Specific surface, 2.22

The specific sur ce, or surface area to volume ratio, of the particles is an inqtortant parameter in solid-liquid separation technology and can be calculated readily. For a munber distribution of heres, the total surface area is  

From a vohune di ribution of heres, the total surface area is  

Specific surface may be e q ressed on a mass basis using the material density to modify the volume. The diameter of the here having the same equivalent ecific sur ce as the particle is sometimes termed the surface volume mean or the Sauter mean diameter. 

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The physics of X-ray refraction are analogous to the well known refraction of light by optical lenses and prisms, governed by Snell s law. The special feature is the deflection at very small angles of few minutes of arc, as the refractive index of X-rays in matter is nearly one. Due to the density differences at inner surfaces most of the incident X-rays are deflected [1]. As the scattered intensity of refraction is proportional to the specific surface of a sample, a reference standard gives a quantitative measure for analytical determinations. 

Variation of Specific Surface Eneigy with Particle Size"... 

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. 

There are complexities. The wetting of carbon blacks is very dependent on the degree of surface oxidation Healey et al. [19] found that q mm in water varied with the fraction of hydrophilic sites as determined by water adsorption isotherms. In the case of oxides such as Ti02 and Si02, can vary considerably with pretreatment and with the specific surface area [17, 20, 21]. Morimoto and co-workers report a considerable variation in q mm of ZnO with the degree of heat treatment (see Ref. 22). 

The surface excess per square centimeter F is just n/E, where n is the moles adsorbed per gram and E is the specific surface area. By means of the Gibbs equation (111-80), one can write the relationship... 

Fig. X-1. Adsorption isotherms for n-octane, n-propanol, and n-butanol on a powdered quartz of specific surface area 0.033 m /g at 30°C. (From Ref. 23.)...

Estimate the specific surface area of the quartz powder used in Fig. X-1. Assume that a monolayer of C4H9OH is present at P/P = 0.2 and that the molecule is effectively spherical in shape. 

One hundred milliliters of an aqueous solution of methylene blue contains 3.0 mg dye per liter and has an optical density (or molar absorbancy) of 0.60 at a certain wavelength. After the solution is equilibrated with 25 mg of a charcoal the supernatant has an optical density of 0.20. Estimate the specific surface area of the charcoal assuming that the molecular area of methylene blue is 197 A. ... 

Explain the behavior of this system, and calculate the specific surface area of the steel. 

Dye adsorption from solution may be used to estimate the surface area of a powdered solid. Suppose that if 3.0 g of a bone charcoal is equilibrated with 100 ml of initially 10 Af methylene blue, the final dye concentration is 0.3 x 10 Af, while if 6.0 g of bone charcoal had been used, the final concentration would have been 0.1 x Qr M. Assuming that the dye adsorption obeys the Langmuir equation, calculate the specific surface area of the bone charcoal in square meters per gram. Assume that the molecular area of methylene blue is 197 A. ... 

For adsorption on Spheron 6 from benzene-cyclohexane solutions, the plot of N N2/noAN2 versus N2 (cyclohexane being component 2) has a slope of 2.3 and an intercept of 0.4. (a) Calculate K. (b) Taking the area per molecule to be 40 A, calculate the specific surface area of the spheron 6. (c) Plot the isotherm of composition change. Note Assume that is in millimoles per gram. 

While a thermodynamic treatment can be developed entirely in terms of f(P,T), to apply adsorption models, it is highly desirable to know on a per square centimeter basis rather than a per gram basis or, alternatively, to know B, the fraction of surface covered. In both the physical chemistry and the applied chemistry of the solid-gas interface, the specific surface area is thus of extreme importance. 

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

Harkins and Jura [21] found that a sample of Ti02 having a thick adsorbed layer of water on it gave a heat of inunersion in water of 0.600 cal/g. Calculate the specific surface area of the Ti02 in square centimeters per gram. 

Make a numerical estimate, with an explanation of the assumptions involved, of the specific surface area that would be found by (a) a rate of dissolving study, (b) Harkins and Jura, who find that at the adsorption of water vapor is 6.5 cm STP/g (and then proceed with a heat of immersion measurement), and (c) a measurement of the permeability to liquid flow through a compacted plug of the powder. 

According to Eq. XVI-2 the specific surface area of an adsorbate should vary... 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

Plot the data according to the BET equation and calculate Vm and c, and the specific surface area in square meters per gram. 

Construct a v versus t plot for the data of Problem 11 (assume that Table XVII-4 can be used) and calculate the specific surface area of the rutile. 

