BET Brunauer, Emmett, and

Wheeler [16] proposed that the mean radius, r, and length, L, of pores in a catalyst pellet (of, for that matter, a porous solid reactant) are determined in such a way that the sum of the surface areas of all the pores constituting the honeycomb of pores is equal to the BET (Brunauer, Emmett and Teller [17]) surface area and that the sum of the pore volume is equed to the experimental pore volume. If represents the external surface area of the porous particle (e.g. as determined for cracking catalysts be sedimentation [18]) and there are n pores per unit external area, the pore volume contained by nSx cylindrically shaped pores is nSx nr L. The total extent of the experimentally measured pore volume will be equal to the product of the pellet volume, Vp, the pellet density, Pp, and the specific pore volume, v. Equating the experimental pore volume to the pore volume of the model... 

XRD and nitrogen adsorption studies reveal that MCM-41 can be synthesized in the presence of niobium and tantalum compounds. In Table 2, the surface area Abet, the pore volume Vp and the pore diameter dp, calculated from nitrogen adsorption-desorption isotherms using BET (Brunauer, Emmett and Teller) and BJF1 (Barrett, Joyner and Flalenda) analysis, are... 

The particle size and surface area distributions of pharmaceutical powders can be obtained by microcomputerized mercury porosimetry. Mercury porosimetry gives the volume of the pores of a powder, which is penetrated by mercury at each successive pressure the pore volume is converted into a pore size distribution. Two other methods, adsorption and air permeability, are also available that permit direct calculation of surface area. In the adsorption method, the amount of a gas or liquid solute that is adsorbed onto the sample of powder to form a monolayer is a direct function of the surface area of the sample. The air permeability method depends on the fact that the rate at which a gas or liquid permeates a bed of powder is related, among other factors, to the surface area exposed to the permeant. The determination of surface area is well described by the BET (Brunauer, Emmett, and Teller) equation. 

BET Brunauer, Emmett, and AGi free energy changes (Dent... 

The total surface area or specific surface area (area/unit weight) is determined by the nitrogen absorption method known as the BET (Brunauer, Emmett, and Teller) absorption isotherm of an inert gas. The principle of this technique is based on the monolayer adsorption of nitrogen at low temperature, which has a fixed spherical volume. Thus, the amount of nitrogen adsorbed is proportional to the total surface area of the sample. 

It has been assumed so far that segregation occurs in a monatomic layer following the McLean model. While this assumption is acceptable for dilute solutions, segregation may also occur across multi-atomic layers and, in particular, for concentrated solutions. The use of a multi-layer adsorption model (BET—Brunauer, Emmett and Teller— model) has been suggested as the most simple and useful approximation for segregation in concentrated solutions. ... 

BET (Brunauer, Emmett and Teller) isotherm and modified BET isotherm... 

A key material property of powders and fibers in particular is the specific surface area. The extent of adsorption from the vapor and liquid states on a solid surface is determined in part by the specific surface area of the solid. Typically, to determine the specific surface area, a gas adsorption isotherm is measured for example, the adsorption of nitrogen is measured on the substrate of interest at 77 K, the boiling point of nitrogen. The experimental isotherm is then analyzed by the BET (Brunauer, Emmett and Teller) model [42,43] to determine the monolayer capacity of the substrate. The specific monolayer capacity multiplied by the cross-sectional area of the adsorbed gas molecule gives the specific surface area. Amorphous silica gel may have a specific area of 200-300 mVg while carbon fibers may have a value of around 0.1 mVg. 

Surface area (BET) n. The total surface area of a solid calculated by the BET (Brunauer, Emmett, and Teller) equation, from nitrogen adsorption or desorption data obtained under specified conditions. 

Surface analysis via physisorption is the appropriate technique to analyze the specific surface of a catalyst The catalyst sample is contacted at different pressures (normally from vaccum to atmosphere) with a gas that physisorbs under appropriate temperatme conditions (normally N2 at 77 K) in a defined manner on its surface. Owing to this physisorption process the pressure in the sample chamber changes. From this pressure drop, the physisorbed amount of gas per sample mass is determined. The adsorbed amount versus the applied pressure is called the sorption isotherm and with different models, such as, for example, the most common BET (Brunauer, Emmett, and Teller) model, the available surface can be calculated from the isotherm. Other models like the BJH (Barrett, Joyner, and... 

Figure 3.3.43 Shapes of adsorption isotherms according to the BET (Brunauer, Emmett, and Teller) theory for various values of Cbet (not considering capillary condensation and surface inhomogeneities) (a) Equation (3.3.47a) for an unlimited number of layers (b) n-layer BET equation for Cbet = 100, if the number cannot exceed Umax, that is, for adsorption in a limited space such as a capillary, Eq. (3.3.47b).

When adsorption takes place in multilayers, adsorption on the adsorbent surface and above the adsorbed molecules is considered to be based on different attractive forces. Monolayer adsorption is formed by the same concept as the Langmuir type adsorption while adsorption above monolayers is equivalent to condensation of the adsorbate molecules, giving rise to the BET (Brunauer, Emmett and Teller, 1938) equation... 

To gain further insight into how the plasma and catalyst interact in this system, we performed some characterisation of the catalysts after a period of treatment in the plasma environment using BET (Brunauer, Emmett and Teller) surface area analysis, SEM (scanning electron microscopy) investigation of the surface morphology, elemental analysis and ATR-IR (attenuated total reflection Infrared) spectroscopy... 

Another example of a DMC-catalyzed esterification reaction is the esterification of free fatty acids with glycerol [32]. This reaction again used Zn-Fe(II)-DMC as a catalyst yet the activity of the material could be tuned by varying the synthesis temperature. As such, DMCs with different acidities (as evidenced by NHj-TPD), crystallite sizes (calculated from the Debye-Scherrer equation), particle sizes (studied with scanning electron microscopy (SEM)), and BET (Brunauer, Emmett and Teller) specific surface areas were obtained. The highest catalytic conversions were observed for the catalysts synthesized at elevated temperatures these materials featured both the highest specific surface area and the largest number of acid sites. 

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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