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Capillary Condensation in 8-nm Deep Channels Junjie Zhong, Jason Riordon, Seyed Hadi Zandavi, Yi Xu, Aaron Harrinarine Persad, Farshid Mostowfi, and David Sinton J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03003 • Publication Date (Web): 11 Jan 2018 Downloaded from http://pubs.acs.org on January 12, 2018

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The Journal of Physical Chemistry Letters

Capillary Condensation in 8-nm Deep Channels Junjie Zhong,† Jason Riordon,† Seyed Hadi Zandavi,‡ Yi Xu,† Aaron H. Persad,†, ‡ Farshid Mostowfi,§ and David Sinton†,* †

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario

M5S 3G8, Canada ‡

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge,

Massachusetts 02139, United States §

Schlumberger-Doll Research, Cambridge, Massachusetts 02139, United States

Corresponding Author *

E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Condensation at the nanoscale is essential to understanding many natural and synthetic systems relevant to water, air and energy. Despite its importance, the underlying physics of condensation initiation and propagation remain largely unknown at sub-10 nm, mainly due to the challenges of controlling and probing such small systems. Here we study the condensation of n-propane down to 8-nm confinement in a nanofluidic system, distinct from previous studies at ~100 nm. The condensation initiates significantly earlier in the 8-nm channels and it initiates from the entrance, in contrast to channels just 10-times larger. The condensate propagation is observed to be governed by two liquid-vapor interfaces with an interplay between film and bridging effects. We model the experimental results using classical theories and find good agreement, demonstrating that this 8-nm non-polar fluid system can be treated as a continuum from a thermodynamic perspective, despite having only 10-20 molecular layers.

TOC GRAPHICS

Liquid

Film

Vapor

8 nm


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Condensation in sub-10 nm systems has garnered increased interest recently due the important role of phase change in climate engineering,1-4 water purification,5-6 energy transport and storage,6-7 shale gas production,8-9 surface treatments,10-12 heat transfer13-14 and nanomaterials1517

. The underlying physics of the condensation process at the sub-10 nm scale, however, remains

poorly understood. For example, condensation initiation within sub-100 nm confinement can be described through the Kelvin equation, where the highly curved liquid-vapor interface introduces a shift in saturation conditions.18 However, there is much debate as to the validity of Kelvin equation below 10 nm since such small systems span a small, discrete number of molecules. While certain studies claim to have validated the Kelvin equation down to sub-10 nm systems,1920

other works indicate otherwise pointing to, for example, the breakdown of the ideal gas and

incompressible liquid assumptions inherent in Kelvin equation.21-22 In addition, the condensate propagation kinetics within a confined sub-10 nm space is difficult to directly observe. Numerical simulations of nanoscale systems23 indicate that condensation propagates by the liquid bridging of films that grow on opposite channel walls, while experiments in nanoporous media suggest that the condensate propagates by capillary flow24 and vapor diffusion.25 The validity of the theoretical approaches at the sub-10 nm scale can only be examined after overcoming the challenges of obtaining accurate experimental data, specifically the difficulties of precisely controlling and probing sub-10 nm systems. Currently, the most established experimental methods for studying nanoscale condensation require measuring adsorption and desorption isotherms in nanoporous media.26 However, these techniques are often affected by nonuniformity in pore size and geometry, and generally do not allow direct observation of condensation dynamics in pores. Other approaches such as electron scanning microscopy,27 atomic force microscopy28 and electrical conductivity29 have been applied to study nanoscale


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condensation of water,30 electrolytes31 and hydrocarbons26 in cylindrical pores,32-33 nanoslits32, 34 or carbon nanotubes.35 However, accurately controlling, changing and probing the thermodynamic conditions within large testing ranges in such systems remains a challenge. Recent advances in nanofluidics have led to excellent control over system geometry,36-37 thermodynamic conditions38-39 and optical accessibility40, providing an opportunity to directly study condensation at the nanoscale. Studies using nanofluidic devices have examined the condensation of water18 and hydrocarbons41 at ~100 nm scales. However, condensation within precisely manufactured, controlled and directly visualized sub-10 nm systems – a scale relevant to a broad range of natural and synthetic systems– has not yet been achieved. In this article, we visualize the condensation of n-propane in precisely fabricated 8-nm silicon nanochannels. A silicon nitride layer is deposited at the base of the nanochannels to form FabryPerot optical resonance cavities,42 enabling the imaging of discrete fluid phases at this scale. We simultaneously observe the phase behavior in microchannels (i.e the bulk phase) and find that the initiation of condensation in the 8-nm channels agrees closely with the Kelvin equation. Condensate propagation in the 8-nm channels is found to be governed by two liquid-vapor interfaces: one that is pinned at the inlet due to capillary condensation and another that grows through capillary filling. The condensation initiation location, film and bridging effects are discussed in detail and compared with previous findings in sub-100 nm systems. In providing a clear picture of condensation phenomena within a well-defined nanosystem, this work provides fundamental insight into the physics behind condensation down to 8-nm confinement, which we find to deviate significantly from the physics at larger scales. The validity of the Kelvin equation down to 8-nm based on close agreement between classical theoretical modeling and the


