Quantitative terms

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. 

Part 2 (Draft) Quantitative terms and definitions (July 1998)... 

Objective Provide a basis to judge the relative likelihood (probability) and severity of various possible events. Risks can be expressed in qualitative terms (high, medium, low) based on subjective, common-sense evaluations, or in quantitative terms (numerical and statistical calculations). 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the eomplexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often neeessary to treat the solvent as a continuous homogeneous medium eharaeterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. This is the basis of the current inability of physical theories to account satisfactorily for the full scope of solvent effects on rates, although they certainly can provide valuable insights and they undoubtedly capture some of the essential features and even cause-effect relationships in solution kinetics. Section 8.3 discusses physical theories in more detail. 

Natural colloid particles in aqueous systems, such as clay particles, silica, etc. may serve as carriers of ionic species that are being sorbed on the particulates (pseudocolloids). It seems evident that the formation and transport properties of plutonium pseudocolloids can not yet be described in quantitative terms or be well predicted. This is an important area for further studies, since the pseudocolloidal transport might be the dominating plutonium migration mechanism in many environmental waters. 

The first step in Mechanism I is the unimolecular decomposition of NO2. Our molecular analysis shows that the rate of a unimolecular reaction is constant on a per molecule basis. Thus, if the concentration of NO2 is doubled, twice as many molecules decompose in any given time. In quantitative terms, if NO2 decomposes by Mechanism I, the rate law will be Predicted rate (Mechanism I) = [N02 ] Once an NO2 molecule decomposes, the O atom that results from decomposition very quickly reacts with another NO2 molecule. 

Not until the 1940 s did suitable methods, both experimental and theoretical, become available for reducing the constitution of polymers, including the nonlinear, network-forming types, to tractable quantitative terms. Since such means are a prerequisite to the quantitative treatment of polymer properties in relation to constitution, advances in this direction necessarily were delayed. 

A detailed study on velocity profiles, pressure drop and mass transport effects is given in [3]. This, in quantitative terms, precisely underlines the advantages (and limits) of the porous-polymer-rod micro reactor concept. 

The volume expansion accompanying the spin-state transition has been demonstrated, at least in quantitative terms, on the basis of multi-temperature crystal structure studies [6]. An alternative method starts from the determination of the lattice constants as a function of temperature and therefrom, the volume of the unit cell may be calculated at each temperature. It has been shown [70] that the variation of the unit cell volume V(T) may be reproduced by ... 

In 1940, Jacobs [4] described the theory of nonionic membrane permeation of organic compounds in quantitative terms. The influence of pH and pKa on drug... 

A quantitative term to describe the (lack of) precision of an analytical procedure (e.g. by standard deviation). 

Melatonin can be metabolized non-enzymatically in all cells, and extra-cellularly by free radicals and a few other oxidants. It is converted into cyclic 3-hydroxymelatonin when it directly scavenges two hydroxyl radicals (Tan et al. 1998). In the brain, a substantial fraction of melatonin is metabolized to kynuramine derivatives (Hirata et al. 1974). AFMK is produced by numerous non-enzymatic and enzymatic mechanisms (Hardeland et al. 2006) its formation by myeloperoxidase appears to be important in quantitative terms (Ferry et al. 2005). 

Figure 3 presents an example of islet functioning inside a particular capsule. A typical two-phase perifusion profile is noted,similar in quantitative terms to that of unencapsulated islets. Clearly the ratio of the membrane thickness to capsule diameter is an important parameter, with low membrane capsule ratios providing rapid transfer of nutrients and the exodiffusion of insulin. Contrarily, for thick walled capsules of diameter less then approximately one-half millimeter the perifusion response, as measured by the stimulation index and retardation in insulin response to a glucose stimulus, is slower for encapsulated islets relative to free islets. 

To illustrate these Semenov diagrams in reasonable quantitative terms, n-heptane was selected with the following properties ... 

In more quantitative terms, the analysis developed in Section 5.3.2 may be applied here. It is, however, necessary to take into account inhibition by the substrate as depicted in Scheme 5.3. At low substrate concentration, however, inhibition can be neglected. When complete control by substrate diffusion prevails, the current-potential response obeys the conditions of total catalysis, being given by equation (5.25) (dotted line in Figure 5.24), as discussed in Section 5.3.2, introducing a stoichiometric factor of 2, while the peak potential is given by equation (5.26). 

In Fig. 5.1.10 the evolution of C-even (a) and C-odd-SPC (b) overtime from the LAS-spiked FBBR is plotted. Their formation starts at day 5 with the entire range of examined SPC observed. The curves show a maximum at day 7 with C7-, C8-, and C9-SPC prevailing. However, it should be noted that in quantitative terms the short-chain homologues C4-C6 are underestimated, as their ionisation efficiency is lower than that of the longer-chain SPC. A relatively constant level of all SPC compounds was achieved on day 15 and maintained until the end of the experiment on day 30 (not all data shown). 

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