Review pubs.acs.org/CR
Fundamental Aspects of Energy Dissipation in Friction Jeong Young Park*,†,‡ and Miquel Salmeron*,§,∥ †
Center for Nanomaterials and Chemical Reactions, Institute for Basic Science, Daejeon 305-701, Republic of Korea Graduate School of EEWS, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Republic of Korea § Materials Sciences Division, Lawrence Berkeley National Laboratory, University of CaliforniaBerkeley, Berkeley, California 94720, United States ∥ Materials Science and Engineering Department, University of CaliforniaBerkeley, Berkeley, California 94720, United States ‡
6.1. Commensurability and Superlubricity 6.2. From Stick−Slip Motion to Smooth Frictionless Sliding 6.3. Influence of Applied Vibration Forces on Lubricity 6.4. Thermolubricity 6.5. Ultralow-Friction of Linear Carbon Nanotube Bearings 7. Friction Anisotropy 7.1. Friction Anisotropy on Periodic Surfaces 7.2. Friction Anisotropy in Organic Molecular Films 7.3. Friction Anisotropy on Quasiperiodic Surfaces 7.3.1. Friction Anisotropy on Atomically Clean Quasiperiodic Surfaces 7.3.2. Friction Anisotropy on Quasiperiodic Surfaces Covered with Oxide Layers 7.4. Friction Anisotropy in Graphene 8. Future Perspectives and Conclusion Author Information Corresponding Authors Notes Biographies Acknowledgments References
CONTENTS 1. Introduction 2. Models and Techniques for Friction Studies 2.1. Contact Models Based on Continuum Mechanics 2.2. Relationship between Nanoscale and Macroscale Friction 3. Experimental Techniques for Friction Studies 3.1. Atomic Force Microscopy (AFM) 3.2. Tribometer 3.3. Quartz Crystal Microbalance 3.4. Surface Force Apparatus 4. Atomic-Scale Origin of Friction 4.1. Phonon Contribution 4.1.1. Theoretical Studies 4.1.2. Experimental and Theoretical Studies of Slippage of Adsorbates 4.1.3. Experimental Studies of Phonon Coupling Using AFM 4.2. Electronic Contributions to Friction 4.2.1. Film Resistivity 4.2.2. Infrared Antiabsorption Peaks 4.2.3. Broadening of Vibrational Peaks 4.2.4. Slippage of Atoms on Surfaces 4.2.5. Noncontact Friction Due to Electric Field Fluctuations 4.2.6. Electronic Friction between Solids in Contact 4.3. Photon and Electron Emission from Electronic Excitation 5. Velocity Dependence of Friction 5.1. Velocity Dependence Due to Thermal Activation 5.2. Velocity Dependence Due to Capillary Effects 5.3. Chemical Effects 5.4. Velocity Dependence of Friction in Polymers 6. Superlubricity © XXXX American Chemical Society
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S U U V W X X Z Z Z AB AB AC AD AD AD AD AE AE
1. INTRODUCTION Tribology is the study of interactions between surfaces or interfaces in relative motion (“tribos” means “to rub” in Greek). It includes the phenomena of friction, adhesion, and wear.1,2 Understanding the physical and chemical mechanisms governing these processes is important for applications in microelectro-mechanical system (MEMS) technologies as well as in all kinds of machines involving mechanical motions (e.g., automobiles, aviation, drilling, sliding, skiing, walking, etc.) which directly impact the quality of life. Elucidating the phenomena behind energy dissipation in friction is a longstanding and challenging issue in physical science. The earliest attempts to understand friction are summarized in Amontons’ law, which states that there is a linear relationship between friction force and load, where the ratio of these two forces define the friction coefficient. According to this law,
L M O P P Q R R S
Received: November 15, 2011
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In section 3, we briefly review some of the tools developed for nanoscale friction research (e.g., atomic force microscopy, the quartz crystal microbalance, and tribometers) and for micro- and macroscale friction research. Fundamental mechanisms involving phonons, molecular deformations (soft phonons), and electronic excitations will be reviewed in section 4. Recent studies of the velocity dependence of friction will be presented in section 5. The concept of superlubricity and its relation to commensurability, atomic stick−slip, and local heating will be described in section 6. The directional dependence of the friction force, an intriguing aspect of friction, will be highlighted in section 7. Finally, prospects for future research directions and conclusions will be presented in section 8.
