Chapter 8 Physics and Physical Chemistry at the Nanotip Scale
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Fundamental Investigation of the Mechanical Response of Soft Materials with an Atomic Force Microscope S. Kopp-Marsaudon, L. Nony, D. Michel, and J. P. Aimé CPMOH-Universitéde Bordeaux, 1-351, Cours de la Libération, 33405 Talence Cedex, France
In the local microscopy's field, a large effort is dedicated to study the mechanical properties which can be accessed with a nanotip. Within this context, soft materials are well adapted to probe mechanical response at the nanometer scale. After a discussion of some experimental and technical key points, we present three different types of experiments done on one model polymer : polystyrene films with different molecular weights. In the experiments, the tip may scan the sample surface (friction loops), or move upward and downward in the vicinity of the sample -in contact mode (force curve) or in an oscillating mode (approach-retract curves)-. The comparison of the results shows the sensitiveness of the tip to local mechanical properties. New routes to explore mechanical properties without touching the sample are proposed.
Since the last few years, the study of soft materials with an atomic force microscope (AFM) has shown that it gives much more than just topography. The idea is either to put the tip in contact with the sample and measure the cantilever deflection variations or to vibrate the tip in the vicinity of the sample and to measure changes of the oscillating behavior. The contact experiments allow probing of friction processes at the nanometer scale, thus providing new information for the tribology field (1-6). Bulk mechanical properties of soft materials can be accessed in contact experiments through the force curve analysis (7-9) and with force modulation (10). The more recent development concerns the use of the oscillating behavior of the tip-cantilever (CL) system when brought close to the sample surface. Two modes can be used in dynamic force microscopy. With one mode, commonly called tapping,
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© 2000 American Chemical Society
Tsukruk and Wahl; Microstructure and Microtribology of Polymer Surfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
125 the tip-CL oscillations are done at a fixed drive frequency and a fixed drive amplitude. In that case oscillation amplitude and phase variations are recorded. In the other mode commonly called non contact AFM (11), the oscillation amplitude is kept constant and the recorded quantity is the shift in resonance frequency. Note that the name "tapping" as opposed to "non contact" mode is confusing, as it is possible to work in non contact in the tapping mode. A large effort has been made to understand the oscillating behavior both theoretically and experimentally (see refs (12-18) for the tapping, (1927) for the non contact). Theoretical and experimental development in the field of dynamical force microscopy allow the measurement to be more quantitative. In particular, phase images is now understood as mechanical as shown on the model samples provided by the copolymers (28-30). For non contact experiments, their main result is the possibility to reach contrast at the atomic scale, which is started to be understood through the study of the oscillating behavior of the tip-CL system. In this paper we will compare different experiments in contact and with an oscillating tip to show their contribution for the study of soft material. In static contact mode, force curves and friction loops are recorded while in tapping a systematic investigation of approach-retract curves is presented. A model sample is used: monodisperse polystyrene films of different molecular weights (M ): bulk mechanical properties and molecular weight dependence of the glass transition temperature. In order to emphasize the inherent difficulties encountered with an AFM, we begin with a detailed discussion of the technical conditions. w
Technical Section. A Presentation. In an AFM experiment, a nanotip is attached to the end of a compliant cantilever. Two types of experiments can be performed, one in which the tip is brought in contact with the sample, and throughout the experiment the tip remains in contact, rubbing the surface. In that case change of the cantilever deflection or torsion is recorded and the study belongs to the field of tribology, the domain of science devoted to the study of friction processes. In a second type of experiment, the tipcantilever is kept vibrating at or near its resonance frequency and during most of the oscillation period the tip does not touch the sample or even never touches the sample. This second method provides additional information, and for very soft materials, as liquid polymers are, becomes the unique way to probe mechanical properties at the nanometer scale. B A F M Key Issues. In both cases, several parameters are not accurately known, making quantitative measurements difficult to achieve. In this section is given a short list of these parameters. The key issues are force calibration, tip characterization with estimation of the contact area between the tip and the sample, and effects of the experimental environments. The behavior of the contact area, either stationary or fluctuating, is a key parameter to have at least robust, reproducible experimental data. We arbitrarily focus on the attempts to design in situ experiments that allow the measurements to be more quantitative. Most of these key issues are far from being resolved or standardized. They still appear to be very dependent of the scale at which the required signal has to be obtained. The experimental constraints will not be the
Tsukruk and Wahl; Microstructure and Microtribology of Polymer Surfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
