evidence and as a parameter to reflect the efficiency of thin film flow. ... Keywords: liquid bridge; water thin film; atomic force microscopy; capillary force; domed.
Apr 29, 2019 - There was a circle centered at the feature with a radius of collection area (can be as large as â¼23.6 Î¼m), inside which all of the liquid seems to ...
for films thicker than 800-1100 A., which agree very closely with Frankel's law relating film thickness to the velocity of pullout (eq. 1). Since Frankel's law is ...
assumption that the viscosity is constant up to the monolayer, this finding is not com- ... depth does any effect extend are old problems. In ... which applies Reynold's formula for solid pistons to ... e1~ewhere.l~ The results presented here deal wi
Liquid Film in Taylor Flow through a Capillary. Said Irandoust and Bengt Andersson*. Department of Chemical Reaction Engineering, Chalmers University of ...
Partial Hydrogenation of Soybean Oil in a Piston Oscillating Monolith Reactor. Yogesh G. Waghmare , Alan G. Bussard , Robert V. Forest , F. Carl Knopf and ...
Nov 1, 1989 - Yogesh G. Waghmare , Alan G. Bussard , Robert V. Forest , F. Carl Knopf ... Joseph W. Bartsch, Hy D. Tran, Anna Waller, Andrea A. Mammoli, ...
High Performance Liquid Chromatography in Environmental Analysis: Present and Future Applications. Badar I. Afghan , Aaron W. Wolkoff. Journal of Liquid ...
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Department of Chemical and Biomolecular Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
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Direct evidence of a radius of collection area for thin film flow in liquid bridge formation by repeated contacts using AFM Tianmao Lai, and Ping Li Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00827 • Publication Date (Web): 29 Apr 2019 Downloaded from http://pubs.acs.org on May 7, 2019
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Direct evidence of a radius of collection area for thin film flow in liquid bridge formation by repeated contacts using AFM Tianmao Lai* and Ping Li School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China *Corresponding author: Name: Tianmao Lai Email: [email protected] Phone: +86-15902018981 The other author： Name: Ping Li Email: [email protected] Phone: +86-15013235125 Abstract A liquid bridge in a nanoscale gap is of considerable significance in lots of scientific and industrial fields. However, the formation mechanism is not well understood, leading to many contradictory experimental results. In this work, contact experiments were carried out between tipless cantilevers coated with potassium hydroxide and a silica surface on an atomic force microscope (AFM) under different relative humidities (RH). Results show that capillary condensation is dominant and thin film flow is difficult or even impossible at low RHs (31-37%). However, at high RHs (62-82%), thin film flow is dominant, and materials were collected with a domed 3D feature in the contact zone. There was a circle centered at the feature with a radius of collection area (can be as large as ~23.6 μm), inside which all the liquid seems to flow into the water bridge. The radius of collection area is used as direct evidence and as a parameter to reflect the efficiency of thin film flow. This fabrication technique of a domed feature may be viewed as a promising additive manufacturing in the microscale, and this work may also shed some light on the study of the controversial RH dependence of capillary force and other related researches.
Keywords: liquid bridge; water thin film; atomic force microscopy; capillary force; domed feature; relative humidity
1. Introduction In atmospheric air, a liquid bridge usually forms in a nanoscale gap. In the past decades, a great deal of attention has paid to behaviors of liquid bridge due to its significance in many scientific and industrial fields: microassembly 1, biochemistry 2, nanotribology 3, dip-pen nanolithography (DPN) 4, and micro-electromechanical systems (MEMS) 5, just to name a few. In DPN, a water bridge between an atomic force microscope (AFM) tip and a substrate is usually used as a transfer medium to transport materials from the tip to the substrate, either due to diffusion caused by differences in concentrations or liquid dynamic or both 6. Reliability of MEMS is greatly influenced by capillary forces due to liquid bridges. The capillary force is a major factor in the failures of MEMS (stiction) 7-8, since it cannot be ignored even at low relative humidity (RH) for hydrophilic surfaces 9. Therefore, the study of liquid bridge behaviors is of considerable significance, and should be carried out both theoretically and experimentally. The growth mechanisms of a water bridge are dominant in the theoretical investigation. Usually, there are two growth mechanisms in the formation of a water bridge: (1) capillary condensation of water vapor from the atmosphere, (2) thin film flow toward a growing water bridge 10-12. Capillary condensation is usually assumed to be a thermally activated process, leading to a logarithmical increase of capillary force with contact time 13-14. Moreover, the characteristic equilibrium time is on the order of several milliseconds 10, 12, 15. Some researchers reported that just capillary condensation can be used to explain their experiments, and the well-known Kelvin equation was used to estimate water bridge sizes in equilibrium 16-18. However, Weeks et al. 19 proposed that the water bridge size directly imaged by an environmental scanning electron microscopy (ESEM) is orders of magnitude larger than that predicted by the Kelvin equation, which may indicate that thin film flow cannot be ignored. Furthermore, some scholars argued that both mechanisms should be considered to explain their experiments 10-12. However, the mechanism of thin film flow is not well studied and