Work of adhesion

The work of adhesion is defined as the reversible thermodynamic work that is needed to separate the interface from the equilibrium state of two phases to a separation distance of infinity. Equation (3.10) shows the work of adhesion for a liquid—solid combination. This definition is attributed to the French scientist A. Dupre. 

7l is the surface energy (tension) of the liquid phase, 7s is the surface energy of file solid phase, 7SL is the interfacial surface tension, and Wg is the work of adhesion. A rise in the interfacial attraction results in an increase in the work of adhesion. Equation (3.10) can be rewritten to determine the work of cohesion (Wc) when the two phases are identical and no interface is present, as shown in Eqn (3.11) for a solid phase. 

If phase 1 represents liquid and phase 2 represents solid, 

Substitution of /gy J sL Equation (3.7) shows that the work of adhesion is related to the contact angle through the %ung-Dupre equation [5], 

The work of adhesion is an important contributor in the important practical subject of the adherence of coatings to substrates. This will be 

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Various means have been developed for prediciting or calculating a yab or a work of adhesion. Two empirical ones are the following. First, an early relationship is that known as Antonow s rule [13],... 

Finally, Newmann and co-workers [30] (see also Ref. 31) have argued that while free energy contributions may not be strictly additive as in Eq. IV-11, there should, in principle, be an equation of state relating the work of adhesion to the separate liquid surface tensions such as... 

Derive the expression (in terms of the appropriate works of adhesion and cohesion) for the spreading coefficient for a substance C at the interface between two liquids A and B. 

Alternatively, in combination with the definition of work of adhesion (Eq. XII-... 

Equation X-17 was stated in qualitative form by Young in 1805 [30], and we will follow its designation as Young s equation. The equivalent equation, Eq. X-19, was stated in algebraic form by Dupre in 1869 [31], along with the definition of work of adhesion. An alternative designation for both equations, which are really the same, is that of the Young and Dupre equation (see Ref. 32 for an emphatic dissent). 

Both here and in Eq. X-19 the subscript SLV serves as a reminder that the work of adhesion and the adhesion tension involve 75 0 rather than 75. 

Water at 20°C rests on solid naphthalene with a contact angle of 90°, while a water-ethanol solution of surface tension 3S dyn/cm shows an angle of 30°. Calculate (a) the work of adhesion of water to naphthalene, (b) the criticd surface tension of naphthalene, and (c) y for naphthalene. 

Ideal adhesion simply means the adhesion expected under one or another model situation of uniform materials having intimate contact over a well-defined area. In these cases, the important quantity is the work of adhesion wab between two phases, which is given by... 

The interesting implication of Eq. XII-24 is that for a given solid, the work of adhesion goes through a maximum as 7b(a) is varied [69]. For the low-energy surfaces Zisman and co-workers studied, )3 is about 0.04, and Wmax is approximately equal to the critical surface tension yc itself the liquid for this optimum adhesion has a fairly high contact angle. 

Returning to more surface chemical considerations, most literature discussions that relate adhesion to work of adhesion or to contact angle deal with surface free energy quantities. It has been pointed out that structural distortions are generally present in adsorbed layers and must be present if bulk liquid adsorbate forms a finite contact angle with the substrate (see Ref. 115). Thus both the entropy and the energy of adsorption are important (relative to bulk liquid). The... 

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. 

Derive from Eq. XU-24 an expression for the maximum work of adhesion involving only and 7c. Calculate this maximum work for 7c = 22 dyn/cm and 0 = 0.030, as well as 7/. for this case, and the contact angle. 

An inversion of these arguments indicates that release agents should exhibit several of the following features (/) act as a barrier to mechanical interlocking (2) prevent interdiffusion (J) exhibit poor adsorption and lack of reaction with at least one material at the interface (4) have low surface tension, resulting in poor wettabihty, ie, negative spreading coefficient, of the release substrate by the adhesive (5) low thermodynamic work of adhesion ... 

Many of these features are interrelated. Finely divided soHds such as talc [14807-96-6] are excellent barriers to mechanical interlocking and interdiffusion. They also reduce the area of contact over which short-range intermolecular forces can interact. Because compatibiUty of different polymers is the exception rather than the rule, preformed sheets of a different polymer usually prevent interdiffusion and are an effective way of controlling adhesion, provided no new strong interfacial interactions are thereby introduced. Surface tension and thermodynamic work of adhesion are interrelated, as shown in equations 1, 2, and 3, and are a direct consequence of the intermolecular forces that also control adsorption and chemical reactivity. 

