Surface tension concept

The critical surface tension concept has provided a useful means of summarizing wetting behavior and allowing predictions of an interpolative nature. A schematic summary of 7 values is given in Fig. X-10 [123]. In addition, actual contact angles for various systems can be estimated since )3 in Eq. X-38 usually has a value of about 0.03-0.04. 

The capillary effect in CNTs was reported originally by Ajayan and lijima [89], who obtained surface tension threshold values for NT wetting based on macroscopic surface tension concepts and immersion experiments of NTs in different liquids (solvents, metals, etc.) [98]. From their results, although liquids with low surface tension (<200 mN/m), including most common organic solvents would fill tubes, those with surface tension higher than 200 mN/m, such as metals, can neither wet CNTs nor initialize the capillary action [99]. 

Explain briefly the critical surface tension concept and how its value for PMMA has been estimated. Which of the following liquids will fully wet PMMA diethylene glycol, formamide and acetone ... 

The theory of repellency is discussed in Chapter 11. The relationship between repellency and the structure of the fluorinated repellent is in agreement with the critical surface tension concept developed by Zisman [319]. Shafrin and Zis-man [320] determined the critical surface tensions of fu-perfluroalkyl-substituted -heptadecanoic acids and the wettabilities of their monolayers. The wettabilities... 

Although the critical surface tension concept has been criticized for its empirical nature [27], critical surface tension data have been very useful in developing water- and oil-repellent finishes. One reason for this practical impact may be the similarity between the systems studied by Zisman and the surfaces of water-and oil-repellent finishes. 

Zisman was one of the first to recognize that the critical surface tension concept is strictly empirical and to suggest that needs to be replaced by parameters having a thermodynamic or statistical mechanical basis [26]. Fox and Zisman [30] have cautioned that jc varies between liquid types and that it is not a measure of the surface energy of the solid yso-... 

Because of the deficiencies and limitations of the critical surface tension concept, the need to determine the surface free energy of solids has remained. Because the surface free energy of solids is difficult to measure, attempts have been made to estimate the surface free energy from interaction with liquids. 

The repellency of fluorocarbon finishes depends on the structures of the fluorocarbon segment, the nonfluorinated segment of the molecule, the orientation of the fluorocarbon tail, the distribution and the amount of the fluorocarbon moiety on fibers, and the composition and geometry of the fabric [101]. The relationship between repellency and the structure of the fluorocarbon segment is in accord with the critical surface tension concept developed by Zisman and co-workers (see Chapter 11). Shafrin and Zisman [102] determined the wettabilities and critical surface tensions of -perfluoroalkyl substituted 77-heptadecanoic acids synthesized by Brace [103]. Once the seven outmost carbon atoms are fully fluorinated x = 7), the wettability of monolayers of the acids F(CF2)a(CH2)i6COOH approaches that of the perfluorocarboxylic acid F(CF2).vCOOH (Fig. 12.2). This suggests that a terminal perfluoroalkyl chain of seven carbon atoms is sufficiently... 

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

Here again, the older concept of surface tension appears since Eq. 11-22 is best understood in terms of the argument that the maximum force available to support the weight of the drop is given by the surface tension force per centimeter times the circumference of the tip. 

A case can be made for the usefulness of surface tension as a concept even in the case of a normal liquid-vapor interface. A discussion of this appears in papers by Brown [33] and Gurney [34]. The informal practice of using surface tension and surface free energy interchangeably will be followed in this text. 

We noted in Section VII-2B that, given the set of surface tension values for various crystal planes, the Wulff theorem allowed the construction of fhe equilibrium or minimum firee energy shape. This concept may be applied in reverse small crystals will gradually take on their equilibrium shape upon annealing near their melting point and likewise, small air pockets in a crystal will form equilibrium-shaped voids. The latter phenomenon offers the possible advantage that adventitious contamination of the solid-air interface is less likely. 

In the models discussed thus far in this section, emphasis has been placed on electrostatic effects and solvent polarity. An alternative view that to some extent takes other forces into account begins with the idea that, in order to dissolve a solute molecule in a solvent, energy is required to create a cavity in the solvent the solute is then inserted into this cavity. In Section 8.2 we saw that the energy to create a cavity can be expressed as a product of the surface area of the cavity and the surface tension of the solvent. An equivalent expression is obtained as the product of the volume of the cavity and the pressure exerted by the solvent, and we now explore this concept. 

The results were presented in the form of isotherms, in which the properties are plotted versus the concentration. Nevertheless analysis of the isotherms was made based on available melting diagrams approach that the melts consist of TaFg3 and TaF7Cl3 complex ions. However, according to this general conception [312-314], the isotherm of the surface tension must, in such a case, have either a minimum or at least display prominence of the dependence in the direction of the concentration axis. 

The derivations of the foregoing equations have been based on the principles of thermodynamics and the macroscopic concepts of density, surface tension, and radius of curvature. They may therefore cease to be appropriate as the mean radius of curvature approaches molecular dimensions. 

This equation, called the Young Equation, is in accord with the concept that the various surface forces can be represented by surface tensions acting in the direction of the surfaces. Eq. (A.4.3) results from equating the horizontal components of these tensions. 

The classical Kelvin equation assumes that the surface tension can be defined and that the gas phase is ideal. This is accurate for mesopores, but fails if appUed to pores of narrow width. Stronger sohd-fluid attractive forces enhance adsorption in narrow pores. Simulation studies [86] suggest that the lower limit of pore sizes determined from classical thermodynamic analysis methods hes at about 15 nm. Correction of the Kelvin equation does lower this border to about 2 run, but finally also the texture of the fluid becomes so pronounced, that the concept of a smooth hquid-vapor interface cannot accurately be applied. Therefore, analysis based on the Kelvin equation is not applicable for micropores and different theories have to be applied for the different ranges of pore sizes. 

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