remains open to debate. Several questions need answering, including: (1) How do surface physical chemical properties (hydrophilcity, organic coating, etc) impact the flow rate? (2) Can an ice-like thin film flow (more exactly migrate) towards a growing water bridge? (3) Can the liquid very far from a water bridge flow towards it? Or is there a circle (centered at a water bridge) with a radius of collection area, inside which all the liquid can flow into the water bridge? Therefore, the growth mechanism of thin film flow demands clarification. Numerous factors can influence capillary forces: contact geometry, surface heterogeneity, local roughness, tip wear, hydrophilicity, adsorbed water, ionic diffusion, temperature, and RH, etc 20. Furthermore, experimental parameters, like piezo velocity, can influence capillary forces measured on an atomic force microscope (AFM) 21. The unclear mechanism of thin film flow may be the reason why the effects of some factors on capillary force are ambiguous. As an example, RH is one of the factors which are widely studied with an AFM but not well understood. RH dependence of capillary force is still ambiguous with different trends: monotonic increase, monotonic decrease, step-wise increase, maximum, and independence 20. Even for the commonly used contact pair between a silicon AFM tip and silicon wafer, previously published results contradict each other in the literature. In some studies, a monotonic increase was observed 22-23. In other studies, however, the RH dependence
exhibits a maximum at different RHs: ~30% RH 24-25, and ~60% RH 26, and ~70% RH 17, 27-28. Therefore, the dependence of capillary force on RH is inconclusive, and may be caused by the unclear mechanism of thin film flow, which will be discussed later. The mechanisms are also related to the contact time dependence of capillary force, which is still not fully understood. Intuitively, if thin film flow does not occur or reaches saturation in a short time, the capillary force is independent on contact time. And, this was supported by the experiments between two silica surfaces 22, 29. For time-dependent capillary forces, the saturation time is in the wide range: ~50 ms at 50% RH 12, ~1 s at 15% RH 18, ~4 s at 30% and 65% RH 10, ~5 s at 42% RH 11, ~60 s at 31% RH 29, ~100 s at 40-60% RH 30, and ~120s at 15% 31. Moreover, the equilibrium time can be as large as ~600 s at 98% RH studied by using an ESEM 32. To understand these behaviors, the flow rate of a thin film in different systems should be studied further. The aim of this work is to investigate growth mechanisms of a water bridge at different RHs. For this purpose, contact experiments with thousands of times were carried out between some tipless cantilevers and a silicon wafer on an AFM. These cantilevers were coated with potassium hydroxide (KOH). Imaging and ex situ chemical characterization of the cantilever surface were carried out with SEM, Auger electron spectroscopy (AES), and energy-dispersive X-ray spectroscopy (EDS). These were used to determine whether materials on the cantilever surface are collected in the contact zone or not. The experimental results at low and high RHs were compared with each other. Outcomes show that materials were collected in the contact zone by thin film flow with a domed three-dimensional (3D) feature at high RHs. And, a radius of collection area was observed as a direct evidence of thin film flow, and may be also used as a parameter to reflect the efficiency of thin film flow. The formation of a domed 3D feature was discussed, which may be viewed as a promising additive manufacturing in the microscale. Furthermore, based on the results, the controversial RH dependence of capillary force was discussed, and this work may also shed some light on this study and other related researches.
2. Materials and Methods 2.1. Preparation and characterization of sample and cantilever The sample used was an N-type silicon wafer of (100) orientation with a native oxide layer. Figure 1 shows a topography image of the sample with a scan size of 2 μm × 2 μm. This image was obtained with a sharp tip (Tap300Al-G, Budget Sensors, Innovative Solutions Bulgaria Limited, Sofia, Bulgaria) by using tapping mode of an AFM (MFP-3D Classic, Asylum Research, Santa Barbara, CA, USA). From this image, the average roughness and root-mean-square roughness were determined as 0.390 nm and 0.518 nm, respectively. The water contact angle of the sample surface was 52.4±2.8°, as determined by using a home-made contact angle goniometer. Before the experiments, the sample was ultrasonically cleaned in an alcohol solution for 15 minutes, and then ultrasonically cleaned in deionized water for 15 minutes. AFM probes (Probe 1#-4#) for contact experiments were tipless silicon cantilevers (TL-CONT, Nanosensors, Neuchatel, Switzerland). The normal spring constants of these cantilevers were varied between 165.23 and 213.75 pN/nm, which were determined with thermal methods by the MFP-3D AFM 33. The images of the cantilevers were obtained by an
ESEM (Quanta 200 FEG, FEI Company, Eindhoven, Netherlands) in high-vacuum mode using the Everhart-Thornley detector (ETD) at ~1.5 mPa and 15 kV high voltage with a working distance of ~10 mm. SEM and AFM images of a typical cantilever before the experiments are shown in Figure 2. From Figures 2(a) and (b), the cantilever has no tip, and three rounded edges intersect in one point (contact point) at its free end. The area around the contact point is the contact zone. Figure 2(c) shows a 3D AFM image of the contact zone, which was obtained by an inverse imaging method using a silicon calibration grating (TGT1, NT-MDT, Moscow, Zelenograd, Russia) 34. More details of this grating are shown in Figures S1 and S2 of Supporting Information. Figure 2(d) shows the cross-sectional profile created by the straight line in Figure 2 (c).
