Water Uptake by NaCl Particles Prior to Deliquescence and the Phase Rule

Abstract

Using an environmental transmission electron microscope (ETEM), we show that a significant amount of water, far exceeding the multilayers caused by surface adsorption, is reversibly associated prior to deliquescence with substrate-supported NaCl particles (dry diameters of ∼ 40 nm to 1.5 μ m; ∼ 18°C). We hypothesize that the water is present as an aqueous solution containing dissolved Na and Cl ions. Water uptake occurs at relative humidities (RH) as low as 70%, and the resulting liquid layer coating the particles is stable over extended times if the RH is held constant. We exposed CaSO ₄ and CaSO ₄ · 2H ₂ O particles to elevated RH values in the ETEM to show that chemically nonspecific condensation of gas-phase water on the TEM substrate does not explain our observations. Furthermore, damage to the NaCl surface induced by the electron beam and small fluctuations in RH do not seem to contribute to or otherwise affect water uptake. We have similar observations of water association for other alkali halide particles, including NaBr and CsCl, prior to deliquescence. To explain the observations, we derive the phase rule for this geometry and show that it allows for the coexistence of liquid, solid, and vapor for the binary NaCl/H ₂ O system across a range of RH values. The derivation includes the effects of heterogeneous pressure because of the Laplace-Young relations for the subsystems. Furthermore, in view of the lever rule and the absence of similar observations for free-floating pure NaCl aerosol particles, we hypothesize that the surface energy necessary to support these effects is provided by sample-substrate interactions. Thus, the results of this study may be relevant to atmospheric systems in which soluble compounds are associated with insoluble materials.

1. INTRODUCTION

The interaction of water vapor with atmospherically relevant aerosol particles has been reported upon extensively in the literature. The impetus for such research lies in the well-recognized fact that the phase (i.e., solid or liquid [Martin 2000]) in which a particle exists in the atmosphere dramatically affects its ability to scatter and absorb light (e.g., Charlson et al. 1992), to catalyze heterogeneous reactions in the atmosphere (e.g., Hu and Abbatt 1997), and to form ice nuclei (e.g., DeMott and Rogers 1990). Because the phase plays an important role in these processes, many investigators focused on the determination of the relative humidity (RH) at which a soluble inorganic aerosol particle spontaneously picks up water to become a solution droplet (deliquescence RH) and the RH at which that solution droplet re-crystallizes (efflorescence RH). Using this information, the RH range in which the particles exist as solutions or solids has been determined, and a prediction of their impact on the atmosphere has been assessed (Martin et al. 2004).

Sea-salt aerosol particles (SSA) are one of the most important types of particles in the troposphere because they comprise a large fraction of the particulate matter introduced into the atmosphere globally (Lewis and Schwartz 2004). Based on the composition of natural seawater, and ignoring reactions that occur in the atmosphere, the ionic composition of SSA is dominated by Cl⁻ (55.04% w/w) and Na⁺ (30.61% w/w) (Seinfeld and Pandis 1998). Therefore, much effort has been directed towards understanding the hygroscopic properties of NaCl particles.

It is widely accepted that phase transitions of pure inorganic salts such as NaCl occur abruptly at either the deliquescence RH (DRH) or efflorescence RH (ERH) (e.g., Biskos et al. 2006a). Therefore, conventional wisdom has it that at a particular RH value an individual particle exists as either a solid or as a solution droplet (Martin 2000). Using a continuous-flow apparatus, Tang et al. (1977) showed that at 25°C NaCl aerosol particles deliquesce at 75.7% RH. This finding has been corroborated (within error) by other studies employing a variety of experimental techniques that include gas chromatography, infrared spectroscopy, particle mobility analysis, electrodynamic balance, environmental scanning electron microscopy, and environmental transmission electron microscopy (e.g., Lee and Chang 2002; Cziczo et al. 1997; Ebert et al. 2002; Krueger et al. 2003; Wise et al. 2005; Biskos et al. 2006b).

Other studies examined water adsorption onto the NaCl surface prior to deliquescence. Ewing (2005) provides an excellent review on the processes taking place on the surface of NaCl as RH is increased to the DRH. He shows that at water vapor pressures of ∼ 20 mbar at 24°C (67% RH), water adsorbs to the surfaces of NaCl crystallites with a surface coverage of ∼ 4.5 monolayers (see Figure 9 of Ewing 2005). Using scanning polarization force microscopy, Luna et al. (1998) determined that on the order of monolayers (i.e., 0.3 to 2 nm) of water adsorbed on the surfaces of NaCl, KCl, KBr, and KF at ∼ 20–70% RH. Romakkaniemi et al. (2001) studied the adsorption of water on 8 to 15 nm NaCl and (NH₄)₂SO₄ particles at room temperature using an ultrafine tandem differential mobility analyzer. They showed that more than one monolayer of water molecules adsorbed on both types of particles below the DRH.

