Surface energy specific

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. 

The surface of silica is covered by a layer of acidic silanol and siloxane groups. This highly polar and hydrophilic character of the filler surface results in a low compatibihty with the rather apolar polymer. Besides, highly attractive forces between silica particles result in strong agglomeration forces. The formation of a hydrophobic shell around the silica particle by the sUica-sUane reaction prevents the formation of a filler-filler network by reduction of the specific surface energy [3]. 

While our arguments are simplified in several respects - three-dimensional clusters will not all have the same shape, and the use of a macroscopic concept like the specific surface energy 7 is not really warranted - they are qualitatively correct, and Eqs. (10.16) and (10.17) are useful estimates. 

This wetting process may be described in terms of a balance of specific surface energies —the Young equation ... 

Specific surface energy or surface tension of a solid Specific free energy of an interface between UC and U vapor Specific energy or tension of a liquid-solid interface Surface tension of a solid in a foreign vapor Surface tension of a grain boundary... 

Only surface energy is mentioned in the title of this review, but surface tension also is considered in the following text. The dimensions of (specific) surface energy (ergs/cm2 or joules/m2 or g/sec2) and of surface tension (dynes/cm or newtons/m or g/sec2) are identical. For typical liquids, also the two absolute values are equal for instance, the surface tension of water 7 at room temperature is about 72 dyne/cm, and the (specific) surface energy is 72 erg/cm2. 

A relation between rupture phenomena and (specific) surface energy 7 was postulated by Dupre 4 almost simultaneously with the hypothesis of Quincke. Let a cylindrical rod be broken in tension. After rupture, two new gas — solid interfaces of vr2 each are present, r being the radius of the rupture surface. Consequently, the work of rupture ought to contain a term 2 nr2 7 . Dupre did not indicate how to separate this term from the main component of the work of rupture, which is the work required to extend the rod to its maximum elongation (or strain). The modern development of Dupre s ideas is reviewed in Section III.3. below. 

The usual procedure, however, does not follow Laplace s precedent, but rather uses Dupre s scheme. Consider a bar, of unit area cross section and containing 2n atomic layers perpendicular to the axis of the bar n is a large number. Let the internal energy of the bar be E0. If the bar is cut in two, so that each half contains n atomic layers, the energy of the system changes to Ey. One-half of the difference between the two energies is considered to be (specific) surface energy of the material, that is 7 = 0.5 (Ex - E0). The factor 0.5 appears, of course, because two rupture surfaces are formed by one act of separation. 

E((ThkiAhki) = Minimum [a = specific surface energy A = surface area) (1)... 

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

Numbers of Neighbor Atoms, Specific Surface Energies, and Work Functions of Different Planes of a Tungsten Crystal (4S)... 

The second column of Table II shows the numbers of the first (wi), second (ni), and third (nj) neighboring atoms for an atom situated inside (in) or located outside (ad) the plane under consideration. Planes having the same numbers of Wi and n2 for in-atoms show identical values of work function increases with packing density of the crystal planes, their specific surface energy a decreases [Straiiski and Suhrmann (48)] in a reverse linear relation to 4> (see Table II, column 3. and Fig. 12). 

Fig. 12. Specific surface energy a as function of the electron work functions of various planes of a tungsten crystal.

Since the electron work functions and the specific surface energies of different planes of the same crystal may have different values, it would be interesting to study the electronic interaction during adsorption of foreign molecules on monocrystals. Investigations of monocrystals, however, encounter many difficulties therefore, one has to restrict oneself in general to poly crystalline surfaces, which also give remarkable results because the force of interaction essentially depends on the nature of the metal and differs for the same metal from one species of adsorbed molecules to the other. 

It is possible to be more definite about the influence of face on the work function, which is a measure of the electron affinity of the metal. The work function has been shown to depend on crystal face (19). The question of the relationship of the work function and the specific surface energy of the surface to its chemical activity has been discussed by Suhrmann (20). 

The addition of surfactants, which can either adsorb on the surface of a nucleus or act as a center for inducing nu-cleation, can be used to control the process of nucleation and the stability of the resulting nuclei. This is due to their effect on the specific surface energy, on the one hand, and their ability to incorporate the material in the micelles, on the other. 

Figure 13.6 shows a schematic for IGC operation. Inverse, in this instance, refers to the observation that the powder is the unknown material, and the vapor that is injected into the column is known, which is inverse to the conditions that exist in traditional gas chromatography. After the initial injection of the known gas probe, the retention time and volume of the probe are measured as it passes through the packed powder bed. The gas probes range from a series of alkanes, which are nonpolar in nature, to polar probes such as chloroform and water. Using these different probes, the acid-base nature of the compound, specific surface energies of adsorption, and other thermodynamic properties are calculated. The governing equations for these calculations are based upon fundamental thermodynamic principles, and reveal a great deal of information about the surface of powder with a relatively simple experimental setup (Fig. 13.6). This technique has been applied to a number of different applications. IGC has been used to detect the following scenarios ...

The specific surface preparation can be checked for effectiveness by the water-break free test. After the final treating step, the substrate surface is checked for a continuous film of water that should form when deionized water droplets are placed on the surface. A surface that is uniformly wet by distilled water will likely also be wet by the adhesive since the specific surface energy of water is 72 dyn/cm and of most organic adhesives is 30 to 50 dyn/cm. However, this test tells little about weak boundary layers or other contaminants that may be present on the substrate s surface but still be capable of wetting with water. 

The specific surface energy of a polymer can be estimated by means of an additive quantity, the Parachor. Alternatively, it maybe calculated from the molar cohesive density (which is also additive). Rules are given for the estimation of the interfacial tension and the contact angle of a liquid on a solid. 

The measurement of the work needed to increase the surface area of a solid material (e.g., an electrode metal) is more difficult. The work required to form unit area of new surface by stretching under equilibrium conditions is the surface stress (g1 ) which is a tensor because it is generally anisotropic. For an isotropic solid the work, the generalized surface parameter , or specific surface energy (ys) is the sum of two contributions ... 

The surface stress (specific surface energy) can be measured by -> bending beam technique or by electrochemical -> Kosters laser interferometry [vii]. (See also -> surface stress measurements.)... 

The considered experimental tfC) dependences cannot be explained satisfactorily by the Derjaguin-Gutop-Prokhorov theory [405-407]. For instance the weak change in the specific surface energy a of the NP20 foam bilayers (less than 0.5% in the C range studied) cannot account for the steep increase in t with C when reasonable values of A and yi are used. 

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