Dynamic friction measurement with the scanning force microscope

Transcription

1 Dynamic friction measurement with the scanning force microscope Othmar Marti and Hans-Ulrich Krotil Hans O. Ribi, Dynamic friction measurement with the scanning force microscope 2001 Scanning Force Microscopes excert lateral forces on the sample during measurement. The recording of the magnitude of these forces as a function of position gives friction maps. The possible scanning speeds of SFM, however, are far below the velocities of practical devices. The dynamic friction force measurement provides a solution to this problem. The sample is modulated laterally at frequencies up to several kilohertz and with amplitudes in the nanometer range. It is shown that the interaction with the sample is not only determined by friction, but also by the viscoelastic response of the sample. The combination of dynamic friction measurement with the intermittent contact measurement mode, the PulsedForceMode, gives full access to the relevant sample parameters: topography, lateral friction forces, adhesion, sample stiffness and relaxations times. 1 Introduction The integrating question since the first friction force measurements with atomic (scanning) force microscopy (Mate et al., 1987) is still without any definitive answer: how does friction on an atomic scale correlate to macroscopic friction measurements? Macroscopic measurements average over many contacts between the two rubbing bodies. The detailed interaction mechanisms are only indirectly accessible (Bhushan, 1999a). The handbook from Bhushan (1999b) contains a wealth of articles describing the many models and experimental findings of microtribology. The scanning force microscope is often considered to be a model system for a single asperity contact. The tip of the cantilever is one member of the materialpairs investigated. Typically one plots of the friction as a function of the (preset) normal force. The optical lever detection system (Marti et al., 1990; Meyer et al., 1990) with its two-dimensional force detection capability is ideally suited for this task. The microscopes are operated in contact mode. The friction signal is calculated by subtracting the lateral force of the backward scan from the lateral force of the forward scan. Unless the microscope has an efficient linearisation accurate to Published in: Bhushan, B. (Ed.), Fundamentals of Tribology and Bridging the Gap between the Macro- and Micro/Nanoscales, Kluwer Academic Publisher, (2001), othmar.marti@uni-ulm.de 1

2 the pixel this method fails. The nonlinearity of the piezo response presents that corresponding pixels on the forward and the backward scan are measured at the same point on the sample. Furthermore the microscope is limited to the very low speed regime ( pm ). To overcome the nonlinearity problems it seems to be advantageous to perform a friction experiment locally (Goddenhenrich et al., 1994; Yamanaka et al., 1995; Colchero et al., 1996; Nurdin et al., 1997; Krotil et al., 1999b). The sample is mounted on a piezo-stage and modulated with nanometer-amplitudes perpendicular to the cantilever axis. The lateral forces induce a signal in the lateral force channel of the microscope. The modulation is detected by synchronous detection (Colchero et al., 1996). Since the cantilever is moving only a few nanometers, the nonlinearity is negligible. Furthermore the synchronous detection implicitly subtracts the forward and backward scan lateral force images. With some tips the lateral movement is much smaller than the contact area. Hence it is possible that the experiments in dynamical friction force microscopy can be understood in terms of the dynamical shear testing of materials. The normal force F involved in these experiments is a sum of the externally applied normal force and the adhesion force. F = F e + F A (1) The adhesion force F A is easily measured using the PulsedForceMode (Rosa et al., 1997; Krotil et al., 1999a). In this paper we present a new method which combines dynamical friction mode imaging and PulsedForceMode to achieve a more complete data set on friction. 2 Theoretical Considerations We investigate the situation, where the sample is modulated laterally with a triangular excitation at the frequency ω. We assume in a first approximation that the tip sticks to the surface until the threshold voltage for static friction, F stick, is reached. The friction force then reduces to F slip, the presumed constant dynamic friction force. The resulting friction signal at the detector of the microscope in dependence of the modulation amplitude A, of the shear piezo is given by the following equations: with t 1 and t 2 given by f(t) = F HA m (cos (t) + 1) qf H 2 π t t 1 (2) = qf H t 1 < t 0 = qf H F HA m (1 cos (t)) 2 0 t t 2 = qf H t 2 < t π ( t 1 = π + arccos q ) A m ( t 2 = arccos q ) A m Provided that the modulation amplitude obeys A m k lat F tick the signal is synchronously detected using a lock-in amplifier. This amplifier detects the in-phase component x and the out-of-phase component y of the resulting signal. (3) 2