FIG. 9 Images of NaCl particles selected to determine the possible presence of contamination. The corresponding EDS spectra were obtained at the locations denoted with an “X.” The particles were prepared using a TSI atomizer and were deposited on a lacey-carbon film (no Formvar).

The presence of water on particles has the potential to influence the uptake and reaction of gas-phase constituents in the atmosphere (e.g., De Haan and Finlayson-Pitts 1997; Ghosal and Hemminger 2004). These studies demonstrate that water uptake from surface adsorption happens on the scale of at most several nanometers. The adsorption of this water layer is a surface process and is therefore largely independent of system size; the nanoscale values are similar whether studying single macroscopic crystals or nanoparticles.

We used an environmental transmission electron microscope (ETEM) to study the hygroscopic behavior of substrate-supported NaCl particles between 0 and 95% RH (Wise et al. 2005; Wise et al. 2007a; Wise et al. 2007b) and found that NaCl particles deliquesce at ∼ 75 % RH. The DRH determined using the ETEM is in agreement with the accepted DRH for NaCl particles having diameters greater than 40 nm (Cziczo et al. 1997; Ebert et al. 2002; Wise et al. 2005; Biskos et al. 2006b; Tang and Munkelwitz 1993; Richardson and Snyder 1994). However, Wise et al. (2007b) found that some NaCl particles underwent morphological transformations from square to rounded shapes at RH values close to but lower than the DRH. Wise et al. (2007b) interpreted particle rounding as an indication that nanoscale water associated with the particle liberated ions, providing some fluidity to the solid and allowing its shape to change (see also Kendall and Martin 2005, 2007).

In the work described here, we take advantage of the ability of the ETEM to image water associated with the surfaces of substrate-supported NaCl particles. We show that under the conditions of our study a significant amount of water, up to a thickness of 100 nm and definitely a different phenomenon from the nanoscale surface-adsorbed water described above, can be reversibly taken up onto the surfaces of submicron-to micron-sized NaCl particles prior to deliquescence. A liquid phase of comparable volume to the original particle is formed. This extensive water uptake differentiates the phenomenon studied here from prior work that focused on nanoscale adsorption (Ewing 2005; Luna et al. 1998; Romakkaniemi et al. 2001).

Studies of ammonium sulfate using an electrodynamic balance have shown about 5% by mass water uptake at 0.2 to 0.8% RH below its deliquescence RH (Richardson and Spann 1984; Colberg et al. 2004). Colberg et al. (2004) explain that 2-to 20-μ m particles of ammonium sulfate crystallize with concave pores as well as crevices between crystallites that can trap water below the DRH. For comparison, sodium chloride particles studied by the electrodynamic balance do not have similar water uptake below the deliquescence RH (Braun and Krieger 2001; Olsen et al. 2006), presumably because sodium chloride (which is the topic of our study) forms as euhedral, smooth crystals so that the morphology effects leading to water uptake are absent. Our results are clearly distinct from both sets of studies. We observe water uptake for sodium chloride as an outer liquid layer of approximately the same volume as the core for relative humidities up to 3% below DRH.

2. EXPERIMENTAL

2.1. Particle Generation and Collection Methods

The methods used to prepare the different particle types in this study are summarized in Table 1. NaCl particles with dry diameters ranging from ∼ 40 nm to 1.5 μ m were generated in a variety of ways. The first involved atomization of a 1 M NaCl solution followed by drying in a diffusion dryer and deposition by diffusion onto TEM grids. The second method involved generating particles by bubbling air through a 0.6 M solution of NaCl. This procedure was used to mimic the natural production of particles over the ocean. Particles generated with the bubbler were pulled through the diffusion dryer and collected onto TEM grids using an MPS-3 microanalysis particle sampler (California Instruments, Inc.). A full description of this generation and collection method is given in Tyree et al. (2007) and Wise et al. (2007b). The third method of generating NaCl particles utilized the vaporization and condensation of granular NaCl. The vaporization-condensation aerosol generation (VCAG) method is described in detail in Biskos et al. (2006b). The NaCl particles thus generated were collected onto TEM grids using a TSI Nanometer Aerosol Sampler (model #3089) operated at a voltage of ∼−10 kV and a flow rate of 1 L/min.

TABLE 1 Particle generation and collection methods

Particle type	Manufacturer, purity %	Medi	Generation methods	Impaction methods
NaCl	J.T. Baker (100)	Aqueous solution, solid	Atomization, bubbler,	Diffusion, MPS-3 ^a , electrostatic
		powder	VCAG ^b	precipitation ^c
CaSO4	J.T. Baker (98.0)	Solid powder	n/d ^d	Physical contact
CaSO4·2H2O	J.T. Baker (98.0)	Solid powder	n/d ^d	Physical contact
NaBr	Sigma Aldrich (99.99)	Aqueous solution	Atomization	Diffusion
CsCl	Sigma Aldrich (99.9)	Aqueous solution	Atomization	Diffusion

Because CaSO₄ and CaSO₄· 2H₂O are relatively insoluble, they could not be atomized to generate particles. Therefore, in order to deposit them onto TEM grids, the grids were physically contacted with a small amount of the solid powder, during which some particles adhered to the grid. NaBr and CsCl particles were generated from 1 M solutions using a TSI model # 3076 atomizer. Following atomization, the particles were passed through a diffusion dryer (TSI model #3062) that reduced the ambient RH to between ∼ 45 and 65%. The particles were then deposited by diffusion onto TEM grids.