The work of adhesion, is the change in energy per unit surface area when two interfaces come into contact, as given in equation 1 where and... 

However, the surface tension of the soHd, y, and the soHd—Hquid interfacial tension, y, caimot be measured direcdy by simple means. The work of adhesion of the soHd to the Hquid usually deterrnined by other techniques. 

Most of the various strategies which have been proposed to predict relative adhesive interfacial strength are based on thermodynamics. One may define, without ambiguity, as shown in Fig. 3, a thermodynamic work of adhesion , Wa,... 

Fig. 3. Definition of thermodynamic work of adhesion, Wa (a) disjoining surfaces in vacuum (b) disjoining surfaces in fluid medium m and (c) disjoining surfaces in presence of vapors from adhesive.

One may also be able to determine the work of adhesion for cases in which the contact angle is zero by using probe liquids, as described later in this chapter. There are also other ways of determining the work of adhesion, such as inverse gas chromatography, which do not depend solely on capillary measurements (surface tension and contact angle). This too will be discussed later. 

The relationship between practical adhesion and the work of adhesion,... 

Assuming the work of adhesion to be measurable, one must next ask if it can be related to practical adhesion. If so, it may be a useful predictor of adhesion. The prospect at first looks bleak. The perfect disjoining of phases contemplated by Eq. 1 almost never occurs, and it takes no account of the existence of an interphase , as discussed earlier. Nonetheless, modeling the complex real interphase as a true mathematical interface has led to quantitative relationships between mechanical quantities and the work of adhesion. For example, Cox [22] suggested a linear relationship between Wa and the interfacial shear strength, r, in a fiber-matrix composite as follows ... 

The most-often cited theoretical underpinning for a relationship between practical adhesion energy and the work of adhesion is the generalized fracture mechanics theory of Gent and coworkers [23-25] and contributed to by Andrews and Kinloch [26-29]. This defines a linear relationship between the mechanical work of separation, kj, , and the thermodynamic work of adhesion ... 

Combination of Eq. 7 or Eq. 8 with the Young-Dupre equation, Eq. 3, suggests that the mechanical work of separation (and perhaps also the mechanical adhesive interface strength) should be proportional to (I -fcos6l) in any series of tests where other factors are kept constant, and in which the contact angle is finite. This has indeed often been found to be the case, as documented in an extensive review by Mittal [31], from which a few results are shown in Fig. 5. Other important studies have also shown a direct relationship between practical and thermodynamic adhesion, but a discussion of these will be deferred until later. It would appear that a useful criterion for maximizing practical adhesion would be the maximization of the thermodynamic work of adhesion, but this turns out to be a serious over-simplification. There are numerous instances in which practical adhesion is found not to correlate with the work of adhesion at ail, and sometimes to correlate inversely with it. There are various explanations for such discrepancies, as discussed below. 

Initial intimacy of contact between the adhesive and adherend must of course precede the formation of a diffusion interphase, but in contrast to contact adhesion, the issue which is dominant is not the maximization of the work of adhesion but instead must be some appropriate measure of the phase compatibility, in the sense of mutual solubility. 

It can be shown, in the context of the assumption that only dispersion forces operate across the interface (i.e. j/l = vt nd ys = vi), that optimal wetting and maximal work of adhesion may not be criteria consistent with one another. Either Eq. 9 or Eq. 11 gives for these conditions ... 

There is much evidence that there are many cases in which the interaction between liquids and solids cannot be described in terms of dispersion forces alone. For example, Dann [75] found significant non-dispersion-force contributions to the work of adhesion between ethanol/water mixtures, mixed glycols, and polyglycols and a mixture of formamide and 2-ethoxyethanol against a variety of solids. The nature of these other interactions , however, were at first the subject of some dispute. We may account for them in a general way with a term /sl inserted into Eq. 11 ... 

The use of the harmonic mean often leads to better predictions of interfacial tensions between polymers and better contact angles between liquids and polymer solids, but the criterion for maximization of the work of adhesion is the same as... 

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