REVIEW OF SCIENTIFIC INSTRUMENTS 85, 123707 (2014)
Nanorheology by atomic force microscopy Tai-De Li, Hsiang-Chih Chiu, Deborah Ortiz-Young, and Elisa Riedoa) School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
(Received 14 June 2014; accepted 24 November 2014; published online 19 December 2014) We present an Atomic Force Microscopy (AFM) based method to investigate the rheological properties of liquids confined within a nanosize gap formed by an AFM tip apex and a solid substrate. In this method, a conventional AFM cantilever is sheared parallel to a substrate surface by means of a lock-in amplifier while it is approaching and retracting from the substrate in liquid. The normal solvation forces and lateral viscoelastic shear forces experienced by the AFM tip in liquid can be simultaneously measured as a function of the tip-substrate distance with sub-nanometer vertical resolution. A new calibration method is applied to compensate for the linear drift of the piezo transducer and substrate system, leading to a more precise determination of the tip-substrate distance. By monitoring the phase lag between the driving signal and the cantilever response in liquid, the frequency dependent viscoelastic properties of the confined liquid can also be derived. Finally, we discuss the results obtained with this technique from different liquid-solid interfaces. Namely, octamethylcyclotetrasiloxane and water on mica and highly oriented pyrolytic graphite. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4903353] I. INTRODUCTION
The behavior of fluids confined within nanometers from the solid interface has received a lot of attention in the past decades due to its importance in tribology, biology, geophysics, and polymer science. Recently, it has been found that the behavior of nanoconfined liquids differs significantly from the bulk. Interesting phenomena occur at the liquid-solid interface where the classical continuum laws break down.1 Liquids confined between two solid surfaces can form ordered layers, leading to structural oscillatory solvation forces2 and nonlinear viscoelastic dynamics.3 A powerful instrument to probe liquids under nano-confinement is the surface force apparatus (SFA).4, 5 Some of the disadvantages of SFA include the limited materials choice and jump-to-contact instability, i.e., when the gradient of the force between two surfaces exceeds the spring constant of the apparatus, one surface snaps into the other one losing force information. The Interfacial Force Microscope (IFM),6 which uses oxide-terminated tungsten tips with radii of about 10 μm,7 was designed to avoid such instabilities with a self-balancing force feedback sensor. The mechanically stable Transverse Dynamic Force Microscope (TDFM), also known as the Shear Force Microscope, is able to probe the viscoelastic behavior of water under nano-confinement, but lacks the resolution in vertical separation smaller than 4 molecular layers owing to instrument limitations.8 Nevertheless, how surface roughness or wettability of the confining surfaces influences the properties of the nano-confined water is not clearly known. Obviously the aforementioned instruments, SFA, IFM, or TDFM, cannot image the surface topography with high lateral resolution to acquire information about surface properties. Therefore, to comprehensively study the properties of nano-confined liquids, an instrument that can perform force measurements for a) Email: [email protected]
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a separation smaller than 1 nm and topography imaging with high lateral resolution is absolutely necessary. Atomic Force Microscopy (AFM), which permits to acquire high resolution topography images and perform high resolution force measurements between an AFM tip and a sample surface, provide an opportunity to investigate the properties of nano-confined water with unprecedented advantage. Indeed, a variety of experimental techniques based on AFM have been utilized to probe the properties of liquid in the vicinity of different substrates.9, 10 The solvation forces in OMCTS (Octamethylcyclotetrasiloxane) and n-dodecanol near Highly Oriented Pyrolytic Graphite (HOPG) are observed using force-distance spectroscopy with the contact mode AFM, but this oscillatory behavior is not seen in water.11 The Frequency Modulation (FM) AFM based technique is employed to measure the solvation forces at the interface between OMCTs and HOPG.12 The FM-AFM equipped with a carbon nanotube probe is also used to study the oscillatory and hydration forces in the vicinity of self assembled monolayers on gold substrate13 as well as on biological membranes.14 Additionally, in FM-AFM, since the oscillating frequency of the cantilever as well as the phase difference with respect to the cantilever driving signal are both recorded, this technique also enables the study of the viscoelasticity of the nano-confined liquids.11, 12 However, in FM-AFM, the interacting forces and the viscoelastic properties of nano-confined liquid are deduced indirectly from the frequency and phase shifts of the cantilever using complicated mathematical formulas with approximations. On the other hand, optical interferometer based AFM method can simultaneously measure the normal and shear stiffness using the vertical and lateral oscillations with high sensitivity, but this method is subject to cross-talk of vertical and lateral signals, cantilever-optical fiber alignment deviations and it is not compatible with commercial AFMs.15 Therefore, a method that is easy to use and can simultaneously, directly, and unambiguously measure the solvation forces and viscoelasticity
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of nano-confined liquid with high resolution is apparently in need. In this paper, we present a new AFM-based technique for simultaneous, quasi-statical normal and lateral force measurements in nano-confined liquid as a function of tip-sample separation distance.2, 3 A lateral shearing signal is applied to the AFM cantilever by a lock-in amplifier while it is approaching the solid surface. The normal and lateral forces experience by the AFM tip in liquid can be recorded at the same time. Thus this technique permits an in situ investigation of the structural and dynamical properties for nano-confined fluids and can be employed easily with most commercial AFM without instrument modification. In addition, with a recently developed correction procedure to account for the linear drift of the piezo transducer, we are able to precisely determine the tip-sample separation down to one molecule layer and investigate the properties of water confined between a gap smaller than 1 nm. To demonstrate the capabilities of this technique, in the following we will present the results obtained from various liquid-solid interfaces. More specifically, we will discuss the normal solvation forces of OMCTS in the vicinity of mica and HOPG, the normal solvation and lateral viscous forces of nano-confined water on mica, as well as the viscoelastic properties of nano-confined water studied with our technique.
II. EXPERIMENTAL A. Experimental setup
In this work, we use a commercial AFM (PicoPlus 5500, Agilent Technologies) equipped with a silicon AFM cantilever (NSC35, MikroMasch) with a typical tip radius, Rtip = 40 ± 10 nm to study the physical properties of the nanoconfined water. The normal and torsional spring constants of the cantilever are kN ≈ 3–4.5 N/m and kT ≈ 50–120 N/m, respectively. These force constants are determined by imaging the cantilevers with a Scanning Electron Microscope (JEOL JSM-5910) to acquire their physical dimensions after each measurement (More details in the text below). In addition, we also perform inspections on the tip apex. We have found that a rough tip surface with protuberances will prevent the observation of solvation forces in liquid.2 An AFM liquid cell is used to contain the sample, liquids, and the AFM cantilever inside an environmental chamber. This chamber is in ambient conditions for experiments with water and is filled with ultrafiltered nitrogen gas for OMCTS. The liquid cell is cleaned by rinsing and sonication first in ethanol followed by Isopropyl Alcohol and then blown dry with compressed nitrogen gas. The mica and HOPG surfaces are prepared by the tape-exfoliation method and then blown with compressed nitrogen gas to eliminate any surface debris. The cleanliness of the surfaces are examined by AFM topography images over areas of 1 μm2 with contact mode AFM imaging. To insure the tip is shearing in parallel to the sample surface, before each measurement, we tilt the sample stage and obtain the AFM topography image of the surface until the difference in height across a surface distance of 1 μm is less than 1 nm. This height difference corresponds to a tilted angle of less than 0.06◦ between the tip and sample surface. This proce-
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FIG. 1. Schematic of the experimental setup. With a lock-in amplifier, a lateral shearing signal is applied to the AFM tip as it approaches the solid surface. The normal and lateral force are recorded simultaneously. Both the tip and the sample surface are immersed in a liquid environment.