Copper-mesh TEM grids with various types of support films were used. The different films included ultra-thin carbon on a holey-carbon support (Ted Pella, Inc. # 01824), carbon Type-A (Ted Pella, Inc. #01820), lacey-carbon Type-A (Ted Pella, Inc. #01890), and silicon monoxide Type-A (Ted Pella, Inc. #01829). The support films (except for the ultra-thin carbon on a holey-carbon support) had a removable Formvar backing for additional support. The Formvar backing was left on the carbon film for some experiments, and for others it was removed. We used the lacey-carbon Type-A substrates with the Formvar backing removed for experiments in which holes free of substrate were desired. The other substrates were used when a continuous support film was desired.

2.2. Hygroscopic Behavior of the Particles

Water-uptake experiments were carried out using a 200-kV FEI Tecnai F20 TEM fitted with a differentially pumped environmental cell. Wise et al. (2005) described the ETEM and the procedure developed to study the hygroscopic properties of deposited particles. The procedure was slightly modified in Wise et al. (2007a) and is identical to that used in the current study. Prior to each water-uptake experiment, the accuracy of RH measurements was verified by measuring the DRH of laboratory-generated NaCl particles. The DRH for these NaCl particles was 75 ± 2%, in agreement with the known DRH of NaCl. Although the day-to-day accuracy of the RH measurements using the ETEM is ≤ 2%, their precision is ≤ 1%. During water-uptake experiments, sequences of images at various increasing and decreasing RH values were recorded for each particle. The hygroscopic behavior of the NaCl particles shown in this study is representative of many hundreds of NaCl particles studied using the ETEM. All water-uptake experiments were performed at 18.2 ± 0.1°C.

2.3. Conventional TEM Analyses

Bright-field images and energy-dispersive X-ray spectrometry (EDS) measurements were recorded for specific particles using a Philips CM200 TEM operated at 200 kV. The microscope was used to provide morphological and chemical information on particles after ETEM analyses. The EDS measurements were obtained using beam size 5 (6 nm) at intervals of 10 s. No distinguishable peaks except those resulting from interaction with the Cu grid were present at energy values greater than 5 eV. The spectra were collected using ES Vision software.

3. RESULTS AND DISCUSSION

3.1. Water Associated with NaCl Particles Prior to Deliquescence

Figure 1 is a typical ETEM image showing water uptake on the surfaces of NaCl particles at RH values lower than the DRH. The particle highlighted with the thin arrow appears to have a shell or halo of water surrounding a solid NaCl core at 74 ± 1% RH. This phenomenon is further demonstrated in Figure 2 for a 0.77-μ m NaCl particle exposed to increasing RH. At 70% RH the sharp edges of the particle became rounded, which we interpret as the effect of it starting to take up an observable amount of water. Furthermore, it appeared that water spread out slightly along the carbon substrate (fuzzy area highlighted by the thin arrow). As the RH was increased to 72%, the particle became more spherical, and additional water spread out along the substrate. Only after the RH was increased to 74 ± 1% did the particle deliquesce. When the RH was lowered to 67%, the particle remained a solution droplet, thereby confirming the particle had indeed deliquesced.

FIG. 1 Water uptake observed on the surfaces of NaCl particles at 74% RH. The thin arrow highlights particle rounding and water surrounding the solid core prior to deliquescence. The solid up arrow indicates increasing RH. The particles were prepared on an ultra-thin carbon film with a holey-carbon support film and generated using the bubbler method.

FIG. 2 Images of NaCl particles as the RH was increased (up arrows) past the deliquescence point and subsequently decreased (down arrows). The particles were prepared on a lacey-carbon support film (no Formvar) using a TSI atomizer.

The ETEM is a powerful analytical instrument for the study of hygroscopic behavior of individual particles because it can resolve morphological features to the nanometer scale. Thus, we have the ability to visibly detect small changes on the surfaces of individual particles prior to deliquescence. However, the use of the ETEM to study the hygroscopic characteristics of aerosol particles is in its infancy. Therefore, it is reasonable to test whether artifacts produced by the ETEM were the cause of the water-uptake phenomenon. The experiments performed to evaluate and test such possible explanations are presented in the following sections.

