Empirical rules

The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

Slater provided a series of empirical rules for choosing the orbital exponents (, which are... 

Cram s Rule JACS 1952, 74,2748 JACS 1959, 84,5828. empirical rule... 

Sets of empirical rules, often referred to as Woodward s rules or the Woodward-Fieser rules, enable the absorption maxima of dienes (Table 7.11) and enones and dienones (Table 7.12) to be predicted. To the respective base values (absorption wavelength of parent compound) are added the increments for the structural features or substituent groups present. When necessary, a solvent correction is also applied (Table 7.13). 

Arachno Clusters 2n + 6 Systems). In comparison to the number of known closo and nido boranes and heteroboranes, there are relatively fewer arachno species. Partly because of the lack of a large number of stmctures on which to base empirical rules, arachno stmctures appear to be less predictable than their closo and nido counterparts. For example, there are two isomeric forms of one with the arachno [19465-30-6] framework shown... 

J. Pabian and H. Hartmann, Eight Absorption of Organic Colorants Theoretical Treatment and Empirical Rules, Springer-Vedag, Heidelberg, 1980. 

The heat capacity, the heat required to raise 1 g-mole drrough one kelvin, can be calculated at temperatures generally above 300 K by two simple empirical rules. The first of these, Dulong and Petit s rule, was discovered in the course of calorimeU ic smdies of the heat capacities of the elements and shows drat the heat capacity has a value,... 

Traditional control systems are in general based on mathematical models that describe the control system using one or more differential equations that define the system response to its inputs. In many cases, the mathematical model of the control process may not exist or may be too expensive in terms of computer processing power and memory. In these cases a system based on empirical rules may be more effective. In many cases, fuzzy control can be used to improve existing controller systems by adding an extra layer of intelligence to the current control method. 

If R = H in the above example, then according to the beta scission rule (an empirical rule) only route b becomes possible, and propylene would be a product ... 

Similarity effect on chemical events may be traced back to the old empirical rule that like dissolves like similia similibus solvuntur). This rule, however, implies the similarity between solute and solvent molecules in polarity or functional group, but not in molecular shape. 

Five percent rule The empirical rule that the approximation a — x a is valid if x 0.05a, 362 Flerov, G. N., 515 Flotation process, 539 Fluids, supercritical, 232 Fluoride, 190,559 Fluorine... 

The empirical rule described above for the enantiofacial differentiation in AE of primary allylic alcohols also applies to secondary allylic alcohols. The new aspect that needs to be taken into consideration in this case is the steric hindrance arising from the presence of a substituent (R4) at the carbon bearing the hydroxy group (Figure 6.3). This substituent will interfere in the process of oxygen delivery, making the oxidation of one enantiomer much faster than the reaction of the other one. The phenomenon is so acute that in practice kinetic resolution is often achieved (Figure 6.4) [27]. 

Benson17 has tried to collect some thermodynamic data based on a number of empirical rules for this class of radicals. He estimated heats of formation for HS02, MeSO 2) PhSO 2 and HOSO 2 as —42, —55, —37 and — 98kcalmor respectively. He also estimated a stabilization energy for the benzenesulfonyl radical of 14 kcal mol"1, which is very similar to that of the benzyl radical. However, recent kinetic studies18 (vide infra) have shown that arenesulfonyls are not appreciably stabilized relative to alkanesulfonyl radicals, in accord with the ESR studies. 

We can summarize these empirical rules by introducing the concept of the activity, zzj, of a substance J ... 

When a substituent is introduced directly into an aromatic molecule, it may enter into certain of the available positions more readily than into others. This phenomenon of orientation has been exhaustively studied, and empirical rules have been found which describe the experimental results fairly satisfactorily. In a monosubstituted benzene CeHjR, for example, the introduction of... 

This theoretical result is completely substantiated by experiment. Goldschmidt,31 from a study of crystal structure data, observed that the radius ratio is large for fluorite type crystals, and small for those of the rutile type, and concluded as an empirical rule that this ratio is the determining factor in the choice between these structures. Using Wasastjerna s radii he decided on 0.67 as the transition ratio. He also stated that this can be explained as due to anion contact for a radius ratio smaller than about 0.74. With our radii we are able to show an even more satisfactory verification of the theoretical limit. In Table XVII are given values of the radius ratio for a large number of compounds. It is seen that the max-... 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

It is often of industrial interest to be able to predict the equilibrium sorption of a gas in a molten polymer (e.g., for devolatilization of polyolefins). Unfortunately, the Prigogine-Flory corresponding-states theory is limited to applications involving relatively dense fluids 3,8). An empirical rule of thumb for the range of applicability is that the solvent should be at a temperature less than 0.85 Tp, where Tp is the absolute temperature reduced by the pure solvent critical temperature. 

At this stage of development of the subject it is appropriate to consider a number of empirical rules which may serve to indicate the important variables. It would seem likely that (i) there will be competitition between each species in the system for the sites available at the electrode surface, and that (ii) for each species in the system there will be an equilibrium between the solution and the adsorbed state. Thus it would be expected that the solution constituents would affect these equilibria in two ways (a) if one of the constituents of the medium is itself adsorbed, the reactant will tend to be displaced (b) if the reactant is strongly solvated, complexed or ion paired by constituents of the medium, the species in solution will be favoured. 

Features of chemical structure that affect the degree of molecular freedom influence both the crystalline melting point and the glass transition temperature. Moreover, such features have roughly similar effects on both properties, so that the empirical rule has been found that for many polymers ... 

In the absence of more elaborate methods of observing of short-lived bromination intermediates, the present results can provide some useful empirical rules, the most important being as follows. 

Because of our inability to analyze the interaction of microscopic QM systems and macroscopic measuring devices to a sufficient degree, we make use of a set of empirical rules that are known as measurement theory. Some day, measurement theory will become a proven set of theorems in QM,, as the proponents of the decoherence theory, among others, claim. Until such time, it is beneficial to introduce the measurement process, and the principles associated with it, separately from the dynamics described by the Schrbdinger equation. 

From these studies of sugars and related molecules, it is possible to derive empirical rules whereby Ri(ns) values can be used as the basis for configurational assignments. These rules are illustrated graphically in Fig. 5, where the relative relaxation-efficiency between two protons is plotted as a function of the interproton distance. 

Apart from the most widely utilized Snyder and Soczewinski semiempirical model of linear TEC, several other physicochemically grounded approaches to the same question exist as well [12]. Also, a choice of the empirical rules in mathematical... 

The common method of treating rod-pumped wells is to periodically batch inhibitor into them. The treatment period for a given well is selected using empirical rules based on well production volumes. A successful and economic corrosion inhibition program must carefully control the inhibitor concentration in the well fluids. Environmental aspects and efficacious inhibitor usage necessitate the measurement of very low corrosion inhibitor concentrations. Inhibitor concentrations as low as one part per million are significant, thus... 

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