Hygroscopic Properties of NaCl Nanoparticles on the Surface: A Scanning Force Microscopy Study

We investigated the hygroscopic growth of Sodium Chloride (NaCl) nanoparticles with curvature related diameters ranging from 10 nm to 200 nm, at different relative humidity by scanning force microscopy. Hygroscopic aerosol nanoparticles play a vital role in the earth climate and human health. We report that 10-nm NaCl nanoparticles adsorbed on silicon surfaces have a higher deliquescence relative humidity than larger NaCl nanoparticles (size > 30 nm). This finding is consistent with observations for airborne nanoparticles by hygroscopicity tandem differential mobility analyzer. Therefore, the presence of a silicon surfaces plays no significant role for the deliquescence relative humidity. Moreover, the study of individual airborne particles by means of scanning force microscopy revealed that the ability of water uptake, i.e. growth factor, of NaCl particles differs by as large as 40 % at the same relative humidity. This finding indicates that the individual nature of NaCl particles influences the growth factor. Our study of individual nanoparticles the corresponding GFs can vary. The that different different uptake. the exact shape, composition the


Introduction
Nanoparticles are a significant component of atmospheric aerosols. Aerosols are proposed to influence Earth's climate and human health [1][2][3][4] . Often atmospheric aerosols are hygroscopic, and they can grow significantly in humid environments 5,6 . Therefore, studying the hygroscopic properties of suspended atmospheric nanoparticles at different relative humidity (RH) has received significant attentions [7][8][9][10] . In particular, the phase state of the atmospheric nanoparticles determines optical properties, cloud-droplet nucleation efficiency and heterogeneous chemistry [11][12][13][14][15][16] . Details of the phase transition at different humidity can be inferred from the analysis of hygroscopic growth curve of individual aerosol particles or aerosol populations.
Atmospheric aerosols can adsorb water on surfaces 17,18 , and the hygroscopic property of the adsorbed nanoparticles may influence chemical and physical processes on the surface. Substantial water sorption by nanoparticles may lead to surface corrosion, which is a serious problem for electronic devices 19 . Therefore, the behaviors of nanoparticles on surfaces at different humidity were studied intensively. Ghorai and Tivanski used X-ray microscopy (STXM) and near edge X-ray absorption fine structure (NEXAFS) spectroscopy to investigate atmospherically relevant NaCl, NaBr, NaI and NaNO 3 nanoparticles on Si 3 N 4 windows 20  However, the role of the surface on the response of aerosol nanoparticles to humidity is still not clear.
Eom et al. 24 examined the hygroscopic properties of micrometer sized inorganic particles on different types of substrates by optical microscopy. They found that the substrate has no influence on the deliquescence relative humidity (DRH) of these micrometer sized particles 24 . The DRH is the relative humidity (RH) value upon the phase transition from a solid to a liquid occurs 25 . In contrast, Morris et al. reported that NaCl particles with a little bit smaller diameters of 0.5 -1 μm on the surface exhibit a different growth behavior compared to airborne particles upon exposure to humidity 22 . In addition, the shape and size of particles varies at different RH 26 . The latter was measured by means of a humidified tandem differential mobility analyzer (HTDMA). These measurements indicate that the diameter of the

4
particles is not the only parameter that controls the growth factor. It seems likely that the morphology and shape of particles play a role in the growth behavior, too. Consequently, methods allowing to measure the size and the shape dependence of the hygroscopicity of nanoparticles are required. In particular, aerosol nanoparticles < 100 nm on surfaces have not been studied, although these particles may be more important for climate change and human health than larger ones 3,27,28 .
In this study, the NaCl particles, which are one of the most important components of atmospheric aerosol particles 29,30 , were chosen. Particles with different sizes were generated and collected onto a silicon substrate. In particular, we focused on small particles with mobility diameter of 200 ± 15 nm, 30 ± 2 nm and 10 ± 0.5 nm, which may be prone to surface effects more than particles > 200 nm 8,31 . The error in sizes is given by the DMA transfer function. The morphology and hygroscopic growth at different RH were analyzed by using SFM. Based on SFM parameters, we calculated the volume of NaCl particles and we introduce a model to calculate the curvature related diameter ( ). Changes in upon humidity exposure allowed us to determine the DRH of different particle sizes. The data from this study was compared to the values for suspended particles from HTDMA. This comparison confirms results of the previously theory about the nano-size effect on particle phase transition 9 and indicates that the method developed for airborne nanoparticles applies to the deliquescence of nanoparticles on surfaces as well.