3.2. Hydrophobic Nature of the TEM Substrate

To evaluate the nature of the TEM substrate, we exposed two relatively insoluble materials to elevated RH on an ultra-thin carbon film with a holey-carbon support film. When CaSO₄ particles were exposed to an RH of 89% (Figure 3, column a), particle morphology did not change. Similarly, the morphology of a CaSO₄· 2H₂O particle (Figure 3, column b) remained the same at 89% RH. Both experiments confirmed the hydrophobic nature of the TEM substrate (at RH values well above the DRH of NaCl) and showed that water did not condense at the substrate/particle boundary based on purely physical effects (i.e., absent the chemical aid of NaCl). Therefore, we are confident that wetting of the substrate does not explain the water associated with the NaCl particles prior to the DRH.

FIG. 3 Images of a 1.3-μm CaSO₄ (column a) and a 2.3-μm CaSO₄·2H ₂O (column b) particle on an ultra-thin carbon film with a holey-carbon support film as RH was raised and held at 89%. The horizontal straight arrows indicate RH was held for an extended period of time.

3.3. Time Dependence of Water Uptake by NaCl Particles Prior to Deliquescence

Krueger et al. (2003) observed particle rounding and water association prior to deliquescence in their environmental scanning electron microscope (ESEM) experiments. They found that at 70.3% RH and ∼ 2-μ m NaCl the particle had a square shape. When the RH was increased to 75.0%, the edges of the particle became rounder. If the RH was held at 75.0% for an extended time (35 minutes), more water gradually associated with the particle, which became more spherical, although a solid NaCl core remained. If the water vapor pressure was then increased by a small fraction (0.1 torr), the NaCl particle deliquesced.

Our observations differ somewhat from those of Krueger et al. (2003). We exposed NaCl particles to 72% RH for extended times (Figure 4). In the initial image at 72% RH, many particles experienced changes in particle morphology, which we attribute to water uptake. After these initial changes, however, the morphologies did not change as the RH was held constant for 16 minutes. We also found that particle morphology did not change with time, implying that the system had reached steady state.

FIG. 4 Images of NaCl particles as the RH was raised and held at 72%. The thin arrows highlight that particle morphology did not observably change during 16 minutes of exposure to 72% RH. The particles were prepared using a TSI atomizer and were deposited on an ultra-thin carbon film with a holey-carbon support film.

3.4. Reversibility of Water Uptake by NaCl Particles Prior to Deliquescence

A decrease of RH following initial water uptake led to dry particles. For example, when NaCl particles (Figure 5) were exposed to an RH of 74%, the particles took up water and became spherical while retaining square cores. The cores appeared to be slightly smaller than their initial sizes at 0% RH, supporting the hypothesis that the layer surrounding the cores is an aqueous solution. When the RH was then decreased to 68%, the particles lost water and reverted to square shapes. This process could be repeated as long as the DRH was not reached. For example, we twice hydrated and dehydrated the NaCl particles in Figure 5 before we reached the DRH of 75%. Following deliquescence, when we reduced the RH, the particles remained spherical.

FIG. 5 Images of NaCl particles as the RH was twice increased and decreased. The particles were prepared using a TSI atomizer and were deposited on a lacey-carbon support film (without Formvar).

3.5. Ruling Out Radiation Damage as an Explanation of Water Uptake by NaCl Particles Prior to Deliquescence

Another possible explanation for the water uptake is that it is related to radiation damage during electron microscopy. It is well established that such damage occurs when materials such as ammonium sulfate and metal halides are studied using a TEM (Allen et al. 1998; Egerton et al. 1987; Li et al. 2003). Using ultraviolet photoelectron spectroscopy, Folsch and Henzler (1991) found that damage caused by electron bombardment induced chemisorption of water to the surfaces of NaCl films. The damaged sites then acted as reactive centers, which caused dissociation of water molecules and production of OH⁻. Dai et al. (1995), using Fourier transform infrared spectroscopy, also found that water physically adsorbs and dissociates at defects on NaCl surfaces to produce bound OH⁻.

The surfaces of the NaCl particles were unavoidably exposed to the electron beam during imaging using the ETEM. In Wise et al. (2005), we describe careful measures taken to minimize beam damage. By comparing particles that were exposed to radiation for different periods of time we did not observe any significant effect from the electron beam. For example, the particles in Figure 6a and Figure 6b are from opposite sides of the same TEM grid and thus were subjected to the same RH (73%), but the first was exposed to the electron beam for significantly longer (∼ 5 minutes) than the second (∼ 5 seconds). We observed comparable water uptake on both particles, independent of radiation dose. Thus, we do not believe the effect of the electron beam is the cause of water uptake prior to deliquescence.

FIG. 6 Images of NaCl particles as the RH was raised and held at 73%. The particles were located at opposite sides of the sample grid and show that water uptake on the surfaces of the particles was independent of electron dosage (i.e., the particle shown in image a was exposed to the electron beam for significantly longer than the particle shown in image b). The particles were prepared using the bubbler method and were deposited on an ultra-thin carbon film with a holey-carbon support film.

