Fowkes theory

The dispersive component is associated with polymer-filler interaction and the specific component is associated with filler networking and agglomeration. The dispersive component of different fillers is more conveniently measured hy inverse gas chromatography although it can also he measured by contact angle methods. The work of adhesion is given by the following equation, which has been modified to account for Fowkes theory. 

Behind this lies the Fowkes theory, in accordance with which the total surface free energy is due to the action of dispersion and polar forces. The contribution of the latter in the free energy can be distinguished. It can be seen that the free surface energy of a liquid is given by... 

The Fowkes theory played an important role in the evaluation of not only the free surface energy of polymers and its relation to Yc, but also in the case of interfacial energy and determination of the relationship between adhesion of polymer solids and their sruface energy. In this respect, it is essential to take into account, apart from dispersive forces, polar forces operating at the interface. De-... 

In the Fowkes theory, the surface tension is divided into dispersion (d) and specific (spec) components ... 

The specific value includes both polar and hydrograi bonding effects. Noticeably, the dispersion value indicates that approximately 30% of the surface tension value of water is due to dispersion forces, which agrees well with theoretical considerations and the molecular theories mentioned in Chapter 2. (The contribution of dispersion to water s potential energy is around 24% at 298 K.) This illustrates the importance of the van der Waals forces even for strongly hydrogen bonding compounds such as water. The dispersion surface tension value of water from the Fowkes theory can be considCTed to be widely accepted and is therefore used in further calculations. 

The Fowkes theory, like other approaches discussed later, has strengths and weaknesses. Success stories have been reported, e.g. for mercury-water and alkanes, or interfaces between water or glycol and n-alkanes (see Example 3.3... 

Calculate, using the Hansen-Beerbower equation, the dispersion and specific (polar and hydrogen bonding) parts of the smface tension of water based on both sets of water solubility parameters. Which set of water solubility parameters results in values for the dispersion and specific surface tensions for water closer to those estimated from the Fowkes theory ... 

One of the major problems of the application of the theory to sohds is the determination of the interfacial tension. For such systems it cannot be determined by direct measurements, it is usually derived from thermodynamic calculations. Good and Girifalco [31] developed the first theory for the calculation of Yab> because it contained an adjustable parameter it did not gain practical use. The most widely accepted solution was suggested by Fowkes [32,33]. He assumed that surface tension can be divided as shown in Eq. 9 ... 

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 ... 

If Fowkes semiempirical interfacial tension theory (as described on pages 65-67) is applied to the solid-liquid interface, then... 

Figure 1.11. Entropy of water, adsorbed on Graphon. The adsorbed volume is in ml standard temperature and pressure and V(mon) is the volume in a saturated mono-layer according to BET theory. (Redrawn from A.C. 2 ttlemoyer, in Hydrophobic Surfaces. F.M. Fowkes. Ed., Academic Press (1969) 1.)...

This theoretical work was utilized by Good and Fowkes who developed theories relating van der Waals forces to surface tension and to the work of adhesion. These concepts are discussed in Chapters 5 14. 

Chen et al. (1999) treated polyester films with plasma in six kinds of gases (O, Nj, He, Ar, H, and CH ). Results in terms of surface tension and three components, and and the critical surface tension of the polyester film are summarized in Table 3.9 (Chen et al., 1999). It is evident that the value of the surface tension of polyester film obtained by the extended Fowkes s equation (Fowkes, 1964) corresponds highly to y of Zisman s plots (Zisman, 1964), which coincides with the theory of (Kitazaki and Hata (1972). Surface tensions of polyester films treated with O, ... 

The logical next step in the process of extending the utility of theory to practical systems is to include polar molecular interactions. For this step, Fowkes suggested that the intermolecular forces contributing to surface and interfacial tensions, and subsequent phenomena such as wetting, could be broken down into independent and additive terms. For example, a polar molecule such as an ester would have two terms making up its surface tension—dispersion forces (d) and dipolar interactions (p)—so that... 

A special type of interaction, the acid-base interaction, is a fairly recent discovery. It is based on the chemical concept of a Lewis acid and base, which is briefly described. The acid/base definition was proposed separately by J. N. Bronsted and G. N. Lewis. Restatement of these definitions by Lewis in 1938 led to their popularity and acceptance. The Lewis definitions are an acid is a substance which can accept an electron pair from a base a base is a substance which can donate an electron pair. By this definition, every cation is an acid in addition to chemical compounds such as BF3 and Si02. Conversely, anions and compounds like NHj, PH3, and CgHjCH2NH2 are bases. According to the acid-base theory, adhesion results from the polar attraction of Lewis acids and bases (i.e., electron-poor and electron-rich elements) at the interface. This theory is attributed to the work by Fowkes et Gutmann, and Bolger and Michaels . ... 

In the modern theory of surface science, Fowkes was the first to propose the theory of acid-base interfacial interaction [37 0]. 

The theory of the Good-Girifalco interaction parameter can be developed to give some support for this relationship. This was not accepted by Fowkes, who argued that the principal non-dispersion interactions are Acid-base interactions, for which a geometric mean relationship does not apply. 

There is also an analogous attempt to separate out these forces in the theory of solutions and solubility parameters. One of the first attempts to separate out the components of interfacial forces was made by Fowkes. His contention was that all materials display van der Waals, or dispersion, forces across interfaces. In particular, certain materials, such as totally saturated hydrocarbons, were assumed to display only van der Waals forces. Equation (87) was written for such materials. 

The authors postulate that a solid and a liquid of similar polarity will give a minimum value of y%. Kitazaki and Hata also discuss the ramifications of their postulates and experimeiital results on adhesion measurements. Overall their conclusion is that a maximum is achieved when the polarities of the solid surface and the adhesive are as similar as possible. From the Good and Girifalco theory, a maximum in would also be expected when the interparticle forces across the interface are at a maximum. Wu has also analyzed the separation of the force components of the interfacial and surface tensions. Wu, however, chooses to make an arithmetic mean approximation rather than the geometric mean approximation used by Good and by Fowkes. He bases this choice on an analogy with the form of the expressions for the interparticle forces, which are more closely mimicked by an arithmetic mean. Wu contends that his use of the arithmetic mean yields results closer to measured values. 

The most significant work to use acid-base theory to understand the surface chemistry of inorganic fillers has been carried out by Fowkes and his co-workers [1-4, 10-12]. 

The interfacial acid-base function theory was put forward the first time in 1962 by Fowks. This theory holds that the filler and polymer matrix of a composite material can be treated as a generalized acid or alkali. When the surfaces of the filler and polymer matrix have different acids or alkalis, they are easy to combine. The greater their difference in pH, the more easily they will combine. When the surfaces of the filler and polymer matrix have the same acid or alkali, the surface of the filler should be modified to change its pH value. The different surface pH values are beneficial to improve the bonding strength between the reinforced material and polymer matrix and improve the performance of filled plastics. 

---