Molecular Dynamics Simulation of Atomic Force Microscopy at the

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Molecular Dynamics Simulation of Atomic Force Microscopy at the Water– Muscovite Interface: Hydration Layer Structure and Force Analysis Kazuya Kobayashi, Yunfeng Liang, Ken-ichi Amano, Sumihiko Murata, Toshifumi Matsuoka, Satoru Takahashi, Naoya Nishi, and Tetsuo Sakka Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b04277 • Publication Date (Web): 28 Mar 2016 Downloaded from http://pubs.acs.org on April 1, 2016

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Molecular Dynamics Simulation of Atomic Force Microscopy at the Water–Muscovite Interface: Hydration Layer Structure and Force Analysis Kazuya Kobayashi,1,2 Yunfeng Liang,2,* Ken-ichi Amano,1 Sumihiko Murata,2,* Toshifumi Matsuoka,2 Satoru Takahashi,3 Naoya Nishi,1 and Tetsuo Sakka1 1

Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto 615-8510, Japan

2

Environment and Resource System Engineering, Kyoto University, Kyoto 615-8540, Japan

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Japan Oil, Gas and Metals National Corporation (JOGMEC), Chiba 261-0025, Japan

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Corresponding author: Yunfeng Liang

Complete postal address: Kyoto University, Room C1-1-110, Kyotodaigaku-Katsura, Nishikyoku, Kyoto 615-8540, Japan Tel:

+81-75-383-3205

Fax:

+81-75-383-3203

E-mail:

[email protected]

*

Corresponding author: Sumihiko Murata

E-mail:

[email protected]

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Abstract

With the development of atomic force microscopy (AFM), it is now possible to detect the buried liquid–solid interfacial structure in three dimensions at the atomic scale. One of the model surfaces used for AFM is the muscovite surface because it is atomically flat after cleavage along the basal plane. Although it is considered that force profiles obtained by AFM reflect the interfacial structures (e.g., muscovite surface and water structure), the force profiles are not straightforward because of the lack of a quantitative relationship between the force and the interfacial structure. In the present study, molecular dynamics simulations were performed to investigate the relationship between the muscovite–water interfacial structure and the measured AFM force using a capped carbon nanotube (CNT) AFM tip. We provide divided force profiles, where the force contributions from each water layer at the interface are shown. They reveal that the first hydration layer is dominant in the total force from water even after destruction of the layer. Moreover, the lateral structure of the first hydration layer transcribes the muscovite surface structure. It resembles the experimentally resolved surface structure of muscovite in previous AFM studies. The local density profile of water between the tip and the surface provides further insight into the relationship between the water structure and the detected force structure. The detected force structure reflects the basic features of the atomic structure for the local hydration layers. However, details including the peak–peak distance in the force profile (force–distance curve) differ from those in the density profile (density–distance curve) because of disturbance by the tip.


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INTRODUCTION Interfacial water structures on solid surfaces are of great interest in a wide range of science fields, such as geochemistry, soil science, biology, tribology, and physical chemistry.1–18 When water comes into contact with a hydrophilic solid, it is strongly attracted to the surface and its properties are different from those in the bulk phase because of significant interactions with the hydrophilic solid.3 The hydration force between two hydrophilic solids measured by surface force apparatuses is a monotonically repulsive force.2,3 It very rapidly increases with decreasing separation at very small separations (below 1–1.5 nm). If the surfaces are hydrophilic and atomically flat, the hydration force shows oscillations with an overall repulsive background.2,3 Israelachvili and Wennerstrom3 hypothesized that the repulsive force is entropic in nature. However, it is difficult to construct molecular images to determine how the entropy actually contributes to the repulsive force. Further experiments and simulations are required to test the validity of this hypothesis with a realistic system. Atomic force microscopy (AFM) is one of the best methods to reveal interfacial structures on solid substrates.10–16,19–36 Three-dimensional solvation structures have been revealed on the hydrophilic muscovite surface.10–16 Because of the high lateral resolution of the technique, not only the solvation structure but also the crystal surface structure of muscovite can be obtained, and the images well reproduce the crystal periodicity.19–24 Furthermore, previous studies have been able to show a clear lateral distribution image of adsorbed ions.14–16 Carbon nanotube (CNT) tips have been integrated in AFM systems, and show promising sensitivity for imaging with nanoscale lateral precision because of the high aspect ratio.28–33 Although force profiles obtained by AFM reveal many interfacial properties, the force profiles are not straightforward because of the lack of a quantitative relationship between the force and the interfacial properties.