3 x = 1 π y = 1 π π π π π f(t) sin(t) dt (4) f(t) cos(t) dt Amplitude r and phase φ of the detected signal can be calculated from x and y by The resulting equations look rather complicated: r = x 2 + y 2 (5) ( ) x φ = arctan (6) y r = x 2 + y 2 ( [ = F H 4q + π A m ] 2 [ ( 2 + 4q + 6q2 Am + A m 2 arccos q A ] ) m 1 2q + Am q 2 + qa m ) 2 (1 + q) A m ( ) x φ = arctan y ] [ ( ) 2 + 4q + 6q2 Am = arctan ([ 4 + A m 2 arccos 2 (1 + q) 1 A m q A ] ) 1 m 1 2q + Am q A 2 + qa m m (7) (8) The signal for a modulation amplitude, small enough to never leave the static friction regime, is proportional to the excitation amplitude. The phase is zero. r = A mf H 2 (9) φ = 0. (10) At the limit of high excitation amplitudes the signal is again a simple function of the sliding friction force. lim r = 4qF H A m π = 4 π F G (11) The above theory is valid only for samples with no viscoelastic behaviour. There one can, to a first approximation, interpret the data in terms of static and dynamic friction forces. Viscoelastic surfaces on the other hand are characterized by their moduli and by characteristic time constants. In many experiments the lateral modulation amplitude is small compared to the diameter of the contact zone. Therefore one can view the experiment as a nanoscopic 3

4 shear compliance testing. The testing of shear compliance involves the three moduli: the bulk modulus B B = hydrostatic pressure volume strain the Youngs modulus or tensile modulus E E = = hydrostatic pressure volume change per unit volume = pv 0 V tensile stress force per unit cross section area = = F/A tensile strain strain per unit length ln (L/L 0 ) and the shear modulus or rigidity G (12) (13) G = shear stress shear strain = shear force per unit area shear per unit distance between shearing surfaces = F/A S/D (14) These equations deal with purely elastic deformations. However, polymers and many other materials have considerable viscous responses to stimuli. Whereas the elastic response is reversible, the viscous response is plastic. Molecules are permanently rearranged, their equilibrium is reached only after a relaxation since characteristic relaxation time. For a sinusoidal forced vibration one gets the following equations for the stress and the strain, respectively. τ = τ 0 sin (ωt) (15) γ = γ 0 sin (ωt ϑ) (16) We can combine these two quantities into one complex modulus. G = τ 0 γ 0 cos (ϑ) (17) G = τ 0 γ 0 sin (ϑ) (18) The real part of this modulus, G, is the storage modulus (named after the fact that energy is stored reversibly in the deformation). It describes the stiffness of the sample. The imaginary part of the complex modulus, G, is the loss modulus or viscous modulus. It describes the dissipation of mechanical energy, i.e. the conversion of mechanical energy to heat. In a similar way one can write down a complex shear modulus E. The definition is analogous to the above definition of the complex G. In both cases one can define a loss tangent and G G = tan (δ G ) (19) E E = tan (δ E ) (20) A dominant relaxation time constant of molecular reorganization under shear conditions shows up as a peak in the imaginary part of the complex shear modulus. This quantity is standard for characterizing polymers and polymer samples. 4