Figure 1. Topographic AFM image of the sample with a scan size of 2 μm × 2 μm.
Figure 2. The characterization of a cantilever before the experiments. (a) SEM image of the entire view of a typical TL-CONT cantilever. (b) SEM image of the cantilever free end. (c) 3D AFM image of the contact zone before the experiments with a straight line to create a profile, which was obtained by inverse imaging method with a silicon calibration grating (TGT1). The scan size is 2 μm × 2 μm. (d) The cross-sectional profile created by the line in (c). The preparation method before the contact experiments was shown in Figure S3 of Supporting Information. As-received cantilevers were firstly rinsed with deionized water for 30 minutes to remove soluble pollutants. Then, they were treated with oxygen plasma for 3 minutes at 30 W and 2.5 mbar pressure to remove organic pollutants in a plasma cleaner
(Femto, Diener Electronic GmbH, Nagold, Germany). After that, they were rinsed in KOH solution with a concentration of 5 or 10 mmol/L. The cantilever surface became very hydrophilic after the plasma treatment, and KOH solution was adsorbed on the surface to some degree. After drying, the cantilevers were ready to be used in the experiments. The used KOH concentration was 5 mmol/L for Probes 1# and 3#, and 10 mmol/L for Probes 2# and 4#. 2.2. Chemical characterization and adhesion force measurements Firstly, images of as-received probes were obtained by the ESEM mentioned above. Then, the probes were treated by the method mentioned above. Since the probes were rinsed in KOH solution, potassium (K) was on the cantilever surfaces. Therefore, K distribution on the cantilever surface was analyzed by AES (PHI 700, ULVAC-PHI, Chigasaki, Japan) with a detection sensitivity of ~0.1 atom %. Then, thousands of force curves were collected by these cantilevers at different RHs. After that, the contact zone of each cantilever was investigated by the ESEM and another AES (PHI 710, ULVAC-PHI, Chigasaki, Japan). The adhesion forces were measured by using another AFM (Being Nano-Instruments BY-3000, Guangzhou, China) at 26±1 °C. The AFM head and base were placed inside a box to adjust RH (Figure S4 of Supporting Information). During the experiments, force curves were collected by monitoring the cantilever deflection as it approaches to and retracts from the sample, and adhesion forces were extracted from these curves (Figure S5 of Supporting Information). The measurements were performed on a scanning area or at a location on the sample surface. All adhesion forces measured are shown in Figures S6-S14 of Supporting Information. During the experiments, the cantilever was tilted with the sample by ~17° to avoid cantilever crash. There are four clear benefits by using a tipless cantilever: (1) A wedge-like gap between a cantilever and a substrate forms after contacting to study thin film flow; (2) The contact point is blunt enough to prevent severe wear (see Figure 2(d)); (3) material transport on the cantilever surface can be easily detected by SEM and AES; (4) Without a tip, the movement of the contact point with a normal load in the direction parallel to the cantilever is very small 31.
3. Results and Discussion Both Probes 1# and 3# were rinsed in KOH solution with a concentration of 5 mmol/L. The adhesion force measurements were carried out for Probe 1# at 34±1% RH and Probe 3# at 73±1% RH. Figure 3 shows adhesion forces versus sequential measurement number of times measured at the same location for both probes. In Figure 3(a), the adhesion force drops a little from ~112 nN to ~104 nN and to ~101 nN. From the lowest value, the adhesion force increases gradually, and then drops to a lower value, then increases again, and so on. Impressively, between measurement number ~1000 and ~1600, the adhesion force increases gradually with a constant rate to the maximum value of ~113 nN. In Figure 3(b), the adhesion force of Probe 3# decreases at first and then increases gradually with measurement number of times. There were also 2048 force curves collected for Figure 3(b). However, only 393 data points are shown here, since the data after 393 are not available due to out of measurement range of this probe. The normal spring constant of Probe 3# is only 0.165 N/m. Therefore, forces larger than ~470 nN cannot be measured by this probe on the AFM. Most probably, after 393, the adhesion force increases and then reaches saturation, and the maximum
adhesion force is much larger than ~470 nN. Other data obtained by Probes 1#-4# can be found in Figures S6-S14 of Supporting Information. Based on Figures S6-S14 of Supporting Information, the behaviors of adhesion force can be summarized as follows: (1) The adhesion forces measured at high RHs are much larger than those at low RHs (see Figure S14 of Supporting Information). It should be noted that, there are 4,152 data points (total number = 7,428, and 3,276 shown in Figure S14(c)) larger than ~470 nN by Probe 3# at 68~74% RHs, which are out of measurement range of this probe. This value (~470 nN) is about ten times as large as the mean adhesion force (48.9±15.7 nN) obtained by Probe 2# at 31~35% RHs. (2) The increasing magnitude and rate of adhesion force at one location at high RHs are much larger than those at low RHs. As an example shown in Figure 3, the adhesion force by Probe 1# at 34±1% RH increases by ~15 nN with ~600 contacts, and that by Probe 3# at 73±1% RH increases by ~410 nN with ~360 contacts. (3) At both low and high RHs, the adhesion force measured at one location can increase, decrease and remain unchanged, and can suddenly change to a lower or higher value. However, the adhesion force measured at one location at low RHs can increase gradually, then drop to a lower value, and then increase again. This behavior was not observed at high RHs.