126 same for a signal measured at the molecular or mesoscopic scale. Also the chosen experimental strategy is very dependent of the mechanical properties of the surface or object analyzed. The following is a list of works aiming to calibrate AFM. There are in many cases attempts that are indicative of the difficulties encountered and cannot be considered as a definite route to make routinely quantitative measurement with an AFM. 1 Deflection and Force Calibration. Deflection measurement of the end of the cantilever is achieved by optical detection as described in Figure la. Care must be. taken to avoid spurious signal due to interference between sample and cantilever and misalignement of the photodiodes. Calibration of the deflection is easily obtained by performing a force curve (Figure 2a) or an approach-retract curve (Figure 2b). Such an operation requires a good calibration of the relationship between the applied voltage on the piezo actuator holding the sample and the vertical displacement. For a good correspondence between the cantilever displacement and the sample one requires that the contact stiffness is much larger than that of the cantilever stiffness, and therefore requires the use of hard materials. Force calibration is much more difficult to achieve. One way to estimate cantilever force constants is to use formulae for the force constants of simple beam geometry (31). For any of these calculations, all the cantilever dimensions and the relevant moduli must be known. The knowledge of the cantilever dimension is a tricky problem, even for a simple geometry as a beam with a rectangular section. The most important parameter is the thickness, typically half a micron, which cannot be accurately controlled during microfabrication. Because the force constants follow a cubic law as a function of the thickness, dispersion in thickness values induces sizable dispersion in force constant (32). Several experimental attempts have been performed (32, 33), which are in many cases time consuming and cannot be easily standardized. In situ evaluation should obviously be more easy, attempts using power spectrum analysis of thermal fluctuations is quite promising., This approach requires a good estimation of the effective mass and geometrical properties and also that the thermal fluctuations can be easily discriminate from other noise sources (34-36). Note also that calibration with an optical beam detection, is dependent of the laser spot location, thus may vary from one measurement to another if optical adjustment takes place. Here again, there are a few simple ways to overcome this difficulty, the most obvious being to have an experimental set allowing to make various measurements still keeping the same optical realignment. 2 Tip Characterization. The tip is the central parameter of any scanning probe microscope, and an accurate knowledge of the size and of the shape of the tip should normally be a necessary requirement to get a quantitative measurement. The nanometer size, or atomic size, of the tip makes scanning probe microscopy attractive, but results in the relevant part of the tip responsible for the interaction to be unknown. Therefore, reproducible experimental data accompanied with a theoretical description will be required to have a robust interpretation of the experimental data. Nevertheless, numerous attempts have been made to estimate the shape and size of the tip, here we
Tsukruk and Wahl; Microstructure and Microtribology of Polymer Surfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
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Figure 1: AFM optical detection method sketches. Figure la: a laser beam is centered on the cantilever free end where the tip is attached. It then reflects on a mirror towards the photodiodes (here four quadrants photodiodes). As the sample moves (we will always in the following consider that the piezo actuator -which induces the relative tipsample movement- is under the sample), the tip deflection or torsion variations are measured through voltage vertical or horizontal difference of the photodiodes signals.
Figure lb: effect of the orientation of the photodiode four quadrants on the measurement of the output signals of the vertical or lateral voltage difference.
Tsukruk and Wahl; Microstructure and Microtribology of Polymer Surfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
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vertical displacement of the sample Figure 2a: Idealized force curve performed in contact AFM: plot of the tip deflection variations with the vertical displacement of the sample. In part a, the tip is far from the sample, the cantilever rests at its equilibrium position. In part b, the tip is in contact with the sample, the cantilever is compressed. The vertical displacement is then reversed. The cantilever deflection reaches then its initial value and continues to decrease while the tip sticks on the sample. If the sample is hard (like for example mica or silica surface), the slope of part b and c should be equal to 1, allowing to transform the photodiodes vertical signal difference from voltage to distance. At the end of part c, the force due to the extended cantilever equals the adhesive force, it snaps back to its equilibrium position. The vertical displacement AZ necessary to unstick the tip from the sample is noted in gray. U
Tsukruk and Wahl; Microstructure and Microtribology of Polymer Surfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
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vertical displacement Figure 2b: Idealized approach-retract curve: plot of the oscillation amplitude variation with the tip-sample distance during the approach and retraction of a sample toward an oscillating tip-cantilever system. First, when the tip is far from the sample, it oscillates with its free amplitude Af as depicted in part a. In part b, the tip-CL system interacts with the surface through an attractive field. If the drive frequency is slightly below the resonance one, the oscillation amplitude increases. Part c corresponds to the so-called A F M tapping mode where the tip comes in intermittent contact with the sample. In this part, the oscillatory amplitude A decreases linearly with the CL-surface distance d with a slope equal to 1 if the sample is hard, that is if d