5 3 Instrumental Aspects We use commercial scanning force microscopes (Topometrix, CSEM) in combination with a PulsedForceMode electronics (Witec). In the Pulsed- ForceMode the cantilever position is modulated with a sinusoidal voltage. The amplitude is typically between nm. It is large enough that the tip is brought into contact and removed from contact in every cycle. Typically the modulation frequency is between 0.1 to 5 khz. It is important that it is below the resonance frequency of the cantilever. The nature of the response curve depends on the interaction of the tip with the sample. The stiffness (a not so well defined quantity) of the sample and the viscous behavior are the most important parameters. If we start at the left side of Figure 2, then the tip is far away from the sample. The force is constant and zero as indicated by the baseline. Shortly before the tip reaches the surface an instability occurs. It is often called snap in. The size of the force jump is indicative of the interaction potential, but also of double layer forces in electrolytes, for instance. The tip is then pressed against the sample. It follows the indentation curves known from the literature. At the point (time) of maximal indentation the force is measured. The feed back electronics of the scanning force microscope keeps this force constant. Hence the indentation curves are stabilized too. Subsequently the tip is withdrawn from the sample. Adhesion forces permit negative total force. The break force in the JKR model is given by F adhesion = 3π 2 W 1,2R (21) where W 1,2 is Dupr s interfacial energy and R the radius of the tip. Hence the maximum negative force after the indication is determined, within the framework of the JKR theory, by the adhesion of the tip to the sample. The cantilever is then relaxed and starts to oscillate at its resonance frequency. This oscillation permits, in theory, the measurement of mass transfer to the cantilever from the sample. To implement dynamical friction measurements one can measure, while measuring in PulsedForceMode, the lateral force signal modulation induced by the sample. The setup of this experiment is shown in Figure 3. The electronics shown in Figure 3 is essentially the PulsedForceMode electronics. Lock-in amplifiers for the normal and the lateral force mode image detects the induced modulation signals even though they are not continuous (Krotil et al., 2000b; Krotil et al. 2000a). Figure 4 shows the setup to measure dynamical friction and adhesion simultaneously. Therefore the AFM is equipped with several piezo actuators which impart oscillations between the probe and the sample such that a vertical oscillation and a relative lateral oscillation are superimposed. These oscillations give the AFM high dynamic components and makes it obvious to name the operating principle COmbined DYnamic Mode or CODYMode R, for short. The lock-in amplifier generates the modulation signal for the sample piezo. The resulting high frequency signals are detected and phase and amplitude are recorded. It is important to use lock-in amplifiers which have a fast frequency response and a fast calculation of amplitude and phase. The lock-in outputs a signal which starts as soon as the tip gets into contact with the sample. The integration line of the lock-in amplifier determines the rise time of the signals (amplitude and phase). Sample and hold circuits measure the peak values of the induced signals. 5

