The Brunauer-Emmett-Teller Isotherm

It is sometimes seen that as p - the saturation pressure, the adsorbed amount 

In Equations 2.41 and 2.42, the left-hand sides denote the rates of adsorption, which are proportional to the pressure and the unoccupied surface. The right-hand sides denote the rates of desorption, which are proportional to the occupied surface. The rate constants are a for adsorption and [b exp(- QIRT) and b exp(-QJRT)] for desorption in the two cases (n = 1 and n 1). 0 is the fractional area covered by the -stack layer. The volume adsorbed per unit area is proportional 

Experimentally v is measnred in volnmes at standard temperature and pressure (STP). If the adsorption is oidy a saturated monolayer, then 0, = 1 and all other 0, are zero. In that case, one has v = v allowing one to interpret v , as the volume 

FIGURE 2.14 (a) Henry s law, (b) the Langmuir adsorption isotherm, and (c) the BET isotherm plotted with parameters such that (b) and (c) reduce to (a) at low p p°. 

Adsorption of a component from a hquid follows similar behavior. In fact, similar adsorption equations are used. An important case is where a component is adsorbed from the bulk hquid onto a sohd surface. The previous equations are altered by replacing the pressure p with c, the concentration of the adsorbed species in the bulk phase. 

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EXAMPLE 9.5 Calculating the Adsorption Energy from the Brunauer-Emmett-Teller Isotherm. The BET analysis uses p/p0 rather than p as a variable just as we used this pressure ratio to compare Langmuir adsorption at different temperatures in Example 9.3. What corrections, if any, are needed in the apparent adsorption energy of about 14 kJ mole-1 as calculated in Example 9.3 ... 

We now cite the types of experimental data in the literature, by which an analysis of surface adsorption effects is carried out. One common experiment involves measuring adsorption isotherms. By weighing or by volumetric techniques one determines as a function of equilibrium gas pressure the amount of gas held on a given surface at a specified temperature. Usually this quantity varies sigmoidally with rising pressure P, as sketched in Fig. 5.2.1 for a variety of temperatures 7). By standard methods that rely on the Brunauer, Emmett, Teller isotherm equa-tion one can determine the point on the isotherms at which monolayer coverage of the surface is complete it is usually is located fairly close to the knee of the isotherm. From the cross sectional area of the adsorbate molecules and from the amount needed for monolayer coverage one may then ascertain more or less quantitatively the surface area of the adsorbent. As-... 

Specific surface area (SSA), total pore volume and average pore diameter were measured by N2 adsorption-desorption isotherms at 77K using Micromeritics ASAP 2020. The pore size was calculated on the adsorption branch of the isotherms using Barrett-Joyner-Helenda (BJH) method and the SSA was calculated using the Brunauer-Emmett-Teller (BET) method. 

Nitrogen adsorption was performed at -196 °C in a Micromeritics ASAP 2010 volumetric instrument. The samples were outgassed at 80 °C prior to the adsorption measurement until a 3.10 3 Torr static vacuum was reached. The surface area was calculated by the Brunauer-Emmett-Teller (BET) method. Micropore volume and external surface area were evaluated by the alpha-S method using a standard isotherm measured on Aerosil 200 fumed silica [8]. Powder X-ray diffraction (XRD) patterns of samples dried at 80 °C were collected at room temperature on a Broker AXS D-8 diffractometer with Cu Ka radiation. Thermogravimetric analysis was carried out in air flow with heating rate 10 °C min"1 up to 900 °C in a Netzsch TG 209 C thermal balance. SEM micrographs were recorded on a Hitachi S4500 microscope. 

