Article pubs.acs.org/Langmuir
Size-Dependent Stiffness of Nanodroplets: A Quantitative Analysis of the Interaction between an AFM Probe and Nanodroplets Shuo Wang,†,§,‡ Xingya Wang,†,§,‡,∥ Binyu Zhao,⊥ Lei Wang,†,§,‡,∥ Jie Qiu,‡,# Limin Zhou,†,§,‡ Yaming Dong,∇ Bin Li,†,‡ Junhong Lü,†,‡ Ying Wang,†,‡ Yi Zhang,†,‡ Lijuan Zhang,*,†,‡,∥ and Jun Hu*,†,§,‡ †
Shanghai Institute of Applied Physics and ‡Key Laboratory of Interfacial Physics and Technology, Chinese Academy of Sciences, Shanghai 201800, China § University of Chinese Academy of Sciences, Beijing 100049, China ∥ Shanghai Synchrotron Radiation Facility, Shanghai 201204, China ⊥ School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China # School of Physical Science and Technology, ShanghaiTech University, Shanghai 201204, China ∇ Life and Environment Science College, Shanghai Normal University, Shanghai 200234, China S Supporting Information *
ABSTRACT: The interfacial properties of nanodroplets are very significant for the exploration of the basic law governing the fluid behavior at the nanoscale and also the applications in some important processes in novel materials fabrication by forming a special and local reaction environment. However, many basic factors such as the interfacial tension or stiffness of nanodroplets are still lacking, partially because of the difficulty of making quantitative measurements of the interfacial interactions at the nanometer scale. Here, we used a novel atomic force microscopy (AFM) mode, PeakForce mode, to control the interaction between an AFM probe and nanodroplets, by which we could obtain the morphology and stiffness of nanodroplets simultaneously. The change in the stiffness with the size of the nanodroplets was observed where the smaller nanodroplets usually had a larger stiffness. To explain this phenomenon, we then established a theoretical model based on the Young−Laplace equation in which the deformation and size-dependent stiffness could be described quantitatively and the experimental observations could be explained with our numerical calculations very well. The general methodology presented here could also be extended to analyze the relevant behavior of nanobubbles and other wetting phenomena at the nanoscale.
1. INTRODUCTION
Dagastine et al. presented the dynamic forces between two deformable droplets.13 Although most of the previous studies were focused on the microscopic droplets/bubbles, very recently the interactions between a nanoscopic probe and nanoscale droplets have attracted more interest in both fundamental fields and potential applications.15,16 Nanodroplets have been used as an ideal system for studying the interactions near the interface of water and a solid at the nanometer scale, which is also thought to be a theoretical analog with nanobubbles.6,15,20−27 Compared to nanobubbles, nanodroplets could be easily and controllable prepared using the recently developed solvent-exchange method.17−19 This allows us to systematically investigate their interfacial properties and enables the wetting theories to be
Research on droplets of water or oils and on bubbles in the bulk or at an interface has become a very hot topic because of their significance in producing diverse and novel materials.1−5 For example, emulsions could be used as templates to produce submicroscopic hollow particles or create a small space for chemical reactions.3,4 In these processes, the interfacial behavior of the droplets is vital, and the study of their interfacial properties is very important. Among them, the interfacial tension or stiffness, as one of the important physical properties, has attracted more attention in recent years.6−8 Studying the interactions between the droplets and a solid particle/probe is becoming a standard method and is thought to be very important in measuring the stiffness and understanding the involved interfacial deformation of droplets. During the last 20 years, the investigation of these interactions using atomic force microscopy (AFM) and relevant colloid probe techniques has been well developed.9−14 In early pioneering works, Ducker et al. investigated the hydrophobic and DLVO forces in bubble−surface interactions.12 Recently, © 2016 American Chemical Society