friction is independent of the contact area and the speed of the moving parts. However, as we will discuss later, studies on single asperities reveal that friction is dependent on both the contact area and scanning speed. Thus, friction is not necessarily linearly proportional to the normal load. Understanding friction implies grasping how mechanical kinetic energy, 1/2mv2, of the moving parts is transferred to various excitations of the surrounding media. The atomic processes that mediate frictional energy dissipation include collective vibrations in the form of acoustic and optical phonons, as well as localized vibrational modes of atoms and molecules at the interface, which may lead to rupture of chemical bonds.3−6 Another process is the excitation of electrons to unoccupied levels (electron−hole pairs), which decay via fluorescence, excitation of phonons, or rupture of chemical bonds. Bond breaking and high-energy electron excitations may result in electron emission in surfaces with low work function or in fluorescence (triboluminescence). Figure 1 depicts energy dissipation in friction as mediated by phonon and electron−hole excitation.
2. MODELS AND TECHNIQUES FOR FRICTION STUDIES 2.1. Contact Models Based on Continuum Mechanics
The discovery of the laws of friction is attributed to Leonardo da Vinci in the 15th century and to Amontons and Coulomb two centuries later.8 These pioneers discovered that the friction force is directly proportional to the load (the ratio being the friction coefficient) and independent of the contact area and the sliding velocity.9 These centuries-old laws are still used today. When new tools emerged that made the exploration of mechanical properties possible at nanoscale, new phenomena and behaviors were discovered. One is that, when the “real” contact area between surfaces can be measured, friction is proportional to it as the product of the area and interfacial shear strength. However, while load is a well-defined and measurable quantity, the contact area is a quantity that is harder to define and subject to interpretation. This has given rise to a controversy over which is the fundamental controlling parameter: load as in the original law or contact area. This controversy is still active today. A first rationalization came from the work of Bowden and Tabor10 who explained the proportionality of friction and load by noting that only a few asperities in the always rough interface enter in contact, as illustrated in Figure 2a. These asperities will deform elastically until the pressure reaches the plastic yield threshold of the softer material. In practical situations, such plastic deformation is usually the norm. The deformation generates a contact area proportional to the load and in this manner the proportionality between friction and both load and “real” contact area is established. Nanoscale tools, including the atomic force microscope (AFM) and the surface force apparatus (SFA), to be described below, made it possible to address single asperities at the level of atoms. In the ideal asperity all of the atoms and molecules are in contact making it possible to define a “real” contact area. While conceptually satisfactory, the weakness of this model is that whether all the atoms are in contact or not (i.e., at distances where their atomic potentials overlap) is difficult to ascertain because the interface atoms are not accessible to direct imaging or spectroscopy. If the contact between two bodies can be modeled as that of an ideal asperity, at low loads, when the deformation is purely elastic, the contact area is not proportional to the load, as has been observed in many experiments. The contact geometry of asperities can be modeled by that of a sphere of radius R and a planar substrate. Classical continuum mechanics describes
Figure 1. Illustration of a tip sliding against a surface and of several types of resulting excitations that can contribute to energy dissipation in friction: phonons, electron−hole pairs, and electronic excitations that decay via emission of electrons or photons.
Electron excitations couple through Franck−Condon processes to nuclear motions and through anharmonic interactions to lower frequency phonons, which ultimately manifest as heat. The symmetry properties of the contacting surfaces and that of the initial excitation give rise to numerous phenomena, including friction anisotropy, velocity dependence, superlubricity, dissipative surface charge trapping, and more. Understanding these excitations and how they contribute to energy dissipation is rather challenging because of many contributing factors: bulk properties (hardness or modulus), conductance, surface structure, surface imperfections (such as dislocations or impurities), and point defects.7 This paper reviews recent experimental and theoretical findings of these phenomena in various systems, including metals, semiconductors, quasicrystals, two-dimensional sheets, and organic molecular films. In section 2, we briefly review the “classical friction laws” derived from contact mechanics, including Amontons’ law, the Hertz model, and its extensions that include interfacial adhesion. The influence of length scale (macroscale and nanoscale) on frictional properties will also be discussed. B
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Figure 2. (a) Diagram of a macroscopic contact interface showing the presence of multiple sharp asperities where atom-to-atom contact is established. (b) Contact of a single sharp asperity that can be modeled by the tip of an AFM on a planar surface. (c) Total contact area arising from multiple asperities that come progressively into contact as the load increases. (d) Plot of the contact area of an ideal spherical asperity as a function of applied load for the JKR, DMT, intermediate and Hertz models of continuum mechanics. Radius R = 100 nm, reduced modulus K = 50 GPa, interface energy γ = 250 mJ m−2, and contact distance z0 = 3 Å were used in the calculations.