Many models have been developed that deal with the sorption properties of wood in the presence of moisture these have been discussed in a number of works (e.g. Skaar, 1972 Siau, 1984). They can be approximately divided into sorption models, such as the Brunauer-Emmett-Teller (BET) model, or solution models (such as the Hailwood-Horrobin, H-H, model). The sigmoidal shapes of sorption or desorption isotherms can be deconvoluted into two components. These are often taken to represent a monomolecular water layer (associated with the primary sorption sites, OH groups), and a multilayer component where the cell wall bound water molecules are less intimately associated with the fixed cell wall OH groups. 

The Brunauer-Emmett-Teller (or BET) adsorption isotherm applies only to the physisorption of vapours but it is important to heterogeneous catalysis because of its use for the determination of the surface areas of solids. The isotherm is given by the following equation,... 

The most common method used for the determination of surface area and pore size distribution is physical gas adsorption (also see 1.4.1). Nitrogen, krypton, and argon are some of the typically used adsorptives. The amount of gas adsorbed is generally determined by a volumetric technique. A gravimetric technique may be used if changes in the mass of the adsorbent itself need to be measured at the same time. The nature of the adsorption process and the shape of the equilibrium adsorption isotherm depend on the nature of the solid and its internal structure. The Brunauer-Emmett-Teller (BET) method is generally used for the analysis of the surface area based on monolayer coverage, and the Kelvin equation is used for calculation of pore size distribution. 

Surface areas are determined by physisorption. The most common procedure to determine surface area is to measure how much N2 is adsorbed onto a certain amount of material. The uptake is measured at a constant low temperature (i.e., 80 K) as a function of N2 pressure, and is usually very well described by the Brunauer-Emmett-Teller (BET) isotherm. After determining the number of N2... 

The Brunauer-Emmett-Teller (BET) nitrogen adsorption isotherms for EG and DG are shown in Fig. 5. Both the samples exhibit Type I + Type II behavior and their surface areas are 925 and 520 m2 g 1 respectively. The pore size distributions of the samples are shown as insets in Fig. 5, and reveal that EG is... 

Equilibrium sorption of water (solubility) is described by the different isotherms of the Brunauer-Emmett-Teller classification. 

The area is an important surface parameter for catalytic studies. It is needed to evaluate the rate constant of the surface reaction from the kinetics as well as to allow a fair comparison to be made of the effectiveness of different catalysts. Areas are commonly determined by nitrogen or krypton gas adsorption interpreted by the Brunauer-Emmett Teller (BET) isotherm [30, 32], A number of other methods has been proposed and utilised including microscopy, isotopic exchange, chromatography, gas permeability, adsorption from solution, and negative adsorption (desorption) of co-ions [30, 33]. 

In principle, isotherms at low partial pressures of the sorbate may be used to determine specific surface areas by the Brunauer-Emmett-Teller (BET) method (G64). In this method, it is assumed that molecules of the sorbate are adsorbed on surfaces that can include the walls of pores, provided that the distance between molecules on opposing walls is large compared with molecular dimensions. From a plot derived from the isotherm, and given the effective cross-sectional area of the sorbate molecule, the specific surface area of the sorbent and the net heat of adsorption are obtained. Using water as sorbate, specific surface areas of about 200 m per g of D-dried paste have typically been obtained for mature cement pastes of normal w/c ratios... 

In the analysis of isotherm data in the literature the so-called BET (Brunauer. Emmett. Teller) isotherm equation is frequently used ... 

Evidence for a specific inclusion process promoted by molecular imprinting is directly given through sensor effects in comparison to non-imprinted layers of equivalent height. Detailed interpretation of specific inclusion or non-specific adsorption phenomena is accessible with the Brunauer-Emmett-Teller (BET) isotherm adsorption analysis [18] a typical BET-isotherm is shown in Fig. 21.2. 

Multilayer adsorption isotherms are usually analyzed in terms of the Brunauer, Emmett, Teller equation C/Cm = cx/(l —x)(l —x-f cx), wherex s P/Pq. where Pq is the saturation vapor pressure of the liquid c is a parameter, and the other symbols have been defined earlier. Find the equation for the spreading pressure for X < 1. Sketch plots of C/Cm and of fvs. x. 