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Moreover, the AFM tip will inevitably displace the water of the detected area. It is not clear how the disturbance by the AFM tip changes the hydration layers on solid surfaces. This microscopic change should influence the total measured force. Simulations are useful to determine microscopic interfacial properties (e.g., hydration structures).14–18,34,35,37–52 Some pioneering studies have discussed the relationship between the force profile and the interfacial structure using molecular dynamics (MD) simulations14–16,34,35,44– 51

and the statistical mechanics of a simple liquid.52 In those studies, it was demonstrated that the

oscillatory force profiles are correlated with the explicitly determined solvation structure.44,45 Hydration layers have been widely discussed based on simulation studies of water–mineral interfacial structures.12,14–16,34,35,46–50 Very recently, the three-dimensional hydration layer structure on muscovite was resolved by AFM experiments12 with the aid of MD simulation results.46 The mechanism of AFM imaging of three-dimensional hydration structures has been discussed for the mineral-water interfacial system.35,47-50 Efforts have been focused on the entropic effect35,47,50 and the contribution from water hydration layers.48,49 However, information about the force from each individual hydration layer is still missing.35 If the contribution of each layer is clear, we should be able to better interpret the experimental data. In this study, we construct a MD simulation system containing a muscovite surface and a water interfacial system with an AFM tip. The aim is to reveal the role of each water layer on the muscovite surface during AFM measurements. For this purpose, we determine divided force profiles, where the total force from water is decomposed into contributions from each hydration layer. The relation between the AFM forces, hydration structure, and disturbance of each hydration layer by the AFM tip is investigated in detail, especially what the dominant role of


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each layer to a measured force is, and how the disturbance of the AFM tip is reflected by the measured force.

Figure 1. Simulation system: (a) snapshot of the whole system, (b) top view, and (c) [1−10] projection of the muscovite surface. The numbers in (b) represent the force-scanning positions of the AFM tip. Yellow balls: Si, blue balls: Al, red balls: oxygen, magenta balls: K+, grey balls: hydrogen. Note that there is a K+ ion below position 4.

COMPUTATIONAL METHODS An AFM tip was constructed by combining a CNT and a fullerene molecule. The tip structure (see Figure S1) was optimized using the empirical force field described below. The chiral vector of the CNT is (30, 0). Thus, the AFM tip contains 3240 carbon atoms and is ~2.3 nm in diameter and 11.4 nm long. The diameter is within the typical diameter range of single-walled nanotubes (1-3 nm).33 This tip structure is similar to that used in the MD study of Argyris et al.49 The


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interface system was constructed using 15,000 water molecules (initially 10.3 nm × 8.9 nm × 5.1 nm in volume). The muscovite crystal structure was taken from the X-ray diffraction measurements of Richardson.53 The hydrogen atoms were randomly inserted to saturate the Al– OH groups in octahedral layers. In total, 20 × 10 × 1 crystal unit cells (see Figure S2) with a size of 10.4 nm × 9.0 nm × 2.0 nm were used with the cleavage basal plane exposed to the water. The constructed water–muscovite interfacial system with the AFM tip is shown in Figure 1. Muscovite has a well-defined (001) cleavage surface, which gives an atomically flat surface in real experiments. In this study, we used the surface with K+ ions, which are uniformly distributed on the cleavage surface according to electrostatic interactions. It has been shown that K+ ions do not randomly adsorb but form preferentially ordered structures such as rows or geometrical domains.15 In this study, the K+ ions are distributed so that each ion has two neighbor aluminum atoms (Si4Al2 ring site) and forms a row structure (Figure 1(b)). This configuration has been used in the previous MD simulations.39,41,42 The basal plane (Figure 1(b)) mostly consists of tetrahedral SiO4. Isomorphous substitution of Al3+ (blue balls) for Si4+ leads to a net negative charge on the muscovite surface. As a result, K+ ions prefer to be located around the substituted sites. We consider that the K+ ion position shown in Figure 1(b) and (c) is the most reasonable choice. First principles study has confirmed the stability of this K+ position.37 The Si4Al2 ring site is more stable for the K+ ion than the Si5Al1 ring site by 14 kJ/mol. The other possible K+ position, which competes with the ring sites, is the on-top site of the substituted tetrahedral Al sites. However, adsorption to this site is 84 kJ/mol higher in energy than adsorption to the Si4Al2 ring site.37 According to the potential of mean force for K+ ions on muscovite calculated using an empirical potential, it has been suggested that inner-sphere adsorption above substituted


