Quantitative considerations

The total efficiency of a LSC is governed by the following physical loss factors  

Critical cone loss corresponds to the fraction (cos c) of the isotropic luminescence passing through the spherical shell (with differential volume 4 r r2 dr with the fluorescent species at the centre) which undergoes consecutive total reflections (see Fig. 2) by being emitted outside the critical cone. 

As numerical examples of the trapping efficiency 7/trap = (1 - L) may serve  

We are discussing quantities of importance for the performance of the LSC, viz. the luminescent efficiency discussed below, as well as the 

Absorption efficiency r/abs is the fraction of incident solar photons absorbed by the luminescent species. The solar photons here occur in direct and diffuse light. In most calculations, air-mass 1 (AM 1) is taken as standard29) but it should be noted that the detectable solar flux depends strongly on the atmospheric conditions. 

Eggert et al. [90] modified Munro s approach by scaling through volume, rather than pressure. They proposed v (P) = 1 + dvldV, t3(P)=l + (5 3dV, with 

Ma et al. [147,162,163] argued that pressure-induced covalency effects can be understood in terms of the radial expansion of the valence electron wavefunc-tions as the nearest neighbor bond length decreases with pressure. They considered an isotropic compression model based on the scaHng of the Slater integrals 

Zhao et al. [ 144,166] proposed an approach based on symmetry restricted covalency [167]. Symmetry restricted covalency attributes covalency effects to the delocalization of d electron density onto ligand orbitals through a and rr molecular orbital formation between metal d orbitals and ligand s, p, and/or d orbitals [168]. The formation of molecular orbitals occurs between metal d orbitals and ligand orbitals of the same symmetry and varies with the coordination environment. The delocalization of d electron density that occurs upon molecular orbital formation leads to a reduction in the Racah B and C parameter values from the free ion values Bg and Cg. The reduction can be expressed by 

Zheng [ 169,170] used an approach based on Zhao s model and scaled the covalency reduction factor through the equation of state of ruby. Zheng proposed 

In a later paper [ 166], Zhao extended his model for ruby to include off-center site displacements of Cr +. The model accounts for the fact that Cr does not substitute exactly into AP+ sites, but rather is displaced along the trigonal axis. Zhao quantitatively included the position of Cr + relative to an AF lattice site as a function of pressure in his model and re-evaluated the R-line shift data up to 1650 kbar. Zhao s extended model predicted a -0.0489 cm /kbar change in B with pressure up to 400 kbar and a constant value (B = 784 cm ) above 400 kbar. 

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Komatsu [478] has put forward the hypothesis that reaction in many powder mixtures is initiated only at interparticle contact and that product formation occurs by diffusion through these contact zones. Here, one of the participating reactants is not covered with a coherent product layer. Quantitative consideration of this model leads to a modified Jander equation. 

Minimizing the total energy E with respect to the MO coefficients (see Refs. 2 and 3) leads to the matrix equation FC = SCE (where S is the overlap matrix). Solving this matrix is called the self-consistent field (SCF) treatment. This is considered here only on a very approximate level as a guide for qualitative treatments (leaving the more quantitative considerations to the VB method). The SCF-MO derivation in the zero-differential overlap approximations, where overlap between orbitals on different atoms is neglected, leads to the secular equation... 

The applications of the idea of resonance which have been made during the last decade are in the main qualitative in nature. This represents only the first step, which should be followed by more refined treatments with quantitative significance. Some rough quantitative considerations, such as those regarding inter-... 

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

It is concluded that MALDI-ToFMS is a suitable method for direct analysis of low-MW additives in complex polymeric materials (in dissolution), in particular as a rapid screening technique (within 0.5 h). However, in order to turn this method into a general tool for identification and quantitation, considerably more work needs to be done. Identification of additives in polymeric matrices by means of MALDI-ToFMS would greatly benefit from reference libraries of additives contained in such matrices. This is not unlike the situation observed for ToF-SIMS. 

Another survey by Ibl (13) in 1963 listed 13 mass-transfer correlations established by the limiting-current method, only four of which were derived from quantitative considerations. At the time of writing the total number of publications is more than 200. The majority of these concern flow conditions under which theoretical predictions are, at best, qualitative. More recently, an increasing number of publications deal with model hydrodynamic studies of more complex situations, for example, packed and fluidized beds. 

