Impact of atomic force microscopy on interface and colloid science

Transcription

1 Advances in Colloid and Interface Science 133 (2007) Impact of atomic force microscopy on interface and colloid science H.-J. Butt, R. Berger, E. Bonaccurso, Y. Chen, J. Wang Max Planck Institute for Polymer Research, Ackermannweg 10, Mainz, Germany Available online 14 June 2007 Abstract Since its invention twenty years ago the atomic force microscope (AFM) has become one of the most important tools in colloid and interface science. The reason for this impact is that the AFM allows doing experiments on length, time, force, and energy scales, which are not accessible by any other technique. These experiments can be carried out under natural conditions, for example in liquid environments. In this paper we specify the length and time scales involved, give examples where by using the AFM relevant questions in colloid and interface science have been solved, and we discuss future perspectives Published by Elsevier B.V. Contents 1. Introduction Length scales Time scales Force measurements Stabilization of dispersions Adhesion Single molecules Nanomechanics Extreme conditions Cantilever applications Perspectives Faster scanning Chemical analysis Tip sharpening Lithography Conclusions References Introduction Corresponding author. Tel.: ; fax: address: (H.-J. Butt). Since its invention two decades ago by Binnig, Quate, and Gerber [1], atomic force microscopy has made a significant contribution to the progress in colloid and interface science. Usually the atomic force microscope (AFM), also called scanning force microscope (SFM), is used to obtain topographic images of solid surfaces in ambient conditions or liquid environment. To obtain topographic images (Fig. 1A) a tip, which is mounted to a micromechanical cantilever spring, scans the sample surface. While scanning, the force between the tip and the sample is measured by monitoring the deflection of the cantilever. The deflection of the cantilever is usually measured by focusing the beam of a laser diode to the back of the cantilever and detecting the position of the reflected beam. This /$ - see front matter 2007 Published by Elsevier B.V. doi: /j.cis

2 92 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) called contact mode. The lateral resolution depends on the conditions of the sample, the properties of the AFM tip, and the interaction between the two. In rare cases atomic resolution is obtained. More typical for applications in soft matter science are 2 10 nm resolution in lateral direction. The vertical resolution is limited by the thermal noise of the cantilever and is usually better than 0.1 nm [2]. A rapidly growing application of atomic force microscopy are force measurements (review [3], Fig. 1B). In a force measurement the sample (or the tip) is periodically moved up and down. The height of the sample (or tip) and the deflection of the cantilever are recorded and converted to distance and force. Force measurements have contributed significantly to our understanding of interparticle interactions, which stabilize dispersions. Furthermore adhesion between particles, forces within single molecules, and mechanical properties of nanostructures were investigated. In addition to imaging and force measurements, the measurement of surface stress is an active field of research. Changes of the surface stress on the top or bottom side of micromechanical cantilevers lead to a bending [4 6]. This principle is used for sensing specific molecules or for material characterization. In sensor applications one side of the microcantilever is coated with receptors. Upon binding of the ligand to the receptors, the surface stress of that side changes (Fig. 1C). The deflection of microcantilevers can be measured with sub-nm precision, which allows detecting tiny changes in surface stress. Furthermore, microcantilevers can be produced in arrays on a single chip enabling the detection of different molecules simultaneously [7]. That the AFM has become one of the main tools in colloid and interface science is obvious, when looking at the large number of papers containing AFM results. Starting at the beginning of the 1990s the relative number of publications in typical journals of the interface science community started to increase and has reached an average of 12% (Fig. 2). It is still increasing with no indication of a saturation. Fig. 1. (A) Schematic of an atomic force microscope used to image the topography of surfaces. (B) For force measurements the sample is moved up and down. No lateral scanning and no height regulation is required. Often the tip is replaced by a colloidal particle. (C) To use microcantilevers as sensors they are coated on one side with a receptor. Binding of the ligand leads to a bending, which can be detected with the usual optical lever technique. is called the optical lever technique. A topographic image of the sample is obtained by plotting the deflection of the cantilever versus its position on the sample. Alternatively, it is possible to plot the height position of the translation stage. This height is controlled by a feedback loop, which maintains a constant force between tip and sample. While scanning, the tip is usually in contact with the sample. Therefore this mode of operation is Fig. 2. Relative number of papers in which atomic force microscope, scanning force microscope, AFM, or SFM appears in the title, abstract or as a keyword. This number is plotted versus the year of publication for Langmuir and the Journal of Colloid and Interface Science.