A third model is the DMT (Derjaguin−Muller−Toporov) model,13,14 which considers only long-range adhesion forces from inside and outside the contact area. This adhesion force (Lad) is related to the work of adhesion, γ, by Lad = 2πRγ, and can be included as an ‘additional load’. In this model, the contact area varies as
exactly the elastic deformation and is the basis of the wellknown Hertzian model11 in which the contact area, A, is given by ⎛ RL ⎞2/3 A = π⎜ ⎟ ⎝K ⎠
(2-1)
where K is the reduced Young’s modulus A=π
2 1 − vt2 ⎞ 1 3 ⎛ 1 − vs ⎟ = ⎜ + K 4 ⎝ Es Et ⎠
{
R [L + 3πRγ + (6πRγL + (3πRγ )2 )1/2 ] K
2/3
}
(2-4)
The JKR and DMT models approximate elastic behavior in two opposite extremes. DMT describes hard and weakly adhesive materials, while JKR describes compliant and adhesive materials. Any real situation is, of course, intermediate between these two extremes. The contact area in this intermediate region was calculated by Maugis−Dugdale15 and later generalized by Carpick et al.7 and by Schwarz.16 Figure 2d shows the contact area as a function of applied load for a given set of parameters for each of these mechanical models. If the friction force is proportional to the contact area, the graph also qualitatively shows the variation of friction force with normal load. For macroscopic systems where multiple asperities are present, it was shown by Greenwood et al.17 that for any statistically reasonable distribution of asperity radii and heights,10 the sum of their contact areas (Figure 2c) approximately follows a linear dependence with applied load,1,17,18 again providing another explanation to the observed universality of Amontons’ law. While the theory bridges the gap between the mechanics of single asperities and that of macroscopic contacts, it does not resolve the question of whether the load or the contact area are the fundamental
(2-2)
Et and Es are Young’s moduli and νt and νs are the Poisson ratios of the sphere and the flat surface, respectively. No adhesion interaction forces are included in this model. A more sophisticated model is the JKR (Johnson−Kendall−Roberts) model,12 which neglects long-range forces outside the contact area but considers short-range forces inside the contact region that manifest in the surface energy or work of adhesion, γ. In this model A=π
{
R (L + 2πRγ ) K
2/3
}
(2-3)
The value of γ can be determined from the pull-off force (Lad) through γ = 2Lad/3πR. The pull-off force is defined as that where the contact is unstable against thermal fluctuations, which causes a transition to zero area. It can be measured from force−distance curves (or the “approach-retraction curve”), as described in Section 3−1. JKR is applicable when contact between the tip has a large radius and the materials are highly adhesive and compliant. C
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impurities breaks down the spatial coherence of identical crystallographic surfaces in commensurate contacts. It also locks the two contacting surfaces when they are incoherent (i.e., rotated or with different lattice constants) which would otherwise lead to zero static friction. The authors showed that impurity molecules give rise to a nonzero value for the shear stress that increases linearly with applied pressure. Incommensurate interfaces lead naturally to low kinetic friction and zero static friction but impurities similarly affect the shear stress, giving rise to a constant value of μ, in line with Amonton’s law. The effect of the atomic discreteness of the surfaces in contact, particularly roughness, crystallinity, and the presence of steps, was examined by Luan and Robbins30 with MD simulations. Their results indicate that low roughness results in a sublinear dependence of friction on load. While the continuum models also predict a sublinear behavior, the contact areas and yield stresses are underestimated and friction and contact stiffness are overestimated. Mo et al.31 showed that the breakdown of continuum mechanics can be understood as a result of the rough nature of the contact. By defining the contact area as being proportional to the number of interacting atoms, they showed that the macroscopic linear relationship between friction force and contact area can be extended to the nanoscale.31 This model predicts that as adhesion between the surfaces is reduced, a transition takes place from a nonlinear to a linear dependence of friction force on load. This transition is consistent with the results of several nanoscale friction experiments.23,24,32 In the same line of connecting friction to the number of atoms in contact, again defined as atoms whose atomic potentials overlap (i.e., within Å), Cheng and Robbins33 reviewed the effects of thermal atomic vibrations in determining the real contact area, Ac. Using molecular dynamics simulations and a Lennard-Jones interaction potential in a mean-field model, they found that the number of atoms exhibiting repulsion at any instant rises linearly with load. As the vibrating atoms collide with the other body, they can exert a very large force so that the load is supported by the small fraction of atoms that have the largest instantaneous height. They discuss the effect of defining contact as that provided by atoms exerting forces larger than a certain value and integrating over different contact times, measured in units of the vibration period of the atoms, τ. For commensurate periodic surfaces, the contact area equals the total area, Ao, after a contact time on the order of 10τ. For incommensurate