O is obviously not affected by the temperature change in our experiments. This is in agreement with recent infrared measurements from Pandelov et al.49 • The approach directly combines the retrieval of n and k with the determination of NNaCl·2H2O and NNaCl, i.e., the temperature-dependent partitioning between the two solid phases of sodium chloride. These results will be discussed in section 5. 3.3. Validation against Independent Measurements. In addition to the observed unique retrieval result for Vs from three different crystallization experiments, the consistency of the retrieval results can be further checked by comparing them to our supplementary measurements. The sum of the optimization parameters NNaCl and NNaCl·2H2O should yield the total particle number concentration as measured with the CPC. As a further benchmark, we have determined the total NaCl mass concentration from the size distribution measurement and the filter sample analysis. This quantity can also be inferred from the retrieval results as follows. First, from the optimization parameters NNaCl·2H2O and σg and with CMD = 1.1 μm, the volume concentration of the NaCl·2H2O particles in the aerosol population can be calculated. Employing the NaCl·2H2O density and the molar mass ratio between NaCl and NaCl·2H2O, the corresponding mass concentration of pure NaCl from the fraction of particles that have crystallized as NaCl·2H2O can be computed. To infer the additional contribution from those particles that have crystallized as anhydrous NaCl, we have fitted the anhydrous NaCl spectrum from Figure 5 with a Mie scattering computation using tabulated refractive indices for NaCl50 and assuming lognormally distributed particles with their number concentration prescribed to the CPC measurement. With the fitted size distribution parameters and the NaCl density, we can then calculate the mass concentration of anhydrous NaCl from the optimization parameter NNaCl. Within their uncertainty range, we have always observed an agreement between the supplementary measurements and the retrieval results. A quantitative example will be given in section 4.1 after having addressed the technical details of our computations in the next section. 3.4. Practical Implementation. For the accurate calculation of the subtractive Kramers−Kronig integral in eq 3, also the frequency dependent behavior of Im{f(ν̃)} outside the 8563



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regime covered by the measurements must be considered.51 Mutter et al.34 have detected a broad librational mode in the NaCl·2H2O infrared spectrum centered at 649 cm−1 (see Table 1 therein; as stated above, the spectrum was erroneously labeled as a new form of ice, ice b). The band has a Δν̃1/2 of 60 cm−1 and a peak intensity equal to that of the 1643 cm−1 band of the doublet signature in the O−H bending mode regime. We have therefore extended our recorded small particle absorption spectrum below 800 cm−1 with a Lorentz band computed from the parameters given by Mutter et al.34 prior to performing the Kramers−Kronig integration. This issue will be further explored in section 4.3. Technically, we have computed the integral with Maclaurin’s formula method as described by Ohta and Ishida.52 The position of the anchor point was set to the high wavenumber end of our measurements at 6000 cm−1. The choice of the anchor point value is another variable in our retrieval approach. Refractive index predictions for NaCl·2H2O at visible wavelengths using Lorentz−Lorenz theory give values for n between 1.43 and 1.49 depending on the assumed density.48 For anhydrous NaCl, the refractive index decreases by a small amount of about 0.02 when going from visible wavelengths to the near-infrared regime at 6000 cm−1. Assuming that the same tendency also holds for NaCl·2H2O, the reasonable range for n at 6000 cm−1 would then be 1.41− 1.47. Together with assuming that k = 0, the corresponding anchor point values of the composite function f, Re{f(ν̃x)}, can then be calculated. In section 4.1, we quantify the variations in the retrieval results for the four optimization parameters with the assumed value for the anchor point and analyze whether its magnitude can be further constrained by our supplementary measurements of the particle number and mass concentration. The Mie calculations of the infrared extinction spectrum of NaCl·2H2O particles with NNaCl·2H2O, σg, and CMD = 1.1 μm were done by extending the code provided by Bohren and Huffman19 to average over a log-normal number distribution of particle sizes. In the overall optimization scheme, the downhill simplex method was used as the optimization technique.53 As demonstrated in the right part of Figure 4, both the wavenumber regimes of the O−H stretching and the O−H bending mode are important to identify a wrong scaling of Vs by the appearance of a spectral mismatch in comparison with the measured extinction spectra. It is therefore necessary to give both spectral regimes equal weight in the optimization procedure to derive a reliable value for Vs. In comparison with the broad frequency range of the extinction feature associated with the O−H stretching mode, the O−H bending mode regime only comprises two narrow extinction bands of low intensity. Its contribution to the overall sum of the rootmean-square deviations for the entire spectral range from 6000 to 800 cm−1, which is minimized in the course of the optimization procedure, will therefore be very small if each wavenumber point of the spectrum is equally weighted. Therefore, a weighting factor, as determined from the ratio of the band intensities and the number of wavenumber points of the O−H stretching and bending mode regimes, had to be applied to the root-mean-square values calculated for the O−H bending mode regime to ensure that its impact in the optimization procedure is comparable to that from the O−H stretching mode regime. With this procedure, consistent retrieval results for Vs were obtained for the three different crystallization experiments at 230.7, 225.7, and 216.0 K.