3 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) Before giving scientific and technical reasons for the impact of atomic force microscopy, we would like to mention one practical aspect. Setting up a basic AFM laboratory requires a financial investment of the order of 200,000 Euro. This is often affordable for young scientists on the level of assistant professors. As a result, many highly active groups of young independent scientists advance the field and lead to rapid progress. This is certainly one factor driving the progress of interface science with the AFM. The main scientific factor for the impact of atomic force microscopy is not easy to identify. It is not as simple as for example for electron microscopy. When electron microscopy came up, it overcame the diffraction limit of light microscopes and improved the resolution by a factor The AFM helped to solve many scientific questions and it is one more tool to characterize microscopic structures. It is, however, more difficult to identify the main underlying reason for the impact. Compared to electron microscopy, in which the sample is exposed to vacuum, the AFM can be operated in air, liquid, and other natural conditions. Compared to diffraction techniques only small surface areas are required; typically the whole sample extends over 100 nm 100 μm. The surface molecules do not need to be arranged as a two-dimensional crystal. In contrast, electron, grazing-incidence X-ray, or He diffraction can only be applied to crystalline, homogeneous surfaces of typically 1 cm size. In atomic force microscopy (and the related scanning tunnelling microscopy) real images are obtained rather than images in reciprocal space, which lack the phase information and which can not be uniquely transformed into real space. The the AFM complements other techniques for structural analysis but does not replace them. If, for example, mean spacings or periodic structures are analysed, scattering techniques are unbeatable. With scanning electron microscopes large areas can be analyzed much faster than with the AFM. In addition to some obvious advantages, we argue that the success of atomic force microscopy is due the fact that now experiments can be done at new length and time scales under natural conditions. As a result of the length scales also new force and energy scales become easily accessible. The concept of length and time scales also helps to design AFM experiments properly and to analyse results. Let us illustrate the significance of length and time scales in one example: the adsorption of surfactants from solution to a solid interface. Many questions concerning the structure of adsorbed surfactants could be solved by imaging them in aqueous medium. This was pioneered by Manne, Gaub, Ducker, and others [8 11]. Fig. 3 shows an AFM image of asymmetric cationic Gemini surfactant, (C 18 H 37 ) (N + (CH 3 ) 2 ) (CH 2 ) 3 (N + (CH 3 ) 2 ) (CH 3 ) 2Br -, adsorbed to mica from a 3 mm aqueous solution [12]. Under these conditions the surfactant adsorbes in the form of complete micelles, which form a hexagonal structure on the silica surface. The diameter of each micelle is 8.8 nm. The fact that stable micelles could be imaged, demonstrates that they are stable over at least the time required to scan one image, in this case s. In fact, micelles could be observed for much longer times. Individual surfactant molecules, however, reside much shorter at a certain position. Fig. 3. AFM image ( nm 2 ) of aggregates of the cationic Gemini surfactant (C 18 H 37 ) (N + (CH 3 ) 2 ) C 3 H 6 (N + (CH 3 ) 2 ) CH 3 on the cleavage plane of mica in contact with a 3 mm aqueous buffer solution [12]. The structure of the surfactant is schematically shown on the left. Typical exchange times of surfactant molecules in a micelle are of the order of 1 μs. Another example of the importance of time and length scales is the success of tapping mode. With its introduction it became possible to image soft structures such as polymers. In tapping mode the cantilever is vibrated close to its resonance frequency. Typically relative stiff cantilevers with resonance frequencies in the range of khz are used. When the tip of such a vibrating cantilever approaches a surface, at some point it will get into contact. This reduces the vibration amplitude, which is used as a feedback signal to record the topography. In addition, depending on the energy dissipation during the short contact time, the phase between the excitation and the actual movement of the tip changes [13,14]. The phase shift allows to deduce mechanical properties of the sample. Even soft samples can be imaged in tapping mode because of two reasons. First, lateral friction of the tip on the sample surface as it occurs in contact mode is avoided. Second, the contact time is short. Taking a resonance frequency of 300 khz and estimating that typically the tip is less than one tenth of a vibration period in actual contact with the sample we obtain typical contact times of 0.3 μs. At that time scale even many soft samples are not deformable and appear hard. To illustrate this we show an example of a film made of a diblock copolymer. Diblock copolymers are linear polymers, which consist of two chemically distinct parts [15]. In the bulk, diblock copolymers tend to microphase separate [15 17]. Depending on the length of each block and on the immiscibility between them different structures are formed, for example spherical phases A arranged in a hexagonal order in a matrix of block B. Other structures formed are cylinders or lamellar phases [18]. On surfaces the structure of thin films can be different due to the interaction with the solid support and the polymer-air surface. Diblock copolymer films have been studied extensively with the AFM [19 23]. As one example Fig. 4 shows a film of a diblock copolymer consisting of polyisoprene

