Mutual Identification between the Pressure-Induced Superlubricity and

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

The Mutual Identification between the PressureInduced Superlubricity and the Image Contrast Inversion of Carbon Nanostructures from AFM Technology Junhui Sun, Keke Chang, Daohong Mei, Zhibin Lu, Jibin Pu, Qunji Xue, Qing Huang, Liping Wang, and Shiyu Du J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00155 • Publication Date (Web): 05 Mar 2019 Downloaded from http://pubs.acs.org on March 6, 2019

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The Journal of Physical Chemistry Letters

The Mutual Identification Between the Pressure-induced Superlubricity and the Image Contrast Inversion of Carbon Nanostructures from AFM Technology Junhui Sun,1,2,3,4 Keke Chang,2 Daohong Mei,5 Zhibin Lu,3* Jibin Pu,1 Qunji Xue,1,3 Qing Huang,2 Liping Wang1* and Shiyu Du2* 1Key

Laboratory of Marine Materials and Related Technologies, Zhejiang Key Laboratory of Marine Materials and Protective Technologies, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China. 2Engineering Laboratory of Nuclear Energy Materials, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China. 3State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China. 4School of Mechanical Engineering, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China. 5School of Science, East China University of Technology. Nanchang 330044, China

ABSTRACT:

Previous studies predict pressure-induced superlubricity, but that is still undetermined due to absence of probing technique. Here, we present an unprecedented mutual identification between the superlubricity and atomic-scale image from Atomic Force Microscopy (AFM) measurement by the first-principles simulation of metallic Cu tip scanning on carbon nanostructures. With the tip height decreasing, the sliding potential evolves from anticorrugated, to substantially flattened, and eventually to corrugated patterns, inducing superlubricity of flatten potential at the critical height. Correspondingly, both the normal forces and the contrast of atomic image patterns also undergo similar inversions at the respective critical tip heights in accord with recent experimental observation. Based on the underlying mechanism elucidated, the mutual identification between the images contrast inversion and the superlubricity is confirmed. This may advance the AFM technology to stimulate the experimental observation of superlubricity from its theoretical studies, and may thus promote the development of theory systems of superlubticity. 1

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TOC graphic Reducing unwanted friction, wear and energy dissipation of moving mechanical components is intriguing for many applications1. Considerable efforts are thus dedicated to design materials and surfaces seeking the possible solutions to frictionless sliding. Conventionally, superlubric sliding for dry friction is mainly achieved by structural lubricity2-4 and continue slide under tiny loading5,6 owing to lower potential corrugation7,8. In terms of the inversion of the potential energy surface (PES) corrugation,9,10

our recent theoretical studies revealed a distinctive

superlubricity.11,12 This unusual superlubric behavior, which is enabled by the pressure induced friction collapse, differs from the daily intuition and the well-known Amontons laws in tribology.13 However, further advances for this approach are limited due to the lack of an efficient access to the superlubric state in real life. In other words, a concise yet efficient technology is urgently needed for the experimental observation of this exceptional superlubricity, which may provide an impetus to its development from the theoretical prediction to practical application in surface sciences. One of the well-known experimental technologies frequently adopted for probing materials surface is Atomic Force Microscopy (AFM). Particularly, the contrast inversions of energy fields, interatomic forces and atomic-scale images of the

