Obtaining force versus distance curves

Comparison of the frost crystals observed via SEM at humidity of 30% (Fig.3a and 3b) prepared with those observed via AFM under similar conditions (Fig.2a, 2b, 2c and 2d) shows very little similarities. The temperature difference between the laser heated tip " and the ice surface has a large impact on the AFM imaging process. When the tip touches the surface covered with frost, melting of frost crystals immediately takes place, so that the tip loses contact with frost/ice (established via force-versus-distance curves). In this case the tip was approached further to the surface. The small size of the crystallites obtained at humidity... 

The accurate and absolute measurement of the distance, D, between the surfaces is central to the SFA technique. In atypical experiment, the SFA controls the base position, Z3, of the spring and simultaneously measures D, while the spring constant, k, is a known quantity. Ideally, the simple relationship A F D) = M (D-z ) applies. Since surface forces are of limited range, one can set F(D = qo) = 0 to obtain an absolute scale for the force. Furthermore, 5F(Z) = qo)/5Z) 0 so that one can readily obtain a calibration of the distance control at large distances relying on an accurate measurement of D. Therefore, D and F are obtained at high accuracy to yield F D), the so-called force versus distance curve. 

In parallel, another important (although less direct) technique for measuring forces between macromolecules or lipid bilayers was developed, namely, the osmotic stress method [39-41]. A dispersion of vesicles or macromolecules is equilibrated with a reservoir solution containing water and other small solutes, which can freely exchange with the dispersion phase. The reservoir also contains a polymer that cannot diffuse into the dispersion. The polymer concentration determines the osmotic stress acting on the dispersion. The spacing between the macromolecules or vesicles is measured by X-ray diffraction (XRD). In this way, one obtains pressure-versus-distance curves. The osmotic stress method is used to measure interactions between lipid bilayers, DNA, polysaccharides, proteins, and other macromolecules [36]. It was particularly successful in studying the hydration... 

Fig. 3 Schematic deflection-versus-piezo translator position curve (Az versus Azc). At large separation, no force acts between tip and sample (a). The cantilever is not deflected. When approaching the surface, it was assumed that a repulsive force is acting (b) and the cantilever is bent upwards. At a certain point, the tip often jumps onto the sample. This happens when the gradient of attractive forces, for example, the van der Waals forces, exceeds the spring constant of the cantilever. After the jump-in, the tip is in contact with the sample surface (c). When retracting the tip, often an adhesion force is observed (d) and the tip has to be pulled off the surface. The deflection-versus-piezo translator position curve has to be transformed as described in the text to obtain a force-versus-distance curve (F versus D).

The nanotribological properties of the SAM films generated from CnOH, CnCHs, and CsCH3 SAM films were characterized through the measurement of frictional forces with a plasma-cleaned silicon nitride tip as a function of load under distilled water. Representative friction-versus-load plots obtained by AFM are presented in Fig. 4a. The force-versus-distance curves obtained from the same three SAM films are shown in Fig. 4b. In order to ensure a statistically valid comparison, the measurements were repeated several times in varying order using the same tip/... 

First, we note that a force versus distance curve may be obtained in two fundamentally different ways. The force can be controlled and the resulting separation measured. This is the principle used in the thin film balance. Alternatively, the distance can be controlled and the resulting force determined, and this is the method utilized in the SFA, AFM and MASIF approaches. The methodology used in these latter techniques does, however, differ in several important respects. Perhaps the most fundamental difference is how the force and the surface separation are determined. 

The surface forces apparatus (SFA) developed by Tabor, Winterton [30], and Israe-lachvili [56] contains two crossed silica cylinders with a radius of curvature of roughly 1-2 an to which thin sheets of mica are glued to obtain atomically flat surfaces (inset of Figure 3.1). One mica-coated cylinder is mounted to a piezoartuator, which is used to change the distance between the two cylinders when recording force versus distance curves. 

The jump to contact (2) and jump-out (5) instabilities have the consequence that not all parts of the interaction potential can be reconstructed from the measurement. Such instabilities can be avoided or suppressed by using stiffer cantilevers, but this would be at the cost of reduced sensitivity. To obtain a real force-versus-distance curve (called force curve ), and Zp have to be converted to force and distance. First, aline fit is done on the zero force region to subtract any offset in the detector signal. Then, a... 

Figure 11.12 Force versus distance curve obtained with a biomimetic DOPA-containing polymer in aqueous solution of 1 mM KNO3 measured with an atomic force microscope between two titanium surfaces [1427]. Approaching (o) and retracting ( ) parts are plotted.

In the spectroscopy mode of AFM force-distance curves F(z) are recorded at one or more scan points after the z piezo has been adjusted to the force setpoint (contact mode). The classical shape, as illustrated in Section 5.3.4 and Figure 63, is obtained mostly with hard materials or simpler molecules. In air a meniscus of water is formed at the jump-to-contact. Due to the meniscus force the jump-to- and jump-oflf-contact separations differ largely and the area of the hysteresis loop becomes quite large. Force-distance curves can have various appearances. An overview is given in Reference [233]. Spectroscopy is rarely employed in the dynamic mode because with an oscillating probe the tip-sample separation is never well-defined. On the other hand the snap-on is avoided and the complete interaction potential can be inferred from the measured frequency versus distance curve employing simulations [234,235]. 

