Surface monolayer capacity

Here, qg and may be roughly interpreted as the micropore (or uniform surface) capacity, and outer surface monolayer capacity, respectively. To avoid using three experimental points to determine q, and C, a fixed value (say 50) is recommended for the BET constant C. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

To obtain the monolayer capacity from the isotherm, it is necessary to interpret the (Type II) isotherm in quantitative terms. A number of theories have been advanced for this purpose from time to time, none with complete success. The best known of them, and perhaps the most useful in relation to surface area determination, is that of Brunauer, Emmett and Teller. Though based on a model which is admittedly over-simplified and open to criticism on a number of grounds, the theory leads to an expression—the BET equation —which, when applied with discrimination, has proved remarkably successful in evaluating the specific surface from a Type II isotherm. 

In practice, the monolayer capacity is of interest, not so much in itself, but as a means of calculating the specific surface with the relation quoted at the beginning of the Chapter, viz... 

When it is desired to evaluate the specific surfaces of a set of closely related samples of solid, however, only one of the samples needs to be calibrated against nitrogen (or argon), provided that all the isotherms of the alternative adsorptive can be shown to have indentical shape. A simple device for testing this identity, by use of the a,-plot, is described in Section 2.13 by means of the a,-plot it is also possible to proceed directly to calculation of the specific surface without having to assign a value to or to evaluate the BET monolayer capacity, of the alternative adsorptive. 

The BET method for calculation of specific surface A involves two steps evaluation of the monolayer capacity n from the isotherm, and conversion of n into A by means of the molecular area a . 

According to the classical Langmuir model, n is actually equal to the monolayer capacity, and can be converted into the specific surface A of the solid by the standard relation A = n a L (cf. Equation (2.1)). A number of lines of argument would suggest, however, that this interpretation is invalid, and that the value of A arrived at does not represent a true specific surface. 

As will be seen shortly, an analogous result is obtained with the silica-water system, where the BET monolayer capacity of water calculated from the water isotherm is roughly equal to the hydroxyl content of the silica surface. 

The relationship between the BET monolayer capacity of physically adsorbed water and the hydroxyl content of the surface of silica has been examined by Naono and his co-workers in a systematic study, following the earlier work by Morimoto. Samples of the starting material—a silica gel—were heated for 4 hours in vacuum at a succession of temperatures ranging from 25 to 1000°C, and the surface concentration of hydroxyl groups of each sample was obtained from the further loss on ignition at 1100°C combined with the BET-nitrogen area. Two complete water isotherms were determined at 20°C on each sample, and to ensure complete... 

In Table 5.3, is compared with the total hydroxyl concentration (Ni, + N ) of the corresponding fully hydroxylated, sample. The results clearly demonstrate that the physical adsorption is determined by the total hydroxyl content of the surface, showing the adsorption to be localized. It is useful to note that the BET monolayer capacity n JH2O) (= N ) of the water calculated from the water isotherm by the BET procedure corresponds to approximately 1 molecule of water per hydroxyl group, and so provides a convenient means of estimating the hydroxyl concentration on the surface. Since the adsorption is localized, n.(H20) does not, of course, denote a close-packed layer of water molecules. Indeed, the area occupied per molecule of water is determined by the structure of the silica, and is uJH2O) 20A ... 

The BET monolayer capacity N, calculated from the first water isotherm included both physisorbed and chemisorbed water, whereas that from the second isotherm iV, included only the physisorbed water. Thus the difference (iV, - N,) gave the amount of chemisorbed water taken up as hydroxyl groups during the isotherm determination. N, + iV ) was therefore the total concentration of hydroxyl groups on the surface when the second water isotherm was being measured. 

The external surface area of the filler can be estimated from a psd by summing the area of all of the equivalent spheres. This method does not take into account the morphology of the surface. It usually yields low results which provide Htde information on the actual area of the filler that induences physical and chemical processes in compounded systems. In practice, surface area is usually determined (5) from the measured quantity of nitrogen gas that adsorbs in a monolayer at the particle surface according to the BET theory. From this monolayer capacity value the specific surface area can be determined (6), which is an area per unit mass, usually expressed in m /g. 

