Semiquantitative theory

Doi and his coworkers have proposed a semiquantitative theory for the swelling behavior of PAANa gels in electric fields [14]. They have considered the effect of the diffusion of mobile ions due to concentration gradients in the gel. First of all, the changes in ion concentration profiles under an electric field have been calculated using the partial differential Equation 16 (Nernst-Planck equation [21]). 

Sabatier and Balandin had predicted a relationship between catal)dic activity and heat of adsorption. If a solid adsorbs the reactants only weakly, it will be a poor catalyst, but if it holds reactants, intermediates or products too strongly, it wiU again perform poorly. The ideal catalyst for a given reaction was predicted to be a compromise between too weak and too strong chemisorption. Balandin transformed this concept to a semiquantitative theory by predicting that a plot of the reaction rate of a catal)Tic reaction as a function of the heat of adsorption of the reactant should have a sharp maximum. He called these plots volcano-shaped curvesl This prediction was confirmed by Fahrenfort et al." An example of their volcano-shaped curve is reproduced in Fig. 9.1. They chose the catalytic decomposition of formic acid... 

The semiquantitative theory was first applied by Dunitz and Orgel to ferrocene (55), where it was found that a value of k 5.0 eV in the expression Hij=kSij gave satisfactory agreement with observed bond energies the inclusion of the 4p orbitals in these calculations was made later (57) and shown to be in accord with observed X-ray absorption data. 

Gas-phase reactions will bo given an emphasis beyond the other areas of kinetics, precisely because the extensive development of quantitative thermodynamic data and semiquantitative theories makes it possible to interpret the details of these complex reactions of gases to a degree far beyond anything now available for reactions in condensed phases. 

Jones, 1936 1958, p. 159), which has long been thought to dominate the electronic structure of the covalent solids. A sketch of that zone is shown in Fig. 18-3,b. The volume contained within it is just sufficient to contain the four electrons per atom, and it would be natural to assume that all Bragg planes other than those bounding the Jones Zone are unimportant and could be neglected in a semiquantitative theory. 

Bartell, L.S. (1964). Semiquantitative Theory of Resonance Using Pauling Bond Orders. Tetrahedron, 20,139-153. 

Fourier component of the pseudopotential, which is the largest matrix element, dominates all others leads to a semiquantitative theory of the bonding properties of the covalent systems. This theory allows us to identify the even and odd parts of that pseudopotential with the covalent and polar energies of the LCAO theory, and provides another rationalization for the d" -dependence of the covalent energy. As we deform the covalent structure into an ionic structure, we see that the covalent energy ceases to contribute to the bonding properties in this approximation. 

Recent research with the II-VI semiconductor material ZnO (band gap = 3.8 eV, similar to those of the heavy-metal azides) has revealed that the ability of the specimen to retain stable ions formed by electrostatic charging is a critical function of the degree of surface order A highly disordered surface allows the formation of stable adsorbed ions a highly ordered surface does not [43]. A semiquantitative theory to account for this has been proposed [44]. Further, with disordered surfaces, the location of the electronic state of the adsorbed ions relative to the band structure of the specimen can be probed by an optical discharge technique to yield information about the electronic properties of the surface [43]. These potentialities, coupled with the field-assisted initiation capabilities of an azide specimen, argue that the electrostatic charging technique should be applied quantitatively to explosive azides. 

If one wants to develop a semiquantitative theory of the resonance, integrals it suffices to study the case of ethylene because the resonance integrals used in the extended theory are supposed to be independent of the number of atoms in the molecule. 

Now we shall consider a semiquantitative theory of the shape of the broad component of the melt spectrum. Since over 70% of the protons are on para-substituted aromatic rings in PET/60PHB and PET/30PHB/30THQ, these protons will contribute most of the spectrum. As a first approximation, the neighboring protons on each ring can be considered to be an isolated proton pair. Pake has discussed the spectrum for an isolated pair of protons. Each pair contributes two lines centered at the same position and separated by... 

The authors of [33] considered their liquid Newtonian. Going back to Fig. 3 and its discussion, it becomes clear that this theory is fully applicable in qualitative and even semiquantitative analysis of thermoplastic foaming. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

Table I shows the values of the relaxation time calculated using Eqs. (249) and (250). Both the inertial time and the long time decrease with increasing density. This is in agreement with the trend of the curves in Fig. 6. Indeed, the actual estimates of the relaxation times in Table I are in semiquantitative agreement with the respective boundaries of the plateaux in Fig. 6. The estimate of Xiong, the upper limit on x that may be used in the present theory, is perhaps a little conservative.

Development of the quantum mechanical theory of charge transfer processes in polar media began more than 20 years ago. The theory led to a rather profound understanding of the physical mechanisms of elementary chemical processes in solutions. At present, it is a good tool for semiquantitative and, in some cases, quantitative description of chemical reactions in solids and solutions. Interest in these problems remains strong, and many new results have been obtained in recent years which have led to the development of new areas in the theory. The aim of this paper is to describe the most important results of the fundamental character of the results obtained during approximately the past nine years. For earlier work, we refer the reader to several review articles.1 4... 

The ability of theory to account for the wide range of spin-forbidden reactivity observed in a near-quantitative way means that the same theoretical models can be trusted to give insight into more complex transition metal systems. For these other systems, detailed experimental data are not always present for comparison, and it is not always possible to carry out high-level ab initio computations in order to calibrate DFT methods. Nevertheless, the dual approach of locating MECPs and using NA-TST will clearly be able to provide lots of qualitative and semiquantitative insight into reactivity. 

This chapter is intended to provide basic understanding and application of the effect of electric field on the reactivity descriptors. Section 25.2 will focus on the definitions of reactivity descriptors used to understand the chemical reactivity, along with the local hard-soft acid-base (HSAB) semiquantitative model for calculating interaction energy. In Section 25.3, we will discuss specifically the theory behind the effects of external electric field on reactivity descriptors. Some numerical results will be presented in Section 25.4. Along with that in Section 25.5, we would like to discuss the work describing the effect of other perturbation parameters. In Section 25.6, we would present our conclusions and prospects. 

The DLVO theory is a theoretical construct that has been able to explain many experimental data in at least a semiquantitative manner it illustrates plausibly that at least two types of interactins (attraction and repulsion) are needed to account for the overall interaction energy as a function of distance between the particles. 

I think it is unique in chemistry that such complicated reactions can be understood semiquantitatively in quite simple physical terms. And I believe it is a great achievement that this very accurate experimental information has been acquired and that it is possible to make such direct successful comparison with theory. 

Bloembergen et al. (S) have presented a relationship between the correlation time for molecular rotation in liquids and the relaxation times assuming that relaxation takes place via mechanism (i) of Section II,A,3. Although the theory can be at best semiquantitative when applied to the protons of water molecules adsorbed on silica gel, values of the nuclear correlation time have been calculated 18) from the T data. These correlation times as a function of x/m show a definite change of slope near a monolayer coverage. This result, if corroborated by data on other solids, may provide a rather unique method for the determination of monolayer coverage. 

Diffusional Dynamics. If the colloidal crystal is stable, does it explain the extraordinarily slow diffusional behavior While some detailed theories of the dynamics of colloidal crystals have been constructed (25.30), they are difficult to apply to our DNA solutions. Therefore, it is of interest to present a much simpler semiquantitative approach. 

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