4. RETRIEVED REFRACTIVE INDEX DATA SET AND SENSITIVITY ANALYSIS 4.1. Sensitivity Study. Before presenting our deduced n and k data sets for NaCl·2H2O in section 4.2, we show the results from sensitivity tests to investigate the uncertainty range of the retrieval results. In addition to the four optimization parameters, our approach includes two variables whose values are initially prescribed: the anchor point value for Re{f(ν̃x)} at 6000 cm−1 and the count median diameter of the NaCl·2H2O particles. The best guess for the latter is 1.1 μm, as derived from the size distribution measurements with the literature value for the NaCl·2H2O density. Concerning the anchor point value, we have estimated that the real part of the refractive index, n, is in the range between 1.41 and 1.47 at 6000 cm−1. Let us first assume that the proper value is in the middle of this interval, i.e., n = 1.44. As already mentioned when summarizing our retrieval approach at the end of section 3.2, we observe a close agreement between the retrieval results for Vs when applying our procedure to the infrared spectra recorded during crystallization experiments at three different temperatures. For the experiments performed at 230.7, 225.7, and 216.0 K with the prescriptions n = 1.44 and CMD = 1.1 μm, we obtain optimized Vs values of 158.3, 147.2, and 152.1 μm3 cm−3, respectively. This yields an average of 152.5 μm3 cm−3 for the NaCl·2H2O volume concentration, the scaling factor of the small particle absorption spectrum. As a check for the consistency of this result, we employ the NaCl·2H2O density and the molar mass ratio between NaCl and NaCl·2H 2 O to compute the corresponding mass concentration of anhydrous NaCl from the dihydrate volume concentration, yielding 153.8 μg cm−3. This value can be compared to the NaCl mass concentration from the ion chromatographic analysis of the filter sample, which yielded 182.0 μg cm−3 and corresponds to the sum of anhydrous and dihydrate NaCl particles that have crystallized in the small particle experiment at 220.9 K. From these two quantities, the mass percentage of NaCl prevalent as NaCl·2H2O can be calculated as 85 ± 9% (assuming a 20% uncertainty for the filter sample analysis). This value is in good agreement with the corresponding mass percentage value of 81% that can be derived from the optimization parameters of the large particle crystallization experiments at 216.0 K (see section 3.3), underlining that an accurate value for the scaling factor Vs has been retrieved. In the following, we analyze the uncertainty range of Vs by modifying the prescriptions for the parameters n and CMD for the large particle crystallization experiment at 230.7 K. Our results are summarized in Table 1, showing the retrieval results for the optimization parameters Vs, NNaCl·2H2O, and NNaCl when either n is varied between 1.41 and 1.47 for a fixed CMD of 1.1 μm or CMD is varied between 1.0 and 1.2 μm for a fixed n of 1.44. Additionally shown is the total particle number concentration, Ntotal, i.e., the sum of NNaCl·2H2O and NNaCl, which can be validated against the independent CPC measurement whose result is shown in the bottom row of the table assuming an uncertainty of 20%. Moreover, we have computed the overall NaCl mass concentration, mNaCl, from the optimization parameters as outlined in section 3.3 and compare it to the average value obtained from the size distribution measurement and the filter sample analysis, which is also denoted in the bottom row with an estimated uncertainty of 8564



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Table 1. Retrieval Results for the Optimization Parameters Vs, NNaCl·2H2O, and NNaCl as Well as Further Resultant Quantities When Varying the Prescriptions for n and CMD, As Applied to the Crystallization Experiment at 230.7 Ka prescriptions n = 1.41, CMD n = 1.44, CMD n = 1.47, CMD n = 1.44, CMD n = 1.44, CMD measurements a

= = = = =

1.1 1.1 1.1 1.0 1.2

μm μm μm μm μm

Vs (μm3 cm−3)

NNaCl·2H2O (cm−3)

NNaCl (cm−3)

Ntotal (cm−3)

mNaCl (μg cm−3)

NNaCl·2H2O/Ntotal

162.2 158.3 155.8 151.6 170.0

231.2 232.2 233.5 270.7 204.4

147.4 138.7 129.0 147.2 123.7

378.6 370.9 362.5 417.9 328.1 335 ± 67

444.8 421.6 398.8 431.3 406.1 390 ± 78

0.61 0.63 0.64 0.65 0.62

The bottom row shows the corresponding results from independent measurements, see text for details.