Alternatively, data points can be collected in the decreasing pressure mode . This procedure is usually applied for the quantification of activated adsorption processes (Reuel and Bartholomew, 1984), such as the adsorption of H2. After the pretreatment of the sample (usually after reduction or reaction, and evacuation for a certain period to remove all the adsorbed surface species) the temperature is lowered to the temperature of measurement. First, a known amount of adsorbate gas is added to the reactor. Subsequently, the pressure in the catalyst compartment is lowered stepwise by expansion of the gas into the repeatedly evacuated reference volume. The adsorbed amount of gas can be calculated for each step. From this procedure, the monolayer capacity of the catalyst can be evaluated. 

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... 

Gas adsorption (physisorption) is one of the most frequently used characterization methods for micro- and mesoporous materials. It provides information on the pore volume, the specific surface area, the pore size distribution, and heat of adsorption of a given material. The basic principle of the methods is simple interaction of molecules in a gas phase (adsorptive) with the surface of a sohd phase (adsorbent). Owing to van der Waals (London) forces, a film of adsorbed molecules (adsorbate) forms on the surface of the solid upon incremental increase of the partial pressure of the gas. The amount of gas molecules that are adsorbed by the solid is detected. This allows the analysis of surface and pore properties. Knowing the space occupied by one adsorbed molecule, Ag, and the number of gas molecules in the adsorbed layer next to the surface of the solid, (monolayer capacity of a given mass of adsorbent) allows for the calculation of the specific surface area, As, of the solid by simply multiplying the number of the adsorbed molecules per weight unit of solid with the space required by one gas molecule ... 

The number of gas molecules can be measured either directly with a balance (gravimetric method) or calculated from the pressure difference of the gas in a fixed volume upon adsorption (manometric method). The most frequently apphed method to derive the monolayer capacity is a method developed by Brunauer, Emmett, and Teller (BET) [1], Starting from the Langmuir equation (monolayer adsorption) they developed a multilayer adsorption model that allows the calculation of the specific surface area of a sohd. The BET equation is typically expressed in its linear form as... 

For non-site-specific physical adsorption processes, Cy will correspond to the monolayer capacity of the entire surface, C, which is of the order 10 mol/cm for many species. However, if selective adsorption is involved, Cy can be considerably less than Cm. At process temperatures in the range 300-1,000 K, the term (kTe /h) R"r) would be of the order 10 cmVmol-s. For the case of Cy = Cm = 10" mol/cm, the corresponds to the maximum level permitted by the TST, that is. 

The experimental isotherms were fitted to the BET and Langmuir isotherms, selecting the best fit. The values of the monolayer capacity, the specific surface and the net heats of adsorption were calculated. 

When the electrostatic surface potential becomes high or when the monolayer capacity of the surface is approached. So far the models agree with experiments up to 60-70 mV but the upper limit is probably below 100 mV. 

When the adsorbate is strongly bound to the surface such that desorption does not occur or occurs at a negligibly slow rate, the monolayer capacity... 

In the Langmuir derivation the adsorbed molecules are allowed to interact with the adsorbent but not with each other The adsorbed layer is assumed to be ideal. This necessarily limits adsorption to a monolayer. Once the surface is covered with adsorbed molecules, it has no further influence on the system. The assumption that adsorption is limited to monolayer formation was explicitly made in writing Equations (72) and (73) for the saturation value of the ordinate. Ii is an experimental fact, however, that adsorption frequently proceeds to an extent that exceeds the monolayer capacity of the surface for any plausible molecular orientation at the surface. That is, if monolayer coverage is postulated, the apparent area per molecule is only a small fraction of any likely projected area of the actual molecules. In this case the assumption that adsorption is limited to the monolayer fails to apply. A model based on multilayer adsorption is indicated in this situation. This is easier to handle in the case of gas adsorption, so we defer until Chapter 9 a discussion of multilayer adsorption. 

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