Brunauer-Emmett-Teller model isotherms

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... 

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... 

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]. 

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. 

Surface Area. In spite of its imperfections, the Brunauer-Emmett-Teller (BET) model is still the most common approach for deriving the specific surface area. It is internationally accepted and recommended by lUPAC that the isotherms be measured with nitrogen gas adsorbent at the boiling point of nitrogen (77.35 K). The monolayer capacity is computed from the intercept and the slope of the linearized BET plot. The agreed cross-sectional area of nitrogen for converting monolayer capacity to surface area is 0.162 nm /molecule. Typically,... 

Nitrogen adsorption/desorption isotherms were measured at 77 K and evaluated using a Quantachrome Autosorb-1 computer-controlled apparatus. (Quantachrome, Boynton Beach, FL, USA) The apparent surface area was derived using the Brunauer-Emmett-Teller (BET) model, Sa.BEx- The total pore volume, Vp at, was calculated from the amount of nitrogen vapor adsorbed, at a relative pressure close to unity, on the assumption that the pores are then filled with liquid nitrogen. The average pore radius, rp, was derived from the total pore volume and the BET surface area on the basis of uniform cylindrical pores. The micropore volumes, and Fo dr, were computed by the Dubinin-Radushkevich (DR) and t methods (Halsey), respectively. The characteristic energy, Eo, was derived from the DR plot as well with P =0.34. The slit size, Lq, was derived from the relation = 10-8/(-Eo-H-4),... 

An adsorption process can be described by isotherms, i.e. by the functional relationship between the adsorbed quantities of a species vs. its activity. A direct consequence of the two possible interactions of a protic electrolyte (e.g. phosphoric, sulfuric or perchloric acid) to a polymer chain with basic groups is a multilayer-like adsorption process. Therefore, the use of an adsorption isotherm as described by the BET model (Brunauer-Emmett-Teller) is convenient. The BET model is originally derived for gas adsorption on surfaces [62, 63]. To derive a multilayer-like adsorption model for a basic ionogen polymer in analogy to the original BET model, we attribute the basic groups of the polymer chains, which can be protonated by the protic electrolyte, as adsorption sites. In case of PBI-type polymers the basic groups are the imidazole centres. 

To obtain the monolayer capacity from the isotherm, it is necessary to interpret the (Type II) isotherm in quantitative terms. A number of theories have been advanced for this purpose from time to time, none with complete success. The best known of them, and perhaps the most useful in relation to surface area determination, is that of Brunauer, Emmett and Teller. Though based on a model which is admittedly over-simplified and open to criticism on a number of grounds, the theory leads to an expression—the BET equation —which, when applied with discrimination, has proved remarkably successful in evaluating the specific surface from a Type II isotherm. 

As we see in the course of the chapter, these two approaches frequently clash. The adsorption isotherm of Brunauer, Emmett, and Teller (BET), which is discussed in Section 9.5, is an excellent example of this. The model on which the BET isotherm is based has been criticized by many theoreticians. At the same time, the isotherm itself has become virtually... 

For most practical purposes, the isotherm can be modeled by an empirical (Brunauer, Emmett and Teller BET) or theoretical (Guggenheim, Anderson, and DeBoer GAB) equation (see below) however, none of the isotherm models in the literature is valid over the entire aw range of 0 to 1. The GAB model is one of the most widely accepted models for foods over a wide range of aw (from 0.10 to 0.90). The details of the different isotherm models with their parameters have been compiled by Rahman (1995). The BET (Eq. A2.3.4) and GAB (Eq. A2.3.5) equations are given as follows ... 

In Langmuir model, the maximal adsorption is that of a monolayer. Langmuir adsorption isotherms all saturate at high vapor pressures. This is unrealistic for many cases. In order to consider the adsorption of multilayers, Brunauer, Emmett, and Teller extended the Langmuir theory and derived the so-called BET adsorption isotherm [378], The basic idea in the BET theory was to assume a Langmuir adsorption for each of the layers (Fig. 9.8). 

The assumption of monolayer adsorption in the Langmuir isotherm model is unrealistic in most cases, and a modification to multilayer adsorption should be considered. In 1938, Brunauer, Emmett, and Teller modified the Langmuir approach of balancing the rates of adsorption and desorption for the various molecular layers [Brunauer et al., 1938], This approach is known as the BET method. The BET isotherm assumes that the adsorption of the first layer has a characteristic heat of adsorption A Ha and the adsorption and desorption on subsequent layers are controlled by the heat of condensation of the vapor, A Hc. The derivation of the BET equation is beyond the scope of this book however, a common form of the BET equation is given as... 

A frequently used adsorption model that allows for adsorption in multilayers has been introduced by Brunauer, Emmett and Teller [10] and is known as the BET equation. With the exception of the assumption that the adsorption process terminates at monolayer coverage, these authors have retained all the other assumptions made in deriving the Langmuir adsorption isotherm. Hence all objections to the application of the Langmuir equation apply here, too. 

Water vapor adsorption isotherms have been obtained on cotton from room temperature up to 150°C [303,304]. Theoretical models for explaining the water vapor sorption isotherms of cellulose have been reviewed [303]. Only adsorption theories will be discussed here at ambient temperatures. The shape of the isotherm indicates that multilayer adsorption occurs and thus the Brunauer, Emmett and Teller (BET) or the Guggenheim, Anderson and deBoer (GAB) theory can be applied. In fact, the BET equation can only be applied at relative vapor pressures (RVPs) below 0.5 and after modification up to a RVP of 0.8 [305]. The GAB equation, which was not discussed in the chapter in the book Cellulose Chemistry and Its Applications [303], can be applied up to RVPs above 0.9 [306]. Initially as the RVP... 

The difficulty of gas adsorption methods lies in the fact that purely monomolecular layers are never formed. Already before the adsorbent is completely covered, multiple layers build up locally. Brunauer, Emmett and Teller derived a relation between gas pressure and the amount of gas adsorbed at the surface which is known as the BET isothermal line. They used both a gas kinetic and a statistical model. 

Total catalyst area is generally determined using a physically adsorbed species, such as N2. The procedure was developed in the 1930s by Brunauer, Emmett and and Teller [7], and the isotherm they developed is referred to as the BET isotherm. In the physisorption process multi-layers are allowed to form. The BET isotherm model treats the first layer differently from all subsequent layers and leads to the following expression... 

The mathematical models that have been applied to the physical adsorption from liquid solutions are generally extensions of the theories that have been developed to describe the sorption of gases on solid surfaces with modifications to account for the competition between the solute and solvent for the adsorption sites. Two of these models have been applied to the adsorption isotherms of nonelectrolytes from solution they are the Langmuir model and the Brunauer, Emmett, and Teller (BET) model in addition the Freundlich empirical equation has also been used. In the Langmuir model it is assumed that the adsorbed species forms a monolayer on the surface of the adsorbent, that the adsorbed molecules... 

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