dure is highly necessary because if there is a large angle between the shearing direction and sample surface, there will be an artifact-like lateral force due to lateral tapping between the tip and the surface, leading to unknown experimental errors. The schematic of experimental setup is shown in Figure 1. A silicon AFM tip approaches a solid surface (mica or HOPG) while a lateral oscillation is applied to it by a lockin amplifier at the same time. A laser projected onto the back of the cantilever is reflected into a 4 quadrant photodiodes, as shown in Figure 1. The normal force FN experienced by the cantilever in liquid can be written as FN = δX · kN ,
(1)
3
where kN = E4 wt is the normal spring constant and δX is the L3 vertical bending of the cantilever due to tip-surface force. In addition, E is the Young’s modulus of silicon16 while L, w, and t are the length, width, and thickness of the cantilever, respectively. The vertical cantilever bending δX = δVN · m, where δVN is the deflection signal measured by the photodiodes shown in Figure 1 and m is the optical lever sensitivity of the cantilever used. During the approach, a lateral oscillation, X0 · sin(ωt), is applied to the piezo-scanner via a lock-in amplifier (Stanford Research Systems, SR830), where X0 and ω are respectively the oscillation amplitude and frequency. The application of lock-in amplifier for data acquisition greatly enhances the signal to noise ratio. The lateral force FL experienced by the cantilever in liquid can be written as FL = kT · hθ, 2
(2)
where kT = 0.4 · kN · (h+L t )2 is the torsional spring constant 2 of the cantilever, h represents the tip height, and θ is the torsional angle of the cantilever due to the presence of the lateral viscous force. The torsional angle θ is also monitored by the laser beam reflected from the backside of the cantilever and recorded by the photodiodes as VL as shown in Figure 1. For a rectangular cantilever used in our AFM system, the torsional angle θ is proportional to VL through the following
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relationship:17 θ (rad) = VL (V)/(7.5 × 103 ) (rad/V).
(3)
Combining Eqs. (2) and (3), we arrive at the lateral force experienced by the cantilever at a given tip-surface separation, L2 FL = 0.4 · kN · 2 · h + 2t
h · V 7.5 × 103
.
(4)
This lateral force, FL (z) = FL sin[ωt+ φ(z)], experienced by the AFM tip in liquid as a function of tip-solid separation distance z, is then measured by the lock-in amplifier, where φ(z) is the phase difference between the applied lateral driving signal and the detected lateral force signal. At φ = 0, the tip is in hard contact with the solid surface and the lateral oscillation amplitude is small enough to guarantee a purely elastic contact deformation without slippage.18
and retracting scanner deformations, respectively. The initial slopes of the approaching and retracting curves in the contact regime, with linear drift present, are Sa 0 and Sr 0 as shown in Figure 2(a) For the approaching curve, we have Sa 0 = ba 0 /Za 0 , where ba 0 and Za 0 are the cantilever bending and piezo deformation when there is linear drift. After applying the new unit, the absolute value of the slope of the force curve at the contact regime should be 1, that is Ub · ba0 U = b · Sa0 = 1, Ua Ua · Za0
0
(5)
such that Ub =
Ua . Sa0
(6)
Similarly, for the retracting curve, we will have Ub = Ur /Sr 0. By combining Eqs. (5) and (6), we arrive at Sr0 · Ua . (7) Sa0 If we assume that the drift velocity, Vdrift , is in the same direction as tip retraction, then the modified approaching (Z[Ua ]) and retracting (Z[Ur ]) distances are Ur = Ub · Sr0 =
B. Drift analysis
Since the tip approaches the solid surface at a rate of only 0.2 nm/s (in water) or 0.4 nm/s (in OMCTS), the linear drift of the piezo scanner becomes important and cannot be neglected in the data analysis. When no linear drift is present, the approaching and retracting FN vs. d curves should overlap and have a slope of “−1” in the range where the tip is in contact with the surface, due to the fact that at hard contact the piezo movement and cantilever bending are equivalent. However, because of the linear drift, the contact lines will not overlap as shown in Figure 2(a) This can be understood as piloting a boat downstream and upstream a river to measure the velocity of the current. The measured velocity of the current going downstream or upstream will depend on the velocity of the boat. When no linear drift is present, the total deformation for the piezo-scanner, Z as shown in Figure 2, should be identical for both tip approaching and retracting movements. The total displacement showed in the raw force curves by the AFM for directions are both “Z nm.” However, owing to the drift, this “Z nm” for the approaching and retracting curve is actually different. This drift can be calibrated by introducing new length units (while the old unit is “1 nm”) for the scanner deformation and cantilever bending such that after correction the slopes of both contact lines shall be “−1.” The new units are Ub , Ua , and Ur for the cantilever bending, approaching
FIG. 2. (a) Typical force distance curves when a constant linear drift is present during measurement. The slopes of the approaching and retracting portions at the hard contact regimes are not the same. This drift can be accounted for using Eqs. (5)–(12). (b) Schematic shows water molecules confined between an AFM tip and a solid surface and form layering structures.
Z[Ua ] = (Vscanner + Vdrif t )T [nm],
(8)
Z[Ur ] = (Vscanner − Vdrif t )T [nm],
(9)
where Vscanner and T are the scanner movement velocity and the time to approach or retract the tip, respectively. From Eqs. (5)–(8), Ua , Ub , and Ur can be determined as Ua = Ur =
2Sa0 [nm], + Sr0
(10)
2Sr0 [nm], + Sr0
(11)
Sa0 Sa0
2 [nm]. (12) + Sr0 A simple home written program has been developed to automate this procedure. A typical example of a normal forcedistance curve is shown in Figure 3. Ub =
Sa0
C. Viscoelasticity of nano-confined water
The obtained lateral viscous forces can also be used to understand the viscoelastic properties of water. When water is confined between two smooth plates with surface area A, separated by a distance d, and with one plate sliding in parallel at a velocity Vshear with respect to the other, the viscosity η of water can be evaluated by η = FL · d/(Vshear · A), where FL is the lateral force required to maintain one plate moving at Vshear with respect to the stationary one.3 If a sinusoidal strain, γ = γ 0 · sin(ωt), is applied to one of the plates while the other is stationary, the resulting shear stress between two plates will be σ = σ 0 sin(ω · t + φ). Since the strain and stress amplitudes can be written as γ 0 = X0 /d and σ 0 = FL /A, respectively, we arrive at the following relationship: FL X = |G∗ | 0 , A d
(13)
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FIG. 3. (a) Typical cantilever bending – Scanner movement curves with constant drift in water. Red is the approaching curve and blue is the retracting curve. (b) After the correction by Eqs. (10)–(12), the approaching curve overlaps with the retracting curve and the slope of the contact regime is −1. (c) The cantilever bending – Distance curve before correction. The contact is not steady and drifts linearly. The oscillation period of the normal force does not match water molecular size, 0.25 nm. (d) The cantilever bending – Distance curve after correction. The curve shows a steady contact and the period of the oscillatory normal force is now with 0.25 ± 0.05 nm, water molecule size.