2


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nanostructures are characteristic phenomena found in AFM investigations.14-17 Owing to the maps evolution, the structures18,19 and bonding forces20 at the atomic-level can be visualized,21-24 which could provide key microscopic details of materials in the investigations for various purposes25-30. Nevertheless, despite the constructive attempts, as an interesting physical phenomenon occurring in the scanning interfaces, the nature behind the observed image contrast inversion has not been explored mechanistically and is far from being understood. This may restrain the improvement of AFM technology for its potentially extended application. Indeed, in an AFM measurement,31 a sharp tip scans over the surfaces when the image with atomic-scale contrasts is created as the response to the tip-surface interaction. In the meantime, frictional forces may arise due to existence of the local potential barrier for the tip sliding. Obviously, the AFM images of the nanostructures and their performance along with tip sliding are strongly associated; however, the fundamental principles governing the mutual identification of friction and imaging are still elusive. In this work, the connection between the pressure-induced superlubricity and the image contrast inversion is identified. For the first time, it is shown mechanistically that the visual frequency modulation AFM (fm-AFM) image contrast inversion of nanostructures can be applicable as a probing technique for the unusual superlubricity. This finding may also improve the AFM technology in quickly acquiring the properties of the materials from their visual images. In the current study, a metallic Cu tip scanning over carbon nanostructures (graphene, graphite and carbon nanotube) as prototypical systems for AFM experiments21,22 is examined by density functional theory (DFT). The tip-sample distance-dependent corrugation landscape of potential energy, surface forces, and AFM images are calculated. The PES corrugation for the sliding reveals an abnormal transition from anticorrugated, to substantially flattened, and eventually to corrugated contacts with decreasing tip height under pressure, resulting in nearly frictionless sliding to superlubricity at the critical height. Owing to the tip-samples potential inversion, the contrast patterns of AFM surface forces and images (force-gradient) also undergo inversions at respectively critical tip heights, 3



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which are in agreement with the experimental observation.22 Due to their underlying principle of correspondence discussed, the pressure-induced contrast inversion of the atomic microscopy image and the friction collapse to superlubricity for the nanostructures can be thus mutually identified. The principle, which rules the inversions of the pattern for PES as well as its first (surface forces) and secondary derivatives (AFM images), may expand the existing theory of superlubricity. The studies also demonstrate that, as a mechanical phenomenon, the pressure-induced superlubricity can be applied for the characterization of nano-materials with hyperfine-structures. These may be an important step for the superlubric phenomenon from its theoretical prediction to the practical application in various fields beyond tribology. We applied the Grimme-vdW corrected PBE (Perdew-Burke-Ernzerhof)32,33 exchange-correlation

functional

for

the

first-principles

energy

plane-wave

calculations. The computational details are shown in the Supporting Information (SI) Section S1. To determine the energies, forces and images in AFM measurements of the noncontact constant height mode, we calculated interaction energy v.s. distance curves for a metal Cu tip models over a gaphene (Cu/graphene), a graphene bilayer (Cu/graphene bilayer), and carbon nanotube (CNT) (Cu/CNT) surface. The graphene bilayer with AB stacking mimics the multilayer graphene and graphite. The properties of carbon nanotube is mimicked by a (17,0) single wall carbon nanotube. The atomic models for the tip scans over the samples are shown in SI (Section S2, Cu/graphene; Section S4, Cu/graphene bilayer; Section S5, Cu/CNT). For the three models, while most of the atoms are relaxed, a few carbon atoms of the nanostructures are fixed to anchor the structures. The anchored nanostructures allow the calculation of the tip-sample interaction at various tip distances. For Cu/graphene, as shown in Fig.S1, the red atom (one of the eight carbon atoms of 2×2 cell) is fixed. For Cu/bilayer graphene, as shown in Fig.S3, the fixed atom (red), i.e. one of the eight carbon atoms of the top layer graphene is fixed, and meanwhile, all the atoms of the lower layer graphene are fixed to reduce computational time. For Cu/CNT, as shown in Fig.S6, 4