Figure 3. Adhesion forces versus sequential measurement number of times measured at the same location on the sample by using (a) Probe 1# at 34±1% RH; (b) Probe 3# at 73±1% RH. The locations for (a) and (b) were different and randomly selected. There were also 2048 force curves collected for (b). However, only 393 data points are shown here, since the data
after 393 are not available due to out of measurement range of this probe. Figure 4 shows SEM images and ex situ AES chemical characterization of Probe 1# before and after contact experiments. The contact zone was clean for the as-received cantilever surface, as shown in Figure 4(a). After the treatment mentioned above, a SEM image of the free end was obtained by PHI 700 AES, as well as the corresponding elemental map of K. An elemental map of K is spatial distribution (peak intensity) of K as pixel intensity. The greater the peak intensity is, the brighter the pixel is. Figure 4(b) shows overlay of the K map as colors on the SEM image, from which it can be seen that K was scattered in bits and pieces on the cantilever surface. After thousands of contacts on the sample at low RHs (32~37%), SEM images were obtained once again, as shown in Figures 4(c, d). After the adhesion force measurements, materials were collected with a stripe-like feature on one side of the contact zone. This feature may be formed by the collection of materials on that side. At last, spatial distribution of K was analyzed again by PHI 710 AES, as shown in Figures 4(e-g). It can be seen that K was still scattered in bits and pieces around the contact zone, indicating that some materials around the contact point cannot be collected in the contact zone. By the comparison between Figures 4(b) and Figures 4(e-g), it seems that PHI 710 AES is more effective in chemical characterization than PHI 700 AES. Figure 5 shows corresponding SEM images and ex situ AES chemical characterization of Probe 2#. It should be noted that, Probe 2# was rinsed in KOH solution with a concentration of 10 mmol/L (5 mmol/L for Probe 1#). K in Figure 5(b) was scattered on the cantilever surface with larger pieces than those in Figure 4(b). Adhesion force measurements of Probe 2# were also carried out at low RHs (31~35%). From Figures 5(c-g), materials were collected on the contact point also with stripe-like features but a very small size, and K was still scattered in bits and pieces around the contact zone after the contact experiments.
Figure 4. SEM images and ex situ AES chemical characterization of Probe 1# before and
after experiments. (a) SEM image of the cantilever free end (as-received). (b) After rinse in 5 mmol/L KOH solution, Auger map of K with a resolution of 256×256 overlaid as colors on the SEM image. After adhesion force experiments at 32~37% RHs, SEM images of the free end were obtained again with (c) enlarged top view and (d) side view, respectively. (e) SEM image of the free end after experiments obtained in AES, and (f) corresponding Auger map of elemental intensity (K) for this area with a resolution of 256×256, and (g) Auger map of K overlaid as colors on the SEM image.
Figure 5. SEM images and ex situ AES chemical characterization of Probe 2# before and after experiments. (a) SEM image of the cantilever free end (as-received). (b) After rinse in 10 mmol/L KOH solution, Auger map of K with a resolution of 256×256 overlaid as colors on the SEM image. After adhesion force experiments at 31~34% RHs, SEM images of the free end were obtained again with (c) enlarged top view and (d) side view, respectively. (e) SEM image of the free end after experiments obtained in AES, and (f) corresponding Auger map of elemental intensity (K) for this area with a resolution of 256×256, and (g) Auger map of K overlaid as colors on the SEM image. AES differential spectra of two points were collected for Probe 2#, as shown in Figure 6(a). One point (Point 1) was on the stripe-like feature, and the other (Point 2) was on a particle about 2 μm away from the contact point. Table 1 shows AES atomic concentrations of these points. The spectra just show that K, carbon (C), silicon (Si), and oxygen (O) are present on both points. However, there was chlorine (Cl) on Point 2 with a small atomic concentration (0.6 atom%), and the atomic concentration of K on Point 2 (23.0%) was much larger than that on Point 1 (5.4%). There are also some other small particles near the contact point, as shown in Figures 5(c, d). These indicate that materials cannot be collected in the contact zone effectively at low RHs, even they are very closed to the contact point.
