Empirical Considerations

The point of the identification of d-ionization bands in complex P.E. spectral patterns of coordination compounds lends itself to several empirical considerations. 

The relative permeability is difficult to quantify. It usually is estimated on the basis of laboratory experiments, as a function of relative saturation. In three-phase NAPL-water-air systems, each relative permeability is dependent on the relative saturation of each of the phases. Modeling based on empirical considerations can be employed. For example. Blunt (2000) discusses a model to estimate three-phase relative permeability, based on saturation-weighted interpolation of two-phase relative permeabilities. The model accounts for the trapping of the NAPL and air (gas)... 

As for direct emulsions, the presence of excess surfactant induces depletion interaction followed by phase separation. Such a mechanism was proposed by Binks et al. [ 12] to explain the flocculation of inverse emulsion droplets in the presence of microemulsion-swollen micelles. The microscopic origin of the interaction driven by the presence of the bad solvent is more speculative. From empirical considerations, it can be deduced that surfactant chains mix more easily with alkanes than with vegetable, silicone, and some functionalized oils. The size dependence of such a mechanism, reflected by the shifts in the phase transition thresholds, is... 

On the basis of empirical considerations and the influence of various coordination centers (see Section 16.3.3.2) on the UV-vis bands of MoS4, the assignments v2 = 312 2e and v3 = /, - 4t2 are probable. The positions of the metal reduction bands can also be related to the redox behavior of the thioanions. 

The problem of reaction mechanism has been attacked from the standpoint of entropies of activation on two somewhat different fronts. On the one hand, mechanistic significance has sometimes been attached to the actual value of AS observed for a given reaction. The value can be compared with that expected for a given transition state structure on the basis of partition function calculations, empirical considerations or thermodynamic data for corresponding equilibria. On the other hand, a change in mechanism between two similar reactants is sometimes indicated by very dissimilar entropies of activation. Both types of information are of a qualified nature. 

The value of n is based on theoretical and empirical considerations and depends on the type of agitation problem. 

Although other methods using such experimental data have been documented,theoretical and/or empirical considerations have led to various expressions involving a dependence on ionic strength, I, which is a major factor influencing the activity of solutes in aqueous solution. 

Although the importance of the ionic strength was first realized from empirical considerations, it is now known to play an important part in the theory of electrolytes. It will be observed that equation (12) on page 83, which gives the reciprocal of the thickness of the ionic atmosphere according to the theory of Debye and Hiickel, contains the quantity where n is the number of ions of the zth kind in unit volume... 

Rejecting the orthodox view - shared by positivists and postpositivists alike - that only empirical considerations are relevant to the justification of scientific theories, Laudan, along with Toulmin and Gerd Buchdahl, recognized the... 

Buckingham and Pople derived the equation from a perturbation treatment of atoms or molecules in a magnetic and a uniform electric field. This treatment requires that the perturbations of the magnetic and the electric field should be of the same order of magnitude. Because of the 1/c prefactor of the magnetic field, only weak electric fields should be considered. In semi-empirical considerations this equation is used to treat perturbations from... 

Undoubtedly, the methods most widely used to solve the Schrodinger equation are those based on the approach originally proposed by Hartree [1] and Fock [2]. Hartree-Fock (HF) theory is the simplest of the ab initio or "first principles" quantum chemical theories, which are obtained directly from the Schrodinger equation without incorporating any empirical considerations. In the HF approximation, the n-electron wavefunction is built from a set of n independent one-electron spin orbitals which contain both spatial and spin components. The HF trial wavefunction is taken as a single Slater determinant of spin orbitals. 

The choice and calculation of the reactor for a specific chemical reaction involves solving the following problems, on the basis of theoretical knowledge or by more empirical considerations ... 

Thus, at this concentration equal amounts of cyclic and open products are formed. A significantly more diluted solution will, therefore, give predominantly the desired macrocycle. Conversely, a solution that is too concentrated will afford almost exclusively polymers. This rigorous procedure is, in practice, not used, and the cyclization reactions are conducted on the basis of more empirical considerations that, nevertheless, respect the necessity to operate in low concentrations. 

The model of TMT is one of the few models solely targeted at predieting conductivity behaviour of a membrane, and in contrast to the model of SZG, is based on physical rather than purely empirical considerations [22]. It is in this vein that they invoke the dusty fluid model (DFM) to model transport in the membrane. Before considering the model of TMT we examine the baek-ground of the DFM and the binary friction model (BFM). 

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