20%. The final column contains the computed number fraction of NaCl·2H2O particles in the crystallized aerosol population. We first note that all retrieval scenarios summarized in Table 1 yield very similar infrared extinction spectra. It is therefore not possible to constrain the values for n and CMD from an apparent spectral mismatch with the measured extinction spectrum within the parameter range given in the table. The variation of n in the regime from 1.41 and 1.47 for CMD = 1.1 μm affects the retrieval result for the scaling factor Vs by less than 5%. The most notable trend is a slight reduction in NNaCl with increasing n. This can be easily understood because an increase in n leads to a higher intensity of the scattering contribution from the NaCl·2H2O particles, as a consequence of which the scattering contribution from the anhydrous NaCl particles has to be reduced. The variations in Ntotal and mNaCl for these three fit scenarios with CMD = 1.1 μm fall within the uncertainty regime of the independent measurements. We are therefore unable to further constrain the value for n from our analysis. Larger variations of Vs are induced when changing the prescribed value for CMD. For CMD = 1.0 μm, Vs decreases by about 4% compared to the retrieval result for CMD = 1.1 μm. As expected, NNaCl·2H2O is increased due to the reduced particle size. Thereby, the retrieved total particle number concentration is already slightly above the uncertainty range of the independent CPC measurement. The opposite trend is observed when increasing CMD to 1.2 μm. This leads to an increase of Vs by 7.4% compared to the retrieval result for CMD = 1.1 μm. The inferred total particle number concentration, however, is still in good agreement with the CPC measurement. When further increasing CMD to 1.3 μm (data not shown), the retrieval result for Ntotal is close to the lower uncertainty limit of the CPC value, and we have computed a significantly higher root-mean-square deviation between the measured and the best fitted extinction spectrum. The prescription for CMD can thus be confined to the 1.0−1.2 μm range. The partitioning of the overall aerosol number concentration between NaCl·2H2O and anhydrous NaCl particles (final column in Table 1) is affected by less than 10% from the various prescriptions for n and CMD. On the basis of the data shown in Table 1, we conclude that the uncertainty of the scaling factor Vs retrieved for the best guess prescriptions for n and CMD of 1.44 and 1.1 μm, respectively, is not larger than 10%. Concluding this section, Figure 6 shows the measured and the best fitted extinction spectrum with these prescriptions for n and CMD. The fit correctly reproduces the measured spectral habitus in the regimes of the O−H stretching and the O−H bending mode, underlining the accuracy of the optical constants inferred from the small particle absorption spectrum. In contrast, the calculated spectrum does not perfectly mimic the purely

Figure 6. Comparison between the measured (black line) and the best fitted (red line) infrared extinction spectrum for the large particle crystallization experiment at 230.7 K, yielding Vs = 158.3 μm3 cm−3 with n = 1.44 and CMD = 1.1 μm.

scattering part of the measured extinction spectrum above about 3600 cm−1. We identify two main reasons for these spectral discrepancies. First, as addressed in more detail in section 4.3, the simplified use of Mie theory to compute the extinction spectrum of nonspherical NaCl·2H2O crystals will particularly influence spectral regimes governed by light scattering. Second, the signature in these scattering regimes will also sensitively depend on the precise shape of the particle number size distribution (Figure 2), and a log-normal approximation will thus not completely reproduce the measured spectral habitus. 4.2. Retrieved Data Set of the Optical Constants for Sodium Chloride Dihydrate. The spectra of the retrieved real and imaginary parts of the infrared complex refractive index for NaCl·2H2O are shown in the left-hand panels of Figure 7. The data set was inferred from the small particle absorption spectrum with n = 1.44 and Vs = 152.5 μm3 cm−3 as the average value for the scaling factor derived from the three independent large particle crystallization experiments at 230.7, 225.7, and 216.0 K. In the O−H stretching regime, the k spectrum reveals three individual peaks at 3552, 3466, and 3404 cm−1. The less intense doublet signature at 3264 and 3242 cm−1 can be interpreted as the overtone of the respective 1643 and 1616 cm−1 peaks in the O−H bending regime.34 Broad absorption bands of very low intensity are additionally observed at about 2100 and 1180 cm−1. All peak positions are in good accordance with those tabulated by Mutter et al.34 One might expect that the hydration water molecules also give rise to a low intensity combination mode at about 5000 cm−1 as observed for ice particles.54 Its intensity, however, was too small to be detected in our experiments, and we have therefore set all k values equal to zero at wavenumbers above 3700 cm−1 beyond the O−H 8565



