Determining the Specific Surface Area

BET method. The most commonly used method for determining the specific surface area is the so-called BET method, which obtained its name from three Nobel prize winners Brunauer, Emmett and Teller (1938). It is a modification of the Langmuir theory, which, besides monolayer adsorption, also considers multilayer adsorption. The equation allows easy calculation of the surface area, commonly referred to as the BET surface area ( bet). From the isotherms also pore-radii and pore-volumes can be calculated (from classical equation for condensation in the pores). 

Two types of instruments are employed to determine the specific surface area by permea-metry. Those of the first type are called constant pressure systems, and the Fisher subsieve sizer is a typical example that belongs to such systems. Instruments of the second type are known as constant volume permeameters, and the apparatus devised by Blain is an example. 

A commonly used method of determining the specific surface area of a solid is by the adsorption of a gas onto the solid and the determination of the monolayer capacity. Most methods make use of the Brunauer, Emmett, and Teller equation, commonly referred to as the BET equation, for calculating the surface area on the basis of monolayer adsorption. The BET equation can be written as... 

Equation 6.2.9 may then be used in determining the specific surface area of an adsorbent. Alternative arrangements of equation 6.2.25 are possible, but they have the inherent disadvantage of placing undue emphasis on the low-pressure data points that are most susceptible to error. 

Because Fe oxides are intimately associated with other soil components, it is not easy to determine the specific surface area of soil Fe oxides. An approximation can be obtained by attributing the surface area difference from before and after selective re-... 

The most well-known method for determining the specific surface area of powders is based on a theory of multimolecular adsorption of gases developed by Brunauer, Emmett, and Teller (BET) (1). The BET method involves the determination of the quantity of a gas which, when adsorbed on the surface of the solid, would completely cover the solid with a monolayer of the gas. 

Porous materials are often analyzed with a mercury porosimeter. With a mercury porosi-meter we can measure the pore distribution of a solid. Thus, we can determine the specific surface area. Mercury is used because of its high surface tension (0.48 N/m) it does not wet... 

From the data given in Table PI.2, determine the specific surface area of 11.32 mg of CaO powder. The data are based on adsorption of nitrogen at — 195.8°C, with S =... 

The most widespread method in determining the specific surface area of solid substrates is without doubt the Brunauer-Emmet-Teller (BET) method.3 It is based on a kinetic model of the adsorption process by Langmuir,7 in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium... 

In a series of experiments (8), we determined the specific surface areas of 14 tohermorite preparations, made from different starting materials (Ca3Si05 and / -Ca2Si04), with different water to solid ratios (0.7 and 9.0), and using different methods of preparation. The BET method was used, with water vapor as the adsorbate. We use nitrogen, too, but it did not measure the total surface, as I will show. The largest specific surface we measured was 376 sq. meters per gram, the smallest was 245, and all the others fell between these limits. We concluded, therefore, that in one preparation practically all of the tohermorite sheets were two unit cells thick, in another practically all of them were three unit cells thick, and in all the rest the particles were either two or three unit cells thick. 

The structure of these pyrogenic silicas has been discussed by Barby [5], particularly with reference to their specific surface area. It was concluded that the initially condensed particles are only about 1 rnn in diameter and that these are so closely packed (high coordination number) to secondary particles of 10 to 30 nm that only a small amount of nitrogen can penetrate the micropores between them. Thus the secondary particles are the ones that are commonly identified in electron micrographs and which determine the specific surface area. They are the primary particles in the voluminous aggregate structure and have a low coordination number of about 3 (see Fig. 8.3). Because of the low level of impurities this type of silica is often used as catalyst support in fundamental studies. 

Porosity is divided by IUPAC (Rouquerol et al. 1994), based on pore size, into the following groups macropores (>50 nm), mesopores (2-50 nm), and micropores (<2 nm). Microporosity may then be subdivided into three subsequent categories supermicropores (1.4-2.0 nm), micropores (0.5-1.4 nm), and ultramicropores (<0.5 nm). Both mineral and organic soil components have pores with different diameter. The holes and channels in the polymer chain of humic substances as well as the interlayer space of the layered mineral have an important role in determining the specific surface area. The size of the interlayer space of layered minerals in a dry state is a few tenths of nanometers, so they are considered as micropores. 