Figure Bl.22.1. Reflection-absorption IR spectra (RAIRS) from palladium flat surfaces in the presence of a 1 X 10 Torr 1 1 NO CO mixture at 200 K. Data are shown here for tluee different surfaces, namely, for Pd (100) (bottom) and Pd(l 11) (middle) single crystals and for palladium particles (about 500 A m diameter) deposited on a 100 A diick Si02 film grown on top of a Mo(l 10) single crystal. These experiments illustrate how RAIRS titration experiments can be used for the identification of specific surface sites in supported catalysts. On Pd(lOO) CO and NO each adsorbs on twofold sites, as indicated by their stretching bands at about 1970 and 1670 cm, respectively. On Pd(l 11), on the other hand, the main IR peaks are seen around 1745 for NO (on-top adsorption) and about 1915 for CO (tlueefold coordination). Using those two spectra as references, the data from the supported Pd system can be analysed to obtain estimates of the relative fractions of (100) and (111) planes exposed in the metal particles [26].

The surface area of a given mass of solid is inversely related to the size of the constituent particles. Thus, for the idealized case where these are equi-sized cubes of edge length /, the specific surface area A, being the surface area of I gram of solid, is given by (cf. p. 26)... 

In discussions of the surface properties of solids having a large specific surface, it is convenient to distinguish between the external and the internal surface. The walls of pores such as those denoted by heavy lines in Fig. 1.8 and 1.11 clearly comprise an internal surface and equally obviously the surface indicated by lightly drawn lines is external in nature. In many cases, however, the distinction is not so clear, for the surfaces of the primary particles themselves suffer from imperfections in the forms of cracks and fissures those that penetrate deeply into the interior will contribute to the internal surface, whereas the superficial cracks and indentations will make up part of the external surface. The line of demarcation between the two kinds of surface necessarily has to be drawn in an arbitrary way, but the external surface may perhaps be taken to include all the prominences and all of those cracks which are wider than they are deep.,The internal surface will... 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

This section is devoted to the relationship between the specific surface of particulate solids and some parameter or parameters which characterize the particle size. Attention will be restricted to particles of simple shapes, but non-uniformity of particle size will be considered. 

Let us take first the ideal case in which a centimetre cube of material is fragmented into equal-sized cubes of edge length 1. Then the area of each will be 6P and their number will be 1//. The total area is thus (1/P)6P, or 6/1 and if the density of the solid is p, then the specific surface A must be... 

We will now consider the dependence of specific surface on particle size for systems composed of particles of simple shape, and exhibiting a distribution of particle sizes. The shapes chosen will, in the first instance, be cubes and spheres, rods, and plates, and will be dealt with in turn. 

From the arguments of the present section it is clear that an inverse relationship holds between the specific surface and the particle size, and if the particles are long or thin it is the minimum dimension, the thickness of the plates or of the rods, which mainly determines the magnitude of the specific surface. 

So far in this section, the specific surface has been taken as the dependent variable and the particle size as the independent variable. In practice one is often more concerned with the converse case where the specific surface of a disperse solid has been determined directly (by methods which will be explained in the subsequent chapters) and one wishes to calculate a particle size from it. 

In all other cases the quantity / calculated from the specific surface is a mean diameter. Unless there is some definite and detailed evidence as to particle shape, the simplest such diameter to aim at is the mean diameter obtained by substituting the measured value of A in Equation (1.79)... 

The numerical values of and a, for a particular sample, which will depend on the kind of linear dimension chosen, cannot be calculated a priori except in the very simplest of cases. In practice one nearly always has to be satisfied with an approximate estimate of their values. For this purpose X is best taken as the mean projected diameter d, i.e. the diameter of a circle having the same area as the projected image of the particle, when viewed in a direction normal to the plane of greatest stability is determined microscopically, and it includes no contributions from the thickness of the particle, i.e. from the dimension normal to the plane of greatest stability. For perfect cubes and spheres, the value of the ratio x,/a ( = K, say) is of course equal to 6. For sand. Fair and Hatch found, with rounded particles 6T, with worn particles 6-4, and with sharp particles 7-7. For crushed quartz, Cartwright reports values of K ranging from 14 to 18, but since the specific surface was determined by nitrogen adsorption (p. 61) some internal surface was probably included. f... 

A Type II isotherm indicates that the solid is non-porous, whilst the Type IV isotherm is characteristic of a mesoporous solid. From both types of isotherm it is possible, provided certain complications are absent, to calculate the specific surface of the solid, as is explained in Chapter 2. Indeed, the method most widely used at the present time for the determination of the surface area of finely divided solids is based on the adsorption of nitrogen at its boiling point. From the Type IV isotherm the pore size distribution may also be evaluated, using procedures outlined in Chapter 3. 

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