Special Issue: Nanobubbles Received: May 1, 2016 Revised: September 4, 2016 Published: September 6, 2016 11230
DOI: 10.1021/acs.langmuir.6b01664 Langmuir 2016, 32, 11230−11235
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Langmuir tested down to the nanometer scale,16,28,29 which is also the basis for their diverse applications.30 Some important work has already been done. For example, AFM force measurements showed that the deformation on a droplet with an AFM probe behaves like a simple Hookean spring,15 similar to a analogous experiment performed on microsized droplets or bubbles.12,31,32 Several reports presented a linear or nearly linear relationship between the interfacial tension and droplet stiffness.7,29 More interestingly, Munz et al. found a negative correlation between the measured stiffness and droplet size.8 Understanding these phenomena requires precise measurements and quantitative analysis. However, different from that in microsized droplets, it is difficult to measure the interaction between a nanodroplet and an AFM probe precisely and quantitatively. Most of the previous studies were quite qualitative and only preliminary information was obtained. In order to obtain a comprehensive understanding of the interactions between the nanodroplets and a nanoscopic probe, a systematic and quantitative study is required on the basis of precise measurements. Recently, PeakForce Tapping, a new AFM mode based on the force feedback signals, has been developed. In this mode, the probe intermittently contacts the sample at a high frequency (typically 2 kHz), and the maximum contact force is controlled at each pixel that is then used as feedback signals. Simultaneously, the individual force curves can be acquired at each pixel and different properties of the sample, such as stiffness, deformation, and adhesion could be analyzed. Here, we systematically investigated the morphology and stiffness of oil nanodroplets as well as the force response loaded on a single nanodroplet using PeakForce and force volume mode AFM, respectively. By analyzing the interaction between the AFM probe and nanodroplets during the approach, we presented the pinning effect that occurred and found the linear relationship between force and deformation. More importantly, we established a theoretical model based on the Young− Laplace equation to give a reasonable explanation of the sizedependent stiffness. The general methodology built in this article would be very helpful for systematic studies on nanoscopic wetting and particularly the pinning behavior of the three-phase line at the nanoscale.
Bruker) with a nominal spring constant of 0.35 N/m were used for imaging and force measurements. The spring constant of cantilevers was calibrated using the thermal noise method prior to use. The cantilevers were treated with plasma using a plasma cleaner (Harrick Plasma, plasma cleaner PDC-32G) for 2 min beforehand. For more details on the force measurements, please see the Supporting Information.
3. RESULTS AND DISCUSSION 3.1. PeakForce Imaging and Stiffness of Nanodroplets. The spherical-cap-shaped nanodroplets on the HOPG surface could be stably imaged by PeakForce AFM. Figure 1a shows the typical morphology of nanodroplets
Figure 1. Morphology and stiffness obtained with Peakforce tapping mode. (a) Typical nanodroplet morphology at the water/HOPG interface over an area of 5 μm × 5 μm with a z scale of 90 nm. (b) The corresponding stiffness image of nanodroplets in (a). (c) The measured stiffness as a function of the radius of the footprint of nanodroplets.