3.6. Estimate of the Amount of Water Uptake by NaCl Particles Prior to Deliquescence

We used the widths of the halos surrounding the particles to estimate the volume percent of water associated with the NaCl particles prior to deliquescence. The calculation is approximate because it assumes that the particles are hemispheres when on the substrate grid. In the absence of a technique to estimate the contact angle between the particles and substrate, we assumed that the particles are hemispheres when on the grid. Therefore, our estimates provide an upper limit. The halos around the 0.4-μ m and 40-nm NaCl particles in Figure 7a and Figure 7b are estimated to comprise approximately 40 and 80% of each particle by volume, respectively, i.e., significant amounts of water were associated with these particles prior to deliquescence.

Many studies (e.g., Biskos et al. 2006c; Cruz and Pandis 2000) use particle growth factors to quantify the extent of water uptake. The growth factor (G _f ) is defined as the ratio of the wet particle diameter at a given RH to the dry particle diameter. Using diameters from two-dimensional ETEM images as a rough estimate for three-dimensional diameters, we calculated the G _f for 13 NaCl particles. The average G _f prior to the DRH is 1.1 ± 0.1 (∼ 73% RH), and the average G _f at the DRH is 1.7 ± 0.3 (∼ 75% RH). For comparison, the volume-based G _f for micron-sized NaCl particles at the DRH is 1.8 (Biskos et al. 2006c). Our observations clearly show that a substantial amount of water, very much beyond a few monolayers, is associated with the particles prior to deliquescence.

3.7. The Possible Role of Particle Contamination in Water Uptake

Although we have no evidence for their presence, contaminants, possibly introduced during particle generation or during exposure to water vapor, in theory could provide an explanation for the water uptake. We estimate that water on the surface of the particle in Figure 7a comprised approximately 40% of the particle by volume at 74% RH. We used the AIM model of Clegg et al. (1998) (http://mae.ucdavis.edu/wexler/aim) to estimate how much contamination with aqueous (NH₄)₂SO₄ (i.e., upper side of its hysteresis loop) would be required to cause this amount of water uptake on an initially dry particle. (NH₄)₂SO₄ was chosen as a surrogate for a possible unknown impurity because it is a salt with well-known hygroscopic properties and because it can be easily handled by the AIM model. Approximately 1% (by dry mass) of the particle would have had to be contaminated with (NH₄)₂SO₄ at 74% RH in order for the water on the surface to comprise 40% of the particle by volume. Because the hygroscopic properties of (NH₄)₂SO₄ are greater than those of many potential contaminants, we believe that 1% is the lower limit of contamination that would have to be present for the observed water uptake.

FIG. 7 (a) NaCl particles generated using the bubbler method at 74% RH. (b) ∼ 40 nm NaCl particles generated using the VCAG method at 75% RH. All particles were imaged on an ultra-thin carbon film with a holey-carbon support film.

Biskos et al. (2006b) discussed that the vaporization and subsequent condensation of granular NaCl is one approach for generating pure NaCl nanoparticles. In the present study, such nanoparticles retained their square shapes when exposed to a RH of 71% (Figure 8). At 75% RH, some particles deliquesced while others had square NaCl cores surrounded by halos of water. When the RH was increased to 76%, all particles deliquesced. Many NaCl nanoparticles exhibited the same pattern of water uptake as that observed for the larger NaCl particles generated by the bubbler (i.e., Figure 1) and by atomization (i.e., Figure 2). Since the same effect was produced independent of the method of particle generation, we do not believe significant amounts of impurities were introduced into our particles during generation.

FIG. 8 ∼ 40 nm NaCl particles as the RH was increased past the deliquescence point. The thin arrows highlight water uptake prior to full deliquescence. The particles were prepared using the VCAG method and were deposited on an ultra-thin carbon film with a holey-carbon support film.

This belief notwithstanding, to test if measurable contaminants were present in the NaCl particles during interaction with water vapor in the ETEM, we performed EDS measurements on freshly deposited NaCl particles using the Philips CM200 TEM (Figure 9a). These measurements confirmed that representative particles contained Na and Cl. A small carbon peak also appeared in the EDS spectrum, presumably from the carbon substrate on the TEM grid. EDS measurements of NaCl particles made after exposure to water vapor in the ETEM (Figure 9b) did not indicate the presence of detectable amounts of other elements or organic impurities. Therefore, we conclude that contamination does not explain our observations.

EDS measurements of the NaCl particles show that the Cl signal from the particles is significantly reduced after exposure to water vapor. In section 3.5 we discussed the mechanism by which sites on the NaCl particle surface, if damaged by the electron beam, can act as reactive centers, causing dissociation of water molecules and production of OH⁻. Although we do not believe the effect of the electron beam is the cause of water uptake prior to deliquescence since the observations of water uptake have no correlation to the extent of beam exposure, this reaction provides a possible explanation for the reduction of the Cl signal measured by EDS after the NaCl particles are exposed to water vapor in the ETEM. If HCl_(g) is liberated from the surface of the NaCl particle, it will be pumped away by the TEM. However, the vapor pressure of NaOH_(s) is negligible at room temperature. Therefore, if NaOH occurs on the surface of the particles, an O signal should be present in the EDS spectrum (Figure 9b). If O is present in the particle shown in Figure 9b, it is below the detection limit. This finding lends more credence to our belief that the electron beam is not the cause of water uptake.

