Pull-off energy

Mangipudi et al. [63,88] reported some initial measurements of adhesion strength between semicrystalline PE surfaces. These measurements were done using the SFA as a function of contact time. Interestingly, these data (see Fig. 22) show that the normalized pull-off energy, a measure of intrinsic adhesion strength is increased with time of contact. They suggested the amorphous domains in PE could interdiffuse across the interface and thereby increase the adhesion of the interface. Falsafi et al. [37] also used the JKR technique to study the effect of composition on the adhesion of elastomeric acrylic pressure-sensitive adhesives. The model PSA they used was a crosslinked network of random copolymers of acrylates and acrylic acid, with an acrylic acid content between 2 and 10%. 

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.

The ratio of to R is known as the normalized pull-off energy, P . The normalized pull-off energy depends only on the surface and interfacial energies. 

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.

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... 

The effect of solvent has been treated quantitatively (for SnI mechanisms, in which the solvent pulls off the leaving group) by a linear free energy relationship "... 

We must imagine that some of the molecules in the crystalline solid have carboxyl groups wetted by the water on the line of contact, these groups although attached to the water cannot pull off the hydrocarbon chain at low temperatures. At 17° C., however, in the case of stearic acid the force of dissolution and the kinetic energy of the molecule are sufficient to permit of rupture. The molecule now floats freely on the surface of the water. During the course of time a number of molecules are so detached, they do not however exert any appreciable action on the tension of the water... 

Since the outer electron in sulfur experiences more shielding, it will be easier to pull off. Therefore, S has the smaller first ionization energy. 

When attempting to relate the adhesion force obtained with the SFA to surface energies measured by cleavage, several problems occur. First, in cleavage experiments the two split layers have a precisely defined orientation with respect to each other. In the SFA the orientation is arbitrary. Second, surface deformations become important. The reason is that the surfaces attract each other, deform, and adhere in order to reduce the total surface tension. This is opposed by the stiffness of the material. The net effect is always a finite contact area. Depending on the elasticity and geometry this effect can be described by the JKR 65 or the DMT 1661 model. Theoretically, the pull-off force F between two ideally elastic cylinders is related to the surface tension of the solid and the radius of curvature by... 

For the Hertzian contact, no force is needed to pull away the contacting sphere from the flat plane in excess of the weight of the sphere. However, for the JKR contact, due to adhesion forces, this does not hold. The value of the nonzero pull-off force represents the adhesion of the contacting sphere with the flat plane. Strictly speaking, this force corresponds to adherence of the surfaces as energy dissipation, surface relaxation, etc. also influence its value. It should be stressed that the value of the JKR pull-off force only depends on the sphere (lens) radius and the work of adhesion in the medium in which the JKR experiment is conducted. Thus, the contact area and mechanical properties for true JKR contacts do not play a role for its value. All the above considerations for contact mechanics were based on pairwise additivity of molecular forces. 

Thus, the different surface free energies ji can, in principle, be experimentally determined based on AFM pull-off force measurements if the surface free energy of the tip is varied in a controlled manner. These equations form the basis for the so-called chemical force microscopy (CFM) approach and allow one to discriminate between different materials [7]. 

In these experiments, individual f-d curves were recorded at various locations of each film using the same tip (i.e., the tip radius is assumed to remain constant). Subsequently, the pull-off forces were evaluated off-line and were plotted in a histogram. The pull-off forces were observed to increase with the extent of oxyfluorination and the concomitant increase in surface energy (shown as values of surface tension). Using different tip functionalities and media on oxidized iPP and... 

Fig. 4.8 (a) Histograms of pull-off force values obtained with an unmodified Si3N4 tip on untreated and oxyfluorinated iPP films in ethanol. The total surface free energy y of the polymer film is shown, (b) Mean values of pull-off force measured with COOH-terminated tips on modified polyolefin surfaces (iPP, isotactic polypropylene LDPE, low-density polyethylene) in ethanol (top) and with OH-terminated tips on oxyfluorinated iPP in water (pH 3.8, bottom) as a function of cos 0 (contact angle measured with water). (Reprinted in part/adapted with permission from [26, 27]. Copyright 1998, 2000, American Chemical Society.)... 

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