Intensive and extensive factors

NMR spectroscopy has shown much promise as a technique for characterizing acid sites. In theory, it should enable the direct characterization of both the intensive and extensive factors of acidity in zeolites. The current limitations of the techniques have to do with the instrumentation not allowing for sufficient resolution for complete analysis of the proton sites. New NMR instrumentation is currently being developed that should allow for more complex experiments with higher accuracy. 

Short chain alkanes (C4 and C5), especially isobutane and neopentane, were frequently used to elucidate the reaction mechanism of catalytic cracking, e.g., in papers by Hall et al. [110,114] and Kranilla et al. [115]. In these publications, however, few comparisons were made to distinguish the intensive and extensive factors of the zeolite acidity. 

The action of particulate fillers on a thermoplastic is dependent on factors that can be classified as extensity, intensity and geometrical factors. The extensity factor is the amount of filler surface area per m of the composite in contact with the plastic. The intensity factor is the specific activity of this solid surface per m of interface, determined by the chemical and physical nature of the filler surface in relation to the plastic. Geometrical factors are the structure including shape of filler (anisotropic such as such as lamellar, plate, needle and isotropic such as spherical), their particle size and size distribution as well as porosity. Among those the chemical nature of the filler surface plays most vital role in determining the degree of plastic-filler interaction. 

Each term on the right-hand side is a product of an intensive factor (one that does not depend on the amount of matter in this system) and an extensive factor (one that does depend on the amount of matter in the system). Thus,... 

Physical properties are termed either intensive or extensive. Intensive properties are independent of the quantity of material present. Density, specific volume, and compressibility factor are examples. Properties such as volume and mass are termed extensive their values are determined by the total quantity of matter present. 

The single-chain structure factors calculated in the previous sections correspond to the infinite dilution limit. This limit also corresponds to zero scattering intensity and is not useful so that concentration effects have to be included in the modeling of polymer solutions. First, Zimm s single-contact approximation [5] is reviewed for dilute polymer solutions then, a slight extension of that formula which applies to semidilute solutions, is discussed. 

Equation (1.75) is a mathematical statement of the second law of thermodynamics for reversible processes. The introduction of the integrating factor for Sq causes the thermal energy to be split into an extensive factor. S and an intensive factor T. Introducing Eq. (1.75) into Eq. (1.56) yields the combined first and second laws... 

A. E. Hirschler (Sun Oil Co., Marcus Hook, Pa. 19061) I should like to make a comment relating to your statement that activity is not a simple function of acidity. This statement appears to contain the implicit assumption that all acid sites able to protonate pyridine would have the same catalytic activity. Actually, one might expect an intensity factor (acid strength) to be operative in acid catalysis as well as an extensive factor, and the apparent lack of correlation you observed may result from an influence of acid strength on catalytic activity. Pyridine adsorption data alone do not completely define Bronsted acidity. One may need also some measure of acid strength. Acidity measurement with Hr indicators, such as we and others have reported, may supply useful information relative to acid strength as well as number of acid sites. 

Structure and Acidity of Zeolites. - Hall and cowoikers have expressed the total acidity of zeolites in terms of an extensive factor, representing the total number of acid sites in the zeolite, and an intensive factor, representative of the strength of the individual sites In a structurally pure H-zeolite, the nature of the acid site is easy to conceptualize, consisting of the bridging hydroxyl group between two tetrahedra, one centered on aluminum and the other on a silicon, viz. 

The purpose of this article is to review recent work concerning the characterization of the acid sites in zeolites, concentrating on the use of various techniques which can give detailed information concerning both the intensive and the extensive factors of acidity in zeolites. Due to the large number of papers being published in the area of zeolite catalysis, this review will certainly not be all-inclusive and the available literature will have greatly expanded by the time of publication. 

The role of any technique used for characterizing acidity is to give a quantitative measurement of the number of acid sites (extensive factor) and their strength (intensive factor). In addition, it should ideally be able to differentiate between Brpnsted and Lewis types of acid sites. Of the techniques most commonly used for this purpose, few are able to characterize the acid sites accurately and quantitatively. Thus, in most instances a combination of characterization techniques become necessary. 

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