The Work of Cohesion and Adhesion

At this point it is convenient to introduce two terms related to Equation (2.1) that will appear in various contexts in later chapters, namely, the work of cohesion and the work of adhesion. The work of cohesion, Wc, is defined as the reversible work required to separate two surfaces of unit area of a single material with surface tension a (Fig. 23a). Based on the distinction between solid and hquid surfaces explained above, the definition applies 

FIGURE 2.3. (a) When new surface is formed by dividing a homogeneous material, a certain amount of work is required. That work, the work of cohesion, is related to the surface tension of the material by Equation (2.2). (i ) If the new surface results from the separation of two different materials, the resulting work of adhesion is given by Equation (2.3). 

Strictly to liquid surfaces, although the concept is useful for solid surfaces as well. Since the process involves the creation of two unit areas of fresh surface, and since the work required for that process is the surface tension, the work of cohesion is simply 

It must be remembered that Wc is a reversible thermodynamic function and represents a minimum amount of work for carrying out the process. Additional work may be expended in associated irreversible processes such as heat generation. Related to Wc is the work of adhesion, Wa(i2 , defined as the reversible work required to separate unit area of interface between two different materials (1 and 2) to leave two bare surfaces of unit area (Fig. 23b). The work is given by 

The nature of the immediate environment of freshly formed surfaces will 

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It is possible to perform a physical analysis to predict either liquid lens or thick him formation, and the strength of adhesion between the two phases. In order to assess the adhesion strength, initially we need to formulate the work of cohesion and adhesion. In Section 2.1, we dehned the term cohesion to describe the physical interactions between the same types of molecule, so that it is a measure of how hard it is to pull a liquid (and solid) apart. In Section 3.5.3, we dehned, the work of cohesion, W), as the reversible work, per unit area, required to break a column of a liquid (or solid) into two parts, creating two new equilibrium surfaces, and separating them to inhnite distance. (In practice, a distance of a few micrometers is sufficient.) The work of cohesion required to separate liquid layers into two parts having unit area can obviously be expressed from the definition of surface tension as... 

From the definitions of the works of cohesion and adhesion given in Chapter 2, it can be seen that 5b/a is the difference between the work of adhesion of B to A and the work of cohesion of B ... 

Although the mathematical relationships encountered in wetting phenomena are usually quite simple, they are found to be very useful in many practical applications. Their combinations and variations have given rise to still more relationships, which further expand their utihty without expanding the amount of information necessary for their application. Two thermodynamic relationships that can be useful in the analysis of wetting and spreading phenomena are the works of cohesion and adhesion. 

The processes of cohesion and adhesion are schematically depicted in Figure 5.5a and b. Cohesion involves the merging of two volumes of a (or P) into one volume in an environment of its vapor. Then, in view of Equation 5.6, the Gibbs energy of cohesion in phase a is defined as the reverse of the isothermal isobaric work per nnit cross-sectional area, indicated by the subscript a, to reversibly separate two volumes of a. 

In addition. Figures 7.4(b) and 7.5 schematically illustrate further thermodynamic expressions for solid-liquid interactions, i.e. the work of wetting or work of immersion and the work of cohesion and the work of adhesion , respectively. As can be easily seen, each of these parameters represents the work associated with a de-wetting process. 

The work of cohesion and the work of adhesion are both defined for a reversible process. Surface tension can be interpreted as half of the work of cohesion. 

The statement was made that the work of adhesion between two dissimilar substances should be larger than the work of cohesion of the weaker one. Demonstrate a basis on which this statement is correct and a basis on which it could be argued that the statement is incorrect. 

Surface energies are also associated with failure of an adhesive bond, because failure involves forming new surfaces and the appropriate surface energies have to be provided. The surface energy term may be the work of adhesion, VTa, or the work of cohesion, VTcoh. depending on whether the failure is adhesive or cohesive. For phases 1 and 2, these are defined as follows [lOj ... 

Harkins defines two terms, the work of cohesion We which is the work done when a bar of liquid of unit cross sectional area is pulled apart against the cohesive forces. It is thus numerically equal to twice the sur ce energy of the liquid. The work of adhesion Wa is similarly defined as the work required to pull apart a composite bar consisting of half of one liquid and half of the other, at the place of junction. 