Figure 6. Ex situ chemical characterization by AES and EDS. AES differential spectra of some points (estimated sampling depth ~2 nm) in the contact zone for (a) Probe 2#, and (b) Probe 4#. The insets of (a) and (b) are SEM images of the contact zone showing the investigated points with Points 1-5. EDS spectrums (estimated sampling depth of ~1 μm) of the materials inside the contact zone after contact experiments for (c) Probe 3#, and (b) Probe 4#. The insets of (c) and (d) show the side views of both probes. The rectangular boxes are used to mark the investigated areas. Table 1. AES atomic concentrations (atom%) of Points 1-5 on Probes 2# and 4# Probes Probe 2#
Figures 7 and 8 show corresponding SEM images and ex situ AES chemical characterization of Probes 3# and 4#, respectively. Both cantilevers were used at high RHs. It can be seen from Figures 7(c, d) and 8(c, d), materials were collected and piled up in a domed 3D feature in the contact zone after contact experiments. The created feature on Probe 3# was like a truncated circular cone with a height of ~2 μm and a volume of ~3.144 μm3. As shown in Figure 7(g), K was also scattered in bits and pieces around the contact points. However, some large particles had not been collected into the contact zone. These particles are away
from the contact point with a radius of collection area (RC) of ~14.5 μm. K pieces with a distance < RC are all with low intensity, which indicates that most of the materials around the contact point had been collected. For Probe 4#, the radius of collection area was ~23.6 μm, as shown in Figure 8(g). By the comparison between Figures 8(b) and (g), even large particles with a distance < RC had been collected in the contact zone. It should be noted that the area with a distance < RC also has K but with a very low intensity. For Probe 4#, AES differential spectra of three points in the contact zone are shown in Figure 6(b), and Table 1 shows AES atomic concentrations of these points. By comparison, there is no distinguished Si peak on Point 3, and no K on Point 4, and no Ca on Point 5. EDS spectrums of the domed features for Probe 3# and Probe 4# are shown in Figures 6(c, d), with corresponding investigated areas shown in the insets. Besides C, O, Si and K, there are Na, Mg, Al, S, Cl and Ca on the features. Some elements may be from atmospheric pollutants (such as dust) collected inside the contact zone. Specially, there is no K on the upper half of the feature on Probe 3#, which indicates that potassium ion (K+) may transfer across the surface with a fast rate and deposit in the lower half of the feature.
Figure 7. SEM images and ex situ AES chemical characterization of Probe 3# before and after experiments. (a) SEM image of the cantilever free end (as-received). (b) After rinse in 5 mmol/L KOH solution, Auger map of K with a resolution of 256×256 overlaid as colors on the SEM image. After adhesion force experiments at 68~74% RHs, SEM images of the free end were obtained again with (c) enlarged top view and (d) side view, respectively. (e) SEM image of the free end after experiments obtained in AES, and (f) corresponding Auger map of elemental intensity (K) for this area with a resolution of 256×256, and (g) Auger map of K overlaid as colors on the SEM image.
Figure 8. SEM images and ex situ AES chemical characterization of Probe 4# before and after experiments. (a) SEM image of the cantilever free end (as-received). (b) After rinse in 10 mmol/L KOH solution, Auger map of K with a resolution of 256×256 overlaid as colors on the SEM image. After adhesion force experiments at 30~82% RHs, SEM images of the free end were obtained again with (c) enlarged top view and (d) side view, respectively. (e) SEM image of the free end after experiments obtained in AES, and (f) corresponding Auger map of elemental intensity (K) for this area with a resolution of 256×256, and (g) Auger map of K overlaid as colors on the SEM image. Under ambient conditions, a liquid bridge forms inside the wedge-like gap between a cantilever and the sample. The side view of the contact scenario is show in Figure 9(b). The growth dynamics of a liquid bridge is essential to understand the phenomena concerning the liquid bridge. As mentioned above, there are two growth mechanisms: capillary condensation and thin film flow 10-12. Capillary condensation is usually viewed as two processes: capillary nucleation and subsequent growth due to water molecule diffusion until thermodynamic equilibrium 35. For a water bridge in equilibrium via capillary condensation, the Kelvin equation holds 36 p kBT ln v rK psat
where, L is the surface energy of water, rK is the Kelvin radius, is the molecular density of water in units of molecules/m3, kB is the Boltzmann constant, T is the absolute temperature, pv is the actual vapor pressure, psat is the saturated vapor pressure of water, and pv / psat is
the RH. The liquid bridge is concave with a negative Kelvin radius. From Equation (1), the