3.8. Observations of Water Uptake by Other Alkali Halide Particles Prior to Deliquescence

We observed water uptake by other alkali halide particles below their respective DRH values. For example, when NaBr particles were exposed to 47% RH (Figure 10, top row), water surrounded the solid NaBr cores. As the RH was increased to 48% the particles deliquesced. Similarly, significant water uptake was associated with CsCl particles at 64 % RH (Figure 10, bottom row). When the RH was increased to 68%, the particles deliquesced.

FIG. 10 Images of NaBr particles (top row) and a CsCl particle (bottom row) as the RH was increased past the deliquescence point of 48% for the NaBr particles and 68% for the CsCl particle. Thin arrows highlight particle rounding and water uptake prior to the DRH. The particles were prepared on a flat carbon film (with Formvar) and were generated using a TSI atomizer.

3.9. The Phase Rule: Derivation

The conventional Gibbs phase rule requires that a NaCl particle in a NaCl/H₂O binary system exists at a particular RH value and temperature as either a solid or a solution droplet, except for precisely at the deliquescence relative humidity (Gibbs 1906; Martin 2000; Jensen 2001). The ETEM images of the present study, however, show that solid and liquid are simultaneously present in substantive amounts from 70 to 75% RH. In this section, we derive the phase rule for our experimental geometry. In section 3.10, we find that it theoretically allows for our observations. In section 3.11, we consider how the lever rule informs us about the possibility of detecting solid and liquid phase simultaneously across a 5% RH range.

The phase rule is a statement of constraints on equilibrium. In a system described by n components in i phases, the definition of equilibrium requires homogeneity of chemical potential of a species among all phases, meaning that μ _1a = μ _2a = … = μ _ia for species a, and we can therefore just write μ _a. The designation μ _1a refers to the chemical potential of component a in phase 1. Chemical potential μ _1a can be calculated provided that all other terms are known, i.e., μ _a = μ _1a = f ₁(μ _b, μ _c,…, μ_n; T,P). This relationship is analogous to calculating the concentration of a species from the concentrations of all other species and an equilibrium constant among them.

The relation μ _a = f ₁(μ _b, μ _c,…, μ _n; T, P) corresponds to 1 equation and n + 2 variables. There is one such equation for each phase present (i.e., μ _a = f ₂(μ _b, μ _c, …, μ _n; T, P), μ _a = f ₃(μ _b, μ _c,…, μ _n; T, P), and so forth), providing a total of i equations. For a uniquely defined algebraic system, we must balance the number of equations with the number of variables: i = n+ 2. For an initially underdetermined algebraic system corresponding to the case of too few defined variables (i.e., n + 2 − i > 0), we may arbitrarily choose values of the excess (n + 2 − i) variables to obtain a determined system. We represent this result, which is the conventional Gibbs phase rule, by F = n − i + 2, where F is called the number of degrees of freedom.

The implicit assumption of the above derivation is uniform temperature and pressure among all subsystems, as indicated by the absence of subscripts on T and P. Macroscopically small phases, however, necessarily have curvature and are therefore under different pressures. The Laplace-Young relation provides the relationship between surface curvature and pressure (Koenig 1950). The chemical potential terms then must be written as: μ _a = f ₁(μ _b, μ _c, …, μ _n; T, P ₁) = f ₂(μ _b, μ _c, …, μ _n; T, P ₂) = … = f _i(μ _b, μ _c, …, μ _n; T, P _i). The subscript i on pressure indicates that each subsystem has its own pressure, the value of which depends on system size and surface tension. This system of equations has i equations and n + i + 1 variables, requiring that the values of (n + 1) variables be declared (i.e., degrees of freedom) for a full determination. The phase rule for heterogeneous subsystem pressures is then: F = n + 1.