4 94 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) length scales have to be considered and these are coupled to distance. Surface roughness defines the first length scale, the overall radius of the particle typically 1 10 μm defines a second length scale. In this context the most useful quantitative definition of surface roughness is the peak-to-valley distance over a typical area, over which surface forces are acting. For distances much larger than the surface roughness the radius of the particle is the relevant length scale. A third important set of length scales is defined by the geometry of the cantilever. Cantilevers are microfabricated and either rectangular or V-shaped. They are typically t c = μm thick, w=15 50 μm wide and L = μm long. Together with the Young's modulus of the material E they determine the spring constant k c and the resonance frequency (see below). For a rectangular cantilever we have Fig. 4. AFM tapping mode phase image of a thin film of polyisoprene-b-poly(2- (N,N-dimethylamino)ethyl methacrylate) [24]. and 2-(N,N-dimethylamino)ethyl methacrylate, denoted by PIb-PDMAEMA [24]. The number average molecular weights of the two blocks were 20.6 kda and 3.8 kda, respectively, so that PDMAEMA as the minority forms small islands in a matrix of PI. PI with a molecular weight of 20.6 kda is a liquid with a viscosity of roughly 0.4 Pa s. In contact mode it would wet the AFM tip and the surface tension of the liquid would attract the tip into the polymer. In tapping mode this is prevented. By keeping the time of each contact short, the liquid PI can not flow around the tip and it practically behaves like a solid surface. In tapping mode with its short contact times even single liquid drops can be imaged. As an example Fig. 5 shows few liquid drops of concentrated aqueous solution of P 2 O 5 on mica imaged in tapping mode [25]. In this way nanoscopic liquid drops could be imaged under natural conditions and for example line tensions could be determined [26]. k c ¼ Ewt3 c 4L 3 The design of an AFM cantilever for contact mode imaging or for force measurements is a compromise between the need to have a soft cantilever and to have a high sensitivity. To obtain a soft cantilever they should be long and thin. High sensitivity on the other hand is achieved with short cantilevers. In addition, short cantilevers with high resonance frequencies tend not to be influenced by vibrations of the building and the table, which are of low frequency. All requirements lead to the conclusion that cantilevers should be small. Only short and thin cantilevers are soft, have a high sensitivity, and a high resonance frequency (see below). 3. Time scales The most important time constant of the AFM is given by the inverse of the resonance frequency ν 0 of the cantilever: τ=1/v 0. For imaging it limits the scan velocity [29 31]. If, for example, ð1þ 2. Length scales Different length scales are relevant in atomic force microscopy. One important length scale is the distance between the tip and the sample surface. For contact mode imaging this is of atomic dimension. In a force measurement the relevant length scale is larger and typically of the order of the range of surface forces. Another relevant length scale is defined by the radius of curvature of the tip. It typically ranges from 1 50 nm depending on the material and the manufacturing process. In imaging, the lateral resolution on crystalline surfaces can be of atomic dimensions. On soft or nonperiodic surfaces the resolution of individual features is given by the radius of curvature of the tip. For many force measurements particles are attached to the end of the cantilever; this is referred to as the colloidal probe technique [27,28]. Usually the particles are spherical. Using microspheres increases the variability of available materials and the geometry of the contact materials is better described. Two Fig. 5. Tapping mode image of a drop of saturated aqueous P 2 O 5. For details see [25].

5 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) we intend to resolve features of Δx resolution the scan velocity should be significantly below v o Δx. Processes, which are faster than τ are difficult to resolve. For a rectangular cantilever in vacuum or gaseous medium the resonance frequency is given by v 0 ¼ 0:1615d t c L 2 d sffiffiffi E q ð2þ Here, ρ is the density of the cantilever material. In liquid, the resonance frequency is reduced by typically a factor 5 10 [29]. Hydrodynamic effects cause the effective mass of the cantilever to increase because the cantilever drags the surrounding liquid with it [32 34]. The higher the viscosity of the surrounding liquid the lower the resonance frequency of the cantilever. This effect can even be used to measure the viscosity of liquids [35]. Typical resonance frequencies are 5 40 khz for contact mode cantilevers and khz for tapping mode, both in air. In many applications it is desirable (or unavoidable) to heat the tip and microcantilever. One unavoidable source of heat is the laser light impinging on the cantilever apex. Heating the microcantilever can be achieved at heating rates of N1000 K/s. In microcantilevers the heat transfer depends on the thermal contact to the media and the heat conductivity to the cantilever support. In the case of typical gold-coated silicon nitride cantilevers the heat is equilibrated within 1 10 ms in vacuum [36]. Under ambient conditions thermal contact to the air further reduces the equilibration time. The thermal contact is even better for liquids and equilibration times much faster 1 ms can be achieved. Bimaterial microcantilevers bend when their temperature is changed. Heat can be generated by reactions on a catalytic layer situated on the microcantilever [37] or by the transition heat of a phase transition within a sample attached to the microcantilever [38]. Active controlled heating of microcantilever sensors allows to investigate thermal decomposition up to temperatures of 1000 C [39]. In many applications it is instructive to relate the instrumental time scales to time scales of processes studied. Often the diffusion of molecules determines the speed of processes. Therefore we consider two typical examples: the diffusion constant of toluene molecules in air at normal temperature and pressure is D t = m 2 /s. Assuming our cantilever has a resonance frequency of 50 khz we have τ=20 p μs. ffiffiffiffiffiffiffiffiffi In 20 μs toluene molecules diffuse an average distance 6D t s ¼ 31Am, assuming they are free to diffuse in all directions equally well. Thus, for gas molecules around a typical AFM tip diffusion is fast enough to equilibrate possible concentration gradients. If we take the same cantilever and analyse a process in water the resonance frequency decreases to typically 5 khz or τ=0.2ms. The diffusion coefficient for ions such as Na + or Cl in water are and m 2 /s, respectively. This leads to a mean diffusion distance of μm. Thus, concentration gradients over 1 μm distance are equilibrated on the time scale of 0.2 ms. As one example Fig. 6 illustrates relevant time and length scales for AFM imaging of biological membranes [40]. To