The BET adsorption isotherm

In Langmuir model, the maximal adsorption is that of a monolayer. Langmuir adsorption isotherms all saturate at high vapor pressures. This is unrealistic for many cases. In order to consider the adsorption of multilayers, Brunauer, Emmett, and Teller extended the Langmuir theory and derived the so-called BET adsorption isotherm [378], The basic idea in the BET theory was to assume a Langmuir adsorption for each of the layers (Fig. 9.8). 

It is assumed that the adsorption heat for the first layer Q has a particular value. For all further layers, the heat of adsorption Qi corresponds to the heat of condensation of the liquid. Another condition is that desorption and adsorption take place only directly between vapor and surface. Adsorbed molecules are not allowed to move from one layer directly to another. In equilibrium, the desorption rate for each layer must be equal to the adsorption rate. We 

n is the total number of moles adsorbed per unit area, nmon is the number of adsorbed moles in one full monolayer per unit area (each binding site is occupied exactly once), Po is the equilibrium vapor pressure, and 

Equation (9.37) shows that, n/nmon becomes infinite for P/Pq — 1. This is what we expect because condensation sets in. For the second part of Eq. (9.38) see exercises. 

Since the BET adsorption isotherm is so widely used, we describe a simple derivation [1], It is convenient to define two parameters, a and / , according to 

---

Specific surface areas are then obtained by dividing by the weight of catalyst employed in the experiments in question. It should be pointed out, however, that it is the BET adsorption isotherm that is the basis for conventional determinations of catalyst surface areas. (See Section 6.2.2.)... 

The surface area increase during refining is also easily demonstrated experimentally. The BET adsorption isotherm, for example, shows that there is an approximately 250% increase in specific... 

Equation 11.60 is the final expression for the BET adsorption isotherm commonly seen in the literature. It gives the total amount of gas phase A that can be absorbed onto a certain surface area of solid material. 

It is easy to see that the BET adsorption isotherm has the correct limits at very high [A] and when multilayer adsorption is negligible. First, consider the case where the pressure of A approaches the value for saturated vapor pressure of A in equilibrium with the liquid. Let the corresponding concentration be designated [A]sa/. The vapor/liquid equilibrium process is written... 

Now consider the form of the BET adsorption isotherm written in Eq. 11.59. If multilayer adsorption were not possible, then Km would be zero. The adsorbed site fraction from Eq. 11.59 becomes... 

Type E is common for the adsorption of gases. Usually the first concave part is attributed to the adsorption of a monolayer. For higher pressures more layers adsorb on top of the first one. Eventually, if the pressure reaches the saturation vapor pressure, condensation leads to macroscopically thick layers. It can be described by the BET adsorption isotherm equation Eq. (9.37) (see below). 

Usually specific surface areas are determined from adsorption experiments. To illustrate this let us assume that adsorption of a specific sample is adequately described by the Langmuir Eq. (9.22). From fitting experimental results we obtain Tmon in units of mol/g. Then we assume a reasonable value for the cross-section area of a gas molecule a a, and obtain the specific surface from J2 = rmon ANA- In most practical applications the BET adsorption isotherm is used instead of the Langmuir Eq. (9.22) because it fits better. From a fit with the BET isotherm we get Tmon or nmon. Some cross-sectional areas for suitable gases in A2 are N2 16.2 02 14.1 Ar 13.8 n-C4Hi0 18.1. 

Suppose that a solid surface is placed in a bulk vapor phase having a pressure Pb and molecular density below the saturation values at the existing temperature. Attraction between the solid and molecules of the vapor favors buildup of an adsorbed film. However, the additional energy associated with the density gradient between the film and bulk vapor phase opposes film formation, an effect not considered in developing the BET adsorption isotherm of the preceding section. 

The BET adsorption isotherm was originated for a definite model of adsorption layer [120], and next it was extended to the finite, n-number of layers [132,133]. 

Figure 7.12. The BET-adsorption isotherm (BET AI), Eq. (7.70) showing for C>2 an inflection point and at the sorptive gas saturation pressure p = Ps(T) a singularity n — 00 indicating pore condensation and the appearance of a bulk liquid phase [7.1-7.5],...

The development of microporosity during steam activation was examined by Burchell et al [23] in their studies of CFCMS monoliths. A series of CFCMS cylinders, 2.5 cm in diameter and 7.5 cm in length, were machined from a 5- cm thick plate of CFCMS manufactured from P200 fibers. The axis of the cylinders was machined perpendicular to the molding direction ( to the fibers). The cylinders were activated to bum-offs ranging from 9 to 36 % and the BET surface area and micropore size and volume determined from the Nj adsorption isotherms measured at 77 K. Samples were taken from the top and bottom of each cylinder for pore sfructure characterization. 