The translation model was refined and developed further in a later article (Lehmann and Kuhn, 1984). It is assumed that in the early stages of evolution, guanosine and cytidine were the most important building blocks for RNA syntheses, as they allow strong base pairing (via three hydrogen bonds). Quantitative considerations lead to an upper limit of about 50 nucleotides for a reasonable chain length. 

TABLE 2 Quantitative Considerations of Selected Polymer Pairs... 

Owing to overlapping of different processes in this range of temperature, quantitative considerations based on data obtained in programmed temperature TG cannot be made. However, it can roughly be estimated that up to 410 C, that is to the end of the process characterised by the narrow DTG peak 3 in Figure 12, about one mole of ammonia 1s evolved per mole of melamine. This would support the formation of melam by Reaction 13, followed by elimination of ammonia (reaction 14). 

For quantitative considerations it is convenient to use atomic units (a.u.), in which h = eo = me = 1 (me is the electronic mass) by definition. They are based on the electrostatic system of units so Coulomb s law for the potential of a point charge is = q/r. Conversion factors to SI units are given in Appendix B here we note that 1 a.u. of length is 0.529 A, and 1 a.u. of energy, also called a hartree, is 27.211 eV. Practically all publications on jellium use atomic units, since they avoid cluttering equations with constants, and simplify calculations. This more than compensates for the labor of changing back and forth between two systems of units. 

In order to explain all the salient features of the key experimental results on ECT (viz. listed as 1. to 6. at the beginning of Section II, Phenomenology of ECT), Vijh25 proposed a detailed electrochemical mechanism in which electroosmosis of the tissue (and thence water movement from anode to cathode) and electrode reactions (thence necrosis of the tissue, pH changes etc.) play the dominant roles. In particular, he presented a model and some quantitative considerations that delineate Nordenstrom s idea of electroosmosis through the narrow interstitial channels lined with fixed charges as the mechanism of the electrochemical destruction of the tumor tissue.10 Also he examined the role of electrode reactions and other events as possible contributory factors, as follows25 in Section III.2. 

Regardless of any quantitative considerations, the presence of two separate peaks in the chromatogram indicates the extent of the resolution and may be quantified using the following equation ... 

Haaijman, J. J. (1988) Immunofluorescence quantitative considerations. Acta Histochem. 35, 77-83. 

That the excited state from which the actual reaction begins would have ir - it rather than n it character was no difficult guess. Semi-quantitative considerations and simple calculations of electron distribution already make it clear that upon n->ir ... 

The key to optimum design for multiple reactions is proper contacting and proper flow pattern of fluids within the reactor. These requirements are determined by the stoichiometry and observed kinetics. Usually qualitative reasoning alone can already determine the correct contacting scheme. This is discussed further in Chapter 10. However, to determine the actual equipment size requires quantitative considerations. 

The magnitude of the allowable temperature for the bake-out process in question will, indeed, be determined essentially by the material in the chamber. Precise pump-down times can then be estimated by calculation only if the quantity of the evolving and pumped vapors is known. Flowever, since this is seldom the case except with drying processes, a quantitative consideration of this question is abandoned within the scope of this publication. 

Dihydrogen complexes, osmium, 37 3(X)-301 Dihydroxo-bridged complexes acid-base equilibria, 32 108-110 quantitative considerations, 32 115-118 binuclear, 32 66-67 crystallographic data, 32 61, 63 stability complexes, 32 103-104... 

The influence of deuterium substitution on the acid base effects in hydrogen bonds has been considered [3], The treatment given here has been designed to enable a more quantitative consideration of these effects to be made and to interpret the known contraction phenomena. 

Numbers for characteristic lake data (volume, surface, area, etc.) and input data are rounded off to facilitate quantitative considerations. 

If nuclei or their surroundings have any mobility, the resonance fine will narrow and become Lorentzian in shape. The cause of this behaviour is an averaging process of the components of the field gradient tensor. Quantitative considerations of the mobility mechanisms in zeolites are difficult to make and are beyond the scope of this article. 

Because the rate is independent of vessel size in the presence of mercury vapor, and inert diluents decrease the rate (1), it is concluded that initiation and termination are gas phase, and peroxides are destroyed at the wall in mercury free systems. A more detailed understanding of the mechanism of formaldehyde oxidation requires quantitative consideration of peroxides such as performic acid, and unequivocal evidence for the identification of chain carriers. 

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