BET expressions

The Type II and Type III isotherms shown in Figure 5.7 can both be described by the so-called infinity-form of the BET expression, which allows for an infinite number of adsoibate layers. The difference in the shsqpes of these two isotherms arises from differences in the strength of the adsorbate-adsorbent interaction. 

The absorption isotherm does not follow the BET expression in the initial part (20) ... 

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. 

An alternative way of deriving the BET equation is to express the problem in statistical-mechanical rather than kinetic terms. Adsorption is explicitly assumed to be localized the surface is regarded as an array of identical adsorption sites, and each of these sites is assumed to form the base of a stack of sites extending out from the surface each stack is treated as a separate system, i.e. the occupancy of any site is independent of the occupancy of sites in neighbouring stacks—a condition which corresponds to the neglect of lateral interactions in the BET model. The further postulate that in any stack the site in the ith layer can be occupied only if all the underlying sites are already occupied, corresponds to the BET picture in which condensation of molecules to form the ith layer can only take place on to molecules which are present in the (i — l)th layer. 

The external surface area of the filler can be estimated from a psd by summing the area of all of the equivalent spheres. This method does not take into account the morphology of the surface. It usually yields low results which provide Htde information on the actual area of the filler that induences physical and chemical processes in compounded systems. In practice, surface area is usually determined (5) from the measured quantity of nitrogen gas that adsorbs in a monolayer at the particle surface according to the BET theory. From this monolayer capacity value the specific surface area can be determined (6), which is an area per unit mass, usually expressed in m /g. 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Probability in Bayesian inference is interpreted as the degree of belief in the truth of a statement. The belief must be predicated on whatever knowledge of the system we possess. That is, probability is always conditional, p(X l), where X is a hypothesis, a statement, the result of an experiment, etc., and I is any information we have on the system. Bayesian probability statements are constructed to be consistent with common sense. This can often be expressed in tenns of a fair bet. As an example, I might say that the probability that it will rain tomorrow is 75%. This can be expressed as a bet I will bet 3 that it will rain tomorrow, if you give me 4 if it does and nothing if it does not. (If I bet 3 on 4 such days, I have spent 12 I expect to win back 4 on 3 of those days, or 12). 

A currently popular alternative <> the ah initio method is density ftmitwnal theory, m which the energy is expressed in terms of rhe electron density rather than the w-ivi-funcron itself. The idvautogc of this approach is that it is less demanding computationally, requires less computer nine-, and m some cases—particularly for d-mctal complexes—gives bet-ter agreement with experimental values than other procedures. 

The number of gas molecules can be measured either directly with a balance (gravimetric method) or calculated from the pressure difference of the gas in a fixed volume upon adsorption (manometric method). The most frequently apphed method to derive the monolayer capacity is a method developed by Brunauer, Emmett, and Teller (BET) [1], Starting from the Langmuir equation (monolayer adsorption) they developed a multilayer adsorption model that allows the calculation of the specific surface area of a sohd. The BET equation is typically expressed in its linear form as... 

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) ... 

Inhaled corticosteroids mediate a variety of immunological actions and are commonly used in the treatment of allergic asthma [28]. However, not all patients respond well to this treatment and some are steroid-resistant. In a recent study, Tantisira et al. [29] described a new genetic non-synonymous variation in TBX21 that encodes for the transcription factor T-bet (T-box expressed in T cells) associated with significant improvement of the airway hyperresponsiveness in children affected by allergic asthma [30]. Noteworthy, the... 

GR inhibitory interaction with T-bet may be an important mechanism underlying the immunosuppressive properties of GCs [27]. It is therefore important to determine the footprint of T-cell-specific transcription factor expression and binding on the IFN-y promoter in asthmatics, resulting in a closer classification of this disease. Allergic asthma is possibly a multifaceted disease that can be further better subclassified and therefore treated with different strategies. 

The onset of asthma might depend on both genetic and environmental components. In childhood the expression of IFN-7 is fundamental in determining the future T-cell development. In fact, defective IFN-7 early in life favors a Th2 cell development probably as a result of increased IL-6 production by DCs or mast cells and/or IL-4 production by natural killer or other cells. The increased GATA-3 expression in the lung of asthmatics points in this direction. The defect in T-bet or its genetic modification in asthmatics underlines the... 

Mehta DS, Wurster AL, Weinmann AS, et al NFATc2 and T-bet contribute to T-helper-cell-subset-specific regulation of IL-21 expression. Proc Natl Acad Sci USA 2005 102 2016-2021. 31... 

Tolbutamide is one of the most widely used antidiabetic agents. Its action is preferably connected with stimulatory action of j3-cells in the pancreas, which results in intensive insulin secretion. It is used for type II diabetes melhtus of medium severity with no expressed microvascular complications. Synonyms of this drug are mebenol, oramid, ora-bet, tolbuton, butamide, rastinon, and others. 

Improvement in symptoms such as cessation of clavicular retractions, quieter and slower respirations, and a relaxed facial expression reduction in the need for rescue shorf-acfing bet aj-agonists... 

Kaupmann, K., Huggel, K., Heid, J., Flor, P.J., Bischoff, S., Mickel, S.J., McMaster, G., Angst, C., Bittiger, H., Froestl, W, and Bet-tier, B. (1997) Expression cloning of GABAb receptors uncovers similarity to metabotropic glutamate receptors. Nature 386 239-246. 

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