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experimental results supports the continuous assumption for a fluid system with only 10-20 layers of molecules.

b

a

A

A 10

A A

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Liquid in Nano

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Vapor in Nano

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6 4 2

Reservoir

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2 4 Position (µ µm)

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VBulk

(i) 340

VNano VBulk (ii)

LNano VBulk

VNano LBulk

Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


320

300 Condensation in Nanochannels Condensation in Bulk Kelvin Equation (R = 4 nm) Saturation Condition (Bulk)43

(iii)

LNano

VNano 280 0.5

1.0

1.5 Pressure (MPa)

2.0

2.5

Figure 1. Thermodynamic conditions for condensation in 8-nm channels and in the bulk scale. (a) Schematic of the nanofluidic device with both nanochannels and bulk microchannels under the same thermodynamic conditions for comparison. (b) AFM profile of a single nanochannel (8.0 ± 0.2 nm). (c) Measured condensation conditions at 8 nm and in the bulk, along with corresponding saturation curves obtained using the Kelvin equation and NIST values.43 Each point for the 8-nm case represents the average of a total of 33 measurements (3 runs with 11 nanochannels). Each point for the bulk case represents the average of 6 measurements (3 runs


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with 2 microchannels). Error bars are smaller than the symbols. Images show system behavior at a pressure of 1.31 MPa at one of three temperatures. When the temperature is above the Kelvin equation prediction, both micro- and nanochannels remain in the vapor phase (light red and light yellow, respectively), (i). When the temperature approaches the Kelvin equation prediction, capillary condensation occurs, with the condensate growing into the 8-nm nanochannels (the dark red phase, Lnano denoting the liquid, replacing the light red phase, Vnano denoting the vapor, while microchannels remain in the vapor phase (light yellow, Vbulk), (ii). When temperature reaches the bulk prediction, condensation occurs and the condensate grows in both the nanochannels and microchannels (dark red and dark yellow, Lnano and Lbulk, respectively), (iii). The scale bar corresponds to a distance of 100 µm and applies to all microscope images. As shown in Figure 1a, parallel dead-end nanochannels (500 µm × 4 µm × 8 nm) were etched (Figure 1b), and flanked by two deep microchannels (500 µm × 20 µm × 20 µm) to allow direct comparison of condensation behavior between sub-10 nm confinement and bulk under the same thermodynamic conditions. All channels connect to the same vapor reservoir and were sealed above via a glass layer, with a 200-nm thick silicon nitride base layer to enhance optical contrast between liquid and vapor phases (see Supporting Information Section 1). During all experiments, the pressure was controlled by a syringe pump and monitored using a pressure transducer. Temperature was controlled using a water bath via a copper chiller fixed at the bottom of the nanofluidic chip and monitored using thermocouples inserted within the device. Before the experiment, the devices were vacuumed for 6 hrs (see Supporting Information Section 2). We measured the highest condensation temperature for different pressures, in both the bulk (i.e., microchannels) and 8-nm nanochannels. In each test, propane was first set to the desired pressure, and then pumped into the nanochannel after the target temperature was established on


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the chip. For each temperature, the system was monitored for up to 1 hr to determine whether condensation initiates, and was then was fully vacuumed for 30 min between measurements (see details in Supporting Information Section 2). Results are shown in Figure 1c, with error bars representing both the experimental uncertainty and the resolution between runs for a given pressure (a zoom-in of the T-P data is provided in Supporting Information Section 3). The condensation initiation temperatures in the 8-nm channels are plotted with those predicted by the Kelvin equation: − −

ln

=

(1)

where is the equilibrium pressure for capillary condensation with a curved meniscus (i.e.,

the Kelvin pressure), is the saturation pressure in bulk, is the universal gas constant, is

temperature of the vapor phase, is the liquid-vapor interface tension and is the main radius of curvature of the liquid-vapor interface. We also assumed that propane fully wets the nanochannel surfaces during condensation42.