obtained from PeakForce tapping mode. The formed nanodroplets have a lateral size range from 100 nm to 2 μm and a height from 10 to 200 nm. The contact angles of these nanodroplets were mainly between 150 and 160°. These results were consistent with the previous reports by tapping mode AFM.19 Figure 1b shows the stiffness images of these nanodroplets. From the stiffness images, we could analyze the stiffness of each nanodroplets and give a statistical distribution of the stiffness versus the sizes as shown in Figure 1c. It was found that smaller droplets had a larger stiffness. The size dependence stiffness obtained here was similar to our previous findings on nanobubbles,6 and a detailed analysis of this behavior is given in section 3.3 and 3.4. 3.2. Force Curve of Single Nanodroplets and Pinning Effects. To understand the size-dependent feature in Figure 1c, a detailed investigation of the whole response while the AFM probe approaches and retracts from a single nanodroplet is required. The model of the interaction between the AFM probe and nanodroplet was described in Figure 2a. We performed the force measurement using the force volume mode of AFM. A typical force curve is presented in Figure 2b, and the interaction
2. EXPERIMENTAL SECTION 2.1. Materials. The decane solution was prepared by mixing ethanol (99.8%, GR Sinopharm Chemical Reagent Co., Ltd.) and decane (99% Sigma-Aldrich) in a volume ratio of 1000:1. Millipore water with a conductivity of 18.2 MΩ cm was obtained from a USFELGA Maxima water purification system. Hightly ordered pyrolytic graphite (HOPG, 1.2 × 1.2 cm2, ZYH grade, Bruker) was used as the substrate of formed nanodroplets and was freshly cleaved before use. 2.2. Formation of Nanodroplets. Nanodroplets were produced by the solvent exchange method,19 whereby decane solution was displaced by water. Mainly, about 2 mL of decane solution was first introduced into the fluid cell and then replaced with more than 5 mL of water. A fluid cell was assembled from an AFM fluid tip holder, a silicone O-ring, and the HOPG substrate. 2.3. AFM Measurements. After the formation of nanodroplets, they were imaged using AFM PeakForce tapping mode (MultiMode 8 equipped with a J scanner, Bruker) in water. The set point and amplitude were set at 600 pN and 100 nm, respectively. The stiffness of each nanodroplet was obtained from the force curve at each pixel. To obtain highly accurate force curves for single nanodroplet analysis, the AFM was switched to force volume mode. The force curve data was obtained from complete force curve cycles at a frequency of 10 Hz scanned across the nanodroplets. Silicon nitride probes (DNP-10, 11231
DOI: 10.1021/acs.langmuir.6b01664 Langmuir 2016, 32, 11230−11235
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feature always held in the weak force ( 2γ/Rc. However, during our experiments, the probe snapped into contact with the liquid interface and penetrated the droplet. The force measurement then became a capillary phenomenon. We adopted the pinning of the three-phase line as a boundary
Figure 3. Size-dependent stiffness of nanodroplets. (a) Normalized stiffness k* = k/γ as a function of the normalized droplet sizes L/r0. Data were obtained with decane nanodroplets using PeakForce tapping mode. The solid line represents the numerical results from the model. The dotted line presents the approximate solution (eq 20) using asymptotic analysis, with parameters of r0 = 7 nm and γ = 0.05 N/m. (b) Model calculations of deformation profiles for the nanodroplet shown in Figure 2b under different external forces. The deformation occurred only in the inner region (small r, near the probe). (c) The total deformation in Figure 3b is a combination of component contributions. The solid line represents a function of the profile shown on the left-hand side of eq 11. The dotted line represented the Laplace pressure term on the right-hand side of eq 11, and the dashed line represents the external force term. The deformation in the inner region was mostly contributed by the external force. In the outer region, the profile followed the Laplace pressure term. 11233
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Langmuir calculations from eq 10, which are in good agreement with the experimental data. A negative correlation could be clearly presented (i.e., smaller droplets were stiffer). However, when L/r0 exceeded 20, the size of the droplet had a relatively weaker effect on the effective stiffness. Because of the pinning, the droplet was laterally confined between two three-phase lines located at the probe and the substrate. As the probe approached the droplet, the lateral boundary of the droplet had an effect on the deformation. Physically, the deformation of the fluid interface was controlled by the Laplace pressure across the fluid interface. To understand the size-dependent stiffness in details, we further analyzed eqs 9 and 10. First, for large droplets, it corresponds to the flat region in Figure 3a. Equation 10 was rearranged to u′(r ) 2
=
1 + u′(r )
r Δp F − 2πrγ 2γ
The stiffness of the droplet was the force over the deformation at r0. K=
2
1 + u1′(r )
=
K≈
⎛r ⎞ u1 = b cosh−1⎜ ⎟ + D ⎝b⎠
2πr0u1′(r0) 1 + u1′(r0)2
36
(13)
γ
■
(14)
If we neglect the Laplace pressure term, then the solution for u1 at the boundary r = r0 is u1′(r = r0) =
F 2πγ
(15)
(16)
■
The boundary condition at L is given by contact line pinning,
u1(r = L) = 0
(19)
() L r0
(20)
ASSOCIATED CONTENT
AUTHOR INFORMATION
Corresponding Authors
(17)
*E-mail:
[email protected]. *E-mail:
[email protected].
