Pull-off force

The value of the pull-off force can he reduced significantly hy imaging under liquids, because of elimination of capillary condensation forces, which pull the tip towards the sample. 

Fig. 3. Schematic of a sphere in contact with a flat surface, (a) The deformation when surfaces are in contact. The radius of the deformed zone is a, and the separation profile is given by D versus r. The central displacement, S, is shown as the distance between the center of the deformed zone and the tip of the undeformed sphere, represented by the bold line. S characterizes the displacement of the applied load, (b) When the applied load is —/ s, the pull-off force, the surfaces jump out of contact, and the undeformed shape of the surfaces is attained.

When the surfaces are in contact due to the action of the attractive interfacial forces, a finite tensile load is required to separate the bodies from adhesive contact. This tensile load is called the pull-off force (P ). According to the JKR theory, the pull-off force is related to the thermodynamic work of adhesion (W) and the radius of curvature (/ ). 

The surfaces jump out of contact when the applied load is equal to the pull-off force, i.e. P — —P. The contact radius at the point of separation, a, is given by... 

In an appropriately designed experiment, it is possible to measure the pull-off force (Ps), contact radius (a versus P, ao and aj, and the separation profile outside the contact zone (D versus j ). From these measurements, it is possible to determine the thermodynamic work of adhesion between two surfaces, if the contacting bodies are perfectly elastic. 

Contrary to spherical contact, the minimum force, or the pull-off force under load-controlled conditions, is dependent on the elastic constant of the system... 

Israelachvili and coworkers [64,69], Tirrell and coworkers [61-63,70], and other researchers employed the SFA to measure molecular level adhesion and deformation of self-assembled monolayers and polymers. The pull-off force (FJ, and the contact radius (a versus P) are measured. The contact radius, the local radius of curvature, and the distance between the surfaces are measured using the optical interferometer in the SFA. The primary advantage of using the SFA is its ability to study the interfacial adhesion between thin films of relatively high... 

Pa, would deform appreciably under the action of loads comparable to the pull-off force given by Eq. 16. It is for this reason that the JKR type measurements are usually done on soft elastic materials such as crosslinked PI rubber [45,46] or crosslinked PDMS [42-44,47-50]. However glassy polymers such as polystyrene (PS) and PMMA are relatively hard, with bulk moduli of the order of 10 Pa. It can be seen from Eq. 11 that a varies as Thus, increasing K a factor of... 

SFA has been traditionally used to measure the forces between modified mica surfaces. Before the JKR theory was developed, Israelachvili and Tabor [57] measured the force versus distance (F vs. d) profile and pull-off force (Pf) between steric acid monolayers assembled on mica surfaces. The authors calculated the surface energy of these monolayers from the Hamaker constant determined from the F versus d data. In a later paper on the measurement of forces between surfaces immersed in a variety of electrolytic solutions, Israelachvili [93] reported that the interfacial energies in aqueous electrolytes varies over a wide range (0.01-10 mJ/m-). In this work Israelachvili found that the adhesion energies depended on pH, type of cation, and the crystallographic orientation of mica. 

Fig. 13. Measurement of surface energies of PS and PMMA. It can be seen that there was a finite adhesion hysteresis. At a given load, the contact radius during loading was less than the contact radius during unloading. From the unloading data, we get yi>s = 45 1 mJ/nr, and yi),viMA = 53 1 mj/m . These number are in good agreement with the values of surface energies determined from the pull-off force measured using the SFA.

Fig. 22. Nomialized pull-off energy measured for polyethylene-polyethylene contact measured using the SFA. (a) P versus rate of crack propagation for PE-PE contact. Change in the rate of separation does not seem to affect the measured pull-off force, (b) Normalized pull-off energy, Pn as a function of contact time for PE-PE contact. At shorter contact times, P does not significantly depend on contact time. However, as the surfaces remain in contact for long times, the pull-off energy increases with time. In seinicrystalline PE, the crystalline domains act as physical crosslinks for the relatively mobile amorphous domains. These amorphous domains can interdiffuse across the interface and thereby increase the adhesion of the interface. This time dependence of the adhesion strength is different from viscoelastic behavior in the sense that it is independent of rate of crack propagation.