Catalyst characterization - Characterization of mixed metal oxides was performed by atomic emission spectroscopy with inductively coupled plasma atomisation (ICP-AES) on a CE Instraments Sorptomatic 1990. NH3-TPD was nsed for the characterization of acid site distribntion. SZ (0.3 g) was heated up to 600°C using He (30 ml min ) to remove adsorbed components. Then, the sample was cooled at room temperatnre and satnrated for 2 h with 100 ml min of 8200 ppm NH3 in He as carrier gas. Snbseqnently, the system was flashed with He at a flowrate of 30 ml min for 2 h. The temperatnre was ramped np to 600°C at a rate of 10°C min. A TCD was used to measure the NH3 desorption profile. Textural properties were established from the N2 adsorption isotherm. Snrface area was calcnlated nsing the BET equation and the pore size was calcnlated nsing the BJH method. The resnlts given in Table 33.4 are in good agreement with varions literature data. 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

The support and the catalysts were characterised by means of nitrogen adsorption, XPS, TPD and SEM. The nitrogen adsorption isotherms were determined at 77 K in a Coulter Omnisorp 1000 CX equipment, and were analysed by the BET equation (SBet), and by the t-plot for mesopore surface area (Smeso) and micropore and mesopore volume (Vmicr0, Vmeso), using the standard isotherm for carbon materials. The catalyst samples were previously outgassed at 120 °C. 

Calculate C and the specific surface area As of a material from the nitrogen adsorption isotherm according to the BET equation from the data points given in the figure. Use the ideal gas equation to convert the adsorbed volumes into moles (STP indicates that the volumes adsorbed are given for standard temperature and pressure, i.e., 273 K and 101.3 kPa). 

In addition to these characterizations of adsorption curves, mathematical descriptions of adsorption isotherms, based on physical models, often are used to study solid interactions with contaminants. The main adsorption isotherms include those of Langmuir, Freundhch, and Brunauer-Emmet-TeUer (BET) they are depicted in Fig. 5.2. 

Fig. 5 (a) shows the nitrogen adsorption isotherms of aluminum hydroxy pillared clays after heat-treatment at 300-500°C. These are of the typical Langmuir type isotherm for microporous crystals. Fig, 5 (b) shows the water adsorption isotherms on the same Al-hydroxy pillared clays [27]. Unlike the water adsorption isotherms for hydrophilic zeolites, such as zeolites X and A, apparently these isotherms cannot be explained by Langmuir nor BET adsorption equations the water adsorption in the early stages is greatly suppressed, and shows hydrophobicity. Water adsorption isotherms for several microporous crystals [20] are compared with that of the alumina pillared clay in Fig. 6. Zeolites NaX and 4A have very steep Langmuir type adsorption isotherms, while new microporous crystals such as silicalite and AlPO -S having no cations in the...

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

Until now, we have focused our attention on those adsorption isotherms that show a saturation limit, an effect usually associated with monolayer coverage. We have seen two ways of arriving at equations that describe such adsorption from the two-dimensional equation of state via the Gibbs equation or from the partition function via statistical thermodynamics. Before we turn our attention to multilayer adsorption, we introduce a third method for the derivation of isotherms, a kinetic approach, since this is the approach adopted in the derivation of the multilayer, BET adsorption isotherm discussed in Section 9.5. We introduce this approach using the Langmuir isotherm as this would be useful in appreciating the common features of (and the differences between) the Langmuir and BET isotherms. 

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... 

The Mg-Al-C03-LDH used as adsorbent and sorbent was prepared with an Mg Al ratio of 2 1 by the coprecipitation method at variable pH [6], The material obtained was characterised by powder X-ray diffraction (PXRD, using a Siemens D-5005 X-ray diffractometer), and elemental and thermal analyses. The material showed the characteristic lamellar structure with a basal spacing of 7.6 A, specific surface area of 87.1 m2 g 1, determined by the N2-BET adsorption isotherm, and an approximate minimum molecular formula [Mg, MAt, (oh) m ](CO, ) 5 2.3 i(h2o) The size distribution and the average size of the LDH particles were determined by light scattering, using a Zetasizer 4 from Malvern. 

The BET specific surface area [28] was calculated in the relative pressure range between 0.04 and 0.2. The total pore volume was determined from the amount adsorbed at a relative pressure of 0.99 [28], The primary mesopore volume and external surface area were evaluated using the as-plot method [24, 28, 29] with the reference adsorption isotherm for macroporous silica [29], The pore size distributions were determined using the Kruk-Jaroniec-Sayari (KJS) equation [30] and the calculation procedure proposed by Barrett, Joyner and Halenda (BJH) [31]. 

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,... 

Figure 9.9 Left BET adsorption isotherms plotted as total number of moles adsorbed, n, divided by the number of moles in a complete monolayer, ri7non, versus the partial pressure, P, divided by the equilibrium vapor pressure, Po. Isotherms were calculated for different values of the parameter C. Right Adsorption isotherms of water on a sample of alumina (Baikowski CR 1) and silica (Aerosil 200) at 20°C (P0 = 2.7 kPa, redrawn from Ref. [379]). The BET curves were plotted using Eq. (9.37) with C = 28 (alumina) and C = 11 (silica). To convert from n/nmo to thickness, the factors 0.194 nm and 0.104 nm were used, which correspond to n-mon = 6.5 and 3.6 water molecules per nm2, respectively.

---