Detailed theory

A more detailed theory of electrophoresis is found in Refs. 9 and 58. The motion of the ions in the double layer due to the field F and due to the relative motion of the particle, cause a retardation of the electrophoretic motion that must be considered to... 

A 1984 volume reviews in detail theories and experiments [37] on nuilticritical points some important papers have appeared since that time. 

The detailed theory of bonding in transition metal complexes is beyond the scope of this book, but further references will be made to the effects of the energy splitting in the d orbitals in Chapter 13. 

Figure 10.13 shows such plots of z versus D/X, where D is r for random coils, R for spheres and disks, and L for rods. More detailed theories permit these curves to be extended to larger values of than is justified by consideration of Eq. (10.97) alone. In the following example we illustrate an application of this simple method for estimating particle dimensions. 

E. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd ed., John Wiley Sons, Inc., New York, 1967. An excellent volume that stresses the reactions of complexes ia solution a background and a detailed theory section is iacluded that is largely crystal field theory, but some advantages and disadvantages of molecular orbital theory are iacluded. 

Foam Drainage and Overflow The rate of foam overflow on a gas-free basis (i.e., the total volumetric foamate rate Q) can be estimated from a detailed theory for foam drainage [Leonard and Lemlich, Am. Inst. Chem. Eng. J., 11, 18 (1965)]. From the resulting relationship for overflow [Fanlo and Lemlich, Am. Inst. Chem. Eng. Symp. Ser., 9, 75, 85 (1965)], Eq. (20-52) can be employed as a convenient approximation to the theory so as to avoid tri and error over the usual range of interest for foam of low liquid content ascending in plug flow ... 

U.S. EPA has documented case histories of full-scale treatment of aluminum forming wastewaters, which are included in Appendixes A, B, C, and D of this chapter for reference. The detailed theories and principles of the full-scale treatment processes can be found in the literature.8-10... 

For example, reactions of the electronically excited state of Cu, a pseudoalkali, are amenable to detailed theory. 

These results are very encouraging. They do, however, emphasize the need to measure flowing bubble texture and surfactant properties independently before rigorous experimental tests of detailed theories can be made. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

Detailed theories include all these effects in the reaction cross-section, which is then a function of all the various dynamic parameters ... 

The senior author of the present paper took up the suggestion of Chmelir, Marek, and Wichterle and developed from it a detailed theory which he presented in the form of three suppositions, accompanied by an account of the origin of the theory and a critical assessment of it [7]. Some further discussions of the theory and an interim report on the evidence for it were presented subsequently [8]. The present paper contains a full account of the theory, its testing, and its application. For the sake of clarity the original three suppositions are now presented as propositions ... 

Table 5.2 compares the dissolution rate of various Al-minerals. The differences are remarkable. At pH = 3, the half life of surface sites of different aluminum (hydroxides varies from 2 years (corundum) to 20 hours (bayerite). The large difference in rates must be due to different coordinative arrangements of the active surface groups. Although no detailed theory is available, it is perhaps reasonable to assume, that the dissolution rate increases with the frequency of surface groups which be present as endstanding =AI-OH groups. 

A detailed theory of energy transfer by the Coulombic mechanism was developed by Forster, so the process is often referred to as Forster resonance energy transfer (FRET). According to the Forster theory, the probability of Coulombic energy transfer falls off inversely with the sixth power of the distance between the donor and the acceptor. For... 

Population genetics has produced a detailed theory of the relationship between frequency, drift, and selective value of genetic variation (Nei, 1975 Hard and Clark, 1989 Li, 1997). The problem with its straightforward application is that the main parameters, such as history of population size, fixation rate, and selective pressure, are difficult to establish. 

Calculations of isotope effects and isotopic exchange equilibrium constants based on the Born-Oppenheimer (BO) and rigid-rotor-harmonic-oscillator (RRHO) approximations are generally considered adequate for most purposes. Even so, it may be necessary to consider corrections to these approximations when comparing the detailed theory with high precision high accuracy experimental data. 

For choosing a suitable cell construction and optimal reaction conditions in the cell, it is inevitable to consider the fundamental correlations between electrode potential and cell current and their influence on selectivity and yield of the electrochemical reactions. Therefore, a simplified overview is given here. The detailed theory is elucidated in Chapter 1. 

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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