Approach-retract curves

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. 

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 (MJ 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. 

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 AFM 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 dcAf, A(d) = d. In part d, the tip is stuck on the sample with an oscillation amplitude down to zero. The tip might be damaged this part is usually avoided.

The second step is to check the tip quality through the measurement of the cycle of hysteresis during an approach-retract curve (20) as shown in figure 2b and 4. 

We divide this part into three sections contact experiments implying tribology and force curves, oscillating tip experiments with approach-retract curves, and lastly the discussion. 

Typical Approach-Retract Curve. All the results presented for the following are focused in Figure 2b part b, at the spot where the oscillation amplitude just starts to change from the free one. Figure 10a shows typical results obtained on a hard surface (PS high molecular weight (M =284000) sample). 

Figure 10a Approach-retract curves (focused in part b of figure2b) obtained on a M =2840(K) sample, for a free amplitude of 42nm, at a frequency of 292.47kHz below the resonance one (v =293.18kHz). Similar results have been obtained on other hard sufaces Ike silica.

Residential time during which the tip interacts with the sample in an approach-retract curve... 

Figure 9.14 shows a typical approach force curve along with schematic drawings of the relative positions of the SPM tip and the sample surface, as related to the force curve. At the start of the experiment, i.e., position A on the right-hand side of the figure, the tip is above the surface of the sample. As it approaches the surface the Z value decreases until at position B the tip contacts the surface. With further downward movement of the piezo the cantilever starts to be deflected by the force imposed on it by the surface. If the surface is much stiffer than the cantilever, we get a straight line with a slope of — 1, i.e., for every 1 nm of Z travel we get 1 nm of deflection (Une BC in Figure 9.14). If the surface has stiffness similar to that of the cantilever, the tip wUl penetrate the surface and we get a nonlinear curve with a decreased slope (line BD in Figure 9.14). The horizontal distance between the curve BD and the line BC is equal to the penetration at any given cantilever deflection or force. The piezo continues downward until a preset cantilever deflection is reached, the so-called trigger. The piezo is then retracted a predetermined distance, beyond the point at which the tip separates from the sample.

It has been shown [56] that if we measure the areas under the approach and retract curves of the force-distance plot we can get quantitative values of the resilience. Resilience is closely related to the ability of the polymer chain to rotate freely, and thus will be affected by rate and extent of deformation, as well as temperature. Different materials will respond differently to changes in these variables [46] hence, changing the conditions of testing will result in a change in absolute values of resilience and may even result in a change in ranking of the materials. Compared to more traditional methods of resilience measurement such as the rebound resiliometer or a tensUe/compression tester. 

A tendon from the wing region of the dragonfly was dissected and a cross-section with exposed resilin was mounted in PBS such that SPM force measurements could be made. The sample was shown to be 92% resilient [29]. When the technique was applied to recombinant resilin, the approach and retract curves were almost superimposed (Figure 9.18a). Analysis yielded a value... 

FIGURE 9.18 Elastic properties of cross-linked recombinant resilin. (a) A single force-extension curve recorded for a sample of cross-linked recombinant resilin (approach curve solid, retract curve dotted). 

FIGURE 20.8 Load-versus-penetration LvP) curves obtained during nanoindentation of ethylene-propylene-diene terpol3nner (EPDM) samples. Approach curves are shown as solid line and retract curves as broken lines. The curves in (a, b) were obtained respectively on the unvulcanized and cross-linked (amount of sulfur curative was 1.0 phr) samples of neat EPDM. The curves in (c, d) were obtained respectively on the unvulcanized and cross-linked (amount of sulfur curative was 1.0 phr) samples of EPDM loaded with oil (50 wt%). 

FIGURE 20.12 (a) Top part shows variations of elastic modulus profile measured in different locations of the polypropylene (PP)-ethylene-propylene-diene terpolymer (EPDM) blend. The locations are shown by white dots in the blend phase image placed at the bottom. Vertical white dashed lines show the components borders and the elastic modulus value for this location. Vertical black dotted lines indicate the locations where elastic modulus E gradually changes between PP (E ) and EPDM (E )- These values are indicated with black arrows on the E axis, (b) LvP curves for PP-matrix, EPDM-domains, and one of interface locations. The approach curves are seen as solid black lines and the retract curves as gray lines. 