3.10. The Phase Rule: Examples

The example of pure water as a system of 1 component can be considered. Cases A–C of Figure 11 are shown for the condition of uniform pressure corresponding to large subsystems, corresponding to the phase rule of F = n − i + 2. Case A shows that temperature and pressure of water vapor may be independently adjusted when no other phases are present. Case B shows that when liquid and its vapor are present in equilibrium, temperature uniquely defines the system (i.e., F = 1). Case C shows that the co-presence of water vapor, liquid, and solid uniquely defines both temperature and pressure (i.e., the triple point). Cases D–F are shown for subsystems of different pressures, corresponding to macroscopically small systems having surface curvature and obeying the phase rule of F = n + 1. Case D collapses to case A since the system and subsystem pressure are identical in the case of one phase and one component. Case E shows that there are two degrees of freedom. Unlike case B, in case E at a specified temperature, pressure remains a free parameter. This result appears quantitatively as the Kelvin effect of liquid droplets. The pressure on the liquid phase is directly related to the diameter of the liquid phase so that as diameter goes down the chemical potential in the liquid phase and hence in the vapor phase goes up (i.e., higher vapor pressure). Case F shows that there are still two degrees of freedom when vapor, liquid, and ice are simultaneously present. Once temperature and the pressure on the liquid phase (i.e., diameter) are specified, the pressure on the solid phase, which is also regulated by its size, is uniquely specified. Ice and liquid water co-exist at equilibrium across a range of temperatures, although the size of the ice phase is dictated by the size of the liquid phase.

FIG. 11 Illustration of degrees of freedom for (A–C) a system having a common pressure and (D–F) a system for which subsystem pressure are heterogeneous. The Gibbs phase rule of F = n − i + 2 specifies the degrees of freedom for a system under common pressure, where n is the number of chemical components and i is the number of phases. The modified phase rule of F = n + 1 holds for subsystems of different pressures. In panels A–F, F is evaluated for n = 1.

Figure 12 shows the two-component NaCl and H₂O system for the cases of uniform pressure throughout the system compared to subsystems at different pressures (i.e., different sizes). In the case of a uniform-pressure, two-phase system (case A), there are two degrees of freedom (F = n −i + 2 = 2), such as temperature and the chemical potential of water vapor (i.e., relative humidity). The three-phase system (case B) has one degree of freedom. Once temperature is specified, all other factors are constrained. Therefore, the simultaneous presence of NaCl_(s), NaCl_(aq), and H₂O vapor at a given temperate uniquely specifies the chemical potential of water, corresponding to the deliquescence relative humidity.

FIG. 12 Illustration of degrees of freedom for a two-component system of NaCl and H₂O having (A–B) a common pressure and (C–D) subsystems of different pressures. Within the thermodynamic system, the water vapor, the aqueous solution, the particle, and the interfaces (including the particle/substrate interface) exchange both mass (practically speaking, H₂O in the vapor, H₂O and NaCl in the solution, and NaCl in the particle) and joules (chemical potential in vapor, solution, and particle and interfacial energies of substrate/particle, solution/particle, solution/vapor, and possibly vapor/particle).

Figure 12 also shows cases for two-phase (case C) and three-phase (case D) systems having different subsystem pressures, for which F = n + 1 holds. Case C and D therefore both have three degrees of freedom since n = 2. Case C represents the simultaneous presence of NaCl_(aq) and H₂O vapor, such as in the study of the hygroscopic growth factor of aqueous NaCl nanoparticles within a tandem differential mobility analyzer (TDMA) (Biskos et al. 2006b, 2006c). In this setup, the three degrees of freedom are (1) the temperature, (2) the chemical potential of gas-phase water (i.e., relative humidity), and (3) subsystem size (i.e., dry particle radius). As RH changes in the TDMA measurement, the aqueous particle size is uniquely defined by the values of 1, 2, and 3. Case D represents the simultaneous presence of NaCl_(s), NaCl _(aq), and H₂O vapor, such as in the ETEM observations. Of the three degrees of freedom, temperature exhausts one. The second is taken by P ₁, which is adjusted during the course of the ETEM observation as the water partial pressure in the environmental cell (thereby setting the chemical potential of H₂O). The system size (i.e., dry particle mass) is the third degree of freedom.

3.11. The Lever Rule

For case D of Figure 12, the mass partitioning of total NaCl between NaCl _(s) and NaCl_(aq) (i.e., the lever rule of this system) is uniquely defined once the three degrees of freedom are taken. An important caveat, however, is whether or not NaCl _(s) and NaCl _(aq) will simultaneously have adequate masses to be detectable over a range of relative humidity beyond experimental fluctuation. For example, if the lever rule essentially runs from one endpoint to the next within 0.1% RH, then the phases will not be detected to coexist except with the most precise instrumentation. Numerous results in the literature, for example, suggest the absence of a detectable NaCl_(aq) co-phase for free floating aerosol particles, at least within typical RH control of 1% (Biskos et al. 2006b, 2006c). However, if the phases coexist across a range of 2% RH or greater, they will be detected by most common experimental procedures. For the substrate-supported particle in the ETEM observations, the phases are observed to reversibly co-exist over a 5% RH range. These differences for aerosol compared to supported particles indicate different regimes for the lever rule in the two geometries. The quantitative terms affecting the RH gamut of the lever rule (for conditions described by the phase rule of F = n + 1) are the surface tensions and sizes of the involved phases, including, in the present case, both NaCl _(s) and NaCl_(aq). The observations therefore suggest a significant role of the sample/substrate interface as an energy term so that phases coexist over a perceptible range in the present experiments. For the observed RH gamut of 70 to 75% RH, an effect on the order of 1.04 is required, which is an order of magnitude smaller than the Kelvin effect on the hygroscopic growth factor observed for nanoparticles (Biskos et al. 2006a, 2006c).