crystals with different lattice constants or for surfaces cut from amorphous solids, Ac increases more slowly and requires contact times of 105 τ, about 10 ns, and saturates at even smaller values for amorphous surfaces, as shown in Figure 3. This is due to the fact that in these later cases, many of the surface atoms are not in direct opposition to atoms of the other surface and thus require larger vibration amplitudes to reach the repulsive regime.34 For nonflat contacts, they found that contact is spread over an area about twice as large as the Hertz prediction. The varying substrate-tip separation for incommensurate and amorphous surfaces reduces the fraction of atoms in contact, almost exactly compensating for the increased radius of contact for the incommensurate surface while the number of contacting atoms is roughly half the Hertz prediction for the amorphous surface. The contact time interval for computing the number of atoms in an average repulsive contact is important, particularly at high temperatures. The area corresponding to atoms in contact at any instant is substantially
parameters that determine the strength of the friction dissipation forces. 2.2. Relationship between Nanoscale and Macroscale Friction
The reason why the contact area is not a well-defined quantity is due to the enormous range of the strength of the various interaction forces between atoms: van der Waals, electrostatic, and chemical bonding. These forces also vary dramatically in their distance dependence. The strong forces responsible for chemical bonding and for repulsion arise from the overlap of atomic orbitals and decay exponentially within angstrom distances. If these were the only forces, then the contact area could be defined as that including only regions separated by atomic distances. In principle, a contact with these characteristics can be achieved experimentally with the AFM and SFA instruments described below. This high degree of control over the contact allows us to go back to the question of whether the continuum mechanics models discussed above can describe the structure and friction properties of nanoscale single-asperity contacts containing a limited number of atoms. Scores of experiments using nanoscale contacts have shown that continuum single-asperity models are remarkably successful in describing the experimental results of friction and deformation down to nanoscale size contacts. DMT models have been used to successfully describe hard and poorly adhesive materials, including diamond, tungsten carbide, silicon, and quasicrystals,14,19,20 while JKR has been effectively used to describe compliant and adhesive layers, such as mica and organic molecules.21,22 The local conductance measurements carried out by Enachescu et al.14 on diamond and by Park et al.19 on silicon demonstrate that the conductance curves, which directly measure the contact area, follow the DMT predictions. Eventually, however, the continuum models will break down when the number of atoms in contact becomes small enough. Deviations from continuum models have indeed been observed, even before reaching the few atoms contact. Several AFM experiments found that friction is linearly proportional to the applied load, L, on various substrates including gold and alkylthiol molecules,23−25 and follow Amontons’ law Ff = μL, where μ is the friction coefficient. Some surface force apparatus (SFA) studies have also shown a linear proportionality between the friction force and the applied load on alumina surfaces26 and on benzyltrichlorosilane monolayers.27 The puzzling discrepancy between the continuum models and observed linear proportionality is probably an indication of the difficulty, even with nanoscale tools, to determine and to reproduce atomic level details of the contact structure, either as a result of contamination with foreign molecules, of inadvertent wear, or from the uncontrolled atomic structure of the tip. At this juncture, it is necessary to resort to theory. Fortunately, given the enormous increase in computational power of recent years, and the availability of new and sophisticated theoretical tools, including density functional theory (DFT) and molecular dynamics (MD) simulations, it is possible to gain a decisive molecular-level understanding of the nature of the contact area and the role of applied load and interaction forces in determining the origin of friction and the laws that govern it. One insight offered by the use of MD simulations is provided by the work of He et al.28,29 who studied the role of interposed third bodies (wear debris and adsorbed molecules) on the friction properties. The presence of D
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complex system where the actual number of atoms in the contact interacting with each other via overlap of their potentials at angstrom distances is the fundamental parameter that determines friction.22,28,30 This number appears to be proportional to the contact area for smooth, atomically flat surfaces where the role of the load is to increase the contact area via elastic or plastic deformation. On rough surfaces, or surfaces with third bodies interposed, the effect of the load is not merely to increase the contact area but to also increase the number of atoms in real contact. With the problem stated in this way, we can foresee further progress in our understanding of friction of bodies in contact, particularly when theoretical methods and future advances in characterization will increase our understanding.
