Fowkes’ method

Table 2.3. Estimation of the dispersion contribution to the surface tension according to Fowkes method (J. Phys. Chem. 67 (1963) 2538). Data in mJ m, temp. 20°C, taken from Fowkes they differ insignificantly from ours in table A1.5.

Solid 7c Critical surface tension (mN/m) from Zisman plot 7s° Dispersion Component (mN/m) from Fowkes method 7s Surface Tension (mN/m) from Fowkes method... 

The first term on the right is the quantity which Fowkes method calculates. 

Fowkes method of evaluation of acid-base component... 

Surface energy was calculated using the Fowkes method [21] to determine the dispersion and polar (or nondispersion) component of Wettability measurements indicate a surface energy close to 20 mJ/m for the hydrophobic wafer (CHj grafted surface), with a polar component equal to zero. This result confirms the hydrophobic character of the grafted wafer. A surface energy equal to 79 mJ/m was obtained for the hydrophilic substrate (polar component = 42 mJ/m ). 

Unfortunately, the PSP method has the same problem as Fowkes method for water-benzene. It predicts an interfacial tension of 52.23 mN m (51.5 mN m with Fowkes) as both methods ignore the acid-base interactions between water and benzene. 

Calculate with the Fowkes method the surface tension of PE and water s contact angle on this pol5uner. 

In addition to their use in determining the critical surface energy Yq, contact angle measurements can also provide information on the polarity of the film surface. In this case the measurements are conducted with a series of liquids of different polarity (for example isopropanol-water mixtures). For evaluating the data a number of procedures have been published (see for example the Good-Girifalco-Fowkes method [30, 31]). 

Keywords Solid surface tension Solid surface energy Contact angle Work of adhesion Zisman method Surface tension component mefliod Fowkes method Owais-Wendt-Rabel-Kaelble mefliod Extended Fowkes mefliod Equation of state... 

Fowkes method. Fowkes [14-16] was the pioneer proposing partition of surface tension. He assumed that the surface tension of a solid or liquid is a sum of independent components, which addresses specific molecular interaction individually. For example, ysv can have a number of contributors and is given by... 

Extended Fowkes method. Kitazaki et al. [23] further refined the OWRK model by splitting the dipole-dipole interactions into polar and H-bonding interactions. Accordingly, both ysv and /lv comprise three components d for dispersion, p for polar, and h for H-bonding (Eq, 7.13), and they all take the form of geometrical mean (Eqs. 7.14 and 7.15). 

In addition to the methods discussed above, there are a few other solid surface tension determination methods, such as the Wu method [29, 30] and the Schultz methods [31, 32], which also fall into the category of partitioning surface tensions into independent components. Wu used the harmonic means to describe the interfacial surface tension instead of the geometric mean, based on a few slightly different assumptions to derive the equations for Wu s model. The Schultz methods can be considered as a special case of the extended Fowkes method. The contact angle of a polar liquid (usually water) on the solid is conducted in another nonpolar liquid medium (e.g., pure hydrocarbon compounds), or the contact angle of a nonpolar liquid on the solid is measured in another polar liquid medium. 

The surface tension component method assumes that surface tension can be partitioned into different components, which address different intermolecular interactions individually. The overall surface tension will be the sum of all the components according to the linear free energy relationship. In the original Fowkes method [14], only the dispersion interaction is considered. The component method has been subsequentiy extended to include polar component and later divided the polar component into dipolar interaction and H-bonding interaction. The vOCG model appeared as a refined version of the surface tension component methodology. It assumes the existence of both additive and nonadditive components. The Lifshitz-van der Waals component (/ ) is additive, and the electron donor and acceptor components (7 and 7" ) are nonadditive. The solid surface tension (7sv) can be calculated by using three Uquids with known y, y and y values. Since this is a semiempirical approach, the calcu-... 

Measurement of the contact angle at a solid-liquid interface is a widely used method for the determination of the surface energy of solid polymers. Fowkes [1] first proposed that the surface energy of a pure phase, y y could be represented by the sum of the contribution from different types of force components, especially the dispersion and the polar components, such that ... 

Rather than pursue the fractions or their composite any further, we turn next to an empirical approach due to Fowkes to estimate the product y for various substances. We use the symbol yd to represent the London contributions to y estimated by his method. The notation is derived from the fact that London forces are also called dispersion (superscript d) forces (see, for example, Chapter 10, Section 10.7b). In this notation Equation (98) can be written... 

Riddle and Fowkes [19] considered that the values of AN, determined by the NMR method, are partly due to the van del Waals forces between Et3P = O and solvent molecules and attributed somewhat large AN values of strongly basic solvents like pyridine to it. 

F.M. Fowkes, J. Adhesion Set Techn. 1 (1987) 7 other liquid = DMSO method used, SD. 

This method allows one to evaluate an unknown system. The following discussion concentrates on the surface properties of different fillers. The current level of understanding has been developed Ifom principles proposed by Fowkes who indicated that the work of adhesion has two components ... 

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 by inverse gas chromatography although it can also be measured by contact angle methods. The work of adhesion is given by the following equation, which has been modified to account for Fowkes theoiy. 

Jensen [9] indicated that there is no evidence that Drago s parameters reflect the relative electrostatic and covalent contributions to the bonding in resulting adducts. They were not correlated with either a physical property (dipole moment, ionization potential) or with a quantum-mechanically calculated index. Drago s approach is a purely empirical method of calculating enthalpy of formation for molecular adducts. Fowkes applied the Lewis E C equation [19] and has attempted to determine E and C parameters for both polymers and surfaces. However, Jensen [9] indicated the potential problem connected... 

Chehimi and Pigois-Landureau [24] compared six methods of evaluating AG where RTln Vn values were related to the abscissa coordinates labelled as follows I, AH p II, AHvap III, Tb IV, log Pq V, a(7 )V2 VI, (hi/)V2aolO . Authors stated that the AH p approach is linked to those of authors of Refs. [48, 50] and, more importantly, takes into account the self-association character of the polar probes, as recommended by Fowkes [51]. 

Kamdem et al. [31] have used the AN values of polar probes as suggested by Riddle and Fowkes in characterization of birch wood meal by IGC method. The reported values of Kd and Ka indicated that white birch wood surface has an amphoteric character and predominantly acidic sites are involved in the adsorption process. 

Geometric-mean approach (Fowkes and later Owens and Wendt s method)... 

Method of Fowkes. Fowkes [l2,13] has proposed that "the surface tensions [are] a measure of the attractive forces between surface layers and liquid phase, and that such forces and their contribution to the free energy are additive." From this he concluded that the surface... 

Table 3 reports the E and C parameters for various polymers and metal oxides using a variety of techniques. Clearly, several methods can be used to determine E and C. Alternatively, it would perhaps be possible to assess these constants by using contact angles of diiodomethane solutions of specific probes such as phenol. Indeed, the determination of for probe-surface systems was suggested by Fowkes et al. [49] on the basis... 

Two methods were developed to determine the first was suggested by Fowkes and Mostafa in 1978 [11] and the second approach was introduced by van Oss and co-workers in 1988 [22]. 

Equation (2.1.6) fails completely for liquids such as water, methanol and formamide. This is not surprising, because in these liquids hydrogen bonds play a substantial role in providing cohesive forces whose effect is not included in the purely dispersive Hamaker constant. One approach to this problem, initiated by Fowkes (1962), has been to assume that each type of intermolecular force makes an additive contribution to the surface tension. So-called group contribution methods have been developed on the basis of this idea, which are of considerable practical use in classifying and predicting surface tension behaviour in a semi-empirical way. 

---