We have recently been exploring this technique to evaluate the adhesive and mechanical properties of compliant polymers in the form of a nanoscale JKR test. The force and stiffness data from a force-displacement curve can be plotted simultaneously (Fig. 13). For these contacts, the stiffness response appears to follow the true contact stiffness, and the curve was fit (see [70]) to a JKR model. Both the surface energy and modulus can be determined from the curve. Using JKR analyses, the maximum pull off force, surface energy and tip radius are... 

One point, which is often disregarded when nsing AFM, is that accurate cantilever stiffness calibration is essential, in order to calculate accurate pull-off forces from measured displacements. Althongh many researchers take values quoted by cantilever manufacturers, which are usually calculated from approximate dimensions, more accurate methods include direct measurement with known springs [31], thermal resonant frequency curve fitting [32], temporary addition of known masses [33], and finite element analysis [34]. 

The magnitude of the pull-off force depends on the natnre of the tip-sample interaction during contact. Adhesion depends on the deformation of the tip and the sample, because attractive forces are proportional to the contact area. Quantifying the work of adhesion is difficult. The measured magnitude of A7 is strongly dependent on environment, surface roughness, the rate of pull-off, and inelastic deformation surrounding the contact. 

Thomas et al. [72] used a modified force microscope in which a compensatory force was applied to the probe to keep its displacement at zero. With this system they studied interactions between organomercaptan molecules with CH3, NH2, or COOH end groups. All measurements were performed in dry nitrogen. From SEM-measured tip radii and pull-off force they calculated the work of adhesion using the DMT model. They found that the work of adhesion values qualitatively scaled as expected for van der Waals, hydrogen bonding,... 

FIG. 17 (A) Histogram of pull-off force from 86,000 force curves. The heavy line is the sum of... 

Vakarelski et al. [88] also investigated the adhesive forces between a colloid particle and a flat surface in solution. In their case they investigated a sihca sphere and a mica surface in chloride solutions of monovalent cations CsCl, KCl, NaCl, and LiCl. The pH was kept at 5.6 for all the experiments. To obtain the adhesive force in the presence of an electrostatic interaction, they summed the repulsive force and the pull-off force (coined foe by the authors ) to obtain a value for the adhesive force that is independent of the electrostatic component. 

FIG. 21 Pull-off force between a hydrophilic Si3N4 tip and mica as a function of the relative humidity (RH) at room temperature. The spring constant of the lever is 0.1 N/m. Estimated tip radius -200 A. Hysteresis is observed between increasing (open circles) and decreasing (closed circles) humidity. (From Ref. 51.)... 

A much easier method has been developed by Padday et al. (1975) (Faraday Trans. I, 71, 1919), which only requires measurement of the maximum force or weight on the rod as it is pulled upwards. It has been shown by using the Laplace equation to generate meniscus profiles that this maximum is stable and quite separate from the critical pull-off force where the meniscus ruptures. A typical force-height curve is shown in Figure 2.24. 

In contrast to pfm, pfs measurements do not allow the two contributions Pz and a to be separated from their sign, which therefore results in summing up over the two signals rather than building the difference as shown in Equation (12.1) [24], Since pull-off force experiments... 

Assuming that adhesion comes from only a van der Waals attraction G = - Afam/(12jrZ2)], neglecting any balancing forces or any elastic properties of the tape, show that when tape-surface separation l = 0.5 nm (5 A), W= z = 0.01 m (1 cm), and G = 0.2 mj/m2 (0.2 erg/cm2), the peeling force is a tiny constant 0.002 mN = 0.2 dyn whereas the maximum perpendicular-pull-off force on this same square patch is an effortful 80 N = 8 x 106 dyn. 

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