6 4 An Example: The Analysis of Thin Aminosilane Films Generated by Micocontact Printing CODYMode R SFM investigations were performed with the atomic scale tribometer (CSEM Instruments, Neuchatel, Switzerland) with an in-house built CODYMode R module. Amplitude and phase were measured with a lock-in amplifier (SR 844 RF, Stanford Research Systems Inc., CA, USA). The lateral sample excitation was done by a piezoelectric transducer (PIC 155, PI-Ceramics GmbH, Lederhose Germany). All data were acquired with rectangular Si 3 N 4 probes (Olympus Optical Co., Ltd. Tokyo, Japan). The spring constant for normal excitation was 0.75 N/m with a fundamental resonance frequency of 85 khz. The transducer was driven by a synthesized function generator (DS 345, Stanford Research Systems, CA, USA). All measurements were done with an amplitude of 5.5 nm at frequencies from 150 khz to 700 khz under ambient conditions ((24 ± 1) C, (42 ± 2)% relative humidity). Microscopic measurements of frictional forces and shear elasticities were performed on samples prepared by transferring aminosilane ((S-amino-propyl) triethoxysilane, provided by P. Barth) by microcontact printing (µcp ) on silicon wafers. The polydimethylsiloxane (PDMS) stamp (SL-GARD 184 Base silicon elastomer, Dow Corning GmbH, Wiesbaden, Germany) was controlled inked (Krotil 2000). After plasma oxidation of the PDMS stamp, the aminosilane was vapor deposited for two hours and brought into contact with the substrate immediately. The silicon substrate (pieces of monocrystalline silicon wafer from Wacker GmbH, Germany) were cleaned by heating at 70 C for 35 min in Pirhana solution (a mixture 7 : 3 (v/v) of 98 % H 2 SO 4 and 30 % H 2 O 2 ), thoroughly rinsed with deonized water and used immediately. Using this technique a monolayer of aminosilanes was generated, with rings of uncoated silicon exposed. The silicon serves as a hard reference in the analysis of the molecules. The topography of the silicon rings is almost indistinguishable from that of the silane layers. We consider that the coverage of the silicon is mostly one monolayer. The detection of the adhesion force is independent of the lateral modulation frequency (Krotil, 2000). Figure 5 shows that the adhesion force of the silane covered areas is around ( 116±6) nn, that of the silicon (unmodified areas) is ( 108 ± 6) nn. The fluctuation of the adhesion force as a function of the excitation frequency is the same for the monolayer and the bare silicon, indicating that other long range forces such as electrostatic forces might be important. Figure 6 shows a series of measurements at selected frequencies from 150 khz to 700 khz. The frictional force (amplitude and phase) depends on the excitation frequency. Figure 7 shows this more clearly. The amplitude of the frictional signal increases monotonically for the silane coated regions and the silicon (water coated) region. The amplitude on the silane film is slightly larger than that on the silicon. It is expected that the frictional force increases in this velocity range, as a consequence of velocity shear strengthening (Baumberger, 1996). Commonly one assumes that viscous damping is important. The phase map shows an interesting behaviour. For low velocities (frequencies) the phase shift of the silane is more pronounced than for the silicon. At speeds of 16 mm/s the phase relation increases, leading to an inverted contrast. Finally above 19 mm/s the differences between silanes and silicon vanishes. Since silicon is covered with native oxide layer there is a water film in the ring areas. Thus, the phase may indicate different elastic behavior between the water and the aminosilane layers. From the amplitude spectra and the phase spectra the storage module G and G can be calculated according to Equations (17) and (18). The qualitative trend is shown in Figure 7. Since the spectra differ slightly only small differences in G and G are observed. Above 6

7 f = 400 khz a significant increase of G is observed for both materials. Further increasing the frequency puts more and more energy in the storage module. The dissipation has a minimum at f = 400 khz, suggesting an optimal speed for minimum friction. 5 Conclusions Dynamical friction force measurements using CODYMode R allow a simultaneous measurement of topography and adhesion along with friction. The intermittent contact mode of friction measurements prevents the damage of delicate samples. CODYMode R is equally suitable to do mechanicaldynamical testing at the nanometer scale. Improved lateral excitation piezos might increase the useful frequency range to several megahertz. 6 Acknowledgements The authors kindly acknowledge the help of and discussions with Peter Barth, Volodymyr Senkovsky, Thomas Stifter, Sabine Hild, Martin Pietralla, Bernd Heise, Markus Hackenberg and Gerhard Volswinkler. Some of the works was made with support of the German Science Foundation (SFB 239). 7