3. EXPERIMENTAL TECHNIQUES FOR FRICTION STUDIES In studies of tribological phenomena of practical interfaces, macroscopic techniques (e.g., pin-on-disk tribometers) are utilized extensively. The atomic force microscope (AFM),38 on the other hand, is used to address nanometer- and atomic-scale phenomena due to its high spatial resolution. AFM can provide important interfacial information at nanoscale, such as atomic structure, adhesion, friction, lubrication, conductance, wear, and tribochemistry.5,20,21,39 Together with the surface force apparatus2,40 and the quartz-crystal microbalance,41 these tools have provided previously unknown information about tribological phenomena, such as atomic-scale stick−slip and the effects of confinement on liquid films. In this section, we briefly describe these instruments and their various operational modes.
Figure 3. Fractional contact area (where atoms enter in repulsive interaction) Ac/Ao versus contact time interval on a log scale for three types of interfaces: commensurate (solid line), incommensurate (dashed line), and amorphous (dotted line). The atomic interactions are assumed to be described by Lennard-Jones potentials. (Reprinted with permission from ref 33. Copyright 2010, Springer.)
reduced from that in the Hertz theory in all cases. The increase with load is also more rapid than the Hertz prediction (i.e., a more linear area-load relation than that found on flat surfaces). Interestingly, while the results for adhesive tips look similar to those for flat amorphous solids, they are also qualitatively similar to continuum predictions for sphere-on-flat contacts, although for a good fit, the values of the surface energy in the JKR or DMT models need to be larger (within a factor of 2) than predicted at zero temperature. According to the authors, this is likely needed to compensate for the increase in contact area due to the atomistic effects discussed above. In other words, a successful fitting to theory does not represent a quantitative success of the continuum theory at the atomic scale.30,31 From these theoretical studies and from experiments, it appears that the validity or the breakdown of continuum mechanics is intimately associated with the nature of contact. If the friction measurement is carried with a single asperity on an atomically flat surface, the frictional behavior follows the sublinear dependence on load predicted by continuum mechanics models. Such contacts also tend to exhibit substantial adhesion, as observed in many single crystal surfaces, including mica, quasicrystals, diamond, and organic molecules.14,19−22 In the case of atomically rough surfaces generated as a result of wear, chemical modification, or oxidation, the number of atoms in contact will increase with the applied pressure, and a linear dependence between the friction and load is observed. For example, the atomically clean 2-fold Al−Ni−Co quasicrystal surface gave rise to a DMT-type behavior,35 but the air-oxidized 2-fold Al−Ni−Co quasicrystal surface exhibited a linear relation due to the high roughness of aluminum oxide.36 Another example of this transition from sublinear to linear friction vs load behavior is the case of Ptcoated tips on mica studied in UHV by Carpick et al.37 These authors observed that continuous scanning of the Pt tip lead to a chemical transformation that decreased the friction and adhesion, and at the same time the friction curve became more linear. In summary, the understanding of the friction laws has evolved from the initial empirical linear F vs L relationship, observed on macroscopic and rough surfaces, to a more
3.1. Atomic Force Microscopy (AFM)
In this technique, a sharp tip is brought into close proximity with a surface, which causes normal bending of the cantilever supporting the tip (z-deflection) due to attractive or repulsive interaction forces (Figure 4a). As the lever is scanned parallel to the surface, frictional forces cause torsional deformations of the lever. The two deformations can be detected simultaneously by a laser beam reflected from the back of the cantilever onto a four-quadrant photodetector by suitable combinations of the signals in the quadrants. This makes it possible to determine load and friction forces if the spring constants of the cantilever and the sensitivity of the photodetector are known. When measuring friction forces this technique is sometimes referred to as friction force microscopy (FFM). Adhesion forces can be obtained by measuring force− distance curves, or “approach-retraction curves”, where the cantilever bending is plotted versus sample displacement,42,43 as shown in Figure 4b. After contact is established, a repulsive