reveal the structure of membrane proteins biological membranes are imaged in aqueous buffer. With sharp tips the best Fig. 6. Illustration of relevant length and time limits of a typical AFM experiment for imaging a biomembrane in aqueous electrolyte. The diagonal p line ffiffiffiffiffiffiffiffiffi in the double-logarithmic plot relates time scales τ and diffusion lengths 6D t s assuming a diffusion coefficient of D t = m 2 /s (Na + ion in water). images show a lateral resolution of 1 nm. This resolution is plotted as a horizontal line. To image such fragile biological structures usually soft cantilevers are used with a typical resonance frequency of 5 khz. This time constant is represented by a vertical line in Fig. 6. The AFM tip might disturb the ion distribution of the membrane. In order to allow for equilibration of the electric double layer by the diffusion of ions we have to consider the diffusion equation, leading to a diagonal line. An upper limit of the san size is given by the geometric construction of the cell and the scanner. A typical maximal scan size for high resolution imaging is 10 μm. These limits define the allowed time and length scales of this particular experiment. The importance of the system and instrumental time constants becomes obvious when studying for example lipid monolayers or bilayers. Lipid layers have been studied extensively [41 43]. The head groups of the lipid molecules were only resolved, when the lipid was in the gel phase, where the molecules form a crystalline order [44,45]. In the fluid phase individual molecules could not be observed and the lipid layer appears as one homogeneous, featureless surface. 4. Force measurements Most force measurements with the AFM in colloid and interface science are carried out for one or more of the following reasons, each one aiming at a different application: Surface forces are important to stabilize dispersions. Simply speaking: if the force between two dispersed particles in a liquid is repulsive, the particles do not aggregate and the dispersion is stable. If the forces are attractive, aggregation will occur and the dispersion is unstable. The time scale of aggregation depends critically on the range and strength of these surface forces. Force measurements are carried out for a better understanding of adhesion. Adhesion is not only important to make adhesives. It is also relevant for the flow of powders and for cleaning surfaces.

6 96 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) AFM force measurements significantly contribute to our understanding of single molecules, for example the rupture of individual bonds or the stretching of polymer chains. Force measurements are used to analyse nanomechanical properties of materials. We discuss these four applications and the related types of experiments in the following and give examples. For details we refer to Ref. [3] Stabilization of dispersions For a dispersion to be stable the dispersed particles need to repel each other, or at least an activation barrier has to be overcome. Attractive forces lead to aggregation. Thus the stability of a dispersion is directly linked to the forces between the particle surfaces. These surface forces can be measured with the AFM [27,28]. In a force measurement the sample is moved up and down by applying a voltage to the piezoelectric translator, onto which the sample is mounted, while measuring the cantilever deflection [3]. In some AFMs the chip to which the cantilever is attached is moved by the piezoelectric translator rather then the sample. This does not change the description at all. For simplicity we assume that the sample is moved. The sample is usually a material with a planar, smooth surface. It is one of the two interacting solid surfaces. The other solid surface is usually a microfabricated tip or a microsphere attached to a cantilever. For simplicity we call this tip. If we explicitly refer to one of the two we mention it as microfabricated tip or microsphere. Repulsive forces responsible for stabilizing dispersions are measured during the approaching part of a force cycle. As one example the force-versus-distance curve between a silica microparticle and a titania flat in aqueous electrolyte containing 1 mm KNO 3 is shown in Fig. 7 [46]. The force is normalized by division through the radius of the silica microsphere. This normalization allows to compare experiments carried out with probes of different sizes. According to Derjaguins approximation [47] the force between a sphere and a planar surface is given by F=2πRW, where W is the energy per unit area for two parallel plates. F/R should therefore not depend on the specific probe size. Derjaguins approximation is valid for conservative interactions with a range much smaller than the radius of curvature of the tip. Force curves shown in Fig. 7 were recorded at different ph values ranging from ph 8.8 for the top curve to ph 3.0 for the bottom curve. The surface charges of both materials are mainly determined by the ph. Silica has an isoelectric point around ph 3.0, while the isoelectric point of titania is ph 5.6. As a consequence at high ph, where both materials are negatively charged, a repulsive electrostatic double-layer force dominates the total interaction. As theoretically predicted the electrostatic force decays exponentially with distance. The characteristic range is characterized by the p Debye length, which for monovalent salts is given by 0:3nm= ffiffi c, where the concentration c of the salt has to be inserted in mol/l. In the presence of 1 mm KNO 3 the Debye length is 9 nm. The repulsion decreases as the ph decreases, and at ph 3.0, i.e. below the isoelectric point of titania, there is an electrostatic attraction as well as a van der Fig. 7. Force between a silica (SiO 2 ) microsphere of 2.5 μm radius and a titania (TiO 2 ) crystal versus distance. The force is scaled by the radius of the sphere. The curves were recorded at ph values of 8.8, 7.2, 6.3, 5.3, and 3.0 from top to bottom with 1 mm KNO 3 background electrolyt. The figure is reproduced with kind permission from ref. [46]. Waals force resulting in an overall attraction between the two surfaces. A relevant question is whether the system is in equilibrium at all times during the force curve. We consider two effects: The diffusion of dissolved molecules and hydrodynamic effects. The force curves plotted in Fig. 7 were recorded with an approaching velocity of the particle and the cantilever of 100 nm/s. Taking the range of the