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tetrahedral Al sites would be stable.43 However, recent X-ray crystal truncation rod (CTR) reflectivity data clearly disprove this suggestion.7 The GROMACS package (version 4.5.6)54 was used for the MD simulations. The SPC/E model,55 CLAYFF force field,56 and Joung and Cheatham monovalent ion model57 were used for water, muscovite, and K+ ions, respectively. An intramolecular potential58,59 for the carbon– carbon interactions of the AFM tip was used to relax the tip structure. The intramolecular force field was developed by fitting the experimental properties of graphite (lattice parameters, elastic constants and phonon frequencies).58 For CNTs, it has been demonstrated that the breathing frequency of CNTs calculated using this force field is in agreement with experiments.59 The Lennard-Jones (LJ) parameters for the carbon atoms in the AFM tip were taken from the paper of Cheng and Steele.60 The LJ parameters for unlike atoms were determined by the Lorentz– Berthelot combination rule.54 The cutoff distances were 1.0 nm for both LJ and electrostatic potentials. The particle mesh Ewald summation method was used for long-range electrostatic interactions.61 For all of the simulations, the temperature was controlled at 298 K by the Nose– Hoover thermostat,62,63 where the time constant was 2.0 ps. The positions of carbon atoms in the AFM tip, silicon and tetrahedral aluminum atoms in muscovite, and K+ ions were fixed unless specified otherwise. By fixing the atoms, we prevented K+ ions from detaching from the surface during the simulations. This makes the lateral position of the AFM tip well defined. We performed an additional simulation to demonstrate that this calculation setting does not affect the hydration structure. The fixation of carbon atoms in the AFM tip enables us to separate force into contribution from different hydration layers. It is regarded as a reasonable approximation, since CNTs have high rigidity and high Young’s modulus, namely hardly to be deformed.33 The oxygen atoms in muscovite were free to move. We changed the separation distance between the


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AFM tip and the muscovite surface by steered MD simulations. In the steered MD simulation, the tip was inserted into and retracted from the middle of the bulk water (to reduce the “macroscopic” flow effect induced by the motion of the tip) with an umbrella potential. Then, force with different separation distance is obtained by equilibrium MD simulations. There are two different approaches to calculate the AFM force, one is direct approach (i.e. a summary of the total force of atoms in the AFM tip); 44–46,49 another is free energy approach (i.e. from the derivative of the potential of mean force).34,35,47,48,50 In this study, the forces were calculated by direct approach from the equilibrium MD simulations. We considered the forces on carbon atoms within 1.4 nm from the top of the tip. The tip has a spherical cap at the top, which is called the top of the tip in this work. It was confirmed that the conclusions of this study do not change by including carbon atoms further away from the top of the tip (within 2.0 nm, see Figure S3). The intramolecular forces on the CNT, including both nonbonded and bonded interactions, were excluded when we calculated the force. Figure 1(b) shows the force-scanning positions of the AFM tip in this study, where we chose eight independent lateral sites considering the crystal periodicity. All of the equilibrium MD simulations were performed for 3.0 ns. The forces and atomic trajectories were recorded every 0.5 ps during the final 1.0 ns for taking the average values. Error bars were estimated on the basis of segments of 0.5 ns. In this study, 24 different configurations at different separation distances (from ~0 nm to ~1.2 nm above the surface) were considered at each lateral position. In total, 576 (3 × 24 × 8) ns MD simulations were performed excluding the steered MD simulations. Snapshots of the simulation systems were prepared by Visual Molecular Dynamics software.64