where G∗ = G + iG is the viscoelastic modulus19 containing both the storage (elastic) modulus (G ) and the loss (viscous) modulus (G ) of the material. Furthermore, with Eq. (13), G∗ can be written as G =
FL d cos φ AX0
and
G =
FL d sin φ. AX0
(14)
III. RESULTS AND DISCUSSION
Figure 4 summarizes the normal forces FN obtained for OMCTS at the interface of mica and HOPG. Figures 4(a) and 4(b) display data acquired without tip shearing during approaching the surface, while Figures 4(c) and 4(d) illustrate data obtained with tip shearing with the same surfaces. Each figure shows the overlap of more than 8 different
FIG. 4. (a) and (c) The approaching normal force-distance curves acquired in OMCTS on Mica with and without tip shearing, respectively. The vertical dashed lines indicate the layering of water molecules confined between the AFM tip and the surface. These data are obtained with shearing amplitude of 0.4 nm with different frequencies (34.9 kHz, 107.4 kHz, 212.3 kHz, and 884.7 kHz). (b) and (d) The approaching normal force-distance curves acquired in OMCTS on HOPG with and without tip shearing, respectively. These data are recorded with a shearing amplitude of 1.18 nm with various frequencies (58.1 kHz, 105.2 kHz, and 397.7 kHz). Excellent overlapping of multiple force-distance curves in all figures demonstrates the reproducibility of our measurements. The insets show the same force curves with larger vertical axes to show that all force curves diverge as d approaches zero.
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measurements demonstrating data reproducibility. When the tip is not laterally sheared with respect to the surface, the structural layering of OMCTS molecule is clearly observed in the FN vs. d data beginning approximately at d ≈ 4 nm from both surfaces. In Figures 4(a) and 4(b), the vertical dashed lines indicate the force maxima which correspond to the first through fourth molecular layers. These oscillatory forces have a period of 0.85–1 nm which is consistent with the diameter of the OMCTS molecules.20 The oscillations in the force curve occur when the tip-sample separation distance decreases and squeezes out a molecular layer of OMCTS, as already demonstrated by SFA5 and several AFM-based measurements.11, 12, 21, 22 Additionally, the oscillatory behavior is more clearly shown on Mica than on HOPG probability due to different surface wettability with OMCTS. The first layer of OMCTS molecules on the surface might not stick well on hydrophobic HOPG, leading to difficulties in forming layered structures of OMCTS molecules. Figures 4(c) and 4(d) show the approaching normal force for OMCTS molecules at the mica and HOPG interface with the tip is laterally sheared with respect to the sample surface (corresponding FL not shown), respectively. The oscillatory behavior of FN vs. d is clearly shown again for OMCTS on Mica but not on HOPG, due to different surface wettability. The force profiles of OMCTS confined between a silicon tip and HOPG are attractive when d < 2 nm, similar to previous results obtained with other AFM based techniques.12, 21, 22 The insets of Figures 4(c) and 4(d) display the same data with larger vertical scale showing that all forces are well converged when d approaches 0. The comparison between the normal forces in presence and absence of shearing indicates that shearing the tip mildly disrupts the layering process, giving rise to less pronounced oscillations. This effect is particular evident on HOPG. Figures 5(a) and 5(b) shows the normal and lateral forces simultaneously captured as a function of the tip-sample separation in deionized ultra filtered (DIUF) water on Mica with the technique discussed in Sec. II. The data were acquired with a lateral shearing amplitude X0 = 0.4 nm and
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a frequency ω = 995 Hz, respectively. The dashed vertical lines highlight the molecular order in the repulsive oscillatory solvation force. The average diameter of water molecule is found to be 0.27 nm, consistent with results reported in the literature.4, 7, 13–15, 23–25 Furthermore, the lateral force FL increases drastically when the tip-sample distance decreases, especially for d < 1 nm. Such increase of FL of liquid at small d has been demonstrated by other experimental techniques.7, 23, 26, 27 The increase of FL is related to the increasing viscosity of water, which can be estimated with Eq. (13), assuming water is confined between two smooth plates. In the case of a spherical AFM tip with radius RTip ≈ 40 nm moving in parallel to a smooth surface with a separation distance d < 1.5 nm and a shearing velocity Vshear , a more rigorous treatment2 leads to η=
FL 2π Vshear (R + d) ln 1 +
h d
− h
,
(15)
for water confined between 0 < z < d + h (See Figure 2(b)). For h ∼ 0.25 nm (size of water molecule) and h = 0.5 nm, the viscosity of the confined water can be estimated to be ∼3 × 102 P, almost 4 order in magnitude larger than that of the bulk water, which is about 10−2 P. This unusual behavior suggests the possibility of lateral order in water molecules, which is usually observed only for spherical non-polar molecules.28 Recent AFM based measurements have also observed laterally organized water on Mica and deduced a molecule diameter of 0.2–0.3 nm.29, 30 Next, by using Eq. (14), the viscoelastic response of the nano-confined water can be derived directly from the lateral force, FL , and phase change, , as shown in Figure 5(b). The obtained elastic component, G , and viscous G component, as a function of tip-sample distance d is displayed in Figures 5(c) and 5(d), respectively. At this experimental conditions, X0 = 0.4 nm and ω = 955 Hz, the elastic component is larger than the corresponding viscous component for d < 1 nm, indicating the glassy state of nanoconfined water, consistent with previous measurements with TDFM8 and other AFM based techniques.30, 31
FIG. 5. (a) and (b) The normal and lateral force curves obtained simultaneously as a function of tip-sample distance in water on a Mica surface, respectively. All curves displayed here are acquired with a shearing amplitude of 0.4 nm and a frequency of 995 Hz. (c) and (d) Elastic and viscous moduli G and G as a function of tip-sample distance determined from one of the lateral force curves (open square) shown in (b).