force bends the lever backward (linear slope line) and the same line is followed during sample retraction. Due to adhesive forces, the line continues beyond the point of first contact found during the approach, until reaching a point, “a” in the graph, where the tensile load of the lever equals the adhesion force of the tip−sample junction. At this point, the probe snaps out of contact with the surface (vertical line from “a” to “b”). The difference in force between “a” and “b” (free position) is attributed to the adhesion force.21,44 Caution must be exercised, however, in the case of small adhesion forces because the value of the jump out of contact will depend on the speed of the retraction motion. When the adhesion is small, a sufficiently long dwelling time near point “a” can cause the tip to snap off due to thermally induced oscillatory fluctuations. This effect is E
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Quantitative measurements of adhesion and friction forces require knowledge of the spring constants for normal bending and lateral twisting. These parameters can be calculated using formulas from continuum mechanics. For a narrow rectangular cantilever, the spring constant for normal bending (kn) and twisting (kl) are given by46 kn =
Ewt 3 4l 3
(3-1)
kl =
Gwt 3 4lh2
(3-2)
where E and G are the Young’s and shear moduli, respectively, w and t are the width and thickness of the cantilever, respectively, l is the length of the cantilever from the base to the tip, and h is the height of the tip.47 Experimental methods for calibrating cantilever spring constants are also used, including the resonance-damping method (Sader et al.),48 the wedge method,49,50 or the force balance method by using a substrate with known slope.51,52 3.2. Tribometer
The pin-on-disk apparatus is one of the most commonly used instruments for macroscale tribological measurements. It consists of a “pin” that is held stationary and a rotating disk containing the sample, as shown schematically in Figure 5. In a
Figure 4. (a) Schematic of the atomic force microscope (AFM). A sharp tip is mounted on a flexible cantilever attached to piezo-electric actuators that provide controlled displacements in x, y, and z directions at the angstrom scale. The displacements of the tip make it possible to image the surface and to measure interaction forces in the directions normal to the surface and in the plane of the nominal surface orientation. (b) Schematic of a measurement to determine adhesion forces: the deflection of the lever is very small before contact (horizontal line). After contact is established, often following an abrupt jump to contact (not seen on the scale of the graph), the lever deflects following the sample displacement (inclined line). Upon reversal of the motion, the tip retraces the inclined line and continues down to point a where it abruptly snaps off to point b. This occurs when the adhesion force cannot compensate for the elastic pulling force of the spring. (c) Schematic of a friction measurement in AFM/FFM showing a front view of the lever twisting left and right due to static friction. The graph below shows a friction force loop. (Reprinted with permission from ref 36. Copyright 2008, Institute of Physics Publishing.)
Figure 5. Schematic of a pin-on-disk tribometer. A tip of well-defined shape (spherical, conical, pyramidal, etc.), typically in the micrometer to millimeter size range, is loaded by a fixed weight while describing a path, either circular or linear to study friction and wear properties. (Reprinted with permission from ref 36. Copyright 2008, Institute of Physics Publishing.)
typical pin-on-disk experiment, the coefficient of friction is continuously monitored by measuring the friction force while a fixed load is applied to the pin-sample contact.53,54 Wear, the removal of material by rupture of chemical bonds, is prevalent in this instrument.
manifested in a clear way in the unfolding of proteins and other organic molecules where weak H-bonding forces determine the adhesion between parts of the molecule or between the molecule and the surface.45 As the tip scans over surface, the lateral signal due to friction forces varies depending on the scanning direction and is recorded as a friction force loop, as shown schematically in Figure 4c for the case of a uniform surface. When scanning begins, the tip is usually stuck to the surface because of adhesion forces, called “stiction” (or static friction), and the lever twists until the lateral force equals the static friction force, a process that is equivalent to snap-off in the approachretraction curves. The friction force per unit contact area is the shear stress.
