Brunauer-Emmett-Teller method, isotherm analyses

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). 

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. 

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. 

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 gas adsorption-desorption technique relates to the adsorption of nitrogen (or, less commonly, carbon dioxide, argon, xenon, and krypton), at cryogenic temperatures, via adsorption and capillary condensation from the gas phase, with subsequent desorption occurring after complete pore filling. An adsorption-desorption isotherm is constructed based upon the relationship between the pressure of the adsorbate gas and the volume of gas adsorbed/desorbed. Computational analysis of the isotherms based on the BET (Brunauer-Emmett-Teller) (Brunauer et al. 1938) and/or BJH (Barrett-Joyner-Halenda) (Barrett et al. 1951) methods, underpinned by the classical Kelvin equation, facilitates the calculation of surface area, pore volume, average pore size, and pore size distribution. 

Gelb LV, Gubbins KE. Characterization of porous glasses simulation studies, adsorption isotherms, and the Brunauer-Emmett-Teller analysis method. Langmuir 1998 14 ... 

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. 

Sorption Analysis. Specific surface areas and porosity can be calculated from the adsorption isotherm of nitrogen at — 196 °C. The method of Brunauer, Emmett, and Teller [4.29] is generally accepted for the evaluation of specific surface areas (BET surface area in square meters per gram). The two-parameter equation is applicable to carbon black. The BET surface area comprises the outer surface area as well as the surface area of the pores. 

Gas adsorption is the preferred method of surface-area determination. An isotherm is generated of the amount of gas adsorbed against gas pressure, and the amount of gas required to form a monolayer is determined. The surface area can tTien be calculated using the cross-sectional area of the gas molecule. Outgassing of the powder before analysis should be conducted very carefully to ensure reproducibility. Commonly, nitrogen at liquid nitrogen vapor pressure is used but, for low surface-area powders, the adsorbed amounts of krypton or xenon are more accurately found. Many theories of gas adsorption have been advanced, but measurements are usually interpreted by using the BET theory [Brunauer, Emmett, and Teller, J. Am. Chem. Soc., 60,309 (1938)]. 

Adsorption isotherms. Isothermal microcalorimetry, in conjunction with an RH perfusion device, is a powerful method for mapping surface properties of solids and especially drugs [32]. The principle of the study is to adsorb and desorb water vapour onto and off the surface of a solid in small steps and measure the associated enthalpy change. At low RH values, monolayer water sorption conforms to a BET (Brunauer, Emmett and Teller) model and can therefore be used to determine surface properties. The analysis of the data can be achieved by plotting the water sorption isotherm as a function of RH and fitting to a modified BET type equation [33]. This can provide information about the surface affinity for water and the hydrophilic surface area, parameters... 

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