Generation and Collection of NaCl Aerosol Nanoparticles
Sodium chloride (NaCl) was purchased from Sigma-Aldrich (reagent grade, 99.99% purity) and prepared in deionized water (18 MΩ·cm). The aqueous solution containing NaCl was atomized using TSI 3076 constant output atomizer (TSI, Inc.), and dried (~ 5% RH) by passing through a diffusion silica dryer. The aim of our study is to measure size dependent hygroscopic properties of particles attached to a surface. Thus, the dehydrated aerosol particles with different values of were selected using a differential mobility analyzer (DMA; TSI, Inc. Model 3081A) and then deposited on silicon substrates (Ted Pella Inc., Part No. 16008) via impaction using a pump running with a flow of 1.5 L/min. Prior to the sampling, the silicon substrates were cleaned in Argon plasma for 2 min. The mobility diameters of the NaCl particles that we collected for later SFM measurements are selected

5
preparation steps is shown in Figure 1a.

Scanning Force Microscopy Analysis
All SFM data were obtained in tapping mode by adjusting the minimum force between tip and sample while imaging (Dimension Icon, Bruker). Silicon substrates with deposited nanoparticles were placed in a custom made SFM Teflon cell (Figure 1b, 1c). This cell has a volume of 25 cm 3 and allowed us to adjust the RH during SFM measurements with a precision of < 5% 26  Then the SFM images of particles were recorded at each RH, respectively. After increasing the RH, we decreased the RH again in order to check reversibility and stability of particles. The raw SFM data were analyzed by the NanoScope Analysis 1.5 package.

Quantifying the Size of Nanoparticles and DRH
Different parameters have been used for quantifying the sizes of airborne particles (aerosol) and deposited particles. The parameter is given by the diameter of a particle having the same electrical mobility 33,34 . Alternatively the Stokes diameter ( ), which is the diameter of a sphere having the same terminal settling velocity and density as the particle, was also used 34 . In addition, the volume equivalent diameter ( ) of non-spherical particles was used to quantify the size of deposited particles at different RH in previous SFM studies 22,35 . The is equal to the diameter of a spherical particle that exhibits an identical volume. Principally, all above parameters are reasonable for quantifying the hygroscopic growth of particles. Therefore, we have analyzed the volume of particles at different RH based on SFM measurements. However, this parameter does not reflect changes of the shape. Many physical properties of nanoparticles are caused by changes of its surface properties, such as curvature, but not solely depend on the change in its volume 36,37 . For example, the equilibrium between water vapor and solution droplet is strongly affected by the curvature of the nanoparticle surface 38 . Additionally, in order to address changes in shape with a single parameter, we used a curvature related diameter to quantify the size of particles ( Figure 2a). In order to In our analysis, we approximated the tip apex shape with a semi-sphere having a radius of 10 nm followed by a cone with an opening angle of 35° 32 (Figure 2b). When the height of a solid particle is higher than the radius of tip, the edge of the cone touches the particle (Figure 2c). In this case, we use = -2h • tan17.5°( equation 1) to calculate L. L m is taken from a line-profile across the particle. It is the distance between the points, which elevate from the substrate plane. When the height of a solid particle is lower than the radius of the tip we use (equation 2) to calculate L (Figure 2d). After the = -20 nm deliquescence, particles are in liquid state ( Figure 2e). In this case, we also use Eq. 2 to calculate L no matter what the size it is. After calculating L for particles with different sizes, we calculated by a geometrical model In particular, the calculation of the shape related diameter , as defined here, reflects geometrical changes given by the transition from a crystalline ( Figure 2a) into a liquid state (Figure 2e), although the volume remains unchanged. Therefore solid-liquid transitions should appear more clearly compared to the analysis of volume changes. We consider these curvatures as first order changes.
Second order changes are attributed to a variation of the curvature along different directions of particles as they are not perfectly symmetric and to local curvatures of the particle surfaces (Table S1 in supporting information). For calculating the volume of dry particles, we use (equation 4) as V = 2 • ℎ these particles are cuboids. Particles become spherical caps after the deliquescence, and thus we use the particles were detected after repeated SFM scans (Figure 3b-d).

