Reversible work of adhesion

G() is related to the reversible work of adhesion obtained using contact angle measurements, but in general is greater than W. This is because once an interface is formed and the adhesive solidifies, strain energy is required to mechanically disrupt the interface. This strain energy arises because of the physical connection between the attachment sites between the adhesive and the substrate and the connectivity between this interface and the adhesive bulk. 

W. quantifies the specific, discrete interactions that exist between a wetting liquid and a substrate. These interactions may be Van der Waals, acid-base, or covalent. The reversible work of adhesion is the product of the areal density of these interaction sites (or attachment points) and the energy per attachment point ... 

Eqs. 1-5 hold whether failure is interfacial or cohesive within the adhesive. Furthermore, Eq. 5 shows that the reversible work of adhesion directly controls the fracture energy of an adhesive joint, even if failure occurs far from the interface. This is demonstrated in Table 5, which shows the static toughness of a series of wedge test specimens with a range of adherend surface treatments. All of these samples failed cohesively within the resin, yet show a range of static toughness values of over 600%. 

Keywords aggregation, interfacial interaction, reversible work of adhesion, wettability, matrix-filler interaction, surface treatment, interphase, surfactant, coupling agent, elastomer interlayer... 

Adhesion is created by primary and secondary forces according to the theory of adsorption interaction. This theory is applied the most widely for the description of interaction in particulate filled or reinforced polymers [30]. The approach is based on the theory of contact wetting and focuses its attention mainly on the influence of secondary forces. Accordingly, the strength of the adhesive bond is assumed to be proportional to the reversible work of adhesion (W ), which is necessary to separate two phases with the creation of two new surfaces. 

Although Eq. 11 tries to take into account the effect of polar interactions, the role of acid/base interactions in adhesion became clear and theories describing them have been more and more accepted [35]. The boimdary case of such interactions is the formation of covalent bonds between the surfaces. Such interactions cannot be described by Eq. 11. As a consequence Fowkes [36] suggested that the reversible work of adhesion should be defined as ... 

The strength of the adhesive bond is described acceptably by the reversible work of adhesion values calculated by the above theory in most cases. Often, especially in apolar systems, a close correlation exists between and the mac-... 

In spite of the imperfections of the approach, the reversible work of adhesion can be used for the characterization of matrix/filler interactions in particulate filled polymers. Debonding is one of the dominating micromechanical processes in these materials. Stress analysis has shown that debonding stress (a ) depends on the reversible work of adhesion [8], i.e. ... 

Interphase thicknesses are plotted as a function of in Fig. 7 for CaCOj composites prepared with four different matrices PVC, plasticized PVC (pPVC), PP and HDPE. The thickness of the interphase linearly changes with increasing adhesion. The figure proves several of the points mentioned above. The reversible work of adhesion adequately describes the strength of the interaction, or at least it is proportional to it, interaction is created mostly by secondary forces and, finally, the thickness of the interphase strongly depends on the strength of interaction. 

The direct determination of matrix/filler interaction is difficult, indirect techniques are used in most cases. These employ the principles discussed in Sect. 3.2. The surface tension of the components and interfacial tension or ac-id/base interaction parameters must be known in order to determine the reversible work of adhesion. Adsorption-desorption techniques, which use small molecular weight materials having an analogous structure to the polymer, can be used for the estimation of interfacial interaction. 

In flow microcalorimetry a small sample is put into the cell of the calorimeter and the probe molecule passes through it in an appropriate solvent. Adsorption of the probe results in an increase in temperature and integration of the area under the signal gives the heat of adsorption [70]. This quantity can be used for the calculation of the reversible work of adhesion according to Eq. 13. The capabilities of the technique can be further increased if a HPLC detector is attached to... 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Eowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usually differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

The interaction of two substrates, the bond strength of adhesives are frequently measured by the peel test [76]. The results can often be related to the reversible work of adhesion. Due to its physical nature such a measurement is impossible to carry out for particulate filled polymers. Even interfacial shear strength widely applied for the characterization of matrix/fiber adhesion cannot be used in particulate filled polymers. Interfacial adhesion of the components is usually deduced indirectly from the mechanical properties of composites with the help of models describing composition dependence. Such models must also take into account interfacial interactions. 

Recently, stress analysis has been carried out for the determination of stress distribution around inclusions in particulate filled composites. A model based on the energy analysis has led to the determination of debonding stress [8]. This stress, which is necessary for the separation of the matrix and filler, was shown to depend on the reversible work of adhesion (see Eq. 16) and it is closely related to parameter B. 

Interfacial Energy of Adhesion. When the polyelectrolyte-grafted nylon surface, in equilibrium with 50% relative humidity, is brought into contact with water or a salt solution, various interactions will occur together they comprise the reversible work of adhesion or free energy of adhesion at the interface of these two phases. This free energy of adhesion should be composed of the following contributions ... 

A measure of the attraction of two solids Si and S2 across an interface is the reversible work of adhesion This quantity is given by the relationship of Dupre... 

Thermodynamic Work of Adhesion. One other important aspect of surface energetics (71, 72) is the use of surface free energy to calculate the maximum reversible work of adhesion, Wad, which has been correlated to the adhesive strength (41, 44) and should not be equated to the strength of an adhesive joint (6). Since neither wetting nor adhesion is controlled purely by thermodynamic factors, we should use the maximum reversible work of adhesion, Wad on the basis of an idealistic approach. When all other variables are equal, we can use Wad to compare the effectiveness of adhesives for a specific substrate. 

Interfacial adhesion can be predicted from available models or from data on the mechanical performance of filled systems. The following equation describes the reversible work of adhesion ... 

The reversible work of adhesion (Wadh) is important in determining whether an interface... 

Another approach avoids specifying the field of inter molecular force between solid and liquid and instead resorts to thermodynamics. The first application of thermodynamics to capillarity appears to have been made by Thompson [101,102] later came the classic and general treatment by J. Willard Gibbs [50]. Nearly 60 years had elapsed after Young s treatment before Dupre [31] introduced the reversible work of adhesion of liquid and solid, and its relation to ygv sl ... 

Equation 4 tells us that if 9 = 0—that is, if liquid L 2 spreads on solid Si—the maximum reversible work of adhesion is always in excess of the work of cohesion by an amount at least - Sivj) >... 

This is the equation for the maximum reversible work of adhesion for two solids in contact and is the counterpart of Equation 4 for the case of a liquid in contact with a solid. Our definition of the final solid-solid state as an equilibrium state implies that there are no residual stresses in either solid produced by the solidification of L2. 

We showed that if L2 spreads on Si, the maximum reversible work of adhesion of L2 to Si is greater than the work of cohesion of L2. Conversely, if the maximum reversible work of adhesion of L2to Si is greater than the work of cohesion of L2, then L2 must spread (initially) on Si. We can write, then, from Equations 3 and 6,... 

In the first part of this section, wetting criteria as well as surface and interface free energies are defined quantitatively. The estimation of a reversible work of adhesion W from the surface properties of materials in contact is therefore considered. Next, various models relating the measured adhesion strength G to the free energy of adhesion W are examined. 

In 1964, Fowkes [4] proposed that both the reversible work of adhesion (W) and the surface tension (y) had additive components ... 

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