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Figure 2. Number density of water oxygen atoms along the direction normal to the muscovite surface compared with results obtained by X-ray CTR experiments and MD simulations.42 For the curves in this work, the solid line is the results from the simulation with fixed K+ ions, and the dashed line is the results from the simulation allowing K+ ions to freely move. Note that the experimental data from Sakuma et al.6 and Lee et al.7 are the electron density profiles, whereas the data from Cheng et al.5 are the number density of water oxygen atoms. The first, second, and third peaks are adsorbed water, the first hydration layer, and the second hydration layer, respectively. RESULTS AND DISCUSSION MD simulations revealed the spatial coordinates of water at the muscovite–water interface. The simulations suggest that there are three water layers at the interface. Figure 2 shows the number density profile of the oxygen atom in water along the direction normal to the interface, in which three peaks can be observed. In the calculation of the number density profile, the cylindrical


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space near the AFM tip was excluded (i.e., the result can be considered as the number density of the interfacial system without the AFM tip). The density profile obtained in this study is in good agreement with previous MD simulations41,42 and X-ray CTR measurements5–7 despite differences in the force fields and simulation settings. It is noted that different definitions on the first, the second and the third peaks have been used.5,12,15 In Refs. 5 and 12, they were named as the adsorbed water, the first hydration layer, and the second hydration layer, respectively. In Ref. 15, they were named as the first hydration layer, the second hydration layer, and the third hydration layer. There are advantage and disadvantage of each definition. Throughout this work, we have followed the convention of Refs. 5 and 12, that is, the water molecules in the first peak are called adsorbed water. They are located at the center of the hexagonal ring (e.g., position 8 in Figure 1(b)), and indeed in the same layer as the adsorbed K+ ions. The water molecules in the first hydration layer (i.e., the second peak) are close to but slightly above K+ ions. The water molecules in the second hydration layer (i.e., the third peak) are on top of K+ ions. Additional simulations were performed allowing K+ ions to freely move, and it was found that the hydration structure is about the same (Figure 2).


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Figure 3. Force–distance curves for the eight positions shown in Figure 1(b). is the force between the AFM tip and water, is the force from the muscovite surface, and is the sum of and . in (a) is the number density of water for comparison. Note that the error bars are mostly smaller than the scatters.


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Force–distance curves obtained for the eight different lateral sites are shown in Figure 3. Note that on the horizontal axis is defined as the distance between the center of mass of the topmost five carbon atoms of the AFM tip (see Figure S1) and the center of the mass of the silicon atoms at the muscovite surface, from which we subtract σOW–C = 0.328 nm. σOW–C is the LJ potential parameter between the carbon atom in the CNT and the oxygen atom in water at which the LJ potential is zero. As expected, the force curves are dependent on the lateral position of the AFM tip. The total force curves ( ) show the same general trend of force curves obtained by AFM at hydrophilic solid–water interfaces using a CNT tip.29,31,32 That is, strong background repulsion can be observed as the tip approaches. Oscillatory forces were obtained for positions 2, 3, 5, and 8 (as shown in Figure 3(b), (c), (e), and (h)), whereas the repulsive force is the major feature for positions 1 and 4 (as shown in Figure 3(a) and (d)). The oscillatory features for sites 6 and 7 (as shown in Figure 3(f) and (g)) are weak but detectable. To obtain insight into the relationship between the hydration layer and the calculated AFM forces, the number density profile of water oxygen ( ) is shown along with the force–distance curve in Figure 3(a). This qualitatively shows that the AFM tip breaks structured water at the interface. We assign the oscillatory peak at = 0.3 nm (ranging from 0.172–0.372 nm) in the force–distance curves to breaking of the first hydration layer. Although the main difference in the total force ( ) comes from the force from water ( ), the force from muscovite ( ) slightly reflects the mineral structure with an attractive force minimum. The distance () that gave the minimum force from the muscovite surface varied with the lateral position. In detail, when the AFM tip is above a K+ ion (at position 4), the distance was the furthest from the surface among the lateral scanning positions (as shown in Figure 3(d)). This suggests that the AFM tip felt the K+ ion in this calculation, similar to an experiment


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resolving ions on top of the muscovite surface.13 Indeed, position 4 presents the strongest (total) repulsive force among all of the tip positions.


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Figure 4. Divided force profiles. The water molecules are categorized by their coordinate normal to the interface: Adsorbed water ( ), first hydration layer ( ), and second hydration layer ( ) correspond to the first, second, and third peaks shown in Figure 2, respectively. is the other water. is the sum of all water contributions (i.e., in Figure 3). in (a) is the number density of water for comparison. Note that the error bars are mostly smaller than the scatters.