The characteristic inflection in Type II behavior occurs when multilayer sorption starts. The Brunauer, Emmett, Teller (BET) equation, shown as Eq. (4), can describe isotherms where multilayer sorption is evident ... 

The sigmoidal shape of the nitrogen isotherm of Figure 1 is quite amenable to analyses by the Brunauer-Emmett-Teller (BET) multilayer theory (8). The BET surface area calculated is 2.8 mVg. This value is quite consistent with the predominant l-to-10- xm size distribution observed on this sample with an optical microscope. Assuming cubic habits and density of about 2.3 g/cm, we find the range of specific surface area to be 0.26 to 2.6 m /g. Apparently the sorbed N2 does penetrate into the internal portion of the particles only to a limited extent. 

Gas adsorption is a suitable method for a fractal analysis because it is sensitive to the fine structure of the pores and has negligible adverse affects on the pore system. The results are usually analyzed by using fractal generalizations of the Brunauer-Emmett-Teller (BET) isotherm (30) or of the Frenkel-nalsey-TfiU (FHH) isotherm (31). The latter may also be seen as a fractal generalization of the Kelvin equation and is therefore also applicable in the capillary condensation regime (32). It has been claimed that the fractal BET theory is more appropriate for mass fractals (see sect. Fractals ), whereas surface fractals are to be analyzed using the fractal FHH theory (33). These methods have been applied to cellulose powders (34) and tablets (35). 

Sorption isotherms of model systems were determined gravimetrically and data were modeled using the Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-deBoer (GAB) models. 

The Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-deBoer (GAB) sorption isotherm models were used to obtain experimental steady-state moisture contents in dry basis by linear regression analysis according to Kouassi and Roos (2002). These equations provide the value of monolayer water content, which is an important parameter in food deterioration studies. 

The point-R method of estimating surface areas was frequently used prior to the development of the Brunauer-Emmett-Teller approach. It entailed choosing from an absorption diagram such as Fig. 8-3 the point at which the central linear section begins. This procedure worked well for some systems, but it was extremely difficult, if not impossible, to select a reliable point B on an isotherm such as that shown for n-butane in Fig. 8-3. In contrast, the Brunauer-Emmett-Teller method was found to be reasonably satisfactory for this type of isotherm. 

The nitrogen adsorption-desorption isotherms for specific surface area and porosity assessment were recorded at -196 C in a Gemini instrument from Micromeritics. The specific surface areas were determined by the Brunauer-Emmett-Teller (BET) method. The pore size distributions were obtained from the desorption branch, and the micropore volume was determined by the t-plot method, using literature software [14]. 

The adsorption isotherms provide information about the surface properties of the fibres or paper in the column. For example, the surface area in the column may be deduced from the shape of the isotherm according to the Brunauer-Emmett-Teller theory for multilayer adsorption (13, lJO. This theory gives the number of molecules, Nm, which forms a layer one molecule thick on the surface of the adsorbent. If the area, am, occupied by each vapour molecule adsorbed on the surface is known, then the total surface area, A, is simply given by... 

The Brunauer-Emmett-Teller (B.E.T.) and B.D.D.T. isotherms [d and e in Table 14.3] account for pore filling via multiple layers instead of just a monolayer, and they use C/Q, that tends toward unity as the pores are completely filled. The B.D.D.T. isotherm includes the number of layers explicitly (m), as well as a heat of adsorption term (q). The B.E.T. isotherm is mostly used to estimate surface areas, not for process calculations [see Equation (14.10)]. 

Multilayer adsorption and other complications are accounted for in the more elaborate Brunauer-Emmett-Teller isotherm (BET isotherm) [28], which involves the heats of adsorption of the first and subsequent layers and with which not only Type I behavior can be approximated. In its simplest form, for an unlimited number of adsorption layers and partial pressures well below saturation, the BET equation can be written... 

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