Adsorption isotherms surface area calculation

Pigna M, Colombo C, Violante A (2003) Competitive sorption of arsenate and phosphate on synthetic hematites (in Italian). Proceedings XXI Congress of Societa Italiana Chimica Agraria SICA (Ancona), pp 70-76 Quirk JP (1955) Significance of surface area calculated from water vapour sorption isotherms by use of the B. E. T. equation. Soil Sci 80 423-430 Rancourt DG, Fortin D, Pichler T, Lamarche G (2001) Mineralogical characterization of a natural As-rich hydrous ferric oxide coprecipitate formed by mining hydrothermal fluids and seawater. Am Mineral 86 834-851 Raven K, Jain A, Loeppert, RH (1998) Arsenite and arsenate adsorption on ferrihydrite kinetics, equilibrium, and adsorption envelopes. Environ Sci Technol 32 344-349... 

BET surface area m2/g ASTM D 3037 DIN 66131 DIN 66132 total specific surface area calculated from the nitrogen adsorption isotherm by using the BET equation... 

Adsorption is often studied using powders or porous materials because the total surface area is large even for small amounts of adsorbent. In a typical experiment the volume (V) or the mass (to = V/p) adsorbed per gram of adsorbent, is measured. Theoretical models always describe an adsorption per surface area. In order to compare theoretical isotherms to experimentally determined adsorption results, the specific surface area needs to be known. The specific surface area (in m2/kg) is the surface area per kg of adsorbent. Once the specific surface area is known, the area can be calculated by A = madT, where mad is the mass of the adsorbent. 

Most commercial instruments using gas adsorption for surface area and porosity determination are based on the BET isotherm. In Eq. (1.45), the monolayer capacity Vm can be used to calculate the surface area on the basis of the area occupied by each adsorbed gas molecule. According to Eq. (1.45), a plot of p/[Va(p0 - p)] versus p/po is linear. From the slope and the intercept, Vm can be obtained. Thus, the specific surface area S can be obtained as... 

The surface areas of the various specimens estimated by applying the Brunauer, Emmett, and Teller equation (4) to the initial adsorption isotherms and using the value of 18 sq. A. (14) are compared with the surface areas calculated from the adsorption of cyclohexane in Table I. The surface areas calculated from the total adsorption of methanol on lepidocrocite as well as its products formed by... 

Similar conditioning treatments for the HT fibers were used prior to IGC and krypton adsorption measurements. Adsorption Isotherms for n-nonane on P-55HT at 70°C are shown In Figure 2. Corresponding BET parameters and the surface areas, calculated using Groszek s molecular area for n-nonane, are given In Table II. 

With respect to the values of the apparent specific surfiice area, we have to note here that modem instmmentation permitting the measurement of nitrogen adsorption isotherms is usually provided with software permitting surface area calculation according to several mathematical models, including the BJH (corresponding to the names of Barrett, Joyner, Halenda) method, Langmuir adsorption isotherms, and the BET theory these methods may provide for the same sample of a porous material, values that may differ by as much as 30%. 

Sorption of inert gases at low temperatures appears to produce more habitual data. Now, the values of the C constants do not significandy differ from those for conventional adsorbents also, they are sufficiendy high to allow a refiable estimation of the surface area (Table 10.1). The calculated monolayer capacities, a, are consistent with the position of the B-points. Also, the surface areas calculated from the adsorption isotherms for inert gases at —196°C prove to be many times greater than those calculated from the isotherms for water or carbon dioxide at room temperatures. 

H. D. Orchiston, Adsorption of water vapor. I Soils at 25 C, Soil Sci. 76 453 (1953). J. P. Quirk, Significance of surface areas calculated from water vapor sorption isotherms by use of the BET equation. Soil Sci. 80 423 (1955). 

The nitrogen adsorption isotherm of the carbon nanofibers (Fig. 2) is of Type II in the BDDT classification, which is normally obtained for carbons, which are predominantly mesoporous. The BET surface area (calculated with the data between 0.05 < p/po < 0.2) equals 91 m g and the BJH mesopore surface area equals 79 m g. The generd view is that a low surface area of the support would limit the metal loading if the purpose is to finely disperse the metal catalyst [22]. As was discussed in the introduetion the highly mesoporous structure of the carbon nanofibers significantly reduces diffusion limitations. 

Surface area calculated from nitrogen adsorption isotherms at 77.3 K using BET equation Pore volume calculated from nitrogen isotherm at P/Po = 0.995 t-Plot micropore volume... 

Surface area calculated from nitrogen adsorption isotherms at 77.3 K using BET equation... 

FIGURE 2.33 DTF IPSDs with respect to (a) the pore volume and (b) the specific surface area calculated on the basis of the water adsorption isotherms for nanooxides. (Adapted from Powder TechnoL, 195, Gun ko, V.M., Zarko, V.L, Turov, V.V. et al.. Morphological and structural features of individual and composite nanooxides with alumina, silica, and titania in powders and aqueous suspensions, 245-258, 2009g, Copyright 2009, with permission from Elsevier.)... 

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. 

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. 

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... 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Surface areas are deterrnined routinely and exactiy from measurements of the amount of physically adsorbed, physisorbed, nitrogen. Physical adsorption is a process akin to condensation the adsorbed molecules interact weakly with the surface and multilayers form. The standard interpretation of nitrogen adsorption data is based on the BET model (45), which accounts for multilayer adsorption. From a measured adsorption isotherm and the known area of an adsorbed N2 molecule, taken to be 0.162 nm, the surface area of the soHd is calculated (see Adsorption). 

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). 

---