Equilibrium isotherms Brunauer-Emmett-Teller

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. 

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

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-... 

The possibility of multilayer adsorption is envisaged in the Brunauer-Emmett-Teller (BET) isotherm. The assumption is made that the first layer is adsorbed with a heat of adsorption H and the second and subsequent layers are all characterized by heats of adsorption equal to the latent heat of evaporation, //l- By considering the dynamic equilibrium between each layer and the gas phase the BET isotherm is obtained,... 

The BET Brunauer, Emmett, Teller) (26-28) method of-calculating speciiic surface area from an adsorption isotherm has been mainly applied to nitrogen as the adsorbate at -196 C, Innes (29) developed a rapid automatic technique for measuring the isotherm. Lippens and Hermans described suitable apparatus in detail (30, 31). Also, commercial equipment has been developed using the static equilibrium method, which does not require calibration and gives surface area by automatic digital readout (e.g., Micromeritics, Inc.). 

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. 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

The BET method (Brunauer, Emmett and Teller, 1938) with N2 as the adsorbate, is by far the most common method of measuring the surface areas of Fe oxides. Various commerical instruments are available for these measurements. The method involves measuring the extent of adsorption of N2 (at the boiling temperature of liquid N2 - 77 K) on the outgassed solid as a function of the relative pressure, p/po. he. the adsorption isotherm p is the partial pressure of the adsorbate and po is its equilibrium vapour pressure. The following linear relationship exists between the amount adsorbed, v, (cm g ) and the relative vapour pressure, p/po, ... 

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