We found that within a wide pressure and temperature range (~0.6-2.3 MPa, 286.15-339.15 K), predictions from the Kelvin equation based on bulk fluid properties matched the experimental initiation of condensation results well, where the measured temperature shift between nanoscale and bulk condensation (gap between red and blue points, Figure 1c, ~1-3 K) was at most 8 % different from that predicted by classical theory (see Supporting Information Section 4). It is important to note that the disjoining pressure might influence the equilibrium contact angle,44 and further affect the Kelvin pressure. However, we estimated the disjoining pressure in our system and found to be less than 0.01 MPa. The capillary pressure can thus change up to 0.4% and is negligible in the context of this experiment (see Supporting Information Section 5).


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This result directly supports the applicability of the Kelvin equation under extreme nanoconfinement, which is an important indication of the validity of classical thermodynamics down to the sub-10 nm scale – a matter of debate in the field. For example, experiments using an interferometer with an ~8-nm gap suggest the applicability of the Kelvin equation for modeling the capillary condensation of cyclohexane.20, 45 In addition, recent experimental results for both water and hydrocarbons adsorption in porous media support the Kelvin equation at this scale.19 In contrast, another adsorption study in porous material46 indicates that the Kelvin equation cannot predict capillary condensation within the mesopore size range because of the instability of the adsorbed liquid film. In addition, the assumptions of an ideal gas phase and an incompressible liquid phase inherent to the Kelvin equation have been questioned, and more complicated models based on equations-of-state have been introduced to explain capillary condensation of both non-polar and polar molecules in sub-10 nm nanoporous media.21-22 In contrast to these works, our method provides direct visual distinction between fluid phases within a well-defined geometry and strong evidence of the applicability of the Kelvin equation on non-polar molecules down to 8-nm.


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a

d

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282.15 K 282.55 K 282.95 K 283.35 K 283.75 K 284.15 K

200 100

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Model Prediction Experimental Results (282.15 K)

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2 3 Time (s)

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0 400 Length (µ m)

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Contact Angle of Condensation Interface,

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4

0 µm 1 µm 2 µm 3 µm 4 µm

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∞

60 45 30 15 0 281.5

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Figure 2. Measurement of condensate growth as a function of superheat at isobaric conditions. (a) Total condensate length versus time for different temperatures, at a pressure of 0.61 MPa. Each point represents the average of a total of 33 measurements (3 runs with 11 nanochannels). For clarity, representative error bars are shown. (b) Images depicting condensate growth over time within a group of 5 nanochannels at 282.15 K. Images were stretched horizontally by a factor of 2.5 and contrast-enhanced in black and white for clarity. Red lines separate each frame (see Supporting Information Movie). (c) Schematic of the condensate growth model. The enlarged image of the interface was stretched vertically by a factor of 4 with respect to the


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original image to highlight the presence of an interfacial film. Liquid (black), film (gray) and vapor (light gray) are distinguished. (d and e) Model predictions compared to experimental results at 282.15 K and 284.15 K, respectively. (f) The change of contact angle at the condensation interface for different temperatures, as predicted using the model. The ability to differentiate phases within the sub-10 nm channels uniquely enables the observation of condensation dynamics. Condensate propagation was studied under isobaric conditions (0.61 MPa), with temperature varying between 282.15 K and 284.15 K at 0.4 K intervals. Condensation initiated at the inlet of the nanochannel and grew into the nanochannel with the interface pinned at the inlet. The total condensate length changing over time was measured, and results for different conditions are shown in Figure 2a. Figure 2b shows the typical filling behavior for a group of 5 nanochannels at 282.15 K. The initiation of condensation within the 8-nm nanochannels is caused by the growth of two adsorption layers on opposite channel walls, until they eventually meet and coalesce (Figure 3); when the pressure is above the Kelvin pressure, vapor molecules enter the nanochannel in a locally-supersaturated condition, and are adsorbed quickly near the inlet to form the liquid phase. This phenomenon is in marked contrast to condensation in channels only ~10 times larger where the condensation has been observed to initiate at the dead end.41 A key difference in the initiation of condensation between sub-10 nm and 100 nm (and larger) channels is due to the role of vapor transport resistance, which scales inversely with the square of the channel dimension.47 Vapor adsorption in larger channels (i.e., sub-100 nm) is thus less limited by the molecular transport and the adsorption rate becomes similar along the entire channel, with the dead end providing the internal corner structure preferential for adsorbed layers to collect. It is worth noting that previous simulations indicate that condensation at the sub-10 nm scale may also initiate from the


