Surfaces estimating surface energies

Section 4.1 briefly describes some of the commonly employed experimental tools and procedures. Chaudhury et al., Israelachvili et al. and Tirrell et al. employed contact mechanics based approach to estimate surface energies of different self-assembled monolayers and polymers. In these studies, the results of these measurements were compared to the results of contact angle measurements. These measurements are reviewed in Section 4.2. The JKR type measurements are discussed in Section 4.2.1, and the measurements done using the surface forces apparatus (SFA) are reviewed in Section 4.2.2. 

Summary of methods for estimating surface energy from the contact angle data... 

The adsorption of gas onto a solid surface can also be used to estimate surface energy. Both inverse gas chromatography (IGC) and isotherm measurement using the BET method [19] have been used. Further discussion and detailed references are given by Lucic et al. [20] who compare the application of IGC, BET and contact angle methods for characterising the surface energies of stearate-coated calcium carbonate fillers. 

No quantitative basis exists at present for determining the value of 6si, and indeed, only a very rough estimate can be made for 6i. But it is evident that 6i and 6si should be of about the same magnitude, and hence they will tend to cancel, in Equation 20. As a result, the method for estimating surface energies may not be extremely sensitive to the effect of orientation on surface entropy. 

Fowkes and Mostafa (51) demonstrated another fruitful approach to the problem of estimating surface energies of solids by separating the surface free energy into different components, of which dispersive and polar acid-base interactions dominate, thus giving the following ... 

Figure 11.1 Schematic illustrations of the atomic configuration of (a) (100), (111), and (b) (110) surfaces of fee symmetry, together with the corresponding unit cell of each surface. The surface energy per atom of a specific surface can be estimated by counting the total number of...

Table 9.3 Number of broken bonds, unit cell area, and estimated surface energies of truncated bulk SI surfaces in the framework of a bond counting picture.

The interface between a solid and its vapor (or an inert gas) is discussed in this chapter from an essentially phenomenological point of view. We are interested in surface energies and free energies and in how they may be measured or estimated theoretically. The study of solid surfaces at the molecular level, through the methods of spectroscopy and diffraction, is taken up in Chapter VIII. 

Theoretical Estimates of Surface Energies and Free Energies... 

The second model is a quantum mechanical one where free electrons are contained in a box whose sides correspond to the surfaces of the metal. The wave functions for the standing waves inside the box yield permissible states essentially independent of the lattice type. The kinetic energy corresponding to the rejected states leads to the surface energy in fair agreement with experimental estimates [86, 87],... 

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

The excess heat of solution of sample A of finely divided sodium chloride is 18 cal/g, and that of sample B is 12 cal/g. The area is estimated by making a microscopic count of the number of particles in a known weight of sample, and it is found that sample A contains 22 times more particles per gram than does sample B. Are the specific surface energies the same for the two samples If not, calculate their ratio. 

It should be noted that one may obtain an estimate for the surface energy of a solid from a single contact angle measurement by combining Eq. 9 or Eq. 11 with Eq. 3. One then has ... 

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