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We divided the force curves into the contribution of each water layer. The results are shown in Figure 4, where the definition of the water layer is based on the coordinate of the water molecule in the direction normal to the interface (Z). The values of Z that distinguish the water layers are Z = 0.248 nm, Z = 0.514 nm, and Z = 0.748 nm (see Figure 2). The force from the bulk ( ) is repulsive at any separation distance between the tip and the surface. The reason why the force is repulsive at all separation distances is because of the hydrophobicity of the CNT. At large separation distances (D > 1.0 nm), is almost constant. This constant value was subtracted as a background in the simulation study of Argyris et al.49 When the tip approached the muscovite surface, slightly increased until = 0.4 nm and then decreased, probably because the tip experienced a different bulk water environment. We have revealed that the repulsive background force from water at short separation distances is mainly from the first hydration layer. This is shown in Figure 4, where the force–distance curve from the first hydration layer ( ) resembles the profile of the total force from water ( in Figure 4 and hence in Figure 3) when the tip approaches the interface. One may think that the repulsive force originates from strongly adsorbed water at the interface (the first peak in Figure 2). However, adsorbed water affects the total force very locally because the contribution of adsorbed water becomes significant only when the tip is above adsorbed water (i.e., position 8, Figure 1(b) and (c)). Note that even if the tip is located on top of adsorbed water (position 8, as shown in Figure 4(h)), the first hydration layer strongly contributes to the total force. It was found that the oscillatory behavior in the total force from water ( in Figure 3 or in Figure 4) at around D = 0.3 nm is from the first hydration layer. Therefore, it can be considered that the first hydration layer is destroyed, when D< ~0.3 nm, as suggested in previous studies of fluorite and calcite surfaces.35,47,48,50 It seems that the first hydration layer pushes up


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the tip even after destruction (i.e., the oscillatory region), which may be caused by the lateral strength of the layer owing to the strong hydrophilicity of the substrate. Differing from the surface force and conventional AFM measurements (where water is in between two hydrophilic solid surfaces), the CNT tip is hydrophobic in nature. However, we were able to determine whether the overall repulsive force results from the first hydration layer. Furthermore, from Figure 4, the second hydration layer, whose structure is less stable than that of the first hydration layer, only slightly contributes to the background repulsion.

Figure 5. Force–distance curve for the topmost five atoms in the AFM tip. Lateral position 2 is chosen as representative. Note that position 2 was selected as representative for detailed study because the density of the first hydration layer at this position is among the highest (as will be shown in Figure 6(a)). All of the other lateral positions (except for positions 4 and 8 in Figure 1(b)) show similar results, as shown in Figure S4.


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Finally, the background repulsion force, which is seen at D < ~0.3 nm, is because of the interaction between the edge of the tip (namely, atoms other than the topmost carbon atoms) and the first hydration layer. In fact, if we use only the topmost five carbon atoms of the AFM tip (i.e., the top of the cap, see Figure S1(a)) to calculate the force, the background repulsive force ( ) is not observed, as shown in Figure 5 for position 2. Instead, a much lower repulsive force is observed with an oscillatory peak (at around 0.27 nm) resulting from the first hydration layer, and a weak oscillatory peak (at around 0.60 nm) resulting from the second hydration layer. We will now discuss how the simulation results will aid in interpreting AFM experiments. It has been suggested that the first hydration layer gives dot-like10,11,20,22 and honeycomb-like patterns12,22 in AFM images. First, many AFM experiments of muscovite surfaces with different atmospheres show dot-like patterns in the presence of the water. The representative experiments of Liu et al. using contact mode AFM demonstrated that the observed patterns varied with the overlying liquid.20 When n-decanol was used as the overlying liquid, the pattern was honeycomb-like, whereas the dot-like pattern was obtained with water as the overlying liquid. In the case of noncontact mode, Fukuma et al. also observed the dot-like pattern in the cross-section near the surface in the three-dimensional scanning force microscope image.10 Even when the muscovite surface is imaged in air, it seems that the dot-like pattern is influenced by water because the strong hydrophilicity of the muscovite surface enhances water adsorption.24,27


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Figure 6. Two-dimensional lateral number density map of water in the (a) first and (b) second hydration layers. Points 1–8 are the same lateral positions as shown in Figure 1(b). The honeycomb-like pattern structure is composed of the red and yellow areas, and the dot-like structure is composed of the red points above K+ ions (magenta balls). This pattern may be influenced by the ionic strength of the aqueous solution and the distribution of K+ ions.


