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Perhaps the most convenient way of interpreting the wettability of a low energy solid is the formulation of the work of adhesion, W_A, defined by Dupré and Dupré [22] as the work required to separate a unit area of the solid–liquid interface.

Consider the wetting of a solid substrate (S) by a liquid (adhesive) “L”. A solid–liquid interface is formed as a result according to the following equation:

(2.2)

If γ_S, γ_L, and γ_SL are the surface free energies of solid substrate, liquid (adhesive), and the interphase, then the free energy change of the process (ΔG_A) can be written as

(2.3)

The work of adhesion W_A = –ΔG can be written as

(2.4)

This is the thermodynamic work of adhesion or the work needed to separate unit area of the solid–liquid interface.

Assuming γ_LV = γ_L and γ_SV = γ_s from Equations 2.1 and 2.4, we get

(2.5)

This is known as Young–Dupre’s equation. Thus, if the contact angle, θ, of a well-defined probe liquid against a solid is measured, the work of adhesion can be determined.

Thus, the thermodynamic work of adhesion (W) is, by definition, the free energy change per unit area required to separate to infinity two surfaces initially in contact with a result of creating two new surfaces at the interface between two materials, for example, an adhesive and an adherend.

It is related to the intermolecular forces that operate

at the interface between two materials, for example, an adhesive and an adherend.

It is related to the intermolecular forces that operate

at the interface between two materials, for example, an adhesive and an adherend.

It is related to the intermolecular forces that operate

at the interface between two materials, for example,

It is related to the intermolecular forces that operate

at the interface between two materials, for example,

Fowkes [23] proposed that both reversible work of adhesion (W) and the surface free energy (γ) had additive components and can be partitioned into individual components. Accordingly, several equations were proposed based on this important approach. This pioneering development of Professor Frederick M. Fowkes regarding the acid–base theory in adhesion have attracted the attention of several laboratories. A Festschrift in his honor on the occasion of his 75th birthday was published in 1991.

The approach is described below:

(1) Partitioning of surface free energies into components

The principle of partitioning is based on the assumption that the surface free energy is determined by various interfacial interactions. These interactions in turn depend on the basic properties of the interacting liquid and that of the solid–liquid interface (SL) [23, 24].

(2.6)

where =

are the dispersion, polar, hydrogen (related to hydrogen bonds), induction, and acid–base components, respectively, while o refers to all remaining interactions.

(2) Mode of combinations of the individual energy components According to Fowkes, the dispersion component of the surface free energy is connected with the London interactions. The remaining van der Waals interactions, i.e., the Keesom and Debye ones, have been considered by Fowkes as a part of the induction interactions.

Fowkes investigated mainly two-phase systems containing a substance (solid or liquid) in which the dispersion interactions appear only. Considering just such systems, Fowkes determined the SFE corresponding to the solid–liquid interface as follows:

For two-phase systems comprising of a solid and liquid, in which only dispersion interactions occur, namely, between , Fowkes employed geometric mean as the mode of combination of these energy components to give the following equation:

(2.7)

Fowkes [25] modified Equation 2.7 by changing from geometric mean to arithmetic mean to arrive at the following equation:

(2.8)

Owens and Wendt [26] significantly changed the Fowkes idea while assuming that the sum of all the components occurring on the right-hand side of Equation 2.11, namely

except that γ^d can be considered as associated with the polar interaction ,

Consequently, the following equation was obtained:

(2.9)

Wu [27, 28] accepted the idea by Owens and Wendt to divide the SFE into two parts, but used the harmonic means of the interfacial interactions instead of the geometric means in Equation 2.9 and derived the following equation:

(2.10)

van Oss, Chaudhury, and Good proposed the latest concept of partition in which surface energy is partitioned into two components [29, 30]:

1 Long range interactions London, Keesom, and Debye called the Lifshitz–van der Waals component (γLW)

2 The short-range interactions (acid–base), called the acid–base component (γAB) = 2(γ+ γ–)0.5 where γ+ and γ– mean the acidic and basic constituents, respectively, which are associated with the acid–base interactions.

Combining van Oss Chaudhury’s concept with Young’s equation (Equation 2.5), we obtain the Young–Fowkes–van Oss–Good acid–base equation referred to as the acid–base approach:

(2.11)

This equation contains three unknowns and, therefore, we need contact angle data of three liquids. Table 2.3 contains the physical properties and surface free energy components of test liquids normally used. One of them must be non-polar and the other two should be polar. The Lifshitz–van der Waals component of the surface free energy is obtained from the contact angle of the apolar test liquid, e.g., diiodomethane.

Table 2.3 Physical properties and surface free energy components of test liquids used at 20°C [31].

Liquid	Density (kg/m3)	Viscosity (mPas)	Surface free energy (mJm–2) (LW–AB approach)
				γlv
Water	1000	1.00	21.8	25.5	25.5	51.0	72.8
Formamide	799	1.02	39	2.28	39.6	19	58
Ethylene glycol	1109	19.9	29	1.92	47	19	48
Diethylene glycol	1130	26.8	44.7	–	–	–	–
Diodomethane	3325	2.8	50.8	0	0	0	50.8
1-Bromonaphthalene	1483	–	44.4	0	0	0	44.4

The acid–base interaction and its relevance to adhesives and adhesive bonding have been reviewed in detail by Chehimi et al. [32].