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IV. CONCLUSION
In the foregoing we have presented a technique with AFM which permits simultaneous measurements of the normal solvation force and lateral viscous forces of nanoconfined liquid as well as its viscoelastic properties. With proper cantilever calibrations and the successful correction of the linear drift of the piezo scanner, we are able to capture the structural and viscoelastic properties of liquid at the solid interface with a confining gap down to ∼0.3 nm, which are difficult to achieve with other techniques summarized in Sec. I. We demonstrate the capability of this experimental technique by studying the oscillatory normal force of OMCTS on Mica surfaces, showing a oscillation period of 0.85–1 nm, which is consistent with diameter, 0.7–0.85 nm, of OMCTS.20 Similar experiments with DIUF water on mica surfaces also show the layered structure of nanoconfined water, finding an oscillation period of ∼0.27 nm, consistent with the diameter of a water molecule and with previously reported values.4, 15, 24, 25 Furthermore, the viscoelastic properties, namely viscous and elastic modulus, as well as relaxation time of confined liquids can be directly obtained from the acquired lateral force data. This novel technique provides an approach to comprehensively study and understand the physical properties of nano-confined liquids.32 ACKNOWLEDGMENTS
T.-D.L., H.-C.C., D.O.-Y., and E.R. acknowledge the financial support of the Office of Basic Energy Sciences DOE (DE-FG02-06ER46293). E.R. acknowledges the National Science Foundation NSF (CMMI-1100290) for partial support. We thank Suenne Kim for extensive discussions. 1 J.
N. Israelachvili, Intermolecular and Surface Forces (Academic Press, 1992). 2 T. D. Li, J. P. Gao, R. Szoszkiewicz, U. Landman, and E. Riedo, “Structured and viscous water in subnanometer gaps,” Phys. Rev. B 75, 115415 (2007). 3 T. D. Li and E. Riedo, “Nonlinear viscoelastic dynamics of nanoconfined wetting liquids,” Phys. Rev. Lett. 100, 106102 (2008). 4 J. N. Israelachvili and R.M.Pashley, “Molecular layering of water at surfaces and origin of repulsive hydration forces,” Nature (London) 306, 249 (1983). 5 R. G. Horn and J. N. Israelachvili, “Direct measurement of structural forces between two surfaces in a nonpolar liquid,” J. Chem. Phys. 75, 1400–1411 (1981). 6 S. A. Joyce and J. E. Houston, “A new force sensor incorporating forcefeedback control for interfacial force microscopy,” Rev. Sci. Instrum. 62, 710–715 (1991). 7 M. P. Goertz, J. E. Houston, and X. Y. Zhu, “Hydrophilicity and the viscosity of interfacial water,” Langmuir 23, 5491–5497 (2007).
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Antognozzi, A. D. L. Humphris, and M. J. Miles, “Observation of molecular layering in a confined water film and study of the layers viscoelastic properties,” Appl. Phys. Lett. 78, 300–302 (2001). 9 M. Abdelhamid and B. Bharat “Nanorheology and boundary slip in confined liquids using atomic force microscopy,” J. Phys.: Condens. Matter 20, 315201 (2008). 10 E. Bonaccurso, M. Kappl, and H.-J. Butt, “Thin liquid films studied by atomic force microscopy,” Curr. Opin. Colloid Interface Sci. 13, 107–119 (2008). 11 S. J. O’Shea, M. E. Welland, and T. Rayment, “Solvation forces near a graphite surface measured with an atomic force microscope,” Appl. Phys. Lett. 60, 2356–2358 (1992). 12 S. J. O’Shea and M. E. Welland, “Atomic force microscopy at solid−liquid interfaces,” Langmuir 14, 4186–4197 (1998). 13 S. P. Jarvis, T. Uchihashi, T. Ishida, H. Tokumoto, and Y. Nakayama, “Local solvation shell measurement in water using a carbon nanotube probe,” J. Phys. Chem. B 104, 6091–6094 (2000). 14 M. J. Higgins et al., “Structured water layers adjacent to biological membranes,” Biophys. J. 91, 2532–2542 (2006). 15 S. Patil et al., “A highly sensitive atomic force microscope for linear measurements of molecular forces in liquids,” Rev. Sci. Instrum. 76, 103705 (2005). 16 E. Meyer, H. J. Hug, and R. Bennewitz, Scanning Probe Microscopy: The lab on a Tip (Springer, 2004). 17 T.-D. Li, Ph. D. thesis, Georgia Institute of Technology, 2008. 18 R. W. Carpick, D. F. Ogletree, and M. Salmeron, “Lateral stiffness: A new nanomechanical measurement for the determination of shear strengths with friction force microscopy,” Appl. Phys. Lett. 70, 1548–1550 (1997). 19 J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, 1980). 20 D. W. Scott “Equilibria between linear and cyclic polymers in methylpolysiloxanes,” J. Am. Chem. Soc. 68, 2294–2298 (1946). 21 W. Han and S. M. Lindsay, “Probing molecular ordering at a liquid-solid interface with a magnetically oscillated atomic force microscope,” Appl. Phys. Lett. 72, 1656–1658 (1998). 22 R. Lim, S. F. Y. Li, and S. J. O’Shea, “Solvation forces using samplemodulation atomic force microscopy,” Langmuir 18, 6116–6124 (2002). 23 R. C. Major, J. E. Houston, M. J. McGrath, J. I. Siepmann, and X. Y. Zhu, “Viscous water meniscus under nanoconfinement,” Phys. Rev. Lett. 96, 177803 (2006). 24 J. R. Bonander and B. I. Kim, “Cantilever based optical interfacial force microscope,” Appl. Phys. Lett. 92, 103124 (2008). 25 S. Jeffery et al., “Direct measurement of molecular stiffness and damping in confined water layers,” Phys. Rev. B 70, 054114 (2004). 26 Y. Zhu and S. Granick, “Viscosity of interfacial water,” Phys. Rev. Lett. 87, 096104 (2001). 27 U. Raviv, P. Laurat, and J. Klein, “Fluidity of water confined to subnanometre films,” Nature (London) 413, 51 (2001). 28 J. Gao, W. D. Luedtke, and U. Landman, “Origins of solvation forces in confined films,” J. Phys. Chem. B 101, 4013–4023 (1997). 29 K. Kimura et al., “Visualizing water molecule distribution by atomic force microscopy,” J. Chem. Phys. 132, 194705 (2010). 30 T. Fukuma, Y. Ueda, S. Yoshioka, and H. Asakawa, “Atomic-scale distribution of water molecules at the mica-water interface visualized by threedimensional scanning force microscopy,” Phys. Rev. Lett. 104, 016101 (2010). 31 S. H. Khan, G. Matei, S. Patil, and P. M. Hoffmann, “Dynamic solidification in nanoconfined water films,” Phys. Rev. Lett. 105, 106101 (2010). 32 D. Ortiz-Young, H. C. Chiu, S. Kim, K. Voitchovsky, and E. Riedo, “The interplay between apparent viscosity and wettability in nanoconfined water,” Nat. Commun. 4, 2482 (2013).