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Figure 7. Left panels: retrieval results of the wavelength-dependent infrared optical constants n and k for NaCl·2H2O. The data set was deduced from the small particle absorption spectrum with Vs = 152.5 μm3 cm−3 and using n = 1.44 for calculating the anchor point value in the Kramers− Kronig transformation. Right panels: deviations Δn and Δk with respect to this data set for different choices of n and Vs as denoted in the legend.

stretching regime. Also Mutter et al.34 gave no record of a combination mode in the NaCl·2H2O spectrum. In the right panels of Figure 7, we show the deviations Δn and Δk with respect to the data set inferred from n = 1.44 and Vs = 152.5 μm3 cm−3 when different values for these two parameters are chosen. The black and red traces depict the retrieval results when Vs is kept equal to 152.5 μm3 cm−3 but n is changed to 1.41 and 1.47, respectively. Because we do not employ the direct Kramers−Kronig transformation between n and k but make use of the relationship between the real and imaginary parts of the composite function f(ν̃) (eq 1), different assumptions for n do not simply lead to a constant offset in the retrieved n spectra but also provoke slight spectral fluctuations in the regions of the anomalous dispersion features. Slight changes are also observed for the k spectra when modifying n but the relative differences compared to the spectrum derived for n = 1.44 are less than ± 2% in the regimes of the strong absorption bands. The green and blue traces correspond to the retrieval results for n equal to 1.44 when changing the scaling factor Vs by minus and plus 10%, respectively, as estimated to be its maximum uncertainty. This leads to mirror imaged changes in the corresponding k spectra, with a lower volume concentration leading to higher k values for the absorption bands and a higher volume concentration leading to lower k values. As already noted by Segal-Rosenheimer et al.,27 the changes in k for a ±10% change in Vs are not strictly symmetric. A 10% increase of Vs decreases the k value by about 0.10 at the 3404 cm−1 peak in the O−H stretching regime. Decreasing Vs by 10%, however, increases k by even 0.12 at 3404 cm−1. Changing the intensity of the absorption bands in the k spectra consequently also influences the amplitude of the dispersion features in the corresponding n spectra. The relative changes in n of the green and blue traces compared to the n spectrum derived for Vs = 152.5 μm3 cm−3, however, do not exceed ± 5%.

In the Supporting Information of this article, we have provided our best guess optical constants data set for NaCl·2H2O derived with n = 1.44 and Vs = 152.5 μm3 cm−3 in the spectral regime from 6000 to 800 cm−1 with an interval of about 2 cm−1. The data set is strictly valid for the temperature of 220.9 K at which the small particle absorption spectrum was recorded. The close agreement between the retrieved Vs values at the three different temperatures of the large particle crystallization experiments and between the measured and the best fitted infrared extinction spectra (Figure 6), however, suggest that the temperature dependence of the optical constants is weak and that the inferred data set can be applied to the entire range of temperatures from 235 to 216 K covered by our experiments. Our best estimate for the maximum uncertainties of the two scaling parameters n and Vs are ± 0.03 and ± 15.25 μm3 cm−3, respectively. The corresponding impact on the uncertainty of the optical constants is obtained by performing the Kramers−Kronig integration with the modified values for n and Vs (Figure 7). We recommend the following simple procedure to generate other consistent n and k data sets if readers want to explore the uncertainty range of their retrieval results by employing different values for n and Vs. By inserting the presented n and k data set into eq 2, our recorded small particle absorption spectrum can be exactly recomputed. This spectrum can then be differently scaled before applying the Kramers−Kronig relationship to attain a revised n and k data set or the anchor point value in the integration can be modified. Moreover, readers may test different extensions of the Im{f} spectrum if becoming available in the future. Otherwise, we recommend extending the spectrum below 800 cm−1 with a Lorentz band centered at 649 cm−1 as outlined in section 3.4. 4.3. Further Error Analysis. Having presented the final data set for n and k, we can now quantitatively analyze the effect of two further issues associated with our retrieval approach, namely, the assumption of a spherical particle shape and the 8566



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Figure 8. Mie and T-matrix computed extinction cross-sections, Cext, of NaCl·2H2O particles for two different number size distributions employing the optical constants shown in the left part of Figure 7. The red and blue colored traces in the bottom part of the panels show the spectral residuals of the two T-matrix computations in relation to the Mie calculation.

