Total surface

The total free energy of the system is then made up of the molar free energy times the total number of moles of the liquid plus G, the surface free energy per unit area, times the total surface area. Thus... 

Finally, the total surface enthalpy per square centimeter is... 

The total surface energy generally is larger than the surface free energy. It is frequently the more informative of the two quantities, or at least it is more easily related to molecular models. 

Fig. III-2. Variation of surface tension and total surface energy of CCU with temperature. (Data from Ref. 2.)...

The surface free energy can be regarded as the work of bringing a molecule from the interior of a liquid to the surface, and that this work arises from the fact that, although a molecule experiences no net forces while in the interior of the bulk phase, these forces become unbalanced as it moves toward the surface. As discussed in connection with Eq. Ill-IS and also in the next sections, a knowledge of the potential function for the interaction between molecules allows a calculation of the total surface energy if this can be written as a function of temperature, the surface free energy is also calculable. 

Fig. Vn-2. Conformation for a hypothetical two-dimensional crystal, (a) (lO)-type planes only. For a crystal of 1 cm area, the total surface firee energy is 4 x lx 250 = 1000 eigs. (b) (ll)-type planes only. For a crystal of 1-cm area, the total surface free eneigy is 4 x 1 x 225 = 900 ergs, (c) For the shape given by the Wulff construction, the total surface free energy of a 1-cm crystal is (4 x 0.32 x 250) + (4 x 0.59 x 225) = 851 ergs, (d) Wulff construction considering only (10)- and (ll)-type planes.

The illustrative data presented in Table VII-3 indicate that the total surface energy may amount to a few tenths of a calorie per gram for particles on the order of 1 /xm in size. When the solid interface is destroyed, as by dissolving, the surface energy appears as an extra heat of solution, and with accurate calorimetry it is possible to measure the small difference between the heat of solution of coarse and of finely crystalline material. 

The basic phenomenon involved is that particles of ore are carried upward and held in the froth by virtue of their being attached to an air bubble, as illustrated in the inset to Fig. XIII-4. Consider, for example, the gravity-free situation indicated in Fig. XIII-5 for the case of a spherical particle. The particle may be entirely in phase A or entirely in phase B. Alternatively, it may be located in the interface, in which case both 7sa nnd 7sb contribute to the total surface free energy of the system. Also, however, some liquid-liquid interface has been eliminated. It may be shown (see Problem XIII-12) that if there is a finite contact angle, 0sab> the stable position of the particle is at the interface, as shown in Fig. XIII-5Z>. Actual measured detachment forces are in the range of 5 to 20 dyn [60]. 

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

Although the rate of dissolving measurements do thus give a quantity identified as the total surface area, this area must include that of a film whose thickness is on the order of a few micrometers but basically is rather indeterminate. Areas determined by this procedure thus will not include microscopic roughness (or fractal nature). 

If the total surface area is small (say, a few hundred square centimeters), the amount adsorbed becomes so little that measurements are difficult by normal procedures. Thus the change in pressure-volume product on admitting gas to the adsorbent becomes so small that precision is impaired. 

The saturation coverage during chemisorption on a clean transition-metal surface is controlled by the fonnation of a chemical bond at a specific site [5] and not necessarily by the area of the molecule. In addition, in this case, the heat of chemisorption of the first monolayer is substantially higher than for the second and subsequent layers where adsorption is via weaker van der Waals interactions. Chemisorption is often usefLil for measuring the area of a specific component of a multi-component surface, for example, the area of small metal particles adsorbed onto a high-surface-area support [6], but not for measuring the total area of the sample. Surface areas measured using this method are specific to the molecule that chemisorbs on the surface. Carbon monoxide titration is therefore often used to define the number of sites available on a supported metal catalyst. In order to measure the total surface area, adsorbates must be selected that interact relatively weakly with the substrate so that the area occupied by each adsorbent is dominated by intennolecular interactions and the area occupied by each molecule is approximately defined by van der Waals radii. This... 

Cube. V = a d = a total surface area = 6d, where a is length of side and d is length of diagonal. 

Water is another adsorptive which has often been used, but its complexity of behaviour renders it generally unsuitable for the evaluation of total surface area. Consideration of this important topic is deferred to Chapter 5. 

The incorporation of the new material without any increase in the overall length of the book has been achieved in part by extensive re-writing, with the compression of earlier material, and in part by restricting the scope to the physical adsorption of gases (apart from a section on mercury porosimetry). The topics of chemisorption and adsorption from solution, both of which were dealt with in some detail in the first edition, have been omitted chemisorption processes are obviously dependent on the chemical nature of the surface and therefore cannot be relied upon for the determination of the total surface area and methods based on adsorption from solution have not been developed, as was once hoped, into routine procedures for surface area determination. Likewise omitted, on grounds of... 

Pore size is also related to surface area and thus to adsorbent capacity, particularly for gas-phase adsorption. Because the total surface area of a given mass of adsorbent increases with decreasing pore size, only materials containing micropores and small mesopores (nanometer diameters) have sufficient capacity to be usehil as practical adsorbents for gas-phase appHcations. Micropore diameters are less than 2 nm mesopore diameters are between 2 and 50 nm and macropores diameters are greater than 50 nm, by lUPAC classification (40). 

The average daily incident solar radiation, or insolation, that strikes the earth s surface worldwide is about 220 W/m (1675 Btu/ft ). The annual insolation on 0.01% of the earth s surface is approximately equal to all energy consumed (ca 1992) by humans in one year, ie, 321 x 10 J (305 X 10 Btu). In the United States, the world s largest energy consumer, annual energy consumption is equivalent (1992) to the insolation on about 0.1 to 0.2% of U.S. total surface. 

Specific Surface. The total surface area of 1 g of powder measured ia cm /g is called its specific surface. The specific surface area is an excellent iadicator for the conditions under which a reaction is initiated and also for the rate of the reaction. It correlates in general with the average particle size. The great difference in surface area between 6-p.m reduced iron powder and 7-p.m carbonyl iron powder (Table 3) cannot be explained in terms of particle size, but mainly by the difference between the very inregular-shaped reduced and the spherical carbonyl iron powders. 

Since catalyst activity is dependent on how much catalytically active surface is available, it is usually desirable to maximi2e both the total surface area of the catalyst and the active fraction of the catalytic material. It is often easier to enlarge the total surface area of the catalyst than to increase the active component s surface area. With proper catalyst design, however, it is possible to obtain a much larger total active surface area for a given amount of metal or other active material in a supported catalyst than can be achieved in the absence of a support. 

Hardness is determined by measuring the penetration (depth or area) when a harder material, such as diamond, is pushed into the surface of the material of interest under a specified load. Tme hardness is defined as the force divided by the projected area. Vickers hardness tests, which employ a pyramid-shaped indentor, are frequently used to characterize ceramics however, Vickers hardness calculations normally employ total surface area rather than projected area (43). Measurements are made on the diamond impression shown in Figure 6. Vickers hardness is calculated using... 

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