Possible Theoretical Developments

Consider the possibility of developing for the new system a rigorous, theoretically based design procedure which will be valid over a wide range of design conditions. 

In this review recent theoretical developments which enable quantitative measures of molecular orientation in polymers to be obtained from infra-red and Raman spectroscopy and nuclear magnetic resonance have been discussed in some detail. Although this is clearly a subject of some complexity, it has been possible to show that the systematic application of these techniques to polyethylene terephthalate and polytetramethylene terephthalate can provide unique information of considerable value. This information can be used on the one hand to gain an understanding of the mechanisms of deformation, and on the other to provide a structural understanding of physical properties, especially mechanical properties. 

Therefore, a possible theoretical concept of using such materials in LIB s is based on the development of various composites (alloys), in which the volume variations of the electroactive constituents of AM during cycling can be compensated by the elastic properties of the electrically conductive matrix (Figure 2). 

We discussed mainly some of the possible applications of Fukui function and local softness in this chapter, and described some practical protocols one needs to follow when applying these parameters to a particular problem. We have avoided the deeper but related discussion about the theoretical development for DFT-based descriptors in recent years. Fukui function and chemical hardness can rigorously be defined through the fundamental variational principle of DFT [37,38]. In this section, we wish to briefly mention some related reactivity concepts, known as electrophilicity index (W), spin-philicity, and spin-donicity. 

It is possible to develop the ideas behind PCR and to a lesser extent behind PLS, based on chemical ideas and intuition. Naturally, this is not the only way and both PCR and PLS methods have been developed on pathways that are theoretically oriented. 

With the improvement of analytical techniques, it is now possible to measure oxygen isotopic profiles in minerals. By analogy to the concepts of bulk mineral closure temperature versus closure temperature at every point in the interior of a mineral for the case of thermochronology, future theoretical development will need to clarify the concepts and meanings of Tc and Tae based on interior isotopic or elemental compositions of two contacting minerals. Furthermore, the principles of the above discussion may also be applied to elemental exchange reactions, such as Fe-Mg exchange between minerals. 

A fiirfcher theoretical development which would seem to be possible concerns what Bernal has called the mediating influence of the groups attached to Ox and 02. If either or both of Ox and G2 are part of a -electron system, then there will be a resonance effect facilitating structures such as (iv) and (v), This is just what is found (see Section 2) in a study of dipole moments. Further, if the ligands attached to Ox and 02 are polar, whether electron-donating or electron-accepting,... 

Matrices are also a great convenience in the theoretical development of quantum chemistry. They make possible an economy of notation, and use of matrix-algebra theorems simplifies derivations considerably. Much of the quantum chemistry literature is formulated in matrix language. The vector-space formulation of quantum mechanics (which we have just touched on) is very fruitful for advanced applications see Merzbacher, Chapter 14 and later chapters. 

Ethylene oxides, like other three-membered ring systems, possess many singular features that invite a basis in theory. To satisfy Hub demand, much effort has boon devoted to the task of determining with precision such fundamental properties of the molecule os bond lengths, bond angles, and bond energies- With the advent of modern instrumental methods it has been possible to develop a dependable physical basis fin- theoretical speculations on the electronic structure of ethylene oxide. The present section is concerned with this aspect of epoxide chemistry. 

For future theoretical developments in the field of transport properties of binary and higher-order mixtures, the simplest case seems to study the influence of the variation in mass of one of the species on the transport properties. Without a full understanding of this pure mass effect on the transport properties, it is not possible to analyze the effect of the translational-rotational coupling in real molecules. Toward this goal the simplest system that can be considered is a binary mixture at infinite solute dilution where the effect of the solute-solvent mass ratio on the solute diffusion can be studied. 

If it were possible to develop a theoretical strength model for reinforced thermoplastics, it would be much easier to measure their poten-... 

The first explanation and use of such a pseudopotential is due to Heilman5 (1935) who used it in atomic calculations. More recently the pseudopotential concept was reformulated by Phillips and Kleinman7 who were interested in its application to the solid state.8-10 Research in both solid- and liquid-state physics with pseudopotentials was reviewed by Ziman,11 and work in the fields of atomic spectroscopy and scattering has been discussed by Bardsley.12 For an earlier review on applications to the molecular environment the reader is referred to Weeks et a/.13 In this article we shall concentrate on molecular calculations, specifically those of an ab initio nature. Our objective in Section 2 has been to outline the theoretical origins of the pseudopotential approximation, and in Section 3 we have described some of the techniques which have been used in actual calculations. Section 4 attempts to present results from a representative sample of pseudopotential calculations, and our emphasis has been to concentrate on particular molecules which have been the subjects of investigation by the various approaches, rather than to catalogue every available calculation. Finally, in Section 5, we have drawn some conclusions on the relative merits of the different methods and implementations of pseudopotentials. Some of the possible future developments are outlined in the context of the likely progress in quantum chemistry. 

Consider the possibility of developing for the new system a rigorous, theoretically based design procedure which will be valid over a wide range of design conditions. Note that commercial software is readily available today to develop a rigorous model in a relatively small amount of time. These topics are further discussed in the subsections that follow. 

There are many different kinds of discharge plasmas4,24-27 and it is not possible to develop a theoretical model applicable to all of them. We must therefore re-... 

The developments of impedance spectroscopy described in this paper highlight that precise investigations of polarization effects under conditions of monotonously distributed potentials are possible. Further development of experimental and theoretical bases of the method will allow direct studies of discontinuity surface states that are of great fundamental and applied interest. 

The problem of diffusion modeling in polymers changes to some degree when one envisages to develop a really atomistic model, with trully predictive capabilities and without making any ad hoc assumption on the molecular behaviour and/or motions in the polymer penetrant system. In principle, a possibility to develop such diffusion modelings, is to simulate theoretically the process of penetrant diffusion in a polymer matrix by computer calculations. 

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