10-nm particles.
When the RH reached about 75%, the particle with a height of ≥ 30 nm still remain unaltered on the surface (Figure 3e). However, the particles with a height of ~ 10 nm disappeared after the first scan ( Figure 3e). After increasing the RH to 78.5%, disappeared particles were still not being found ( Figure   3f). One possibility is, that the SFM-tip while scanning sweeps these particles away. However, we could not find traces of particles at the edge of the scan window. Another possibility would be that these small particles are dissolved by water that forms a meniscus between the particles and the surface e.g. due to Kelvin equation 39 . Weeks et al. observed by environmental scanning electron microscopy that such a water meniscus starts to form at RH >70% between a Silicon-nitride SFM-tip and a Silicon substrate 39 . The appearance of such a water meniscus at a RH >70% coincides with our observation that small NaCl particles disappear at a RH of 75 %. In addition, it is noteworthy, that several previous studies of hygroscopic NaCl particles by SFM were all limited to particle diameters larger than hundreds nanometer at different RH conditions 22,24,40,41 . Thus, it might be impossible to image such small airborne NaCl particles at a RH > 70% by SFM owing to the formation of a water meniscus between the particle and the substrate and/or between the particle and the SFM-tip. Although the exact mechanism is unclear, the reason for the disappearance of airborne NaCl particles with a of ~10 nm is the increase in RH above 70%.

30-nm particles.
The little larger particles which corresponds to a of 30 nm could be imaged above a RH of 75% (Figure 3d). The size of the particles increases, and the phase becomes liquid at a high RH. After decreasing the RH we found that the particles which are attributed to a of 30 nm (Figure 4a) and decreased in height to < 10 nm (Figure 4b). It is possible that some of the liquid was removed by scanning the SFM-tip leaving a smaller fraction of NaCl behind. These residual NaCl particles exhibit a height of ~ 4 nm at 10% RH. Correspondingly, its is ~ 10 nm. These small particles are immobile on the surface and possibly adhere much stronger to the surface as they were in a liquid state before (Figure 5a). A subsequent stepwise increases in RH again to 90% lead to an increase in size until finally they became round at a RH of 90% (Figure 5b). Interestingly, these small particles can be imaged reproducibly by SFM, which is different from the case of 10-nm particles from DMA directly.
They do not disappear. Possibly adhesion of such particles is much stronger. We hereby use these residual NaCl particles to study the hygroscopic growth at at ~10 nm.

200-nm particles.
Next, we recorded images of larger particles to examine the change of morphology of particles.
Firstly, the morphology of a cuboid NaCl particle with of 210 nm (RH~ 5%) was analyzed ( Figure   6a). This particle corresponds most likely to one of the particles with of 200 nm. It retains a cuboid shape with corners that are rounded. Rounded corners were also observed by Bruzewicz et al.'s using non-contact environmental SFM 41 . Using Eq. 3, we calculated a of 208 nm. For such large NaCl particles a DRH of 75% was determined by HTDMA 7,42 . Therefore, the SFM exhibits a clear shape change of the cuboid NaCl particle into a semispherical object at a RH of 90% (Figure 6b).
The semispherical shape indicates the formation of a liquid droplet on the surface. Correspondingly, we calculated an increase in to 543 nm. This interpretation is supported by the simultaneously recorded phase variation of the oscillating SFM cantilever (Supporting Information S1).
To summarize, we can image and analyze NaCl nanoparticles with in from 10 nm up to 772 nm at RH from 5% up to 90%, Next, we analyzed the changes in dependence of RH in more detail with the aim to calculate the growth factors (GFs) and the deliquescence relative humidity (DRH).