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Nanorheology by atomic force microscopy Tai-De Li, Hsiang-Chih Chiu, Deborah Ortiz-Young, and Elisa Riedoa) School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
(Received 14 June 2014; accepted 24 November 2014; published online 19 December 2014) We present an Atomic Force Microscopy (AFM) based method to investigate the rheological properties of liquids confined within a nanosize gap formed by an AFM tip apex and a solid substrate. In this method, a conventional AFM cantilever is sheared parallel to a substrate surface by means of a lock-in amplifier while it is approaching and retracting from the substrate in liquid. The normal solvation forces and lateral viscoelastic shear forces experienced by the AFM tip in liquid can be simultaneously measured as a function of the tip-substrate distance with sub-nanometer vertical resolution. A new calibration method is applied to compensate for the linear drift of the piezo transducer and substrate system, leading to a more precise determination of the tip-substrate distance. By monitoring the phase lag between the driving signal and the cantilever response in liquid, the frequency dependent viscoelastic properties of the confined liquid can also be derived. Finally, we discuss the results obtained with this technique from different liquid-solid interfaces. Namely, octamethylcyclotetrasiloxane and water on mica and highly oriented pyrolytic graphite. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4903353] I. INTRODUCTION
The behavior of fluids confined within nanometers from the solid interface has received a lot of attention in the past decades due to its importance in tribology, biology, geophysics, and polymer science. Recently, it has been found that the behavior of nanoconfined liquids differs significantly from the bulk. Interesting phenomena occur at the liquid-solid interface where the classical continuum laws break down.1 Liquids confined between two solid surfaces can form ordered layers, leading to structural oscillatory solvation forces2 and nonlinear viscoelastic dynamics.3 A powerful instrument to probe liquids under nano-confinement is the surface force apparatus (SFA).4, 5 Some of the disadvantages of SFA include the limited materials choice and jump-to-contact instability, i.e., when the gradient of the force between two surfaces exceeds the spring constant of the apparatus, one surface snaps into the other one losing force information. The Interfacial Force Microscope (IFM),6 which uses oxide-terminated tungsten tips with radii of about 10 μm,7 was designed to avoid such instabilities with a self-balancing force feedback sensor. The mechanically stable Transverse Dynamic Force Microscope (TDFM), also known as the Shear Force Microscope, is able to probe the viscoelastic behavior of water under nano-confinement, but lacks the resolution in vertical separation smaller than 4 molecular layers owing to instrument limitations.8 Nevertheless, how surface roughness or wettability of the confining surfaces influences the properties of the nano-confined water is not clearly known. Obviously the aforementioned instruments, SFA, IFM, or TDFM, cannot image the surface topography with high lateral resolution to acquire information about surface properties. Therefore, to comprehensively study the properties of nano-confined liquids, an instrument that can perform force measurements for a) Email: [email protected]
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a separation smaller than 1 nm and topography imaging with high lateral resolution is absolutely necessary. Atomic Force Microscopy (AFM), which permits to acquire high resolution topography images and perform high resolution force measurements between an AFM tip and a sample surface, provide an opportunity to investigate the properties of nano-confined water with unprecedented advantage. Indeed, a variety of experimental techniques based on AFM have been utilized to probe the properties of liquid in the vicinity of different substrates.9, 10 The solvation forces in OMCTS (Octamethylcyclotetrasiloxane) and n-dodecanol near Highly Oriented Pyrolytic Graphite (HOPG) are observed using force-distance spectroscopy with the contact mode AFM, but this oscillatory behavior is not seen in water.11 The Frequency Modulation (FM) AFM based technique is employed to measure the solvation forces at the interface between OMCTs and HOPG.12 The FM-AFM equipped with a carbon nanotube probe is also used to study the oscillatory and hydration forces in the vicinity of self assembled monolayers on gold substrate13 as well as on biological membranes.14 Additionally, in FM-AFM, since the oscillating frequency of the cantilever as well as the phase difference with respect to the cantilever driving signal are both recorded, this technique also enables the study of the viscoelasticity of the nano-confined liquids.11, 12 However, in FM-AFM, the interacting forces and the viscoelastic properties of nano-confined liquid are deduced indirectly from the frequency and phase shifts of the cantilever using complicated mathematical formulas with approximations. On the other hand, optical interferometer based AFM method can simultaneously measure the normal and shear stiffness using the vertical and lateral oscillations with high sensitivity, but this method is subject to cross-talk of vertical and lateral signals, cantilever-optical fiber alignment deviations and it is not compatible with commercial AFMs.15 Therefore, a method that is easy to use and can simultaneously, directly, and unambiguously measure the solvation forces and viscoelasticity
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of nano-confined liquid with high resolution is apparently in need. In this paper, we present a new AFM-based technique for simultaneous, quasi-statical normal and lateral force measurements in nano-confined liquid as a function of tip-sample separation distance.2, 3 A lateral shearing signal is applied to the AFM cantilever by a lock-in amplifier while it is approaching the solid surface. The normal and lateral forces experience by the AFM tip in liquid can be recorded at the same time. Thus this technique permits an in situ investigation of the structural and dynamical properties for nano-confined fluids and can be employed easily with most commercial AFM without instrument modification. In addition, with a recently developed correction procedure to account for the linear drift of the piezo transducer, we are able to precisely determine the tip-sample separation down to one molecule layer and investigate the properties of water confined between a gap smaller than 1 nm. To demonstrate the capabilities of this technique, in the following we will present the results obtained from various liquid-solid interfaces. More specifically, we will discuss the normal solvation forces of OMCTS in the vicinity of mica and HOPG, the normal solvation and lateral viscous forces of nano-confined water on mica, as well as the viscoelastic properties of nano-confined water studied with our technique.
II. EXPERIMENTAL A. Experimental setup
In this work, we use a commercial AFM (PicoPlus 5500, Agilent Technologies) equipped with a silicon AFM cantilever (NSC35, MikroMasch) with a typical tip radius, Rtip = 40 ± 10 nm to study the physical properties of the nanoconfined water. The normal and torsional spring constants of the cantilever are kN ≈ 3–4.5 N/m and kT ≈ 50–120 N/m, respectively. These force constants are determined by imaging the cantilevers with a Scanning Electron Microscope (JEOL JSM-5910) to acquire their physical dimensions after each measurement (More details in the text below). In addition, we also perform inspections on the tip apex. We have found that a rough tip surface with protuberances will prevent the observation of solvation forces in liquid.2 An AFM liquid cell is used to contain the sample, liquids, and the AFM cantilever inside an environmental chamber. This chamber is in ambient conditions for experiments with water and is filled with ultrafiltered nitrogen gas for OMCTS. The liquid cell is cleaned by rinsing and sonication first in ethanol followed by Isopropyl Alcohol and then blown dry with compressed nitrogen gas. The mica and HOPG surfaces are prepared by the tape-exfoliation method and then blown with compressed nitrogen gas to eliminate any surface debris. The cleanliness of the surfaces are examined by AFM topography images over areas of 1 μm2 with contact mode AFM imaging. To insure the tip is shearing in parallel to the sample surface, before each measurement, we tilt the sample stage and obtain the AFM topography image of the surface until the difference in height across a surface distance of 1 μm is less than 1 nm. This height difference corresponds to a tilted angle of less than 0.06◦ between the tip and sample surface. This proce-
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FIG. 1. Schematic of the experimental setup. With a lock-in amplifier, a lateral shearing signal is applied to the AFM tip as it approaches the solid surface. The normal and lateral force are recorded simultaneously. Both the tip and the sample surface are immersed in a liquid environment.