forces to be 30 nm this distance is passed in 0.3 s. Small ions in water diffuse with a diffusion coefficient of roughly D t 10 9 m 2 /s. Thus in 0.3 s ion concentrations p ffiffiffiffiffiffiffiffiffi are equilibrated over length scales of the order of 6D t s ¼ 41lm and we can safely assume that the system is in equilibrium with respect to the distribution of ions. Hydrodynamic effects become important when the flow of the liquid influences the deflection of the cantilever. A repulsive hydrodynamic force is for example generated when a microsphere, attached to the end of a cantilever, approaches the flat surface and the liquid in the closing gap is squeezed out. It is proportional to the real velocity dd/dt, and inversely proportional to the separation D: F hy ¼ 6pgR2 D d dd dt Here, η is the viscosity of the liquid and R is the radius of the microsphere. Eq. (3) is valid for Newtonian fluids (for a Newtonian fluid the viscosity is constant and does not depend on the shear rate) and assuming a no-slip boundary condition at the solid surfaces. As an example demonstrating the significance of hydrodynamic forces Fig. 8 shows the force-versusdistance curve for a glass microsphere of 10 μm radius and a flat surface for two different approaching velocities. With increasing velocity the hydrodynamic repulsion increases. Hydrodynamic force measurements have attracted considerable interest during the last years because a systematic deviation between measured forces and the theoretical prediction of Eq. (3) were observed by most [48 50] but not by all researchers [51]. This ð3þ

7 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) Fig. 8. Hydrodynamic force-versus-distance curves measured at low velocity (v 0 =4 μm/s) and high velocity (v 0 =40 μm/s) in aqueous electrolyte (200 mm NaCl, ph 5) between a glass microsphere (R=10 μm) attached to the cantilever and mica. The force was normalized by dividing it by the radius of the glass particle. Only each 15th point is shown. Approaching and retracting parts of force curves are indicated by arrows. For details see ref. [49]. deviation indicates that the no-slip boundary condition is not precisely valid and slip occurs at the solid-liquid boundary [52,53] Adhesion When retracting the tip from the sample surface, the tip will stay in contact with the surface until the elastic restoring cantilever force of the bent cantilever overcomes the adhesive tip-sample interaction. First measurements of this pull-off or adhesion force F ad were performed by Martin et al. [54] and Erlandsson et al. [55]. Adhesion forces are relevant in many different applications [56,57]. For example, the flow of granular materials depends on the interaction between the particles. Adhesion is critical for cleaning of surfaces in semiconductor industry and for the characterization of surfaces. In general, the adhesion force is a combination of different components. In gaseous environments, significant contributions from electrostatic forces [58 62] are to be expected mainly on insulators and at low humidity, when charge dissipation is ineffective. In aqueous solutions, most surfaces are charged due to dissociation of surfaces groups and electrostatic double-layer forces are important. Van der Waals forces always contribute and in almost all cases they are attractive. Adhesion forces critically depend on the precise contact geometry of the interacting surfaces. Surface roughness [63 68] and the adsorption of contaminants has a pronounced influence. As one example we discuss the influence of humidity on adhesion forces in gaseous environment. It is well known that humidity influences the cohesion in powders and the adhesion of particles to surfaces [69 73]. One reason is certainly the meniscus force. Water condenses into the gap at the contact region between hydrophilic particles. This is described by the Kelvin equation, which relates the relative vapor pressure to the curvature of the condensed liquid surface. The reduced Laplace pressure in the meniscus and the surface tension of the liquid cause an attractive force [74]. Many experiments showed a significant dependency of the adhesion force on the vapor pressure [75 79]. The results were, however, often conflicting. A continuous increase was for example observed for the interaction of a silicon nitride tip with mica [80], between silica particles [81], a silica particle and a silicon wafer [82] between a silicon nitride tip and molybdenum trioxide [83], silicon tips and hydrophilic surfaces, hydrophilic glass spheres and glass [84,85], or pharmaceutical substances [86,87]. In other cases adhesion-force-versus-humidity curves showed a maximum [85,88 91], or a step-like increase [92]. Only recently it was realized that the humidity dependence of the adhesion force is determined sensitively by the structure of the interacting surface on the 1 nm scale [93 95]. As one example Fig. 9 shows the calculated adhesion force-versushumidity for a perfectly smooth sphere of 2 μm radius interacting with a planar surface. For a smooth planar surface the capillary force is almost constant. Only at very high relative humidity it decreases. This changes qualitatively as soon as surface roughness is introduced. To calculate the effect of surface roughness the planar surface was assumed to be covered with an hexagonal array of asperities. Surface roughness leads to a reduced capillary force at low humidity. As a result the adhesion force-versus-humidity curve increases. Depending on the specific shape of the asperities this increase can be different. Conical asperities for example lead to a steep increase while spherical asperities and in particular elastically deformable spherical asperities lead to a more gradual increase Single molecules In 1994 another type of AFM force measurements emerged, to study single molecules. Forces to stretch single polymer molecules [96 98], to unfold proteins [99,100], or to break Fig. 9. Calculated meniscus force between a smooth sphere of R=2 mm radius with a smooth planar surface and with a surface covered with 2 nm high asperities [95]. The asperities were arranged in a hexagonal two-dimensional array with a spacing 20 nm. Three cases were considered: Conical asperities with a half opening angle of 70, spherical caps with a radius 10 nm, and spherical caps which are elastically compressed according to Hertz theory (E=73 GPa, ν=0.17). The particle is positioned directly on top of a central asperity. The contact angle of all surfaces was set to 10.