particle spectrum that is entirely dominated by light absorption, there is only one narrow spectral regime where the T-matrix computations markedly deviate from the Mie calculation. As highlighted by the vertical dashed line in the right panel of Figure 8, this is at the low wavenumber tail of the most intense absorption peak at 3404 cm−1 whose spectral habitus slightly changes when considering aspherical particle habits instead of spheres. As demonstrated by Bohren and Huffman,19 the assumption that extinction spectra of small irregularly shaped particles can be adequately approximated by spheres breaks down in the surface mode region where the term N2(ν̃) + 2 in eq 2 vanishes. This resonance condition is strictly fulfilled for n = 0 and k = √2. The spectral regime that comes closest to this condition in the case of NaCl·2H2O is in fact the strongest absorption peak at 3404 cm−1. Small shape-dependent distortions of this peak are therefore an inherent uncertainty in our retrieved data set, which cannot be exactly quantified without knowledge about the actual shape of the small particles in our crystallization experiment, but because only a narrow spectral range is affected, this will hardly influence the results of a retrieval that is applied to a broad spectral regime. We now turn to the second subject of this section, namely, the sensitivity of the result of the Kramers−Kronig integration with respect to the assumed spectral behavior of Im{f(ν̃)} below 800 cm−1. The black trace in the left panel of Figure 9 shows the small particle absorption spectrum of NaCl·2H2O recorded during the crystallization experiment at 220.9 K with our best estimate for the spectral extension below 800 cm−1, thus including the 649 cm−1 librational mode detected by Mutter et al.34 with a peak height that matches the intensity of the 1643 cm−1 band. The Kramers−Kronig transformation then yields our best guess for the optical constants n and k as already shown in Figure 7 and again plotted as a reference in the two right panels of Figure 9 (black lines). The further colored lines show the results of the Kramers−Kronig integration for different assumptions on the spectral behavior below 800 cm−1 (left panel) as well as the spectral residuals of n and k with respect to the black spectra. The green and red traces represent scenarios where the intensity of the 649 cm−1 librational mode was scaled by minus and plus 50% compared to the intensity of the 1643 cm−1 peak, respectively. Completely omitting the librational mode and setting all optical depth values equal to zero below 800 cm−1 yields the n and k spectra shown in magenta. At wavenumbers below the librational mode regime, there will be another absorption feature of unknown intensity in the lattice mode

influence of the spectral extensions of Im{f} beyond the measurement range on the results for Re{f} after the Kramers− Kronig integration. We start our discussion with the sphere approximation. The assumption of spherical particles occurs twice in our retrieval approach, namely, at the analysis of the small particle absorption spectrum with eq 2, which is only valid for spheres, and at the Mie theory based calculation of the extinction contribution of the NaCl·2H2O particles when fitting the large particle infrared spectra. For both cases, we have to assess the influence of particle asphericity. Wise et al.6 have recorded optical microscope images of the crystallized aqueous NaCl solution droplets in their experiment series. Whereas the anhydrous NaCl crystals appeared as cubes, the crystal structure of NaCl·2H2O is monoclinic,55 and a particle that was identified to be hydrated NaCl by Raman spectroscopy was described as round and bumpy and its envelope did not reveal much eccentricity. We therefore assume that the particles do not preferentially crystallize in a plate-like or needle-like habit with extreme asphericity but that moderate aspect ratios, ϕ, of 0.5 (prolate particle shape) or 2.0 (oblate particle shape) are reasonable estimates to exemplarily analyze the shape dependency of the infrared extinction spectra. In Figure 8, we compare the Mie computed extinction spectra of NaCl·2H2O crystals to those calculated with the Tmatrix code17 for randomly oriented cylindrical particles employing aspect ratios of 0.5 and 2.0. Two different number size distributions are employed. The left panel shows the computed extinction cross-sections, Cext, for log-normally distributed particles with CMD = 1.1 μm and σg = 1.3, as typical for the large particle crystallization experiments. For the representative calculation of a small particle infrared spectrum as shown in the right panel of Figure 8, we have assumed the parameters CMD = 0.08 μm and σg = 1.8, as inferred from a log-normal fit to trace a in Figure 2 and scaling the fitted CMD value by eq 4. Concerning the large particle extinction spectrum, the Tmatrix computations only reveal very small changes compared to the Mie result. Most notably, particle asphericity leads to a small decrease of the intensity in the spectral regimes governed by light scattering. The spectral signatures in the O−H stretching and O−H bending extinction bands remain almost unchanged when introducing a moderate particle asphericity, and we therefore conclude that the retrieval result for the scaling factor Vs is not notably influenced by employing Mie theory in the optimization scheme. Addressing the small 8567



