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Work of Adhesion and Cohesion

If a bulk material is subjected to a sufficient tensile force. the material will break, thereby creating two new surfaces. If the material is completely brittle, the work done on the sam­ple is dissipated only by creating the new surface. Under those assumptions. if the failure is truly cohesive (where both sides of the broken material

molecular forces present before the materials were split apart. This interfacial energy can be represented as 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">₁₂ W_A  the work of adhesion, may be defined by  are of the same composition). then:  

Wc == 2 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">

In this expression We is defined as the work of cohe­sion Now similarly consider separating an adhesive(material 1) from a substrate (material 2) as illustrated in Fig. 2.4. The energy expended should be the Sum of the two surface energies 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">₁and 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">₂ However, because­ the two materials were in contact, there were inter­ the surface energies of the adhesive and the adherend

FIGURE 2.4 Failure of an adhesive

joint creates two new surfaces. The energy expended per unit area should be the sum of the two surface energies

This is the classical Dupre equation, which was developed in 1869.7 This equation could also be represented as:

W_A = 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">_LV + 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">_sv - 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">_SL

Substitution of the Young equation into the Dupre equation results in the Young-Dupre  equation, which states

W_A = 12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">_LV (1 + Cos 12خ¸" style="WIDTH: 10.5pt; HEIGHT: 25.5pt" type="#_x0000_t75">)

This equation relates a thermodynamic parameter, w,-\. to two easily determinable quanti­ties: the contact angle and the liquid-vapor surface tension. Solidification of the adhesive would generate this strength if it were not for the development of stress concentrations. There is some modification of the above equation necessary to consider the roughness of the surface

  Bond Failure Energy

In practice, bond failure energy is composed of two parts: (1) a reversible work of adhesion and (2) an irreversible work of adhesive deformation. Thus, the strength of styrene-butadiene rubber adhesive depends on two components:

-          A viscoelastic energy dissipation term, which is a function of test rate and temperature ­

-          The intrinsic failure energy that agrees closely with the work of adhesion, WA, when the bond failure is apparently interfacial

Much work in adhesion science has centered on the relationship between WA, the cal­culated work of adhesion, and practical adhesion or the real measured adhesion. Ahagon and Gent indicate that practical adhesion can be related to the work -of adhesion plus a function describing the energy dissipation mechanisms within an adhesive bond.

Practical Adhesion = W_A + f (W_A) ?_

?  (zeta) is a factor related to the viscoelastic properties of the adhesive and, thereby, is related to the mechanical energy absorption characteristics of the joint. This is sometimes related to the amount of energy absorbed by the deformation of the joint. As shown in Fig. 2.5, the practical work of adhesion is equal to the theoretical work of adhesion as determined by interfacial effects and to the mechanical work that is absorbed within the joint. Thus, with a completely nondeformable adhesive, interphase, and adherend, the practical work of adhesion is equal to the theoretical work of adhesion.

Adhesives that have a high viscoelastic property are very valuable in many applications. Their ductility will provide for higher impact and peel strength. They are also less sensitive

  W Experimental = W Expected     +   W Additional

                                        Interfacial bonding           Viscoelastic deformation

FIGURE 2.5 The measured work of adhesion is made up of thermodynamic (interfacial bonging) and mechanical (viscoelastic deformation ) components

to defects in the bonded area that may be related to poorly wetted regions, dirt inclusions, and microcracks. The viscoelastic properties provide an energy dissipation when a joint is stressed in the presence of such bonding defects.

It should be realized that the above discussion is very simplistic and summarizes a great deal of science to a fault. There are also significant debates over the applicability and direct usefulness of these relationships. However, the following conclusions can be derived and are of significant assistance to the user of adhesives and sealants:

1. The work of adhesion is a maximum when the contact angle, e, equals 0°, that is when the liquid spreads completely on the surface of the solid. This condition implies that there are stronger forces between the molecules of the liquid and the substrate than between the liquid molecules themselves.

2. Adhesion will tend to go to zero as the contact angle increases above 90°.

3. Under conditions of perfect wetting of a surface by a liquid, WA = 2 _{12خ³" style="WIDTH: 9.75pt; HEIGHT: 25.5pt" type="#_x0000_t75">L v}. Hence W_A = W _C

These conclusions will be discussed further in the following sections.