Figure 2.35 Schematic illustrations of the processes for which AG equals (a) the work of cohesion, (b) the work of adhesion, and (c) the work of spreading. Reprinted, by permission, from P. Heimenz, Principles of Colloid and Surface Chemistry, 2nd ed., p. 316. Copyright 1986 by Marcel Dekker, Inc.

It is informative to apply Equation (60) to low-energy surfaces for two extreme values of 0, 0° and 180°, for which cos 0 is 1 and — 1, respectively. For 0 = 0°, WSL = 2yLV = WAA the work of solid-liquid adhesion is identical to the work of cohesion for the liquid. In this case interactions between solid and solid, liquid and liquid, and solid and liquid molecules are all equivalent. At the other extreme, with 0 = 180°, WSI = 0. In this case the liquid is tangent to the solid there is no interaction between the phases. 

Define the following terms and their relation to surface energies (a) work of adhesion, (b) work of cohesion, and (c) spreading coefficient. 

The free surface of pure liquids. There is some evidence in favour of a tendency for the hydrocarbon ends of molecules to be oriented outwards when one end of the molecule is hydrocarbon in character and the other has a greater residual affinity.1 The most direct evidence is gained by comparing the work of cohesion, or twice the surface tension (Chap. I, 8), of compounds of related constitution with their work of adhesion to water. The surface tension is half the work that must be done in order to pull apart a bar of the liquid of 1 sq. cm. cross-section, for 2 sq. cm. of fresh surface are formed in this operation. The work of cohesion therefore measures the intensity of the attraction between two free surfaces of the same liquid about to come into contact. 

For further thermod)mamic elaboration it is useful also to bring the work of cohesion into the picture. Generally speaking, upon spreading, as in fig. 5.8a, the internal cohesion of the liquid has to be overcome in order to achieve adhesion between liquid and solid. Figure 5.9 Indicates how the work of cohesion is defined. An infinitely long column of unit cross-section is cut into two halves and is the isothermal reversible work required to achieve that. Only for liquids or c... 

Fowkes proposed in 1964 that the work of cohesion, W), and the work of adhesion, Wa, can be separated into their dispersion, d, polar, p, induction, i, and hydrogen-bonding, h components ... 

For a granulating agent to be effective, it is vital that it is able to form a film on the particle surface. Rowe (1989) has suggested that binders should be selected on the basis of their spreading coefficients, where the spreading coefficient is defined as the difference between the work of adhesion of the binder and the substrate and the work of cohesion of the binder. The commonly used granulating agents are listed in Table 11.13. 

The work of adhesion (see Chapter 1,1) reflects the degree to which unsaturated molecular interactions between solids and liquids in contact are balanced. The value of cos 9, which is symbatic to the work of adhesion, is also a measure of the degree of similarity between the solid surface and a liquid (liophilicity). Polar surfaces that are wetted by water well are hydrophilic, while those poorly wetted (solid hydrocarbons, and particularly fluororinated polymers) are hydrophobic. Since the value of 0 is determined by both the work of adhesion and the work of cohesion, a comparison of the contact angles formed by different liquids at the same solid surface does not allow one to compare the works of adhesion (the degree of similarity in the nature of the liquid and solid) directly. For example, polar surfaces are equally wetted well by both water and hydrocarbons. 

As the Gibbs energy of adhesion between the phases a and increases, decreases. When = 0, there is no resistance to the extension of the interface between phases a and the two liquids mix spontaneously. In this case, the work of adhesion is the average of the work of cohesion of the two liquids. 

If 0 = 0, then Wa = 2y that is, the work of adhesion between solid and liquid is equal to the work of cohesion of the liquid. Thus the liquid can spread indefinitely over the surface, since energetically the system is indifferent to whether the liquid is in contact with itself or with the solid. On the other hand, if 0 = 180°, cos 0 = — 1, and = 0. No Gibbs energy expenditure is required to separate the solid and the liquid. The liquid does not wet the solid and does not spread on it. The spreading coefficient f or one liquid on another is defined in the same way as for a liquid on a solid, Eq. (18.23), except that cos 0 = 1. Thus... 

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