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Figure 9. Left panel: small particle absorption spectrum of NaCl·2H2O from the crystallization experiment at 220.9 K with various spectral extensions below 800 cm−1 as detailed in the text. The two right panels show the corresponding spectra for the optical constants n and k after performing the Kramers−Kronig integration. The spectral residuals shown in the bottom parts of these panels are calculated in relation to the black traces which represent our best guesses for the optical constants.

a retrieval that is applied to a broad spectral regime also covering the intense absorption bands of NaCl·2H2O.

region, which we have not yet taken into account. For anhydrous NaCl, the absorption in the lattice mode regime peaks at 165 cm−1 with a maximum k value of 7.41.50 Two peaks at 211 and 148 cm−1 are observed for ice with maximum k values less than one.56 We thus consider the lattice mode vibration in NaCl as an upper estimate for the intensity of its unknown counterpart in NaCl·2H2O and have calculated with eq 2 its contribution to the small particle absorption spectrum using the tabulated optical constants for NaCl and setting Vs equal to 152.5 μm3 cm−3. The blue spectrum shown in the left panel of Figure 9 is identical to the black spectrum at wavenumbers above 400 cm−1 and additionally includes this estimated lattice mode vibration below 400 cm−1. The effect of the various extensions on the retrieved k spectra is very small. When comparing, e.g., the black and blue traces, the additional inclusion of the lattice mode vibration at 165 cm−1 changes the peak intensity of the O−H bending mode by less than 1%. With respect to the n spectra, these two traces diverge by less than 1% for wavenumbers above 1400 cm−1 and only when approaching the low wavenumber limit of our measurement at 800 cm−1 their relative difference increases to 4%. The analysis thus demonstrates that the spectral regime covering the O−H bending mode, including the anomalous dispersion feature in the n spectrum from 1800 to 1400 cm−1 and the doublet absorption peak in the k spectrum at 1643 and 1616 cm−1, remains almost unaffected by the unknown spectral behavior below 800 cm−1. This is important for the accuracy of our retrieval approach because the relative scaling of the O−H bending and stretching mode extinction regimes was used to deduce the scaling factor Vs from the large particle infrared spectra (see right panel of Figure 4). The small variations in the n spectrum when approaching 800 cm−1 due to the unknown extension of Im{f(ν̃)} are another inherent uncertainty of our approach. As with the slight shape induced distortions discussed before, they will not notably influence the results of

5. TEMPERATURE-DEPENDENT PARTITIONING BETWEEN NACL AND NACL·2H2O In this section, we compare our results on the temperaturedependent crystallization of aqueous NaCl solution droplets with respect to the partitioning between anhydrous and dihydrate particles to those from Wise et al.6 Our inferred values for the percentage of NaCl·2H 2 O particles, 100·NNaCl·2H2O/Ntotal, are shown as black squares in Figure 10. The black line represents a best fit function to our data as indicated in the figure graph. The percentages measured by Wise et al.6 are shown as the blue line. As outlined in section 3, the three data points at 230.7, 225.7, and 216.0 K were a direct outcome of our retrieval approach to deduce the optical

Figure 10. Retrieved percentages of NaCl·2H2O particles from the present study (black) in comparison with the relationship found by Wise et al.6 (blue). See text for details. 8568