absolute value of the Kelvin radius increases with RH, and the Kelvin radius is between -0.23 nm and -4.95 nm with 10~90% RHs at T = 26 °C. In addition, the characteristic equilibrium time of capillary condensation is just several milliseconds 15, 37. On a silica surface, a thin liquid film is adsorbed via chemical or physical interactions, as shown in Figure 9(c). It was reported that the thin film is ice-like at 0-30% RHs, and one more layer forms in the range of 30-60% RHs, and liquid water layer grows above 60% RH 38. After the formation of a concave liquid bridge by capillary condensation, the thin liquid film can flow towards it. The flow is governed by Laplace pressure and disjoining pressure. Since the pressure inside a concave liquid bridge is smaller than that of a thin film, the surrounding water film flows toward a growing liquid bridge, which is driven by the Laplace pressure. However, the disjoining pressure tends to draw liquid away from the liquid bridge. Therefore, the driving pressure can be expressed as 39 1 1 A pdriving p L H 3 R1 R2 6 h
where, p is the Laplace pressure, R1 and R2 are the principal radii of curvature of the liquid bridge (note that
R21 0 for a concave liquid bridge), is the disjoining pressure,
AH is the Hamaker constant, and h is the water film thickness. In Equation (2), the disjoining pressure is assumed to be only from the van der Waals (vdW) force 40. For a liquid bridge with a small size, the Laplace pressure is much larger than the disjoining pressure, leading to a high flow rate of a thin film. With the increase of the liquid bridge size, the driving pressure decreases gradually with decreased Laplace pressure (absolute values of R1 and R2 increase) and increased disjoining pressure (film thickness decreases as the film flows into the contact zone). At last, the water bridge reaches saturation and ceases to grow with a vanished driving pressure. If the liquid film can be assumed as a Newtonian fluid, the liquid bridge volume increases with contact time, and can be estimated as 41
p h3t V (t ) Vm 1 exp 0 Vm
where, Vm is the maximum volume, p0 is a constant coefficient with a pressure dimension, and η is the dynamic viscosity of the film, t is the contact time. It can be seen from Equation (3), it will take a long time to reach equilibrium with a large viscosity, and the equilibrium time is short with a small viscosity. At low RHs (31-37%), the thin film adsorbed on a silica surface is ice-like with poor fluidity. It is very difficult or impossible for such a thin film to flow toward a liquid bridge. Therefore, insoluble materials on the surface are not collected in the contact zone. Moreover, soluble materials on the surface cannot be dissolved to migrate to the contact zone, too. Therefore, there are only a few materials collected in the contact zone by thousands of contacts, as shown in Figures 4 and 5. Furthermore, the liquid bridge size formed by capillary condensation is small due to a small Kelvin radius, leading to small adhesion force at low RHs, as mentioned above. Without the flow of liquid film, the water bridge cannot grow with repeated contacts, and then the increasing magnitude and rate of adhesion force at one
location are also small. The change of adhesion force at low RHs was attributed to the attachment and detachment of materials in the contact zone. At high RHs (68-82%), the thin film is liquid-like with good fluidity. Both insoluble and soluble materials can be collected in the contact zone with thin film flow, which is driven by the driving pressure, as schematically shown in Figure 9(a). It is assumed that, the adhesion force (Fad) consists of the vdW force (FvdW) and capillary force, and the capillary force is due to both Laplace pressure and surface tension. Then, the adhesion force can be expressed as 42 1 1 Fad FvdW R22 L 2 R2 L R1 R2
The vdW force is much smaller than the capillary force due to the liquid medium, and can be neglected. With the flow of liquid film, the liquid bridge size increases gradually, eventually leading to the increase of adhesion force. As shown in Equation (2), since the driving pressure is large with a small bridge size, the adhesion force can increase with a large rate. Furthermore, the water bridge can reach to a large size due to liquid flow, resulting in much larger adhesion forces at high RHs. To make a rough calculation, it is assumed that L = 0.072 J/m2, R1 = -0.2 μm and R2 = 0.5 μm. Then, the capillary force calculated by Equation (4) is ~400 nN, which is in the same order of magnitude as the experiment results at high RHs. It should be noted that, the driving pressure decreases with the increase in the distance from the contact point, which may handicap the transport of the materials far away from the contact zone. However, the soluble materials may also be dissolved on a thin liquid film, and then travel toward the contact zone due to a difference in concentration. This diffusion may be possible, since soluble materials near the contact zone may transport at first to the liquid bridge, leading to low concentration near the contact zone. This may be one of the reasons why the radius of collection area can be as large as ~23.6 μm, as shown in Figure 8(g). A radius of collection area not only is used as a direct evidence of thin film flow, but also may be used as a parameter to reflect the efficiency of thin film flow. However, more experiments are needed to clarify whether the radius of collection area will increase with RH at high RHs, or this parameter will be influenced by other factors.
