Capillary Condensation in 8 nm Deep Channels

Zhong, Junjie; Riordon, Jason; Zandavi, Seyed Hadi; Xu, Yi; Persad, Aaron H.; Mostowfi, Farshid

doi:10.1021/acs.jpclett.7b03003

Cited by 67 publications

(45 citation statements)

References 57 publications

(102 reference statements)

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“…It routinely occurs in granular and porous media, can strongly alter such properties as adhesion, lubrication, friction and corrosion, and is important in many processes employed by microelectronics, pharmaceutical, food and other industries [1][2][3][4] . The century-old Kelvin equation 5 is commonly used to describe condensation phenomena and shown to hold well for liquid menisci with diameters as small as several nm [1][2][3][4][6][7][8][9][10][11][12][13][14] . For even smaller capillaries that are involved in condensation under ambient humidity and so of particular practical interest, the Kelvin equation is expected to break down because the required confinement becomes comparable to the size of water molecules .…”

mentioning

confidence: 99%

Capillary condensation under atomic-scale confinement

Yang

Sun

Fumagalli

et al. 2020

Nature

210

146

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Capillary condensation of water is ubiquitous in nature and technology. It routinely occurs in granular and porous media, can strongly alter such properties as adhesion, lubrication, friction and corrosion, and is important in many processes employed by microelectronics, pharmaceutical, food and other industries [1][2][3][4] . The century-old Kelvin equation 5 is commonly used to describe condensation phenomena and shown to hold well for liquid menisci with diameters as small as several nm [1][2][3][4][6][7][8][9][10][11][12][13][14] . For even smaller capillaries that are involved in condensation under ambient humidity and so of particular practical interest, the Kelvin equation is expected to break down because the required confinement becomes comparable to the size of water molecules . Here we take advantage of van der Waals assembly of two-dimensional crystals to create atomic-scale capillaries and study condensation inside. Our smallest capillaries are less than 4 Å in height and can accommodate just a monolayer of water. Surprisingly, even at this scale, the macroscopic Kelvin equation using the characteristics of bulk water is found to describe accurately the condensation transition in strongly hydrophilic (mica) capillaries and remains qualitatively valid for weakly hydrophilic (graphite) ones. We show that this agreement is somewhat fortuitous and can be attributed to elastic deformation of capillary walls [23][24][25] , which suppresses giant oscillatory behavior expected due to commensurability between atomic-scale confinement and water molecules 20,21 . Our work provides a much-needed basis for understanding of capillary effects at the smallest possible scale important in many realistic situations.The Kelvin equation predicts that capillaries become spontaneously filled with water at the relative humidity RHK = exp (-2σ/kBTdρN)where σ ≈ 73 mJ m -2 is the surface tension of water at room temperature T, ρN ≈ 3.3×10 28 m -3 is the number density of water, kB is the Boltzmann constant, and d is the diameter of the meniscus curvature. For a two-dimensional (2D) confinement created by parallel walls separated by a distance h, d = h/cos(θ) where θ is the contact angle of water on the walls' material. For capillary condensation to occur at relative humidity (RH) considerably below 100%, equation 1 dictates that d must be comparable to 2σ/kBTρN ≈ 1.1 nm. For example, under typical ambient RH of 40-50%, water is expected to condense in slits with h < 1.5 nm and cylindrical pores with diameters < 3 nm, if θ is close to zero. Even stronger confinement is required for capillaries involving less hydrophilic materials. So far, a broad consensus has been reached that the Kelvin equation remains accurate for menisci with d ≥ 8 nm [1][2][3][4][6][7][8][9][10][11] and can also describe condensation phenomena in hydrophilic pores as small as 4 nm in diameter 12-14 . To achieve agreement with the experiments at this scale, the Kelvin equation is usually modified to account for so-called wetting films that are adsorbed on...

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mentioning

confidence: 99%

Capillary condensation under atomic-scale confinement

Yang

Sun

Fumagalli

et al. 2020

Nature

210

146

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“…In the framework of TSC, capillary condensation is governed by the chemical potential ( 23 ) in the interaction region, which, using ( 22 ) and ( 27 ), may be expressed in terms of the surface tension as

where

is the density in the interaction phase, defined, like ( 22 ) and ( 23 ), as

is the density of the system, and

is the density of the surrounding bath. If we consider the system to be a vapor bubble with saturated vapor pressure

inside a liquid phase with vapor pressure p , then

and

, which inserted in ( 28 ) and ( 29 ) results in the Kelvin equation

This result is valid for bubbles and, as shown by recent nanoscale experiments [ 26 ], even in capillary tubes that are far too narrow for bubbles to form.…”

Section: The Interaction Regionmentioning

confidence: 87%

“…Just like expression ( 27 ) is valid in the strong coupling regime described by TSC, recent experiments in capillary tubes with radii as small as 8 nm [ 26 ] have shown the nanoscale validity of Kelvin’s classical relation for vapor pressure and capillary condensation. In the framework of TSC, capillary condensation is governed by the chemical potential ( 23 ) in the interaction region, which, using ( 22 ) and ( 27 ), may be expressed in terms of the surface tension as

where

is the density in the interaction phase, defined, like ( 22 ) and ( 23 ), as

is the density of the system, and

is the density of the surrounding bath.…”

Section: The Interaction Regionmentioning

confidence: 99%

Strong Coupling and Nonextensive Thermodynamics

Miguel

Rubı́

2020

Entropy

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We propose a Hamiltonian-based approach to the nonextensive thermodynamics of small systems, where small is a relative term comparing the size of the system to the size of the effective interaction region around it. We show that the effective Hamiltonian approach gives easy accessibility to the thermodynamic properties of systems strongly coupled to their surroundings. The theory does not rely on the classical concept of dividing surface to characterize the system’s interaction with the environment. Instead, it defines an effective interaction region over which a system exchanges extensive quantities with its surroundings, easily producing laws recently shown to be valid at the nanoscale.

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“…2017; Zhong et al . 2018; Al-Kindi & Babadagli 2019 a ) than those in bulk media. Thome (2004) studied the evaporation behaviour and two-phase flow in microchannels and provided experiments and theory related to the evaporation in confined channels.…”

Section: Introductionmentioning

confidence: 98%

“…This was first formulated by Lord Kelvin (Thomson 1872) indicating that the saturation pressure and temperature are inversely proportional to the capillary size. This yields lower temperatures for boiling (Al-Kindi & Babadagli 2018, 2019b or lower pressures for condensation (Tsukahara et al 2012;Bao et al 2017;Zhong et al 2018; Al-Kindi & Babadagli 2019a) than those in bulk media. Thome (2004) studied the evaporation behaviour and two-phase flow in microchannels and provided experiments and theory related to the evaporation in confined channels.…”

Section: Introductionmentioning

confidence: 99%