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constants of NaCl·2H2O. The retrieved n and k data set was then further used to estimate the small dihydrate particle fraction in the crystallization experiment at 235.7 K (solid green line in Figure 5). The various fit results given in Table 1 underline that the retrieved dihydrate percentages are rather insensitive to the prescriptions for n and CMD, and we have therefore assumed 10% as an upper estimate for the uncertainty of 100·NNaCl·2H2O/Ntotal, as indicated by the error bars. The data point at 244 K originates from our previous crystallization and ice nucleation experiments with binary and ternary solution droplets in the NaCl/oxalic acid/H2O system.35 Neither in the FTIR extinction spectra monitored during crystallization nor when probing the deliquescence behavior of the effloresced aerosol population in a subsequent expansion cooling experiment have we detected any evidence for dihydrate formation after crystallization of binary aqueous NaCl solution droplets at 244 K and 70% RHw. The left panel of Figure 5 in Wagner et al.35 shows that the elevated depolarization signal due to the crystallized particle ensemble drops to the background value characteristic for spherical solution droplets at a relative humidity with respect to supercooled water, RHw, of 72 ± 5%. This corresponds to the deliquescence relative humidity of anhydrous NaCl. A further deliquescence step at about 82% RHw due to NaCl·2H2O particles was not detected. The same behavior was observed after the deliquesced aerosol population had again crystallized while cooling the AIDA chamber from 244 to 235 K (see left panel of Figure 7 in Wagner et al.35). The experimental procedure was thus different from the present study where we have performed a crystallization experiment at a constant temperature of 235.7 K and could detect the formation of a minor percentage of NaCl·2H2O particles. Notwithstanding the apparently different results for the NaCl·2H2O percentages, it should first be emphasized that the general trend for the temperature-dependent partitioning between anhydrous and dihydrate NaCl particles is similar in both studies. For a wide temperature range below the peritectic at 273.3 K, exclusively anhydrous NaCl crystals are formed upon efflorescence. The transition to an aerosol population dominated by NaCl·2H2O particles then occurs in a quite narrow temperature range. The position of this transition regime, however, is shifted to lower temperatures in our study compared to the results from Wise et al.6 At the temperatures for 50% dihydrate particle formation, this shift is about 13 K. This indicates that the transition from anhydrous NaCl to NaCl·2H2O is also affected by the experimental conditions and it is not straightforward to predict which study is a better proxy for the real atmosphere. There are three main differences between the experimental conditions of the two studies. At first, Wise et al.6 have considered a broad particle size range from 1−10 μm in diameter, whereas the large particle crystallization experiments from our study featured a narrower size range centered at about 1 μm. Second, we have probed airborne particles whereas the Wise et al.6 study has involved particles deposited onto a quartz surface. The surface obviously did not affect the efflorescence relative humidity of the deposited aqueous NaCl solution droplets because its value was in good agreement with previous literature findings. Nonetheless, one cannot exclude that the surface modifies the partitioning between the two solid phases of NaCl. As outlined in the introduction, there are indications that available surfaces favor the formation of NaCl·2H2O instead of anhydrous NaCl, which would be consistent with the

fact that the transition between both phases is shifted to higher temperatures in the Wise et al.6 study. Third, we must consider that the two studies feature different humidity conditions. Wise et al.6 have performed a classical efflorescence mode experiment by lowering the ambient relative humidity to below about 40% RHw upon which crystallization of the solution droplets was detected. In the AIDA experiments, crystallization of the particle ensemble was observed over long time periods at RHw between 61 and 52%, i.e., above the generally accepted efflorescence relative humidity of NaCl. So the crystallization mechanism might be different in the AIDA experiments and could therefore explain the modified partitioning between the two solid phases of NaCl. As discussed in our previous work,35 it is tempting to explain the gradual crystallization in AIDA by heterogeneous effects, e.g., heterogeneous crystallization on available surfaces inside the vessel like the mixing fan or sampling and injection tubes protruding into the chamber interior. Alternatively, a small subset of the particles might homogeneously nucleate on the few hot spots that are present in the chamber like heated sampling tubes where the NaCl solution droplets temporarily experience a lower relative humidity compared to the average value. These effloresced particles might then further trigger the crystallization of the aerosol population by collisions with still unfrozen supersaturated NaCl solution droplets. Under the assumption that heterogeneous effects favor the precipitation of NaCl·2H2O, this picture of heterogeneous crystallization in AIDA is however not in agreement with the observed low temperature shift of the NaCl−NaCl·2H2O transition regime compared to Wise et al.6 As a further check, we have performed a different type of crystallization experiment where the AIDA chamber was kept at 244 K and 34% RHw for aerosol injection. For this experiment, the chamber walls were not coated by an ice layer but a definite amount of water vapor was added to the chamber to establish the desired RHw value. Under these conditions, the injected supercooled NaCl solution droplets instantly crystallized in AIDA because RHw was below the efflorescence relative humidity. This experimental procedure thus better matches the classical efflorescence mode experiment performed by Wise et al.,6 but similar to the long-term crystallization experiment at 244 K and 70% RHw,35 the spectral signatures due to NaCl·2H2O particles were not detected in the simultaneous FTIR extinction measurements. A fully consistent interpretation of the different experimental findings shown in Figure 10 can therefore not be given at this instant. As already mentioned in the introduction, we will report an additional analysis of the ice nucleation ability of the crystallized NaCl and NaCl·2H2O particles in a succeeding article and compare our findings to those from Wise et al.6 The ice nucleation behavior was investigated by expansion cooling experiments where RHw was increased by reducing the chamber pressure to establish ice supersaturated conditions inside the vessel. Considering the subject of our present work, it is important to note that the partitioning between anhydrous NaCl and NaCl·2H2O crucially influences the response of the aerosol population upon increasing relative humidity. We will demonstrate that there are two competing processes, namely, deliquescence and heterogeneous ice nucleation. For example, in the expansion experiment started at 230.7 K, the fraction of anhydrous NaCl particles deliquesces, whereas the NaCl·2H2O crystals act as heterogeneous ice nuclei before deliquescence occurs. Further studies on the partitioning between the two 8569