3.3. Quartz Crystal Microbalance
The quartz crystal microbalance (QCM) is a piezoelectricbased device used to monitor thin film growth with submonolayer sensitivity.41,55 The QCM derives its great sensitivity from the sharp resonance frequency of the quartz oscillator due to its large Q-factor, which makes it possible to measure mass changes caused by the adsorption of submonolayer amounts of adsorbates.56,57 Another interesting parameter that can be derived from QCM measurements is damping due to dissipative forces acting to oppose the inertial force of adsorbates. Such damping leads to a change in the QF
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transparent metal film evaporated on their back sides, Fabry− Perot interference fringes of color are created when the wavelength matches the local separation. In this way an image of the contact geometry can be obtained. The displacement of the interference fringes in the spectrometer provides a measurement of the separation with angstrom precision. One of the cylindrical lenses can be supported by piezo bimorphs to impart a lateral displacement or oscillations for friction and viscosity measurements. The SFA is ideal for the study of molecular-level structural and rheological properties of liquids and tribological properties of lubricants under compression. For example, it has been shown that when simple fluids (e.g., linear hydrocarbons) are confined between atomically flat surfaces, their behavior is mainly governed by the repulsive interaction with the hard walls. This results in a stepwise thinning of the film with increasing pressure, where the liquid film is squeezed out of the contact area one molecular layer at a time. These changes in thickness are called layering transitions,63 which have been extensively studied experimentally and theoretically64−70 since the phenomenon was first observed by Gee, McGuiggan, and Israelachvili.71 The SFA is also well suited to investigate whether the viscosity of a liquid changes under confinement from that of the bulk liquid when the number of layers decreases to a few. Klein and Kumacheva investigated this question using octamethylcyclo-tetrasiloxane (OMCTS) and found that the confined film displayed a liquid-like shear viscosity for large surface separations (more than 100 nm) down to a separation corresponding to seven molecular layers. However, as the surface separation decreased further, the film became very rigid and its “effective viscosity” increased by at several orders of magnitude.68 In contrast, in a similar experiment, Damirel and Granick65 observed a monotonic increase in the shear relaxation time, elastic modulus, and effective viscosity for separations of less than about 10 molecular diameters between the mica surfaces, with a smooth transition to solidity. The discrepancy between these two experimental results highlights several important weaknesses of the SFA instrument. These include the difficulty of ensuring local surface parallelism and of preventing the attachment of foreign particles that may become trapped in the gap in a contact area that is several micrometers in diameter.72 Trapped particles of subwavelength size and contaminant molecules do not affect the visible light interference fringes and can thus falsify the distance measurement.73 Heuberger and Spencer introduced several improvements in the operation of the SFA, including the tracking of fringes, precise control of position, and multidimensional scanning capability. With their improved instrument, they measured the confinement of cyclohexane74,75 and could detect 6−8 layering transitions with steps that correspond roughly to the expected diameter of the cyclohexane molecule (0.53 nm).76 Zhu and Granick studied the shear viscosity of water confined between mica surfaces separated by 1 or 2 water molecules77 using a SFA78 equipped with piezoelectric bimorphs to produce controlled shear motions (Figure 6). An anisotropic response of the effective viscosity was observed when changing the orientation angle of the two mica surfaces. This angular dependence could not be observed for films thicker than three monolayers, which indicates that the intrinsic liquid structure dominates at larger separations. This result is consistent with the epitaxial organization of fluids next to solid
factor and is manifested in broadening of the resonance curve. From these experiments, a “slip time” (the characteristic time required for an adsorbate layer to come to rest) can be estimated. The damping coefficient, η, can be related to slip time, τ
η=
δf0 1 = 4π τ δ(Q−1)
where f 0 is the resonance frequency. The slip time is typically on the order of nanoseconds. 3.4. Surface Force Apparatus
The surface force apparatus (SFA) consists of a pair of atomically smooth sheets (usually mica) mounted on crossed cylindrical lenses that can be pressed together to form a contact, as shown in Figure 6.58−61 The gap between the two
Figure 6. Schematic of the surface force apparatus (SFA). Two transparent surfaces of mica, with their back side coated with a thin (∼100 nm) silver layer, are shaped in the form of two cylinders with their axis at 90°. White light illuminates the contact between the mica surfaces producing interference fringes with colors that follow the topography of the contact with angstrom precision due to the high wavelength selectivity of the Fabry−Perot interferometer effect of the semitransparent silvered mica. The mica surfaces mounted on lenses can be displaced vertically and horizontally by springs actuated by magnets or piezo-transducers to measure compressive and shear forces acting on fluids trapped between the two curved mica surfaces.