The specific surface areas, 5bet, as estimated from the BET theory for the pure materials and for each mixture are given in Table 1. This method consists in determining the specific surface area from the monomolecular layer volume of the adsorbed nitrogen. It is clearly seen on Figure 2a that the specific surface area, 5 bet, is a linear function of the mixing proportions. As discussed in the introduction this observation suggests that the BET surface is a reliable parameter. 

The BET model is used to determine the specific surface area of solids with the properties mentioned above. Thus, solids for which specific surface areas can be determined using this model are limited to meso- and macroporous solids. In the case of microporous solids, the adsorption phenomenon cannot be described using the above hypotheses. However, in the absence of a universally accepted model, the BET equation is usually used to calculate the specific surface of a microporous solid. 

The first domain is used to determine the specific surface area (5 bet(H20)) and the BET constant values. Moreover, the large number of available experimental points allows the calculation of the corresponding adsorption energy distribution function of water on silica. 

The size of the colloidal non-porous particles determines the specific surface area of an adsorbent (Eq. 3.12) and the porosity of particles is controlled by the average contact number of non-porous primary particles. 

Details of several different methods for determining the specific surface area of carbon black are described in ASTM D 3037. The different types of equipment used and procedures are included in separate sections. Another standard gives full details of procedure of conventional Brunauer, Emmett, and Teller (BET) method based on multilayer gas adsorption. The results of determination are in both cases given in the surface area in square meters per gram of substance. 

The methods of column packing preparation well known in gas chromatography practice [24] give the possibility to coat the silica gel surface with the monolayer of a given surface concentration or with the monolayer in SC state with a well-defined threedimensional excess if the specific surface area of adsorbent is known. On the other hand, inverse gas chromatography allows to determine the specific surface area of silica gel if aliphatic alcohol is used as a liquid stationary phase [25]. 

Surface phase capacity, i.e., the total amount of substances in the adsorbed phase is the second factor determining the sorption properties of the solid sorbents. This quantity is useful for calculating thermodynamic functions which characterize competitive adsorption at the liquid - solid interface and for determining the specific surface area of the sorbents. 

The most relevant characteristic of porous materials is the disposal of a high effective surface/volume relationship, usually expressed in terms of their specific surface area (area per mass unit), which can be determined from nitrogen adsorption/desorption data. Different methods are available for determining the specific surface area (Brunauer-Emmett-Teller, Langmuir, and Kaganer), micropore volume (f-plot, ttj, and Dubinin-Astakhov), and mesopore diameter (Barrett-Joyner-Halenda Leroux et al., 2006). Table 1.1 summarizes the values of specific surface area for selected porous materials. 

To elucidate how the particle size obtained from equation (3.6.63) agrees with the actual particle sizes we determined the specific surface area of CaO, PbO, ZnO and CdO powders by the BET method and estimated the values of their molar surface areas (in m2 mol-1) as 594 (CaO), 705 (PbO), 560 (ZnO) and 193 (CdO). On the basis of the obtained values we estimated the effective radii of the oxide particles (/tm) according to formula (3.6.63) as 0.28 (CaO), 0.33 (PbO), 0.26 (ZnO) and 0.82 (CdO). Taking into account the fact that, as a rule, the average radius of oxide particles obtained commercially is of the order of 1 /rm, it should be concluded that the investigated powders possess a developed surface and, in this case, the use of equation (3.6.59) seems to be more appropriate. 

Commercial colloidal silicas are commonly available in the form of sols or powders. The powders can be xerogels, dry precipitates, aerogels, aerosils, or dried and calcined coacervates. The ultimate unit for all of them is a silica particle, the size of which determines the specific surface area of the product. 

BET adsorption and desorption is usually performed with liquid N2 and is a widespread technique for determining the specific surface area of porous materials [28]. In fact, only surfaces that are accessible to the N2 molecules are detected. The Kelvin equation correlates the curvature of the liquid surface with the applied partial pressure and pore size distributions can be derived [29]. However, this method is successful only for pore structures below about 20 nm. Thus, in aerogels with typical pore sizes in the 1—100 nm range, only a fraction of the total available pore space is detected. For an aerogel with a den-... 

The ionized surface of the particles is possibly associated with the sodium ions as ion pairs. The amount of alkali thus determines the specific surface area and thus limits the particle diameter vdiich varies inversely with Si02 Na20 ratio. 

A plot of P/Va (Po - P) versus P/Po gives a straight line from which V , and C can be determined. The specific surface area, S, of the powder can then be calculated using... 

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