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Figure 6 shows the number density map of the first and second hydration layers parallel to the interface. Overall, they are similar to the reported images from MD simulations.15 However, the high-density spots differ because the previous study used a muscovite surface only a single row of K+ ions (on the surface area of 4.1 nm × 5.5 nm), that is, with a lower coverage of K+ ions than that in our study. The interesting point is that the structure of the first hydration layer has a honeycomb-like pattern, although it can be considered dot-like by taking the highest-density areas (Figure 6(a)). The density contrast seems to be enhanced by K+ ions (shown as magenta balls) and substituted tetrahedral Al sites (shown as blue balls), which agrees with the previous simulation results.15 There is some correlation between the oscillation feature for positions 2, 3, and 5–8 (as shown in Figure 3(b), (c), and (e)–(h), respectively) and the high-density spots of the first hydration layer with the exception of position 8, where adsorbed water molecules are present (Figure 4(h)). This water adsorption site is the only site that also significantly contributes to the repulsive force and may actually influence the nearby first hydration layer structure. Overall, the number density maps are similar to the AFM images.10–12,22 For example, the highdensity areas of the first hydration layer are on bridging oxygen atoms, similar to the image of Fukuma et al.10 Meanwhile, the structure of the second hydration layer can be considered dotlike by taking the highest-density areas (Figure 6(b)). When considering both the hydration layers together, it can be concluded that the measurement by Kobayashi et al.12 is reproduced well in our simulations; that is, the first and second hydration layers present honeycomb-like and dot-like patterns, respectively. In an early report, Fukuma et al. showed that the AFM images were either honeycomb-like or dot-like depending on the frequency shifts (i.e., different levels of tip–sample interaction force) and the amplitude of the tip motion used in their experiments.22 A small frequency shift resulted in a honeycomb-like pattern, while a relatively large frequency


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shift resulted in a dot-like pattern. This fact corresponds well with the density map for the first hydration layer, as shown in Figure 6(a).

Figure 7. Local number density profiles for water molecules confined between the AFM tip and the muscovite surface for lateral position 2. Four local number density profiles in which the top of the tip is in (a) the first hydration layer and (b) the second hydration layer are compared with the profile when the tip is at D = 1.172 nm. The vertical dotted lines in (a) and (b) show the local density peak position when the tip is at D = 1.172 nm, and the vertical dashed lines show the local number density peak position when the force in Figure 5 is the maximum for the two peaks (i.e., (a) D = 0.322 nm and (b) D = 0.622 nm resulting from two hydration layers).


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The force–distance curve in Figure 5 suggests that the top of the tip feels the local hydration structure because three distinct peaks are observed from each water layer contribution. This serves as an excellent example to investigate how the displacement of water in the detected area affects the AFM force. Figure 7 shows the local number density profile of water molecules along the direction normal to the surface plotted for various separation distance D. The local number density is calculated for water molecules within the lateral range around the AFM tip (within a diameter of 0.7 nm) located at position 2, when the separation distances between the tip and the surface are around the force peaks shown in Figure 5. Figure 7(a) shows the water density profiles when the top of the tip is in the first hydration layer, and Figure 7(b) shows the water density profiles when the top of the tip is in the second hydration layer. The vertical dotted and dashed lines show the positions of the local density peaks of the hydration layers when the tip does not affect the interfacial structure (i.e., the tip is sufficiently far from the surface) and when the force shows the peaks in Figure 5, respectively. The peak positions are estimated from the fitting of a Gaussian function to the peaks. In brief, our results show that the water layers are displaced from the original position toward the surface until the moment of destruction, at which time the force shows a peak. We call the displacement the “yielding displacement” in the following discussion. Figure 7(a) shows that the local density peak of the first hydration layer gradually moves toward the surface. The peak intensity first increases and then suddenly decreases (and almost disappears) after the force peak as the tip moves toward the surface. The hydration layer of the AFM tip has been widely discussed in the previous simulation works.34,35,49,50 It can be observed when D = 1.172 nm at Z = 1.2 nm in Figure 7. As the separation distance is shortened, interference between the hydration layer of the AFM tip and the first hydration layer firstly occurs. It leads an increase of the peak intensity when they overlap