We examined NaCl particles supported on several different types of TEM substrates to see if we could detect differences in water uptake. The support films included three different types of carbon films and a silicon monoxide film. We show the hygroscopic behavior of NaCl particles supported by an ultra-thin carbon film with a holey-carbon support film and a lacey-carbon support film (no Formvar) in Figure 1 and Figure 2, respectively. We show the hygroscopic behavior of other alkali halide particles on flat carbon films (with Formvar) in Figure 10. Although not illustrated in this manuscript, NaCl particles on silicon monoxide films also exhibited water uptake prior to deliquescence. No matter the type of support film, a significant amount of water was associated with the NaCl particles at approximately the same RH values. In this sense, our observations of water uptake prior to deliquescence are general across all substrates. In a finer sense, in this first report we could not tell differences among the substrates, possibly because our precision for RH measurement is approximately 1% at best whereas the phenomenon we have observed occurs over a range of 2 to 3% RH. If our explanation for the observed effects is correct, future studies with finer controls on RH or a greater variety of substrates and salts may discern differences among substrates.

The above, for the sake of simplicity, makes no distinction between solid and liquids in discussion of the effects of surface curvature on pressure. A relationship also exists between size and pressure for solids, although it is less precisely specified mathematically than the Laplace-Young relationship since it depends on the nonspherical shape of the solid as well as other factors pertaining to the resistance to flow of solids and possibly nonisotropic stress (e.g., requiring up to 6 variables to describe pressure). Energies for solids are difficult to obtain and vary depending on surface preparation (hence the difference in discussion of surface energy for solids and surface tension for liquids). In general surface energies of solids are much higher than for liquids, such as 5000 mJ m⁻² for mineral oxides or estimated as 400 mJ m⁻² for NaCl. Therefore, effects such as size-dependent solubility for solids are apparent for larger particle sizes than for effects such as vapor pressure increases for liquids.

The above discussion also omits line tension and disjoining/conjoining pressure (Bergeron 1999). These factors have been considered but ruled out in the literature as a hypothesis for nonprompt phase transitions for nanoparticles (Djikaev et al. 2001). Later experimental measurements further demonstrated prompt transitions for nanoparticles (Biskos et al. 2006a). Notwithstanding the absence of application to nanoparticles, the ideas may still have applicability to the coexistence of solid and aqueous NaCl phases across an RH range, especially when those particles are supported on substrates such as in our experiments.

4. CONCLUSIONS

The images obtained using the ETEM provide detailed visual information about what happens on the surfaces of alkali halide particles as RH is increased. We find that a significant amount of water can be reversibly associated with the surfaces of NaCl particles at RH values as low at 70%. We hypothesize that the liquid layer on the surfaces of the particles is an aqueous NaCl solution. Experimental artifacts such as damage to the NaCl surface by the electron beam and small fluctuations in RH are not sufficient to explain the observations. A derivation of the phase rule for our experimental geometry shows that subsystems under heterogeneous pressures, which can be caused by different subsystem sizes and surface energies, have additional degrees of freedom that allow the coexistence in a binary chemical system of three phases (i.e., gas, liquid, and solid) across a range of water vapor pressures. Consideration of the lever rule suggests a significant role of the sample/substrate interface as an energy term so that aqueous and solid phases of NaCl coexist over a perceptible range in the present experiments, in distinction to observations of free-floating pure NaCl aerosol particles.

Aerosol particles in the atmosphere are complex mixtures of inorganic and organic components. Many are associated with insoluble materials and organic compounds. In that regard, TEM substrates may be rough surrogates of insoluble materials, and the results of this study may therefore be relevant to those atmospheric systems.

Acknowledgments

This work was supported by the National Science Foundation under Grant No. 0304213 from the Division of Atmospheric Chemistry. Any opinions, findings, and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the views of the National Science Foundation. We gratefully acknowledge the use of the facilities at the John M. Cowley Center for High Resolution Electron Microscopy within the LeRoy Eyring Center for Solid State Science at Arizona State University. In particular, we thank Karl Weiss, John Wheatley, Grant Baumgardner, Renu Sharma, and Peter Crozier for their assistance with developing our ETEM technique at ASU. We also thank Jonathan Abbatt, Daniel Cziczo, Margaret Tolbert, Melinda Beaver, George Biskos, and John Armstrong for their help in the development of this article. The anonymous reviewers and the editor provided important guidance that improved the article.

Notes

^a MPS-3 microanalysis particle sampler (California Instruments, Inc.).

^b Vaporization-condensation aersosol generation.

^c TSI Nanometer Aerosol Sampler (model #3089).

^d CaSO₄ used as received from the manufacturer.