After inserting eq 17 into eq 13, we obtained D:
⎛L⎞ D = −b cosh−1⎜ ⎟ ⎝b⎠
L r0
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b01664. Details of experiments and data processing, parameters of the pinning model, and other properties of the force response (PDF)
After inserting eq 15 into eq 13, we obtained b as b=
()
S Supporting Information *
F (2πr0γ )2 − F 2
2πγ ln
4. CONCLUSIONS We imaged the formed nanodroplets at the solid/water surface and obtained their stiffness in AFM PeakForce mode. It was found that the stiffness of the nanodroplets had a strong size dependence and smaller droplets were usually stiffer. We then performed the force measurements and analyzed the force curves of nanodroplets approached by the AFM probe. We proposed the pinning effect near three-phase lines during approach, and a theoretical model was built on the basis of the Young−Laplace equation. The deformation and size-dependent stiffness could be described quantitatively, and the experimental observations could be explained with our numerical calculations very well. We could also derive an asymptotic relationship between the stiffness and droplet sizes for large droplets but failed for small ones because of the significant contribution of Laplace pressure. The general methodology presented here could also be extended to analyze the relevant behavior of nanobubbles and other wetting phenomena at the nanoscale.
Here, b and D are two constants that could be determined by the boundary condition. The boundary condition at r0 was given by the force balance, which related the profile to the force as F = πr0 2Δp +
≈
This expression shows the asymptotic relationship between the stiffness and droplet size for large droplets. Here, the stiffness decayed as ln(L/r0) as observed in Figure 3a (the dotted line). This explained the flat region of the curve well in Figure 3a. For small droplets that corresponded to the left side of the curve of the size-dependent stiffness (Figure 3a), the Laplace pressure was increased rapidly because of the narrow lateral confinement of the droplets. The contribution from the Laplace pressure was comparable to the external force in eq 11 and cannot be neglected. The increased Laplace pressure for small droplets would result in an increase in the stiffness with the decreased sizes of nanodroplets.
(12)
which had a general solution known as a catenary curve,
0
2πγ ln
(11)
F 2πrγ
2πγ
( rb ) − cosh−1( Lb )
Thus, in the case of a large droplet, the stiffness is
where F was the applied external force and Δp was the Laplace pressure, indicating that the profile was a function of the force and the Laplace pressure as plotted in Figure 3b. It could be found that the deformation occurred only in the inner region (small r, near the probe) and the deformation in the outer region was negligible. Figure 3c shows that the profile is dominated by the external force in the inner region and Laplace pressure in the outer region. As shown in Figure 3b, the deformation in the outer region is negligible. This allowed us to solve eq 11 for the case of large droplets. The external force dominated the u1(r) deformation profile, u1′(r )
F = u1(r = r0) cosh−1
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are grateful for support from the Key Laboratory of Interfacial Physics and Technology, Chinese Academy of Sciences, and the Open Research Project of the Large Scientific Facility of the Chinese Academy of Sciences: Study on SelfAssembly Technology and Nanometer Array with Ultrahigh Density. We also thank the beamline 08U1A staff at the Shanghai Synchrotron Radiation Facilities (SSRF) for the sample preparation and discussion. We gratefully acknowledge generous financial support by the National Natural Science Foundation of China (grant nos. 11079050, 11290165, 11305252, 11575281, and U1532260), the National Basic Research Program of China (grant no. 2013CB932801), the National Natural Science Foundation for Outstanding Young Scientists (grant no. 11225527), the Shanghai Academic Leadership Program (grant no. 13XD1404400), the 973 project (grant no. 2012CB825705), and the Knowledge Innovation Program of the Chinese Academy of Sciences (grant nos. KJCX2-EW-W09 and U1532260).
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