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dead end when the channel length is close to the channel depth.23 The result observed here is thus limited to the channel geometry where the length is orders of magnitude larger than the depth dimension. In addition to clearly identifying the vapor-liquid interface location, the imaging method used here allowed for sub-8 nm resolution at the interface. Specifically, a sharp high-contrast transition at the leading edge of the liquid film to the vapor phase was observed (Figure 2b and c). This sharp onset indicates a non-zero, finite advancing contact angle during the condensate growth, with the radius of curvature of the interface on the order of ~1 nm (the inferred filling interface shape is illustrated in Figure 2c). Similar observations have been made in other systems featuring long, highly confined geometries, most notably in water condensation in carbon nanotubes with diameters of

~200 nm.48 This stepwise transition of the light intensity at the

interface lies in contrast to the more gradual signal decay expected for a near-zero film contact angle assumed in previous research, notably for capillary filling tests in nanochannels.49-50 As is shown in Figure 2c, once the initial condensate forms at the inlet, there are two effects that combine to drive condensate growth in the nanochannel: (i) the accumulation of vapor molecules at the condensation interface as a result of capillary condensation, and (ii) the liquid flow as a result of the capillary pressure at the filling interface. We modeled (i) and (ii) with the HertzKnudsen equation and Poiseuille law, respectively, and linked these with the conservation of mass (details in Supporting Information Section 6). The resulting model expresses condensate length () as a function of time ():

!"#$% & ) '(

=

!

-

/0

, *+ .

− 1

23

( 4(

5

(2)


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where 0 , the main radius of curvature of the condensation interface, can be expressed as: 7

7:

= 89 −

'

+

2'3

8 < =&2>?( 4

(3)

where ℎ is the depth of the nanochannel, A is the condensation coefficient (assumed to be unity for non-polar molecules51), B is the liquid phase density, C is the molar mass of the fluid, is

the temperature for the system, 0 is the vapor pressure at the condensation liquid-vapor

interface, D is the viscosity of the liquid phase, and E is the thickness of the liquid film in front of

the filling interface (Figure 2b and c). The film thickness was measured through imaging and assumed to be uniform (see details in Supporting Information Section 6). Solving this system of equations (eq 2 and 3) numerically for the highest and lowest temperature cases provides the model predictions in Figure 2d and e (results for other conditions are shown in Supporting Information Section 6). In all cases, the model predicts the total condensate growth well. For example, the predicted time for full condensate filling of the nanochannel was within 6% of the experimental time (See Supporting Information Section 6). The change of the contact angle at the condensation interface (F, Figure 2c) is essential in condensate propagation kinetics, as it affects both capillary condensation and capillary filling and can be determined directly from the main radius of curvature of the condensation interface (0 ) (Supporting Information Section 6). Within the first ~20 µm of condensate length, the contact angle at the condensation interface (F) increases rapidly from zero to ~97 % of the equilibrium value (F VL. An initial liquid bridge forms and a nanobubble (with the main radius of curvature of a few nanometer) is trapped, (ii). Secondary liquid bridge forms as a result of adsorption at a pressure above the Kelvin pressure, (iii). Nanobubble collapses as a result of liquid bridging at multiple locations within the nanochannel, (iv). For low subcooling conditions, liquid bridging effects were observed in addition to continuous condensate growth (Figure 3a).

Liquid bridging during condensation has been previously

reported at the ~100 nm scale, where the liquid bridge formed at relatively high subcooling conditions as a result of capillary pressure-driven flow.41 However, within an 8-nm deep channel, multi-liquid-bridging was observed at low subcooling. This result cannot be explained through similar condensate growth theory developed for ~100 nm confinement or larger systems.41 Figure 3b shows a series of schematics illustrating the mechanisms behind the liquid bridging phenomenon was observed here. At any given condition above the Kelvin pressure, two liquid formation mechanisms act within the nanochannel: (i) the propagation of the liquid column as a result of both capillary condensation and capillary filling (VL, shown in Figure 3b (i)), and (ii) the molecular adsorption of vapor onto the solid channel surfaces (Va, shown in Figure 3b (i)). When subcooling is high (e.g., 2.3 K at 282.15 K/0.61 MPa), continuous condensate growth is observed because VL is larger than Va (Figure 2b). When subcooling is low (e.g., 0.3 K at 284.15 K/0.61 MPa), VL is reduced significantly (here by a factor of ~10 based on both experimental observations (Figure 2a) and model predictions), while Va will remain largely unchanged since it