8 References and Notes Baumberger, T. (1996). Physics of Sliding Friction chapter Dry Friction Dynamics at Low Friction, Kluwer Academic Publishers, l-26. Bhushan, B. (1999a). Handbook of Micro/Nanotribology chapter Introduction - Measurement techniques and applications, CRC Series Mechanics and Materials Science, Boca Raton, Florida. Colchero J., Luna, M., and Baro, A. M. (1996). Lock-in technique for measurement friction on a nanometer scale, Appl. Phys. Lett. 68, Gddenhenrich, T., Mller, S., and Heiden, C. (1994). A lateral modulation technique for simultaneous friction and topography measurements with the atomic force microscope, Rev. Sci. Instr. 65(9), Krotil, H.-U. (2000). CODYMode R scanning force microscopy: The concurrent measurement of adhesion, friction and viscoelasticities, PhD Thesis, University of Ulm. Krotil, H.-U., Stifter, Th., and Marti, 0. (2000). Concurrent measurement of adhesive and elastic surface properties with a new modulation technique for scanning force microscopy, Rev. Sci. Instr. 7, Krotil, H.-U., Stifter, Th., and Marti, 0. (submitted 2000). Combined Dynamic adhesion and friction measurement with the scanning force microscope, Applied Physics Letters. Krotil, H.-U., Stifier, Th., Waschipky, H., Weishaupt, K., Hild, S., and Marti, 0. (1999a). PulsedForceMode: A new method for the investigation of surface properties, Surface and Interface Analysis 27, Krotil, H.-U., Weilandt, E., Stifter, Th., Marti, O., and Hild, S. (1999b). Dynamic friction force measurement with the scanning force microscope, Surface and Interface Analysis 27, Marti, O., Colchero, J., and Mlynek, J. (1990). Combined scanning force andfriction microscopy of mica, Nanotechnology 1, Mate, C. M., McClelland, G. M., Erlandson, R., and Chiang, S. (1987). Atomic-scale friction of a tungsten tip on a graphite surface, Physical Review Letters 59, Meyer, G. and Amer, N. M. (1990). Simultaneous measurement of lateral and normal forces with an optical-beam-deflection atomic force microscope, Appl. Phys. Lett. 57, Nurdin, N., Weilandt, E., and Descouts, P. (1997). Scanning force microscopy of surface phase separation ofpolymer blends, Chimia 51(7), 405. Rosa, A., Weilandt, E., Hild, S., and Marti, 0. (1997). The simultaneous measurements of elastic, electrostatic and adhesive properties by scanning force microscopy.. Pulsed- ForceMode operation, Meas. Sci. Technol. 8, Yamanaka, K. and Tomita, E. (1995). Lateral force modulation atomic force microscope for selective imaging of friction forces, Jpn. J. Appl. Phys. 34,

9 Figure Captions Figure 1. The idealized friction loop shown as a function of time. Two surfaces are moved one past the other. The friction force f(t) increases until the maximum static friction force F H (stick) is reached. The force level reduces down to F G (slip) and stays constant until the backward movement reduces the speed to the point where the tip starts to stick again. The same behaviour is also observed on the backward scan. Figure 2. Scheme showing the modulation voltage (dotted line) and the force signal (straight line) over a complete modulation period in PulsedForceMode. The arrows indicate the points where the baseline, adhesion force, stiffness and the maximal applied normal force F max are taken. Time and force are given by arbitrary units. Figure 3. Block Diagram of the CODYMode R scanning force microscope. Figure 4. Schematic view of a microscope setup in CODYMode R to measure friction and adhesion simultaneously. Figure 5. Adhesive forces in CODYMode R SFM. The detection is not affected by the lateral modulation. Figure 6. Qualitative overview of high velocity friction investigations of aminosilane, microcontct printed on native silicon. The first column represents the adhesion forces, the second column is the frictional amplitude and the third one the frictional phase. The rows are measurements at different frequencies (from 700 khz, top row, down to 150 khz, bottom row). The excitation amplitude was kept constant. All measurements were performed at ambient conditions ((24 ± 1) C, (42 ± 2) % relative humidity). A Si 3 N 4 tip on a rectangular cantilever was used. Figure 7. (a) Starting from the detected amplitude and phase spectra as a function of the maximum lateral sliding velocity one can estimate (b) the storage modulus G and loss modulus G of the silane and silicon (water coated). 9

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