surfaces may be filled with a liquid and the interfaces covered with lubricating films. Actuators attached to the surface supports are used to apply load/shear forces and to control spacing between the sheets down to the angstrom level. The contact area and relative surface separation are measured using either optical or capacitive methods.62 When white light passes through the mica sheets, which are covered by a semiG
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Chemical Reviews
Review
of the layers increases and converges toward the flow resistance of a thin liquid film in the hydrodynamic limit as n becomes infinite. One important characteristic of the SFA is that its large contact area and transparent substrates allow for its combination with optical vibrational spectroscopies. The first demonstration of this capability was the combination of SFA with sum frequency generation spectroscopy by Du et al.86 and by Fraenkel et al.87 The authors showed that pressure leads to the reversible disordering of the terminal methyl groups of long alkyl chains molecules. Similarly, Beattie et al.88 used Raman spectroscopy to study the effects of the confinement of OMCTS and n-hexadecane between a prism and a lens at contact pressures of 40 MPa. Experiments of this type could provide much-needed spectroscopic information on the structure of lubricant molecular films under applied pressure and shear forces. Improvements in SFA instrumentation are continuing to this day. One is the combination of SFA with X-ray diffraction and scattering used by Koltover et al.89 to reveal the alignment of complex fluid thin films under confinement. The authors studied the structure of compressed phospholipid monolayers at the air−water interface with varying amounts of polymer lipid and found that the lateral packing stress increased as the hydrophilic polymer chains relaxed, predominantly through an increase in lipid protrusions rather than by increasing the area per lipid molecule.90,91 Another interesting improvement is the implementation of fluorescence correlation spectroscopy by Granick et al.,88 who used it to study diffusion in molecularly thin liquids confined between mica surfaces. Spatially resolved measurements showed that translational diffusion slows exponentially with increasing pressure from the edges of the Hertzian contact toward the center. This result suggests that friction reflects a disproportionate contribution from the more sluggish molecules that reside near the center of a contact zone.92−94 The nanomechanical properties of liquids confined between two surfaces have been also studied with AFM, which offers the advantage of investigating much smaller areas than with SFM, opening the way for studies of surfaces that are not atomically flat over areas of many micrometers. Another advantage of AFM is that, due to its much higher mechanical resonance, it allows for dynamic measurements into the kilohertz regime and higher. In this manner, the “effective” viscosity between the tip and sample can be measured, for example, by acoustic amplitude modulation measurements.95,96
surfaces predicted from computer simulations of Lennard-Jones particles and molecules.79,80 The spatial structure and dynamics of the layering transition was studied for the first time by Mugele et al.77,81 using undecanol. They showed that the transition follows predictions based on two-dimensional hydrodynamics; they also showed that trapped two-dimensional pockets are formed, which undergo shape transformations to minimize elastic and interfacial energy. Later, Becker et al.82−84 imaged the layerby-layer expulsion of molecularly thin films of OMCTS up to several layers, as shown in Figure 7a. The dynamics of the
Figure 7. (a) Optical images showing the time evolution of the expulsion of single layers of OMCTS, a silane-type liquid of nearly spherical molecules, during compression of a thin film of the liquid in the gap of a SFA. The bright spot in the center is due to the hole created by the expulsion of one layer of molecules. The scale bar represents 25 μm. (b) Plot of the effective drag coefficient versus film thickness (in units of the thickness of one monolayer (∼0.9 nm)). (Reprinted with permission from ref 84. Copyright 2003, American Physical Society.)
4. ATOMIC-SCALE ORIGIN OF FRICTION Friction is the result of the conversion of mechanical energy of moving bodies in contact into other forms of energy such as heat, i.e., molecular vibrations of surface atoms, electronic excitations, and chemical reactions. These excitations couple to lattice vibrations (heat). Electronic excitations can also give rise to emission of light (triboluminescence) or electrons (exoelectron emission). These elementary processes contributing to energy dissipation are fundamental topics in tribology, often with incomplete theoretical and experimental understanding.3,5,21,97 While normally one thinks of friction as a phenomenon of bodies in repulsive contact, even before ‘physical’ contact is established, or more precisely before shortrange (
