Brunauer Emmett Teller model

Brunauer-Emmett-Teller (BET) adsorption describes multi-layer Langmuir adsorption. Multi-layer adsorption occurs in physical or van der Waals bonding of gases or vapors to solid phases. The BET model, originally used to describe this adsorption, has been applied to the description of adsorption from solid solutions. The adsorption of molecules to the surface of particles forms a new surface layer to which additional molecules can adsorb. If it is assumed that the energy of adsorption on all successive layers is equal, the BET adsorption model [36] is expressed as Eq. (6) ... 

Many models have been developed that deal with the sorption properties of wood in the presence of moisture these have been discussed in a number of works (e.g. Skaar, 1972 Siau, 1984). They can be approximately divided into sorption models, such as the Brunauer-Emmett-Teller (BET) model, or solution models (such as the Hailwood-Horrobin, H-H, model). The sigmoidal shapes of sorption or desorption isotherms can be deconvoluted into two components. These are often taken to represent a monomolecular water layer (associated with the primary sorption sites, OH groups), and a multilayer component where the cell wall bound water molecules are less intimately associated with the fixed cell wall OH groups. 

Popper and Bariska (1972) studied the moisture sorption properties of wood chemically modified with acetic (or phthalic) anhydride and analysed the results using Brunauer-Emmett-Teller (BET) theory and the H-H model. Acetylation was found to reduce the number of sorption sites, whereas little effect was noted with phthaloylation. By dividing the sorption isotherm into a monolayer component and a multilayer component using the H-H model, it was shown that there was a large reduction in the... 

Another common model which also describes multilayer adsorption is the Brunauer-Emmett-Teller equation [Eqs. (4.3) and (4.4), often called the BET equation or the BETmethod], published in 1938 [82], Here Vis the amount adsorbed, Vm is the amount adsorbed in one monolayer, p is the pressure, p° is the saturation pressure, C is a constant which relates to the net heat of adsorption, and N [in the cases of Eq. (4.4)] is the maximum number of layers which can form in a pore. 

Because the Langmuir isotherm is not an adequate description of most systems, Equation (2.9) is not used much for area measurement. A number of other isotherm formulations utilize adsorption in surface area measurements, however (cf. Young Crowell, 1962, for example). The best known and most widely used is the BET (Brunauer, Emmett Teller, 1938) theory, a generalization of the Langmuir model to multilayer absorption. Assuming that for the second and succeeding molecular... 

The Brunauer-Emmett-Teller (BET) gas adsorption method has become the most widely used standard procedure for the determination of the surface area of finely-divided and porous materials, in spite of the oversimplification of the model on which the theory is based. 

The Brunauer-Emmett-Teller (BET) adsorption model was developed to account for multilayer adsorption. The BET model can be thought of as the sum of two terms the Langmuir model is used to account for coverage from zero to the completion of the first monolayer, while the second and all subsequent layers (not treated by the Langmuir model) are assumed to have a heat of adsorption equal to the heat of vaporization of the bulk liquid phase of the adsorbing species. The heat of adsorption of the first monolayer usually exceeds the liquid s heat of vaporization. Although it might seem a erode oversimplification, the BET model works well for many systems that involve physisorption of simple molecules,... 

The Langmuir and Volmer equations are special cases of the Fowler-Guggenheim and Hill-de Boer equations, respectively, in which lateral interactions are allowed to vanish the Brunauer-Emmett-Teller equation is a special case of the Broekhoff-van Dongen equation with n = oo and null lateral interactions the model in which all layers are mobile is a special case of Broekhoff-van Dongen model with n = 0. 

Many different equations have been used to interpret monolayer—multilayer isotherms [7, 11, 18, 21, 22] (e.g., the equations associated with the names Langmuir, Vohner, HiU-de Boer, Fowler-Guggenheim, Brunauer-Emmett-Teller, and Frenkel-Halsey-Hill). Although these relations were originally based on adsorption models, they are generally applied to the experimental data in an empirical manner and they all have Hmitations of one sort or another [7, 10, 11]. 

The specific surface area of solid materials is usually determined by applying the Brunauer-Emmett-Teller (BET) equation to nitrogen adsorption data between relative pressures (P/Pq) approximately 0.05 and 0.3 [51]. However, there are many shortcomings of the BET model. For example, it does not consider adsorption in pores. It is well known that the BET method seriously overestimates the specific surface area for many porous materials. For carbons, the theoretically highest possible specific surface area is approximately 2630 m /g... 

Sorption isotherms of model systems were determined gravimetrically and data were modeled using the Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-deBoer (GAB) models. 

The Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-deBoer (GAB) sorption isotherm models were used to obtain experimental steady-state moisture contents in dry basis by linear regression analysis according to Kouassi and Roos (2002). These equations provide the value of monolayer water content, which is an important parameter in food deterioration studies. 

A electronic nose based on an array of eight quartz microbalance-based (QCM) sensors coated with modified MPPs (5,10,15,20-tetraphenylporphyrin) was used for apple aroma measurements [13], The response of each QCM sensor was modeled with Brunauer-Emmett-Teller (BET) adsorption isotherms. By means of multivariate analysis on all sensor responses, the different compounds could be discriminated well and quantified accurately. This calibration protocol can be used to characterize the sensors for the vapors of complex mixtures. 

The use of the Brunauer-Emmett-Teller (BET) sorption model by TMT is problematic due to the faet that the BET is fit to sorption data at 30°C and does not consider the temperature dependence of sorption behaviour. One way the model of TMT eould be improved is by using more recent models for sorption isotherms, e.g. that of Choi and Datta [29], or by using conductivity data measured as a funetion of water content. 

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