8 98 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) single bonds [ ] had been measured before, but the ease and accuracy possible with the AFM greatly stimulated the field (review [107,108]). The wealth of experimental results has also triggered the development of a much refined theory of bonding and bond breaking (e.g. [ ]). AFM allows specific forces of the molecular events to be investigated with piconewton sensitivity and subnanometer accuracy. As one example Fig. 10 shows the stretching of a single poly (ferrocenyldimethylsilane) (PFS) in an aqueous solution [106]. The polymer chains are covalently attached on one end to a gold surface by a thiol group. At zero distance the usual contact adhesion peak is observed, where the tip and the gold surface are separated. After separation the force decreases to zero. Only after a distance of typically nm another adhesion peak is observed. This is due to the stretching of the polymer chain. When stretching a flexible polymer chain the number of possible configurations the chain can assume is reduced. Thus its entropy decreases and work has to be done. In particular at the end of the stretching process, where the chain is elongated close to its contour length, the entropy decrease is drastic and the force required increases to the observed peak. PFS has one special property: it can be reduced/oxidized electrochemically. Depending on the oxidation state the stiffness of the chain and thus its force-distance curve changes. This was used by the authors [106] to build the prototype of a single molecule motor [114]. Single molecules and adhesion are not two distinct, separated topics but in many cases they are related. This is demonstrated in the following example (Fig. 11), in which the interaction between two solid surfaces, a silicon nitride tip and a silicon wafer, across a polymer melt was studied. In general, the interaction of solid surfaces across polymer melts is important to understand confined polymers and for making composite materials. The example (Fig. 11A) shows a typical force curve measured across the diblock copolymer poly(dimethyl siloxane)-poly(ethylmethyl Fig. 10. Superposition of typical force curves of individual stretching events of poly(ferrocenyldimethylsilane) in aqueous solution of 0.1 M NaClO 4 [106]. The curve was recorded when retracting the tip from a gold surface, to which the polymer was linked via a thiol group. Attractive forces are plotted here positive. The distances of all force curves are normalized by dividing them by the distance at which the force has reached 200 pn. Fig. 11. (A) Typical force curve measured in PDMS-b-PEMS on silicon oxide. Approaching ( ) and retracting parts ( ) are shown. Each adhesion peak is stepwise fitted with the worm-like chain model (continuous lines). (B) Superposition of 20 individual force curves (retracting parts). Attractive forces are plotted here negative. For details see [115]. siloxane) (PDMS-b-PEMS) [115]. This diblock copolymer is fluid at room temperature. Since the blocks are not very much different it forms a homogeneous phase and does not microphase separate. When the tip approaches the planar surface a repulsive force is observed. The reason is that PDMS adsorbs to the silicon surfaces, which results in a steric repulsion. More surprising is the interaction upon retraction. Several distinct adhesion peaks are observed in each force curve. Each adhesion peak is attributed to a single polymer chain adsorbed with one end to the sample and with the other end to the tip. These bridging polymer chains lead to an attractive force when they are stretched until one end desorbes from its surface and the bridge breaks. The occurrence of multiple adhesion peaks result from several polymer bridges. Since adsorption can take place at different positions on the polymer chain, sample, and tip the distances of the peaks show a random distribution. When plotting several retraction curves on top of each other (Fig. 11B) one gets a visual average of the attractive forces. Results such as the one plotted in Fig. 11 demonstrate that it is conceptually useful to distinguish two types of adhesion: One that is maximal at contact such as the capillary force (Fig. 9) and one that has a maximum at a large distance (N1 nm) away form contact such as the bridging by polymer chains. While contact adhesion is acting when the two solid surfaces are in direct contact (zero distance), bridging adhesion has a maximum at a

9 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) distance of the order of the contour length of the polymer. This has a direct consequence when trying to separate the two surfaces. In contact adhesion the force required to overcome adhesion is high (Fig. 12). In bridging adhesion the work required to overcome adhesion, which is dashed area in the right plot of Fig. 12, can be higher compared to contact adhesion Nanomechanics Fig. 13. Cantilevers and tips for the Millipede storage system: Scanning electron microscope images of three-terminal integrated cantilevers (70 μm long and 75 μm wide). The outer arms of the cantilevers are 10 μm wide (close to their fixation) and 250 nm thick. For details see: imagegallery/st/millipede. The first force measurements with the AFM were carried out to measure the nanomechanical properties of solids [116]. Mechanical testing of materials on the nanometer scale is relevant for friction and wear, in particular for materials which are not homogeneous on the macroscopic scale. It is also important because scratching was the first method of nanolithography. Today, different methods are known to change surfaces on the sub-100 nm scale with the AFM [117,118]. One prominent example of mechanical modification of a surface is the millipede project of IBM [119]. The millipede project aimed to develop a new data storage technology [120]. The idea was to write small indents into thin polymer layers by pressing a heated tip into the polymer [121]. Each pit of typically 20 nm