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each other. The following decrease of the peak corresponds to destruction of the first hydration layer. Figure 7(b) shows that in the case of the second hydration layer, the local density peak height increases when the tip approaches the force peak (D = 0.622 nm in Figure 5) and gradually decreases after the force peak. Similarly, the increase of the peak intensity is attributed to the interaction between the hydration layer on the AFM tip and the second hydration layer on the muscovite surface. The decrease of the peak intensity indicates destruction of the second hydration layer. We now show how the yielding displacement may aid in better understanding experimental results; namely, how the measured force structures differ from the actual atomic structures. From the local density profile (Figure 7), the peak distance between the first and second hydration layers is 0.26 nm, which is calculated from the difference in the coordinates of the vertical dotted lines in Figure 7(a) and (b). Meanwhile, the peak distance between the first and second hydration layers from the force–distance curve is 0.32 nm (Figure 5). We suggest that this difference is caused by the difference in the amount of yielding displacement between the first and second hydration layers. The amount of yielding displacement is determined by the distance between the vertical dotted lines and the vertical dashed lines in Figure 7(a) and (b). These distances are 0.07 and 0.02 nm for the first and second hydration layer, respectively. That is, the force peak from the second hydration layer can be detected 0.02 nm closer to the surface than its original position. In contrast, the first hydration layer can be detected 0.07 nm closer to the surface than its original position. The larger yielding displacement for the first hydration layer (0.07 nm) than for the second hydration layer (0.02 nm) results from the fact that the first hydration layer is more stable than the second hydration layer. Furthermore, the difference leads to a 0.05 nm increase in the peak distance when we look at the force curve, which agrees with the discrepancy


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between the two hydration layer distances from the local density profile and the force (i.e., 0.06 nm). When the z coordinate of the force curve is calibrated against the muscovite surface, we recommend that the second hydration layer or water structures far from the muscovite surface are used, as in previous experiments,12 because the force peak is expected to be at almost the same position as its original position according to our simulation results. CONCLUSIONS We performed MD simulations of the muscovite–water interface with a CNT tip. The calculations reveal the contribution of each component (e.g., the force from muscovite and water, and the force from each water layer) to the observed force. There are three water layers at the interface, among which the first hydration layer dominates the total force. The force is largest between the edge of the AFM tip (namely, atoms other than the top carbon atoms) and the first hydration layer even after destruction of the first hydration layer. Our simulation results show that the first and second hydration layers have honeycomb-like and dot-like patterns, respectively. These findings are in agreement with the most recent AFM measurement by Kobayashi et al.12 Furthermore, the first hydration layer can be considered dot-like if we only take the highestdensity areas. This agrees with early experimental findings, where a dot-like pattern was often obtained by AFM when the muscovite surface was immersed in water,10,11,20,22 but the honeycomb-like pattern can be obtained with relatively small frequency shifts and a small amplitude (A = 0.2 nm) of the tip motion.22 Analysis of the local density between the tip and the surface provides further insight into the difference between the original hydration structure (i.e., the density profile) and the measured hydration structure (i.e., the force–distance curve). We show that the peak–peak distance in the force–distance curve between the first and second hydration layers is greater than the corresponding peak–peak distance of the original density


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profile of water. The difference is caused by the different displacements of the hydration layers by the AFM tip before destruction (the yielding displacement). CNT tips used in this study can be functionalized in real experiments.33 Force calculations with various tips (chemically functionalized or different apex) will be required for future study. The present study provides atomic-scale information about how to improve the interpretation of AFM experiments of the muscovite–water interface system. ASSOCIATED CONTENT Supporting Information Supporting Information Available: optimized carbon nanotube structure, snapshots of the muscovite unit cell, force–distance curves with different ranges of carbon atoms for force calculation, and force–distance curves from the topmost five atoms of the AFM tip for all of the eight lateral sites. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENT The authors acknowledge financial support from the Japanese Society for the Promotion of Science (JSPS) through a Grant-in-Aid for Scientific Research A (no. 24246148), JOGMEC, JST/JICA-SATREPS, and JAPEX.


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Table of Contents Graphic and Synopsis


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Molecular Dynamics Simulation of Atomic Force Microscopy at the

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