This theory relates the force needed to separate the two surfaces to the mucoadhesive strength and is widely applied in research, where force of detachment versus distance is normally measured. In general, the fracture stress (considered to be equivalent to the mucoadhesion stress) is calculated by dividing the fracture force by the area of contact in the mucoadhesive bond. In the same study, fracture energy (or work of mucoadhesion) can be obtained as the area under the curve in the force versus distance plot. Nowadays, instruments measure directly the force of mucoadhesion between two surfaces in contact as a function of distance and time. 

Figure 2. Representative force-versus-separation curves obtained with a fibrinogen-modified Si3N4 probe (k = 0.03 N/m) in PBS solution on (a) treshly cleaved mica surface, (b) hexadecanethiol SAM on gold, (c) EG3-OMe SAM on gold, and (d) EG3-OMe on silver showing attractive interaction and multiple pull-offs (representative of 20% of the force-distance data taken).

Thus, it was questioned if there were any intrinsic hydration layers on a lipid membrane. The oscillatory profile observed in the A/ versus distance curve obtained by FM-AFM revealed the existence of the hydration layer on a DPPC bilayer (Fig. 18.8a). In FM-AFM, the force is measured with a tip having a nanometer-scale cross section, while the force measured by SFA and the osmotic pressure method is averaged over a micrometer-scale area. Such global averaging may smear out the local distance dependence, showing the oscillatory profile. The result clearly showed the importance of having local spatial resolution in the investigations on interfacial phenomena. 

Force Versus Distance Measurements with an AFM Force measurements with AFM, in the contact mode, consist in detecting the deflection of a spring (or cantilever) bearing a tip at its end, when interacting with the sample surface. The deflection of the cantilever is detected by an optical device (four quadrant photodiode) while the tip is vertically moved forward and backward thanks to a piezoelectric ceramic (or actuator). Thus, provided that the spring constant of the cantilever is known, one can obtain a deflection-distance (DD) curve and then a force-distance (FD) curve, by using Hooke s law. The DD curves presented in this chapter were performed in air. A schematic representation of a DD curve obtained when probing a hard surface is reported in Fig. 3.6. 

Since the first AFM applications, researchers have examined so-called force curves. In the contact mode, these are deflection-versus-distance (DvZ) curves, as seen in Figure 20.2a. Initially, DvZ curves were employed to check whether a particular deflection set point used for imaging corresponds to a net repulsive or net attractive force [25]. This curve can also be obtained in tapping mode... 

Quantitative evaluation of a force-distance curve in the non-contact range represents a serious experimental problem, since most of the SFM systems give deflection of the cantilever versus the displacement of the sample, while the experimentalists wants to obtain the surface stress (force per unit contact area) versus tip-sample separation. A few prerequisites have to be met in order to convert deflection into stress and displacement into tip-sample separation. First, the point of primary tip-sample contact has to be determined to derive the separation from the measured deflection of the cantilever tip and the displacement of the cantilever base [382]. Second, the deflection can be converted into the force under assumption that the cantilever is a harmonic oscillator with a certain spring constant. Several methods have been developed for calibration of the spring constant [383,384]. Third, the shape of the probe apex as well as its chemical structure has to be characterised. Spherical colloidal particles of known radius (ca. 10 pm) and composition can be used as force probes because they provide more reliable and reproducible data compared to poorly defined SFM tips [385]. 

Interactions between a spherical colloid and a wall can be measured by bringing probe and substrate together and monitoring the cantilever deflection as a function of the interparticle distance. The photodetector voltage versus piezo position curve can be converted into a force-distance curve. The force acting on the cantilever follows from the deflection of the cantilever and its known spring constant. The zero force is defined by the deflection of the cantilever as the colloidal probe is far from the surface of the substrate. To obtain the force-distance dependence on an absolute scale the zero distance, i.e., where the colloid touches the wall, has to be determined. Commonly, the zero distance is obtained from the force curve itself and not through an independent method [68]. 

The SFB is a specialized apparatus, developed by Tabor and Winterton (50) and refined by Israelachvili and Adams (51), to study basic colloidal forces—specifically in this case to measure the interaction of orthogonally positioned hemicylinders (generally mica) as they are brought together (or separated) in aqueous solutions. Separations (D) can be measured with a precision of better than 5 A and forces (F) to a precision of 10 p,N. Data are presented in plots of F/R versus D where R is the radius of curvature of the cylinders. Force/distance curves have been measured in the presence of electrolytes, adsorbing surfactants, and, as mentioned in Chapter 2, polymers. Here we will briefly discuss some of the results obtained in four studies (52-55) concerned with the adsorption of conditioning polymer-type polyelectrolytes. 

Figure 10.14 Force per unit area versus distance between two lipid bilayers of EPC at 30°C, DMPC at 30°C, and DPPC at 50°C (redrawn from Ref [1237]). The force curves were fitted with a sum of hydration forces (Eq. (10.18)), van der Waals attraction (Eq. (10.20)), and undulation forces (Eq. (10.23)). To obtain the van der Waals pressure we applied/ —dV /dx (see Exercise 10.4). The parameters were lcc = 0.55 x 10 ),...

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