diameter represents one bit of information. A bit can be read by scanning the tip over the pit. It can also be erased by additional pits written adjacent to the previously inscribed pit. To increase the data rate many cantilevers are operated in parallel (Fig. 13). Mechanical properties on the nanometer scale can differ significantly from the bulk properties as extrapolated from the macroscopic scale [122,123]. In general, AFM technology has been extensively explored for characterizing mechanical properties of materials down to nanometer scales, e.g. bending of nanowires and nanotubes, indentation of polymer films and living cells [124]. Due to its versatile capability of nanoscopic mechanical measurement, it has been developed as a powerful tool for studying the properties of carbon nanotubes (CNT) [125,126]. Carbon nanotubes, as first observed by Iijima in 1991 [127], have shown excellent mechanical properties as compared with almost any other known material. Wong et al. have realized the direct determination of Young's modulus of multi-walled carbon nanotubes (MWCNT) by bending the protruding part of a one-end-pinned MWCNT laterally using an AFM tip [128]. Salvetat et al. have also measured the mechanical properties of single-walled carbon nanotubes (SWCNT) by loading AFM tips on top of the SWCNTs laid across holes on a surface of an alumina ultrafiltration membrane [129]. High flexibility due to the hexagonal network and the buckling of the tube walls enables large fully reversible bending angles [130]. This stability of CNTs allows to form two-dimensional structures on surfaces. Avouris et al. have used the AFM tips to bend, straighten, translate, rotate and even cut individual MWCNTs, although the tube-surface interaction was quite strong [131]. They also showed a promising prospect for nano eletromechanical applications, e.g. nano field-effect transistors (FET) [132]. Yu et al. have reported the breakage of SWCNTs by tensile loads of 30 GPa and Young's modulus ranging from 0.32 to 1.47 TPa [133]. Considering the ultra small size and outstanding mechanical properties of carbon nanotubes, they have been used as tips for force measurements and imaging [ ]. Not only carbon nanotubes are interesting targets for nanomechanical studies, but also nanostructures of many other materials, e.g. those in macromolecular and biomolecular systems, have been investigated using the AFM. For example, Lee and co-workers studied mechanical properties of polypyrrole (PPy) nanotubes and helical polyacetylene (HPA) nanofibers [137]. Bikker et al. investigated the self-assembly of righthanded helix protein nanotube with wall thickness of 3 nm [138]. 5. Extreme conditions Fig. 12. Schematic illustration of retracting force curves detected when separating to surfaces which adhere because of contact adhesion and bridging adhesion. The shaded area on the right represents the energy required to separate the two surfaces. In this subchapter we highlight an often neglected effect in atomic force microscopy. In AFM imaging and in force measurements extreme pressures, stresses, and temperatures might occur. If such conditions were applied for long times they would usually lead to total destruction of the material. Only the fact that they are applied in a small, confined volume of the order of less than (1 μm) 3 and for a short time, typically less then 1 ms,

10 100 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) prevents destruction. With the introduction of atomic force microscopy and nanoindentation experiments it became apparent, that the yield strength increases as the size of the indentor decreases [139]. To quantify this we estimate the pressure and pressure gradient between a tip of radius of curvature of 20 nm and a flat when applying a force of 5 nn. This is a typical situation occurring in many studies of hard solids. We can estimate the pressures using the Hertz model for an elastic sphere interacting with an elastic planar surface [140]. For a Hertz contact the pressure shows a parabolic profile in the circular contact region, P ¼ P 0 1 r 2 =a 2 H, with a maximal pressure P0 in the center. The radius of this contact region a H is given by a 3 H ¼ 3R 4E F with 1 E ¼ 1 v2 1 E 1 þ 1 v2 2 E 2 ð4þ Here, E 1 and E 2 are the Young's moduli for tip and planar sample and ν 1 and ν 2 are the corresponding Poisson ratios. The Young's modulus of silicon nitride is GPa, the Poisson's ratio is , depending on conditions and precise content of silicon and nitrogen. For silicon, the values are E= GPa and ν = , depending on crystallographic orientation. Silicon oxide has a Young's modulus of 72 GPa and a Poisson's ratio of 0.17; all values at room temperature. If we insert F=5 nn, E=100 GPa and ν=0.25 for tip and sample and with a tip radius R=20 nm we get E =53 GPa and a contact radius of a H =1.1 nm. This leads to a maximal pressure of P 0 = 2F/πa H 2 = Pa and to huge pressure gradients of up to dp/dr =2P 0 /a H = Pa/m. 6. Cantilever applications The results obtained with the AFM show that sub-nm deflection of micromechanical cantilevers can be measured, corresponding to pn forces. However, not only forces acting on the tip lead to a deflection, also surface stress changes acting on one side of the cantilever surface result in a bending [5]. In addition to bimaterial cantilevers, which respond to temperature changes (Fig. 14A), one side adsorption of molecules results in a change of surface stress (Fig. 14B). This effect can be used to build micromechanical sensors for artificial nose applications [141]. Hereby one side of the cantilever surface is coated by specific receptor molecules. Upon binding of the corresponding ligands the cantilever bends (Fig. 14C). Additional molecular labels that potentially alter molecular properties are not required. In particular, surface stress changes can be measured in liquids, which is a requirement for most biochemical applications. The use of arrays of cantilevers is advantageous since several cantilevers