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is only proportional to the saturation ratio, here from 1.032 to 1.008.52 In addition, VL decreases as the condensate length increases (Figure 2a). Also, surface defect may exist from the nanochannel fabrication process, and adsorption onto such defects may further increase the sensitivity of Va to subcooling (similar to the sensitivity observed during capillary evaporation in larger nanochannel).53 As a result, liquid bridging is most likely to occur at lower subcooling conditions for longer liquid columns, as observed here (Figure 3a). Once the initial liquid bridge forms (Figure 3b (ii)), the vapor pressure in the resulting nanobubble will be above the Kelvin pressure due to the pinned interface,54 resulting in internal adsorption and condensation. Fast adsorption and condensation within the nanobubble can lead to secondary liquid bridging (Figure 3b (iii)), which continues to repeat until the nanobubble collapses (Figure 3b (iv)). Such a multiliquid-bridging effect is also expected from previous unstable liquid film theories, where the sudden coalescence of two wetter surfaces can happen when the channel depth is below a certain threshold (~10 nm).55 Our experimental results shed new light on liquid bridging phenomena at the sub-10 nm scale and provide direct support for the predictions of previous simulations.23, 56-57 It is also worth noting that, for theoretical analysis, sub-100 nm and larger fluidic systems are typically assumed to act as continuous systems.39, 41 However, the validity of such an assumption in sub-10 nm systems is not immediately clear. Here, the theoretical explanations for both the initiation of condensation and condensation dynamics inside 8-nm high channels are based entirely on classical thermodynamics and continuum fluid mechanics. Since the experimental results agree well with classical and continuum theories, the assumption of treating a non-polar fluid system with only 10-20 molecular layers as a continuous system appears valid from a condensation perspective. Furthermore, the condensate initiation, the film formation, and the liquid bridging phenomena were rendered observable in real time by our nanofluidic system and


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indicate fundamental deviations of the condensation phenomena at the sub-10 nm scale compared to the sub-100 nm scale, even though both systems may be treated as continuous. In summary, we directly measured condensation initiation and dynamics within 8-nm deep silicon nanochannels. The initiation of condensation deviates from the bulk condition and was found to agree closely with predictions from the Kelvin equation. The condensation dynamics at the sub-10 nm scale are distinct from those of similar systems that are just 10 times larger (~100 nm). Specifically, adsorption dominates the condensation initiation in sub-10 nm channels, resulting in liquid formation starting from the channel's entrance. A model combining capillary condensation and capillary filling has been developed and was found to give good predictions of the condensation propagation observed experimentally. Additional bridging dynamics were observed at low subcooling conditions – also in contrast to sub-100 nm and larger systems. Collectively, these results characterize condensation at the sub-10 nm scale. With direct, realtime imaging of condensation phenomena within a well-controlled environment, we also provide strong support of the applicability of classical theory in these systems down to the 8-nm scale.


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ASSOCIATED CONTENT Supporting Information Nanofluidic chip fabrication procedure/Experimental setup and procedures for measuring the initiation of condensation and condensation propagation/Zoom-in of the testing saturation conditions for condensation at 8 nm and bulk scale/Deviation of condensation temperature shift of 8-nm confinement from bulk between theoretical predictions and experimental results/Estimation on disjoining pressure and its effect on Kelvin pressure/Condensate growth model and model predictions/Condensation propagation and liquid bridging video. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT The authors gratefully acknowledge support from Schlumberger Canada Ltd., Alberta InnovatesEnergy and Environment Solutions, and from the Natural Sciences and Engineering Council of Canada through a Collaborative Research and Development Grant, as well as on-going research funding through the Discovery Grants program and the Canada Research Chairs program. In addition, infrastructure funding provided by the Canada Foundation for Innovation and Ontario Research Fund is gratefully acknowledged. REFERENCES (1). Tröstl, J.; Chuang, W. K.; Gordon, H.; Heinritzi, M.; Yan, C.; Molteni, U.; Ahlm, L.; Frege, C.; Bianchi, F.; Wagner, R. The Role of Low-volatility Organic Compounds in Initial Particle Growth in the Atmosphere. Nature 2016, 533, 527-531. (2). Ehn, M.; Thornton, J. A.; Kleist, E.; Sipilä, M.; Junninen, H.; Pullinen, I.; Springer, M.; Rubach, F.; Tillmann, R.; Lee, B. A Large Source of Low-volatility Secondary Organic Aerosol. Nature 2014, 506, 476-479.


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