Theoretical Survey

Recalling the equations shown in Chapter 1 devoted to the theoretical basis of the diffusion process, there are the following equations to consider  

The solution of the problem, whatever the partition factor, is given as follows  

The kinetics of transfer of diffusing substance, by using the dimensionless number M/M , is expressed in terms of the dimensionless number D-t/L by the following Equation (1.52)  

In order to point out the error from using such a software based on the infinite value of the coefficient of convective transfer of the substance at the polymer-liquid interface, the kinetics of the absorption (or desorption) of the same substance are calculated by using the same operational conditions, except for the value of the dimensionless number R which is taken either as finite or infinite. Moreover, the curves are expressed in different ways by selecting two different scales for the time put in the abscissa. 

The kinetics are shown in the following six figures for different values of R selected within the 10-2 range, and for R infinite, as well as for different values of the thickness of the film, so as to compare them. These sheets are in contact with the liquid on both sides. 

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Tancrede, M., R. Wilson, L. Zeise, and E. A. C. Crouch, The Carcinogenic Risk of Some Organic Vapors Indoors A Theoretical Survey, Atmos. Environ., 21, 2187-2205 (1987). 

B. T. Luke, J. A. Pople, M.-B. Krogh-Jespersen, Y. Apeloig, J. Chandrasekhar, and P. v. R. Schleyer,/. Am. Chem. Soc., 108,260 (1986). A Theoretical Survey of Singly Bonded Silicon Compounds. Comparison of the Structures and Bond Energies of Silyl and Methyl Derivatives. 

The potential of the m-benziporphyrin skeleton to produce aromatic macrocycles, foreseeable in the above discussion of its hypothetical tautomers, was actually revealed by introduction of hydroxy groups on the phenylene ring. These functionalities serve as additional tautomerization sites, which become effective aromaticity switches in appropriately designed systems. Theoretical insight into the switching capabilities of hydroxybenziporphyrins was gained from a theoretical survey of relative stabilities and aromatic character of various hydroxybenziporphyrin tautomers [287, 288], which was concurrently verified by experimental work (Table 2) [250],... 

Besides various detection mechanisms (e.g. stimulated emission or ionization), there exist moreover numerous possible detection schemes. For example, we may either directly detect the emitted polarization (oc PP, so-called homodyne detection), thus measuring the decay of the electronic coherence via the photon-echo effect, or we may employ a heterodyne detection scheme (oc EP ), thus monitoring the time evolution of the electronic populations In the ground and excited electronic states via resonance Raman and stimulated emission processes. Furthermore, one may use polarization-sensitive detection techniques (transient birefringence and dichroism spectroscopy ), employ frequency-integrated (see, e.g. Ref. 53) or dispersed (see, e.g. Ref. 54) detection of the emission, and use laser fields with definite phase relation. On top of that, there are modern coherent multi-pulse techniques, which combine several of the above mentioned options. For example, phase-locked heterodyne-detected four-pulse photon-echo experiments make it possible to monitor all three time evolutions inherent to the third-order polarization, namely, the electronic coherence decay induced by the pump field, the djmamics of the system occurring after the preparation by the pump, and the electronic coherence decay induced by the probe field. For a theoretical survey of the various spectroscopic detection schemes, see Ref. 10. 

In this chapter we draw attention to some of the problems in this area and outline a few methods of approach, which are amplified in the advanced text by Ward [2]. A theoretical survey, using sophisticated mathematical methods, is given in the text by Lockett [3], and the contrasting approach of the practical engineer is typified in the work of Turner [4]. Ferry s textbook [5] covers both theoretical and practical aspects of pol3mier viscoelasticity. The more recent work of Lakes [6] covers some aspects of non-linearity. 

The following theoretical outline is limited to a presentation of the definitions and equations necessary for the description of the diffraction of electrons from free molecules. More detailed theoretical surveys, including the deduction of the equations, have been given by various authors. > ... 

I have already examined these problems in a rather compressed manner in earlier publications (Medvedev, 1963,1965). More recently certain individual aspects have been dealt with in a number of theoretical surveys, but the progress now being made in this field is so rapid that many aspects of the problem demand a thorough reappraisal. 

I shall examine this group of theoretical surveys which have recently appeared very selectively and briefly for two reasons. 

The existence of termination (and conventional initiation) provides the rate equations of LRP v th several unique features depending on activation-deactivation mechanisms and experimental conditions, as will be theoretically surveyed in this section. 

The binary alloy of platinum and rhodium is especially known for the catalytic properties of its surfaces [123-126]. Therefore, various publications have already attended to this system for example. Refs [125-130] discuss the relevancy of Pt-Rh in three-way catalysts, and some empirical models about the catalytic process are developed in Refs [131-133]. Here, we take two steps back first, because the whole alloy Pt-Rh will be brought down to its atomic constituents, and second, because not the dynamics of the catalytic process itself wiU be under investigation but, more fundamentally, the equilibrium properties of a Pt-Rh surface. This approach joins other atomistic works on Pt-Rh surfaces, experimental papers such as Refs [1, 134], as well as numerous theoretical surveys such as Refs [2,106, 135-137]. 

Pantony, D. A. and Vasu, K. L. (1968), Studies in the Corrosion of Metals Under Melts - 1. Theoretical Survey of Fire-Side Corrosion of Boilers and Gas-Turbines in the Presence of Vanadium Pentoxide , J. Inorg. Nucl. Chem., Vol. 30, pp. 423-32. 

Robeyns, I. (2005). The capability approach - A theoretical survey. Journal of Human Development, 6(1), 94-114. 

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