Brunauer-Emmett Technique equation

The surface area of a solid material is important in that it provides information on the available void spaces on the surfaces of a powdered solid [48]. In addition, the dissolution rate of a solid is partially determined by its surface area. The most reproducible measurements of the surface area of a solid are obtained by adsorbing a monolayer of inert gas onto the solid surface at reduced temperature and subsequently desorbing this gas at room temperature. The sorption isotherms obtained in this technique are interpreted using the equations developed by Brunauer, Emmett, and Teller, and therefore the technique is referred to as the B.E.T. method [49]. The surface area is obtained in units of square meters of surface per gram of material. 

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. 

Colloid chemists commonly measure surface area by the adsorption of N2 gas. The adsorption is conducted in vacuum and at temperatures near the boiling point of liquid nitrogen (—196° C). The approach is based on the Brunauer-Emmett-Teller (BET) adsorption equation, and has been adapted to a commercially available instrument. Unfortunately, the technique does not give reliable values for expansible soil colloids such as vermiculite or montmorillonite. Nonpolar N2 molecules penetrate little of the interlayer regions between adjacent mineral platelets of expansible layer silicates where 80 to 90% of the total surface area is located. Several workers have used a similar approach with polar H2O vapor and have reported complete saturation of both internal (interlayer) and external surfaces. The approach, however, has not been popular as an experimental technique. 

An important parameter of bulk powders is the specific surface area S, expressed per unit weight. The specific surface area measurement includes the cracks, crevices, nooks, and crannies present in the particles. To include these features in the surface-area measurement, methods have been developed to probe these convoluted surfaces through adsorption by either a gas or a liquid [95-97]. The most widely used surface area measurement technique is the absorption of a monolayer of gas, typically krypton or nitrogen as the adsorbate gas in helium as an inert diluent, using the method developed by Brunauer, Emmett, and Teller [98], known as the BET method. This method utilizes the BET equation... 

Of all existing GC techniques for determining the specific area of a solid, the heat desorption method is the one most often used. This method was developed by Nelson and Eggertsen and modified by a number of workers. In principle, the heat desorption method is based on the traditional Brunauer, Emmett, Teller (BET) technique in which the quantity of adsorbed gas (usually nitrogen) at a temperature near its boiling point is determined. By determining the adsorption at various pressures, it is possible, using the BET equation, to calculate the amount of adsorbate required for the formation of a monolayer. 

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. 

We learned from the previous section that electrochemical active surface area can be determined from the CV method. The accurate measurement of surface area of the electrolyte membrane or electrodes is done by a technique known as the Brunauer-Emmett-Teller (BET) method (Brunauer et al., 1938). It is based on the physical adsorption of gas molecules on a solid surface. It is assumed that gas molecules physically adsorb on a solid in layers infinitely and there is no interaction between each adsorption layer. The BET equation is expressed as... 

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