dure is highly necessary because if there is a large angle between the shearing direction and sample surface, there will be an artifact-like lateral force due to lateral tapping between the tip and the surface, leading to unknown experimental errors. The schematic of experimental setup is shown in Figure 1. A silicon AFM tip approaches a solid surface (mica or HOPG) while a lateral oscillation is applied to it by a lockin amplifier at the same time. A laser projected onto the back of the cantilever is reflected into a 4 quadrant photodiodes, as shown in Figure 1. The normal force FN experienced by the cantilever in liquid can be written as FN = δX · kN ,
(1)
3
where kN = E4 wt is the normal spring constant and δX is the L3 vertical bending of the cantilever due to tip-surface force. In addition, E is the Young’s modulus of silicon16 while L, w, and t are the length, width, and thickness of the cantilever, respectively. The vertical cantilever bending δX = δVN · m, where δVN is the deflection signal measured by the photodiodes shown in Figure 1 and m is the optical lever sensitivity of the cantilever used. During the approach, a lateral oscillation, X0 · sin(ωt), is applied to the piezo-scanner via a lock-in amplifier (Stanford Research Systems, SR830), where X0 and ω are respectively the oscillation amplitude and frequency. The application of lock-in amplifier for data acquisition greatly enhances the signal to noise ratio. The lateral force FL experienced by the cantilever in liquid can be written as FL = kT · hθ, 2
(2)
where kT = 0.4 · kN · (h+L t )2 is the torsional spring constant 2 of the cantilever, h represents the tip height, and θ is the torsional angle of the cantilever due to the presence of the lateral viscous force. The torsional angle θ is also monitored by the laser beam reflected from the backside of the cantilever and recorded by the photodiodes as VL as shown in Figure 1. For a rectangular cantilever used in our AFM system, the torsional angle θ is proportional to VL through the following
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relationship:17 θ (rad) = VL (V)/(7.5 × 103 ) (rad/V).
(3)
Combining Eqs. (2) and (3), we arrive at the lateral force experienced by the cantilever at a given tip-surface separation, L2 FL = 0.4 · kN · 2 · h + 2t
h · V 7.5 × 103
.
(4)
This lateral force, FL (z) = FL sin[ωt+ φ(z)], experienced by the AFM tip in liquid as a function of tip-solid separation distance z, is then measured by the lock-in amplifier, where φ(z) is the phase difference between the applied lateral driving signal and the detected lateral force signal. At φ = 0, the tip is in hard contact with the solid surface and the lateral oscillation amplitude is small enough to guarantee a purely elastic contact deformation without slippage.18
and retracting scanner deformations, respectively. The initial slopes of the approaching and retracting curves in the contact regime, with linear drift present, are Sa 0 and Sr 0 as shown in Figure 2(a) For the approaching curve, we have Sa 0 = ba 0 /Za 0 , where ba 0 and Za 0 are the cantilever bending and piezo deformation when there is linear drift. After applying the new unit, the absolute value of the slope of the force curve at the contact regime should be 1, that is Ub · ba0 U = b · Sa0 = 1, Ua Ua · Za0
0
(5)
such that Ub =
Ua . Sa0
(6)
Similarly, for the retracting curve, we will have Ub = Ur /Sr 0. By combining Eqs. (5) and (6), we arrive at Sr0 · Ua . (7) Sa0 If we assume that the drift velocity, Vdrift , is in the same direction as tip retraction, then the modified approaching (Z[Ua ]) and retracting (Z[Ur ]) distances are Ur = Ub · Sr0 =
B. Drift analysis
Since the tip approaches the solid surface at a rate of only 0.2 nm/s (in water) or 0.4 nm/s (in OMCTS), the linear drift of the piezo scanner becomes important and cannot be neglected in the data analysis. When no linear drift is present, the approaching and retracting FN vs. d curves should overlap and have a slope of “−1” in the range where the tip is in contact with the surface, due to the fact that at hard contact the piezo movement and cantilever bending are equivalent. However, because of the linear drift, the contact lines will not overlap as shown in Figure 2(a) This can be understood as piloting a boat downstream and upstream a river to measure the velocity of the current. The measured velocity of the current going downstream or upstream will depend on the velocity of the boat. When no linear drift is present, the total deformation for the piezo-scanner, Z as shown in Figure 2, should be identical for both tip approaching and retracting movements. The total displacement showed in the raw force curves by the AFM for directions are both “Z nm.” However, owing to the drift, this “Z nm” for the approaching and retracting curve is actually different. This drift can be calibrated by introducing new length units (while the old unit is “1 nm”) for the scanner deformation and cantilever bending such that after correction the slopes of both contact lines shall be “−1.” The new units are Ub , Ua , and Ur for the cantilever bending, approaching
FIG. 2. (a) Typical force distance curves when a constant linear drift is present during measurement. The slopes of the approaching and retracting portions at the hard contact regimes are not the same. This drift can be accounted for using Eqs. (5)–(12). (b) Schematic shows water molecules confined between an AFM tip and a solid surface and form layering structures.
Z[Ua ] = (Vscanner + Vdrif t )T [nm],
(8)
Z[Ur ] = (Vscanner − Vdrif t )T [nm],
(9)
where Vscanner and T are the scanner movement velocity and the time to approach or retract the tip, respectively. From Eqs. (5)–(8), Ua , Ub , and Ur can be determined as Ua = Ur =
2Sa0 [nm], + Sr0
(10)
2Sr0 [nm], + Sr0
(11)
Sa0 Sa0
2 [nm]. (12) + Sr0 A simple home written program has been developed to automate this procedure. A typical example of a normal forcedistance curve is shown in Figure 3. Ub =
Sa0
C. Viscoelasticity of nano-confined water
The obtained lateral viscous forces can also be used to understand the viscoelastic properties of water. When water is confined between two smooth plates with surface area A, separated by a distance d, and with one plate sliding in parallel at a velocity Vshear with respect to the other, the viscosity η of water can be evaluated by η = FL · d/(Vshear · A), where FL is the lateral force required to maintain one plate moving at Vshear with respect to the stationary one.3 If a sinusoidal strain, γ = γ 0 · sin(ωt), is applied to one of the plates while the other is stationary, the resulting shear stress between two plates will be σ = σ 0 sin(ω · t + φ). Since the strain and stress amplitudes can be written as γ 0 = X0 /d and σ 0 = FL /A, respectively, we arrive at the following relationship: FL X = |G∗ | 0 , A d
(13)
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FIG. 3. (a) Typical cantilever bending – Scanner movement curves with constant drift in water. Red is the approaching curve and blue is the retracting curve. (b) After the correction by Eqs. (10)–(12), the approaching curve overlaps with the retracting curve and the slope of the contact regime is −1. (c) The cantilever bending – Distance curve before correction. The contact is not steady and drifts linearly. The oscillation period of the normal force does not match water molecular size, 0.25 nm. (d) The cantilever bending – Distance curve after correction. The curve shows a steady contact and the period of the oscillatory normal force is now with 0.25 ± 0.05 nm, water molecule size.