can be coated with the same receptor molecules to average the sensor signal (Fig. 14D). This reduces noise attributed to the read-out technique and helps to discriminate artefacts from a measured signal. Furthermore, some cantilevers within the same array can be coated with a reference layer not responding specifically to the target molecules. Consequently, by calculating the differential signal between the receptor coated and reference cantilevers unspecific adsorption is cancelled out. Fig. 14. Schematic outline of operating principles of nanomechanical cantilever sensors. (A) Bimaterial micromechanical cantilevers form a calorimeter which can measure small temperature variations. (B) Adsorption of molecules can lead to surface stress changes owing to a change of surface energy. (C) Binding of an analyte to a specific receptor can cause a bending of the cantilever. (D) Scanning electron microscope image of an array consisting of 8 micromachined nanomechanical cantilever sensors (Octosensis, Micromotive GmbH, Germany). Microcantilevers are typically 1.0 μm thick, 90 μm wide and 750 μm long. In the field of biotechnology, DNA hybridisation between self complementary strands leads to conformational changes of the DNA transducing a cantilever sensor bending. Fritz and coworkers pioneered the micromechanical cantilever sensing technique to differentiate a single base mismatch between 12-mer oligonucleotides and to study surface stress upon hybridization of different lengths of oligonucleotides [142]. In this case the differential deflection signal between a cantilever sensors coated with synthetic 5 thio-modified oligonucleotides 12 mer and 16 mer were monitored (Fig. 15). The cantilever array chip was immersed in hybridization buffer (step I in Fig. 15) and the complementary 16-mer oligonucleotide solution (400 nm) was injected into the liquid cell (step II in Fig. 15). The hybridization reaction of the 16-mer caused a differential deflection of roughly 10 nm after 15 min. After washing the cantilevers with

11 H.-J. Butt et al. / Advances in Colloid and Interface Science 133 (2007) Fig. 15. The difference in deflection of oligonucleotide functionalized micromechanical cantilevers [142]. The deflection in step II is attributed to the hybridization reaction of a 16 mer thiol-functionalized coating. The reaction in step III corresponds to the hybridization reaction of a 12 mer thiol-functionalized coating. hybridization buffer the complementary 12-mer was injected (step III in Fig. 15). This step changed the deflection by approximately 17 nm after 15 min in the negative direction. These measurements show that biomolecular recognition of molecules can be transduced directly into a nanomechanical effect. The use of micromechanical cantilever sensors has now become an active field in biotechnology (Review: [143]). Another application of microcantilevers is the analysis of the evaporation of liquid microdrops. The evaporation of macroscopic, volatile, pure liquids from inert solid surfaces has been studied extensively and is well understood (e.g. [ ]). Much less is known about the evaporation of microdrops because the classical techniques do not give reliable results on the sub μm scale. Also an extrapolation from the macroscopic to the microscopic scale is not meaningful because qualitatively new effects might influence the process. These effects are an increased vapour pressure due to the increasing curvature of evaporating drops and the fact that surface forces come into play once the distance between the solid-liquid interface and the liquid surface decreases below 100 nm. To monitor the evaporation kinetics, water drops with diameters below 100 μm, generated with an inkjet nozzle, were deposited onto AFM cantilevers (Fig. 16) [149]. As a result, the cantilever bends and is deflected by typically a few hundred Fig. 16. Model of a spherical drop sitting on a cantilever, with related nomenclature. Fig. 17. Top: comparison of experimental (continuous line), analytic ( ) and FEM model ( ) cantilever inclinations. Drop properties: initial contact angle Θ=93 and contact radius a=41 μm. Cantilever properties: L=750 μm, w= 100 μm, t c =0.937 μm. Bottom: Contact angles ( ) and radii ( ) of the evaporating drop, as determined from video microscope images. nanometers (Fig. 17). During the evaporation of the liquid the forces exerted by the drop become continuously weaker, so the cantilever relaxes back to its equilibrium shape. The process of drop deposition onto a cantilever and evaporation can be divided into different phases [150]: impact and spreading of the drop on the surface, damped cantilever vibration, and quasi-static drop evaporation. Impact and spreading is a complex process. The drop is deformed by the impact and, depending on the liquid-solid interaction, considerable vibrations of the liquid-gas interface might occur. Due to its high velocity of 2 m/s it might splash and satellite drops might be ejected so that it loses part of its mass. Moreover, the impact of the drop causes the cantilever to vibrate. The initial vibration is rapidly damped and the amplitude decays exponentially with a time constant τ d of 2 10 ms in air. The spreading process is characterized by a time constant τ s, which for drops of the dimensions we use is about 1 ms. Finally, the drop attains a quasi-static shape and evaporates. The evaporation of the drop occurs on a characteristic time scale τ e. For instance, for a water drop of about 100 μm diameter complete evaporation lasts of the order of 1 s, thus being orders of magnitude slower than the two other processes discussed above. For drop diameters below about 100 μm, the by far most important contribution to cantilever deflection is due to the Laplace pressure inside the drop, which is compensated by the normal component of the liquid's surface tension γ. These forces impose a torque on the cantilever, which is compensated by its elastic response and causes its bending. The inclination at