Growth Factor and Deliquescence Relative Humidity
The growth factor (GF C ) of particles can be defined by where is the GF at a particular RH, is the calculated curvature related (RH) ( ) diameter at a particular RH (Eq. 3), is the curvature related diameter at the ( ) lowest RH (5 -20%) studied for the corresponding particle. Here we plotted the GF C of two populations of particles, i.e. ~ 200 nm and ~ 10 nm (Figure 7a). In addition, GFs from HTDMA measurements for particles with of 100 nm and 10 nm at different RH conditions were plotted for comparison, as well as curves based on the Köhler theory 7,9,42 . For comparison, we 9 also calculated the GF based on the change of volume of particles (GF V ) by using Eq. 7 22,43 , and results were presented (Figure 7b) and discussed below.
For the population of particles with ~ 200 nm, we calculated GFs of about 1 up to a RH of 77% (Figure 7a). The RH at which nanoparticles become significantly larger is defined as the DRH.
For particles with a ~ 200 nm, we measured a steep increase of the GF C at a RH of 78±1%.
This RH corresponds to the DRH and is indicated by a red dashed line in Figure 7. For the population of particles with ~ 10 nm we measured a constant growth factor of 1 up to a RH of 86±1 % which is 8 % higher in RH compared to the particles having diameters ~ 200 nm. After a RH of 86±1 %, a significant increase of the GF C to values > 1.5 was observed. The DRH of particles with a ~ 10 nm corresponds to 86±1% (black dashed line in Figure 7). Our measurements indicated that GF for larger particles are higher than GF for smaller particles at the same RH condition after the deliquescence. This observation also holds for the GFs, which are calculated by the volume change Notably, the magnitude of the GF calculated by volume changes is in good agreement with the HTDMA data ( Figure 7b). However, the GF magnitude calculated by the curvature related diameter is significantly higher for 200-nm sized NaCl nanoparticles. The latter probably indicate that the calculation of accentuates changes from a crystalline state into a liquid state, where solid to liquid phase transition could be resolved more clearly. The calculation of latter is enabled by using an imaging technique where the height and the width of nano-scale particles can be measured.
The SFM method allowed us to analyze different particles of almost the same .
Interestingly, the GF of particles with the same can be different at the same RH. NaCl nanoparticles exhibit different abilities for water uptake. In other words, the parameter of , as well as the volume, does not solely define the growth factor of particles, and the population of particles with the same may behave differently. This difference has been rarely reported so far because the HTDMA method yields an ensemble average of thousands of particle measurements. SFM allows to study individual particles, though at a significantly reduced statistic.
The HTDMA method revealed a DRH of ~ 87% and ~ 75% for airborne particles with of 10 nm and 100 nm, respectively 7,42 . Both DRH values are not much different from those measured for smaller and larger particles on surfaces, i.e. 86±1%, and 78±1%. Therefore, we conclude that the substrate has a negligible influence on the DRH of NaCl nano-particles down to a size of 10 nm. This conclusion is in agreement with the finding of Eom et al. who reported that the substrate has no influence on the DRH of micrometer sized particles 24 . In addition, the size dependence of DRH of nanoparticles, i.e. DRH increases as the size decrease, were explained by our previous study 9 , and the same size dependence was confirmed here in this study. Therefore, we conclude that the theory that developed there to explain the size dependent phase transition for airborne nanoparticles and the Differential Köhler Analyses (DKA) can be applied to the NaCl nanoparticles on the surface as well.

Summary
Earlier experimental and theoretical studies have reported a change of DRH for airborne particles of different sizes 7,9,25,44,45 . For airborne NaCl particles, the DRH increases by ~ 5 % when the diameter decreases from 100 nm to 10 nm. Our measurements confirm this dependence for particles deposited on silicon surfaces. Thus, we conclude that the theory that developed in our previous study 9 to explain the size dependent phase transition for airborne nanoparticles can describe the deliquescence of airborne nanoparticles on surfaces as well.
Particles on hydrophobic surfaces at high humidity might behave differently. Small particles on hydrophobic surfaces could be more stable. SFM is a suitable tool for comparing similar sized airborne nanoparticles surfaces with different surface energy at high humidity. Our study of individual nanoparticles revealed, that the corresponding GFs can vary. The latter indicates that different airborne particles have different ability for water uptake. Here possibly the exact shape, composition or orientation of the particle plays a role.  Figure 5. SFM images of one NaCl particle with of ~10 nm. (a) SFM topography image of a residual NaCl particle having a of ~10 nm imaged at a RH of ~10%. (b) The same NaCl particle imaged at a RH of ~90%. At this RH the round particle is a deliquesced NaCl solution droplet. Figure 6. SFM images of one NaCl particle with of ~200 nm. Images are shown in height mode here. (a) Image at the RH of ~5%. The particle is solid. (b) Image at the RH of ~90% ( ~ 540 nm). The round particle is supposed to be a deliquescent NaCl solution droplet.