Figure 9. (a) An enlarged view showing the transport of soluble and insoluble materials due to thin film flow. (b) Side view of the contact between a cantilever and the sample. A growing liquid bridge is inside the wedge-like gap due to thin film flow. The angles are ~13° and ~17° on the left and right sides, respectively. Principal radii of the water bridge R1 and R2, film thickness h, and flow directions of liquid film are also shown. Two enlarged views are displayed in (a) and (c), respectively. (c) Schematic diagram showing the structure of water molecules on the silica surface. Hydroxyl groups (−OH) are bound via valence bonds with Si atoms on the silica surface. Water molecules are physically adsorbed via hydrogen bonds. Liquid water layers form on some “icelike” layers at a high RH. Only one liquid-like layer is shown here. Some more water layers will be adsorbed at a higher RH. (d-j) Schematic illustrating contact scenarios in the formation of a domed 3D feature in the contact zone. (d) A cantilever approaches to the sample. (e) A water bridge forms in the contact zone. (f) Two liquid droplets form on both surfaces after separation. The liquid flows out of the contact zone and water molecules evaporate into the air. (g) Both soluble and insoluble materials remain in the contact zone with vanished water. (h) By repeated contacts, there are increasing materials collected in the water bridge. (i) After drying, more materials remain in the contact zone. (j) By thousands of contacts, the feature is fabricated layer by layer, eventually leading to a domed 3D feature. The figures are not to scale.
A domed 3D feature in the contact zone was formed by repeated contacts due to thin film flow at a high RH. Figures 9(d-j) schematically show the formation process. A liquid bridge forms inside the wedge-like gap between a cantilever and the sample due to capillary condensation and thin film flow. After separation, there are two liquid droplets formed on both surfaces, as shown in Figure 9(f). From Equation (2), the Laplace pressure is positive for a convex droplet, since the principal radii of curvature are both positive. That is, the pressure inside a droplet is larger than that inside a flat thin film, resulting in the liquid flow out of the contact zone. Furthermore, the vapor pressure of a convex droplet is also larger than that of a flat thin film, leading to the evaporation of water molecules into the air. Therefore, before the next contact, the droplets with a micrometer size may become very small or completely disappear, depending on the length of non-contact time between two consecutive contacts. The non-contact length time is measured from the time of pull-off in the previous force curve until jump-in-contact in the next force curve, and depends on the dwell time, piezo velocity and normal load. If there is some liquid remained in the contact zone, the liquid bridge size for the next contact will become a little larger than that of the previous contact. That is, liquid bridge volume increases with repeated contacts. It seems that, the contact time has an accumulating effect with repeated contacts 29. The liquid bridge volume cannot only increase by increasing contact time of one contact as shown in Equation (3), but also by repeated contacts due to dynamic behaviors of a liquid 42. In this way, the liquid bridge grows gradually with repeated contacts, which then leads to the increase of adhesion force with measurement number of times, as shown in Figure 3(b). Under different conditions, the increasing behaviors by repeated contacts can be different 29, 31, 42. If the droplets completely disappear or the liquid bridge reaches saturation, the adhesion force will remain almost the same or change slightly. However, the adhesion force may change suddenly due to the formation of a domed 3D feature and variations in contact area during contacts (see Figure S11, Supporting Information). Furthermore, more and more materials are collected in the contact zone, and the feature is formed layer by layer with repeated contacts for thousands of times. It should be noted that most materials will be attached on a cantilever, since the surface energy of the cantilever surface after plasma treatment (water contact angle < 5°) was much larger than that of the sample surface (~52.4°). In order to compare the results with different KOH concentrations under low and high RHs, some images shown in Figures 4, 5, 7 and 8 are demonstrated again as a table (see Figure S15, Supporting Information). No doubt, the materials around the contact zone are collected by thin film flow to form a domed 3D feature at high RHs. However, one may wonder, why the domed 3D feature on Probe 3# is higher than that on Probe 4#, and why the materials are less on Probe 4# with a higher KOH concentration. These were attributed to the contact methods during the experiments. For Probe 3#, the cantilever contacted the sample at one location at first for thousands of time, then scanned the sample in an area in force-volume mode. However, it was just the opposite for Probe 4# (see Figures S11-S13, Supporting Information). The domed feature can be formed layer by layer with repeated contacts at one location without interruption. However, in force-volume mode, the cantilever has to move under a normal load from one point to another to collect force curves over and over again. This movement may influence the formation of a domed feature due to friction. That is, the newly formed layer may be left on the sample during the movement. That is why the domed