where G∗ = G + iG is the viscoelastic modulus19 containing both the storage (elastic) modulus (G ) and the loss (viscous) modulus (G ) of the material. Furthermore, with Eq. (13), G∗ can be written as G =
FL d cos φ AX0
and
G =
FL d sin φ. AX0
(14)
III. RESULTS AND DISCUSSION
Figure 4 summarizes the normal forces FN obtained for OMCTS at the interface of mica and HOPG. Figures 4(a) and 4(b) display data acquired without tip shearing during approaching the surface, while Figures 4(c) and 4(d) illustrate data obtained with tip shearing with the same surfaces. Each figure shows the overlap of more than 8 different
FIG. 4. (a) and (c) The approaching normal force-distance curves acquired in OMCTS on Mica with and without tip shearing, respectively. The vertical dashed lines indicate the layering of water molecules confined between the AFM tip and the surface. These data are obtained with shearing amplitude of 0.4 nm with different frequencies (34.9 kHz, 107.4 kHz, 212.3 kHz, and 884.7 kHz). (b) and (d) The approaching normal force-distance curves acquired in OMCTS on HOPG with and without tip shearing, respectively. These data are recorded with a shearing amplitude of 1.18 nm with various frequencies (58.1 kHz, 105.2 kHz, and 397.7 kHz). Excellent overlapping of multiple force-distance curves in all figures demonstrates the reproducibility of our measurements. The insets show the same force curves with larger vertical axes to show that all force curves diverge as d approaches zero.
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measurements demonstrating data reproducibility. When the tip is not laterally sheared with respect to the surface, the structural layering of OMCTS molecule is clearly observed in the FN vs. d data beginning approximately at d ≈ 4 nm from both surfaces. In Figures 4(a) and 4(b), the vertical dashed lines indicate the force maxima which correspond to the first through fourth molecular layers. These oscillatory forces have a period of 0.85–1 nm which is consistent with the diameter of the OMCTS molecules.20 The oscillations in the force curve occur when the tip-sample separation distance decreases and squeezes out a molecular layer of OMCTS, as already demonstrated by SFA5 and several AFM-based measurements.11, 12, 21, 22 Additionally, the oscillatory behavior is more clearly shown on Mica than on HOPG probability due to different surface wettability with OMCTS. The first layer of OMCTS molecules on the surface might not stick well on hydrophobic HOPG, leading to difficulties in forming layered structures of OMCTS molecules. Figures 4(c) and 4(d) show the approaching normal force for OMCTS molecules at the mica and HOPG interface with the tip is laterally sheared with respect to the sample surface (corresponding FL not shown), respectively. The oscillatory behavior of FN vs. d is clearly shown again for OMCTS on Mica but not on HOPG, due to different surface wettability. The force profiles of OMCTS confined between a silicon tip and HOPG are attractive when d < 2 nm, similar to previous results obtained with other AFM based techniques.12, 21, 22 The insets of Figures 4(c) and 4(d) display the same data with larger vertical scale showing that all forces are well converged when d approaches 0. The comparison between the normal forces in presence and absence of shearing indicates that shearing the tip mildly disrupts the layering process, giving rise to less pronounced oscillations. This effect is particular evident on HOPG. Figures 5(a) and 5(b) shows the normal and lateral forces simultaneously captured as a function of the tip-sample separation in deionized ultra filtered (DIUF) water on Mica with the technique discussed in Sec. II. The data were acquired with a lateral shearing amplitude X0 = 0.4 nm and
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a frequency ω = 995 Hz, respectively. The dashed vertical lines highlight the molecular order in the repulsive oscillatory solvation force. The average diameter of water molecule is found to be 0.27 nm, consistent with results reported in the literature.4, 7, 13–15, 23–25 Furthermore, the lateral force FL increases drastically when the tip-sample distance decreases, especially for d < 1 nm. Such increase of FL of liquid at small d has been demonstrated by other experimental techniques.7, 23, 26, 27 The increase of FL is related to the increasing viscosity of water, which can be estimated with Eq. (13), assuming water is confined between two smooth plates. In the case of a spherical AFM tip with radius RTip ≈ 40 nm moving in parallel to a smooth surface with a separation distance d < 1.5 nm and a shearing velocity Vshear , a more rigorous treatment2 leads to η=
FL 2π Vshear (R + d) ln 1 +
h d
− h
,
(15)
for water confined between 0 < z < d + h (See Figure 2(b)). For h ∼ 0.25 nm (size of water molecule) and h = 0.5 nm, the viscosity of the confined water can be estimated to be ∼3 × 102 P, almost 4 order in magnitude larger than that of the bulk water, which is about 10−2 P. This unusual behavior suggests the possibility of lateral order in water molecules, which is usually observed only for spherical non-polar molecules.28 Recent AFM based measurements have also observed laterally organized water on Mica and deduced a molecule diameter of 0.2–0.3 nm.29, 30 Next, by using Eq. (14), the viscoelastic response of the nano-confined water can be derived directly from the lateral force, FL , and phase change, , as shown in Figure 5(b). The obtained elastic component, G , and viscous G component, as a function of tip-sample distance d is displayed in Figures 5(c) and 5(d), respectively. At this experimental conditions, X0 = 0.4 nm and ω = 955 Hz, the elastic component is larger than the corresponding viscous component for d < 1 nm, indicating the glassy state of nanoconfined water, consistent with previous measurements with TDFM8 and other AFM based techniques.30, 31
FIG. 5. (a) and (b) The normal and lateral force curves obtained simultaneously as a function of tip-sample distance in water on a Mica surface, respectively. All curves displayed here are acquired with a shearing amplitude of 0.4 nm and a frequency of 995 Hz. (c) and (d) Elastic and viscous moduli G and G as a function of tip-sample distance determined from one of the lateral force curves (open square) shown in (b).