The average of the approach and retract curves determined experimentally are fitted with the Hertz model the combination of the two equations above yields... 

The area between approach and retract curves (hysteresis) reflects the energy loss of the cantilever, for example due to deformation of the surface. The shape of force-distance curves changes when repulsive forces dominate (no jump-to and jump-off) or when measuring in liquids. 

Figure 7 A typical force curve acquired by monitoring cantilever deflection as the piezoelectric raises and withdraws the sample surface from the tip. The approach and retract curves are dissimilar when strong chemical and/or physical attraction between the tip and the surface exists. Illustrations of the cantilever bending at various scanner positions are depicted above and below the force curve to assist the reader in interpreting the force curve.

Figure 14. LEFT typical force curve (black - approach curve, red - retract curve) RIGHT t5 pical plot of the extracted parameters as a function of measurement duration (approach labels were removed to increase plainness of the scheme). Reproduced with permission of the Royal Society of Chemistry from [57].

Another contact technique that can be used to analyze multiphase polymer films (i.e., local variations in the elastic properties of the surface) is force-distance spectroscopy. In this mode, the force-distance curves are plots of distance dependent on the forces that act on the tip in the vicinity of the surface. They are registered when the tip approaches the surface or is retracted from it (Maver et al. 2013). Typical approach/retract force-distance curves and their stages are presented in Figure 8.4 (1) the cantilever starts to approach the surface (2) the tip approaches the surface ... 

The data in Fig. 11 show an offset between the force and stiffness minima in the approach and retraction curves. The explanation for this is shown in Fig. 12, which illustrates the relationship between potential, force and interaction stiffness. These curves provide a basis for determining where the contact point with the surface is located. One definition of contact is the position on the curve where the repulsive force can first be detected (see 24), typically identified by a change in curvature of the force-displacement data (3). Therefore, the force gradient (stiffness-displacement data) reveals more clearly the attractive to repulsive transition. The initiation of repulsive contact is thus found from the minimum of the stiffness approach curve (marked at 0 nm), which marks the maximum attractive interaction stiffness. The stiffness data represent a convolution of force gradient and contact stiffness and is... 

For example, the force curve experimental procedure is not as controlled as the tribological and approach-retract ones for two major reasons ... 

For instance, for a cantilever oscillating at its resonance frequency, below an amplitude threshold, the oscillator may only experience the attractive regime at proximity of the surface (curves A in Fig. 9.8). The amplitude and phase signals are superimposed for approach and retraction curves, while when the amplitude is increased above this threshold, which depends on the RH and hydrophilicity of the tip, a h eresis shows up both in amplitude and phase signals. At given tip-sample distances, the system switches from attractive to repulsive interaction. ... 

Figure 13 Idealized force-distance curve describing a single approach-retraction cycle of the AFM tip. Modified from Shahin, V. etal. J. Cell. Scl. 2006, f f9,23-30. The AFM tip is approaching the sample surface (a). The initial contact between the tip and the surface is mediated by the attractive van der Waals forces (contact) that lead to an attraction of the tip toward the sample (b). Hence, the tip applies a constant and default force upon the sample surface that leads to sample indentation and cantilever deflection (c). Subsequently, the tip tries to retract and to break loose from the surface (d). Various adhesive forces between the sample and the AFM tip, however, hamper tip retraction. These adhesive forces can be taken directly from the force-distance curve (e). The tip withdraws and loses contact with the sample upon overcoming the adhesive forces (f). Inset experimental approach curve recorded fora silicon surface electrografted by poly(/V-succinimidyl acrylate) (PNSA) (from a 0.1 M NSA solution in DMF) with a silicon nitride tip.

Adhesion (pull-off force) data are calculated as the largest negative force detected during the retraction curve. In addition to directly extracted data on the maximum adhesive force, further data may be calculated from the force-displacement eurve. The area enclosed between the approach force curve and the retract force curve accounts for the dissipation of the energy per oscillation cycle. Finally, the maximum deformation of the sample is calculated as the difference in the piezo-displacement between the points of maximum and zero foree, measured along the approach curve, and corrected for the ehange in the deflection of the cantilever. The ealculated value includes both elastic and plastic contributions and reaches its maximum at the peak force. 

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