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the carbon atoms (red) at the periodic edge are fixed to anchor the nanotube. The interaction between the probe and the sample is calculated with a fixed height z, which is the operating distance from the tip atom closest to the sample surface. As shown in Fig.S1, for Cu/graphene, we only included the graphene layer and a simple two atom Cu tip in our calculations for AFM simulation. Because the interaction between graphene and substrate usually plays an important role in friction of graphene,34-36 thus, we tested the effect of including a Cu(111) substrate. The studies of the sliding system Cu/Graphene-Cu(111) in Fig.S8, namely, a Cu tip sliding over the surface of a graphene on Cu(111), are shown in Fig.S9 in Section S7 in SI. The results (Fig.S9) also exhibit the similar energy crossing as in Fig.1(a) for the system Cu/Graphene. Thus, despite making a slightly larger critical tip height zc (Fig.S9), the underlying substrate would make insignificant impact on the contrast inversion of AFM image and PES pattern discussed. Therefore, for computational efficiency, the underlying substrate is neglected18,24,37 and the contribution of the other Cu atoms in actual AFM tip was not included in the calculations,18,24,37 and the tip kept rigid and not tilt,18,24 since the fixing of the two atoms of the tip also make insignificant impact18,24,37 on the contrast inversion of AFM image and PES pattern of the energy crossing. The reliability of the two atom model for the tip may be stated as follows. In fact, in the really tip-sample system for the experimental studies of nanoscale friction, the contact radius is tens of nanometer scale depending on the hardness of the materials, the contact may comprise of the thousand atoms. Then, frictional simulations for the big tip are computationally expensive for DFT calculation. Thus, the simulations in the current study are performed for the simplified model of two atom tip. Noteworthy, the simplified models may capture the critical features of AFM image and PES corrugation. Specially, we studied the sliding of periodic models for a Cu(111) surface sliding over a graphene layer with multi-atoms contact (abbreviated as Cu(111)/Graphene, Fig.S10), the results of the surfaces interaction energy (Fig.S11)

5



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calculated exhibit reveal the similar feature of the energy across as the system with the model of the two atom Cu tip (Fig.1a, Cu/Graphene). Moreover, the model of the two atom tip has been proven to be reliable in previous studies,18,24

which reveal

that more complex tip geometries produce bare changes in tip-sample interaction for AFM imaging18,24. Indeed, with tip geometry as Cu4 tetramer in their DFT calculation, Lee et al24 did not observe any significant change in the tip-sample interaction comparing with the two atom model. By using few atoms metallic tip with a terminal atom in the calculation, Martin et al23 reproduced the experimental observation of atomic AFM image evolution. Additionally, for the tip and sample in real AFM measurement with a much larger tip with many atoms, the long-range vdW forces would be stronger which mainly supply a non-bonding attractive background, however, the atomic contrast patterns of the tip-graphene interactions are typically dictated by short-range chemical bonding and Pauli repulsion.23 Consequently, the simplified tip apex of the two atom model24 may be able to capture the pivotal information of tip-sample interaction for AFM contrast inversion and PES surfaces for friction. The results calculated are thus validated by the fact that they reproduce experimental characteristic curves of frequent shifts and AFM images as discussed later. The bond length between the two Cu atoms is 2.216 Å. To determine the PES corrugation for friction studies, we then calculated the binding energies Eb between the tip and the graphene at the relative horizontal and vertical positions with a step of 0.31Å. We also calculated the binding energy at different tip heights z, and then obtain the vertical force Fz acting on the Cu tip and the frequency shift Δf for AFM image simulation. The crossings for the curves of the tip-sample interaction energy, vertical force and frequency shift.

6


(b)

-450 -900

500

Carbon(DFT) Hollow (DFT)

zc1

0

Carbon (DFT) Hollow (DFT)

24 16 8



-500

32



zc0

0

(c)

-Eb/z(pN/cell)

450

Carbon (DFT+vdW) Carbon (DFT) Hollow (DFT+vdW) Hollow (DFT)



(a) Binding energy Eb (meV/cell)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


 Eb/z (10 pN/Å)

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zc2

0 -8

1.5

2.0 2.5 3.0 3.5 Tip height z (Å)

4.0

2.0

2.5 3.0 3.5 Tip height z (Å)

4.0

2.0

2.5 3.0 3.5 Tip height z (Å)

4.0

Fig.1 The binding energy (a), vertical force (b) and frequency shift (c) on tip as a function of tip height at the high-symmetry locations for Cu/graphene. The binding energies Eb are obtained by subtracting the total energies of the Cu tip and the sample from the total energy of the tip/sample system, namely, Eb(z)=Etip-sample(z)-Etip-Esample

(1)