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IV. CONCLUSION
In the foregoing we have presented a technique with AFM which permits simultaneous measurements of the normal solvation force and lateral viscous forces of nanoconfined liquid as well as its viscoelastic properties. With proper cantilever calibrations and the successful correction of the linear drift of the piezo scanner, we are able to capture the structural and viscoelastic properties of liquid at the solid interface with a confining gap down to ∼0.3 nm, which are difficult to achieve with other techniques summarized in Sec. I. We demonstrate the capability of this experimental technique by studying the oscillatory normal force of OMCTS on Mica surfaces, showing a oscillation period of 0.85–1 nm, which is consistent with diameter, 0.7–0.85 nm, of OMCTS.20 Similar experiments with DIUF water on mica surfaces also show the layered structure of nanoconfined water, finding an oscillation period of ∼0.27 nm, consistent with the diameter of a water molecule and with previously reported values.4, 15, 24, 25 Furthermore, the viscoelastic properties, namely viscous and elastic modulus, as well as relaxation time of confined liquids can be directly obtained from the acquired lateral force data. This novel technique provides an approach to comprehensively study and understand the physical properties of nano-confined liquids.32 ACKNOWLEDGMENTS
T.-D.L., H.-C.C., D.O.-Y., and E.R. acknowledge the financial support of the Office of Basic Energy Sciences DOE (DE-FG02-06ER46293). E.R. acknowledges the National Science Foundation NSF (CMMI-1100290) for partial support. We thank Suenne Kim for extensive discussions. 1 J.
N. Israelachvili, Intermolecular and Surface Forces (Academic Press, 1992). 2 T. D. Li, J. P. Gao, R. Szoszkiewicz, U. Landman, and E. Riedo, “Structured and viscous water in subnanometer gaps,” Phys. Rev. B 75, 115415 (2007). 3 T. D. Li and E. Riedo, “Nonlinear viscoelastic dynamics of nanoconfined wetting liquids,” Phys. Rev. Lett. 100, 106102 (2008). 4 J. N. Israelachvili and R.M.Pashley, “Molecular layering of water at surfaces and origin of repulsive hydration forces,” Nature (London) 306, 249 (1983). 5 R. G. Horn and J. N. Israelachvili, “Direct measurement of structural forces between two surfaces in a nonpolar liquid,” J. Chem. Phys. 75, 1400–1411 (1981). 6 S. A. Joyce and J. E. Houston, “A new force sensor incorporating forcefeedback control for interfacial force microscopy,” Rev. Sci. Instrum. 62, 710–715 (1991). 7 M. P. Goertz, J. E. Houston, and X. Y. Zhu, “Hydrophilicity and the viscosity of interfacial water,” Langmuir 23, 5491–5497 (2007).
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Antognozzi, A. D. L. Humphris, and M. J. Miles, “Observation of molecular layering in a confined water film and study of the layers viscoelastic properties,” Appl. Phys. Lett. 78, 300–302 (2001). 9 M. Abdelhamid and B. Bharat “Nanorheology and boundary slip in confined liquids using atomic force microscopy,” J. Phys.: Condens. Matter 20, 315201 (2008). 10 E. Bonaccurso, M. Kappl, and H.-J. Butt, “Thin liquid films studied by atomic force microscopy,” Curr. Opin. Colloid Interface Sci. 13, 107–119 (2008). 11 S. J. O’Shea, M. E. Welland, and T. Rayment, “Solvation forces near a graphite surface measured with an atomic force microscope,” Appl. Phys. Lett. 60, 2356–2358 (1992). 12 S. J. O’Shea and M. E. Welland, “Atomic force microscopy at solid−liquid interfaces,” Langmuir 14, 4186–4197 (1998). 13 S. P. Jarvis, T. Uchihashi, T. Ishida, H. Tokumoto, and Y. Nakayama, “Local solvation shell measurement in water using a carbon nanotube probe,” J. Phys. Chem. B 104, 6091–6094 (2000). 14 M. J. Higgins et al., “Structured water layers adjacent to biological membranes,” Biophys. J. 91, 2532–2542 (2006). 15 S. Patil et al., “A highly sensitive atomic force microscope for linear measurements of molecular forces in liquids,” Rev. Sci. Instrum. 76, 103705 (2005). 16 E. Meyer, H. J. Hug, and R. Bennewitz, Scanning Probe Microscopy: The lab on a Tip (Springer, 2004). 17 T.-D. Li, Ph. D. thesis, Georgia Institute of Technology, 2008. 18 R. W. Carpick, D. F. Ogletree, and M. Salmeron, “Lateral stiffness: A new nanomechanical measurement for the determination of shear strengths with friction force microscopy,” Appl. Phys. Lett. 70, 1548–1550 (1997). 19 J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, 1980). 20 D. W. Scott “Equilibria between linear and cyclic polymers in methylpolysiloxanes,” J. Am. Chem. Soc. 68, 2294–2298 (1946). 21 W. Han and S. M. Lindsay, “Probing molecular ordering at a liquid-solid interface with a magnetically oscillated atomic force microscope,” Appl. Phys. Lett. 72, 1656–1658 (1998). 22 R. Lim, S. F. Y. Li, and S. J. O’Shea, “Solvation forces using samplemodulation atomic force microscopy,” Langmuir 18, 6116–6124 (2002). 23 R. C. Major, J. E. Houston, M. J. McGrath, J. I. Siepmann, and X. Y. Zhu, “Viscous water meniscus under nanoconfinement,” Phys. Rev. Lett. 96, 177803 (2006). 24 J. R. Bonander and B. I. Kim, “Cantilever based optical interfacial force microscope,” Appl. Phys. Lett. 92, 103124 (2008). 25 S. Jeffery et al., “Direct measurement of molecular stiffness and damping in confined water layers,” Phys. Rev. B 70, 054114 (2004). 26 Y. Zhu and S. Granick, “Viscosity of interfacial water,” Phys. Rev. Lett. 87, 096104 (2001). 27 U. Raviv, P. Laurat, and J. Klein, “Fluidity of water confined to subnanometre films,” Nature (London) 413, 51 (2001). 28 J. Gao, W. D. Luedtke, and U. Landman, “Origins of solvation forces in confined films,” J. Phys. Chem. B 101, 4013–4023 (1997). 29 K. Kimura et al., “Visualizing water molecule distribution by atomic force microscopy,” J. Chem. Phys. 132, 194705 (2010). 30 T. Fukuma, Y. Ueda, S. Yoshioka, and H. Asakawa, “Atomic-scale distribution of water molecules at the mica-water interface visualized by threedimensional scanning force microscopy,” Phys. Rev. Lett. 104, 016101 (2010). 31 S. H. Khan, G. Matei, S. Patil, and P. M. Hoffmann, “Dynamic solidification in nanoconfined water films,” Phys. Rev. Lett. 105, 106101 (2010). 32 D. Ortiz-Young, H. C. Chiu, S. Kim, K. Voitchovsky, and E. Riedo, “The interplay between apparent viscosity and wettability in nanoconfined water,” Nat. Commun. 4, 2482 (2013).
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