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the crystallization mechanism and thereby change the partitioning between the two crystalline species. In a succeeding article on the ice nucleation ability of the NaCl and NaCl·2H2O particles, we will demonstrate that knowledge of the partitioning is crucial to predict the behavior of the crystallized particle ensemble upon increasing relative humidity.

solid phases of NaCl and its influence on the experimental conditions are therefore highly recommended.

6. SUMMARY We have investigated the low-temperature crystallization behavior of about 1 μm sized aqueous NaCl solution droplets with respect to the partitioning between the two solid phases of sodium chloride, anhydrous NaCl, and NaCl·2H2O. Crystallization was monitored by in situ infrared extinction and depolarization measurements after the solution droplets had been injected into a large aerosol chamber at temperatures between 235 and 216 K. As a prerequisite to quantify the relative number fractions of both species from the infrared spectra recordings, the so far unknown infrared optical constants of NaCl·2H2O had to be determined. For this purpose, a well established approach was employed that relies on the Kramers−Kronig relationship for the complex function f(ν̃) = (N2(ν̃) − 1)/(N2(ν̃) + 2) whose imaginary part is directly proportional to the optical depth of a small particle absorption spectrum within the Rayleigh approximation. We have therefore additionally performed a small particle crystallization experiment where the crystallized particles featured a median diameter of less than 0.1 μm. In the case of NaCl·2H2O, this basic methodology is complicated by the fact that an unknown fraction of anhydrous NaCl particles is formed upon crystallization of the injected solution droplets which do not reveal any absorption signatures at mid-infrared wavelengths. Therefore, the scaling factor between the recorded optical depth and Im{f}, i.e., the volume concentration of NaCl·2H2O, cannot be directly determined. This apparent difficulty of deriving the optical constants of NaCl·2H2O without prior knowledge of the partitioning between NaCl and NaCl·2H2O was solved by optimizing the scaling factor using a fitting algorithm applied to the infrared extinction spectra of the crystallization experiments with the 1 μm sized particles. These spectra contained a significant scattering contribution and were thus sensitive to the proper scaling of the NaCl·2H2O volume concentration so that its value could be unambiguously retrieved. The large particle spectra were modeled as a superposition of extinction due to NaCl·2H2O and scattering due to NaCl. The outcomes of the optimization procedure were therefore not only the scaling factor for Im{f} but also the number concentrations of anhydrous and dihydrate NaCl particles, i.e., the partitioning between the two solid phases of NaCl was derived concomitantly with the optical constants of NaCl·2H2O. The k spectrum of the retrieved optical constants of NaCl·2H2O reveals several sharp absorption bands due to the hydration water molecules in the O−H stretching and bending mode regimes and thus clearly contrasts with the broad signatures observed for liquid water. Concerning the partitioning between NaCl and NaCl·2H2O, we have shown that there is a transition regime in a quite narrow temperature range from 235 to 216 K where the composition of the crystallized aerosol population changes from almost only NaCl to almost only NaCl·2H2O particles. This general trend is in agreement with the results from a recent study by Wise et al.6 However, the transition regime between NaCl and NaCl·2H2O is shifted by about 13 K to lower temperatures in our experiments compared to those from Wise et al.6 This is presumably due to differences in the experimental conditions including, e.g., particle size, medium (airborne versus deposited particles), and ambient relative humidity, which could influence

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ASSOCIATED CONTENT

* Supporting Information S

Complex refractive indices of NaCl·2H2O from 6000−800 cm−1. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful for the continuous support by all members of the AIDA staff. In particular, we thank Elisabeth Kranz for doing the ion chromatographic analyses, Olga Dombrowski and Rainer Buschbacher for assistance with the aerosol generation and characterization, as well as Tomasz Chudy and Georg Scheurig for the technical maintenance of the chamber. The work has been funded by the Helmholtz-Gemeinschaft Deutscher Forschungszentren as part of the program “Atmosphere and Climate”.

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REFERENCES

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