As shown in Fig.1(a) for Cu/graphene, with decreasing height z, both DFT+vdW and DFT calculated the binding energies Eb decreases to minimum at equilibrium, and then increases. Although DFT+vdW calculation gives a larger binding energy compared to DFT, both of the results for Eb v.s. z curves have similar features with an equilibrium binding height ze ～2.0 Å, and the Cu tip prefers carbon site of graphene. Meanwhile, the DFT+vdW and DFT calculated Cu/graphene interactions give a similar energy difference between the carbon and hollow sites. Accordingly, as shown in Fig.1(a), the contrast patterns of the tip-graphene interactions are typically dictated by chemical bonding and Pauli repulsion, while long-range vdW corrections contribute an attractive background.23 Thus, the discussions in the following sections are mainly based on DFT calculation results unless otherwise stated. Noteworthy, the curves of Eb vs. z acquired on the two high-symmetry positions of carbon and hollow sites show a crossing at the critical height zc0~1.67 Å (zc0 0, and 𝑚 > 𝑛. Specifically, the potential is Lennard-Jones-type (L-J) when m=12 and n=6. Its first-order derivative and second-order derivative are mB

nA

𝑈′(𝑟) = ― 𝑟𝑚 + 1 + 𝑟𝑛 + 1, 𝑈′′(𝑟) =

m(m + 1)B 𝑟𝑚 + 2

―

(6)

n(n + 1)A 𝑟𝑛 + 1

,

(7)

In order to make the intersections of two different potential functions exist, let

𝑈1(𝑟) =

𝐵1

𝐴1 𝐵2 𝐴 2 ― , 𝑈 (𝑟) = ― 2 𝑟𝑚 𝑟𝑛 𝑟𝑚 𝑟𝑛

and 12


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𝑈1(𝑟) = 𝑈2(𝑟) This gives

𝑟0𝑚 ― 𝑛 =

𝐵1 ― 𝐵2 𝐴1 ― 𝐴2

Therefore, if the right hand side satisfies the condition 𝐵1 ― 𝐵2 𝐴1 ― 𝐴2

>0

(I)

Then the two L-J type functions 𝑈1(𝑟) and 𝑈2(𝑟) intersect at a finite r. We can obtain the requirements that their first (Fz) and second order derivative (Δf) intersect by making 𝑈1′(𝑟) = 𝑈2′(𝑟), which results in

𝑟1𝑚 ― 𝑛 =

𝑚(𝐵1 ― 𝐵2) 𝑛(𝐴1 ― 𝐴2)

> 0,

(II)

and 𝑈1′′(𝑟) = 𝑈2′′(𝑟), which results in

𝑟2𝑚 ― 𝑛 =

𝑚(𝑚 + 1)(𝐵1 ― 𝐵2) 𝑛(𝑛 + 1)(𝐴1 ― 𝐴2)

>0

(III)

Obviously, if Condition I is satisfied, both Conditions II and III are satisfied automatically. Therefore, the three inequalities tell us that (a) If two binding energy 13



curves have one intersection, their first and second order derivatives must also have intersections, but at a different point further away from the origin (from m > n); (b) If condition III is satisfied, condition II and I are true. This means the potentials and their first order derivatives do intersect if the second order derivative functions intersect. Briefly, if energy crossing occurs for the curve of Eb, so does Δf and vice versa. With the sufficient and necessary condition discussed (assuming the interatomic interaction approximates to an exponential form), the pressure-driven superlubricity and contrast inversion of AFM forces and imaging could be identified mutually. For Cu/graphene as shown in Eq.2 and Eq.4, both the force crossing (Fig.1b) and the frequency shift crossing (Fig.1c) thus result from the energy crossing in Fig.1(a). Similar Fz and Δf intersections are also presented for other systems e.g. Cu/graphene bilayer (Fig.S4 b and c) and Cu/CNT (Fig.S7 b and c) due to the energy crossing. In fact, the tip height dependent contrast inversions of images in graphene like structures have been observed. Indeed, the currently calculated frequency shift crossing is in agreement with recently experimental observations22 and theoretical studies24. Additionally, for the tip height zc1

Mutual Identification between the Pressure-Induced Superlubricity and

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