3D feature on Probe 4# has lower height and less material. As can be seen from Figures 7(e-g), there are still some K scattered in bits and pieces with low concentration inside the radius of collection area for Probe 3#. There may be three reasons for this phenomenon: (1) The liquid of two droplets formed on both surfaces after separation will flow out of the contact zone. K may return back due to the flowing. (2) The efficiency of thin film flow on the cantilever surface may be reduced after the formation of the domed 3D feature, since the water bridge may be formed at the top of this feature (see Figure S16, Supporting Information). As a contrast, the efficiency may be not reduced due to low height of the feature for Probe 4#. Note that, as shown in Figure 6(c), there is no K on the upper part of the feature for Probe 3#, which may be caused by this reason. (3) The diffusion due to concentration difference may occur, if K is dissolved in a thin liquid film. And K diffuses into the area inside the radius of collection area. The formation of a domed 3D feature may be regarded as a technique of additive manufacturing in the microscale 43. Moreover, it is similar with DPN. However, there are several differences between DPN and the technique introduced here: (1) Usually a sharp tip is used in DPN, while a tipless cantilever is used in the technique; (2) The materials are transported from a tip to a substrate via a formed liquid bridge between them in DPN, while materials are transported from a cantilever surface into the contact zone, and most of materials are remained on the cantilever in the technique; (3) Usually a 2D feature is formed on a substrate in DPN, while a domed 3D feature can be fabricated in the technique; (4) Only one contact is needed for the material transport with varied lengths of contact time to control a feature size in DPN, while thousands of contacts are needed to form a 3D feature layer by layer in the technique. Although it may be a promising technique, there are some unknown matters: (1) Can reproducible features be patterned by this technique? (2) Other materials (such as polymers, colloids, biomaterials, ceramics and metals) can be easily collected in the contact zone to form a 3D feature or not? (3) How to transfer such a 3D feature to other substrate? Therefore, further experimental studies are needed to clarify the merits and demerits of the technique. If things go well, this technique may have an outstanding value in additive manufacturing in the microscale. As mentioned in Introduction, RH dependence of capillary force is still ambiguous with different dependencies. It was reported by Ondarçuhu and Fabié 44 that these contradictory results are reconciled by Köber et al. 45 by detecting actual tip shapes using SEM. That is, the ambiguous dependence was attributed to contact geometry and tip size. However, this may be true just for sharp AFM tips in the nanoscale, but not for colloid probes in the microscale. In our experiments here, capillary condensation is dominant at a low RH, while thin film flow is dominant at a high RH. That is, the formation mechanism of a water bridge may be different for low and high RHs. As mentioned above, the equilibrium time for capillary condensation is in the millisecond range, but that for thin film flow can be as large as hundreds of seconds. Therefore, the contact time may be a crucial experimental parameter in the experiments concerning the RH dependence of capillary force. Unfortunately, to our knowledge, experimental parameters of AFM (such as dwell time, piezo velocity, and normal load) were unreported for most experiments in the literature. If a short contact time is used at high RH, the system may be not in equilibrium with a small water bridge, leading to an undervalued capillary force. Furthermore, the thin film adsorbed on a surface should be in equilibrium
with vapor atmospheres with an adjusted RH during the experiments. When the RH is adjusted to a new one, the film thickness will increase or decrease by the adsorption or desorption of water molecules. It takes time for the adsorption and desorption. Especially, desorption may be difficult and time-consuming because of the disjoining pressure. Therefore, if the waiting time after adjusting RH is not long enough, the system between the thin film and vapor may be not in equilibrium, leading to undervalued or overvalued capillary forces. It should be noted that, the equilibrium of the system was usually neglected in most experiments, mainly due to very short equilibrium time for capillary condensation (thin film flow was usually neglected). That also means, careless choice of experimental AFM parameters may cause these contradictory results. However, things become very different, when thin film flow is taken into account due to its long equilibrium time. Therefore, based on the results here, thin film flow and the equilibrium of the whole system (liquid bridge, thin film and vapor) should be taken into consideration in the study of RH dependence of capillary force.
4. Summary In this work, some tipless cantilevers were used to repeatedly contact a silicon wafer by thousands of times on an AFM under different RHs. These cantilevers were coated with KOH by rinsing in KOH solution after plasma treatment. Before and after the contact experiments, imaging and ex situ chemical characterization of the cantilever surface in the contact zone were carried out by SEM, AES and EDS to investigate growth mechanisms of a water bridge. The conclusions can be listed as follows: (1) At low RHs, the dominant mechanism is capillary condensation, and the thin film adsorbed on surfaces is difficult to flow or even impossible to flow. This was confirmed by scattered K in bits and pieces around the contact zone and only a few materials collected after contact experiments. (2) At high RHs, the dominant mechanism is thin film flow towards a growing water bridge, and materials were collected in the contact zone with a domed 3D feature and almost no scattered K around the contact zone. (3) At high RHs, there was a circle centered on the feature with a radius of collection area s, inside which all the liquid seems to flow into the water bridge. The radius of collection area can be as large as ~23.6 μm. The radius of collection area not only is used as a direct evidence of thin film flow, but also may be used as a parameter to reflect the efficiency of thin film flow. (4) When studying RH dependence of capillary force, much attention should be paid to different mechanisms at low and high RHs and the equilibrium time between thin water film and vapor after changing a RH. Supporting Information Detail of TGT1 calibration grating; Preparation methods of cantilevers; A box to adjust relative humidity (RH); Force-displacement curve; Adhesion forces measured by Probes 1#-4#; Comparison of SEM and AES characterization of Probes 1#-4#; Comparison of possible contact scenario of Probes 3# and 4# (PDF) Acknowledgments
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