Experimental Trends and Theoretical Interpretation

Our primary objective has been to present the experimental results in a convenient, combined form rather than to discuss their significance in great detail. In view of the extreme physical and chemical complexity of anthracite and the limited amount of experimental investigation to which the material has been subjected at present, an elaborate theoretical discussion would be pointless. Indeed, it is improbable that the kinetics of volatile matter release for such a complex material will ever submit to a satisfactory correlation by simple functional relationships. In spite of these difficulties, it is of interest to discuss some of the general trends exhibited by the experimental data and their interpretation by suggesting approximate theoretical and mathematical models for the release mechanism. 

The alkali metals form a homogeneous group of extremely reactive elements which illustrate well the similarities and trends to be expected from the periodic classification, as discussed in Chapter 2. Their physical and chemical properties are readily interpreted in terms of their simple electronic configuration, ns, and for this reason they have been extensively studied by the full range of experimental and theoretical techniques. Compounds of sodium and potassium have been known from ancient times and both elements are essential for animal life. They are also major items of trade, commerce and chemical industry. Lithium was first recognized as a separate element at the beginning of the nineteenth eentury but did not assume major industrial importance until about 40 y ago. Rubidium and caesium are of considerable academic interest but so far have few industrial applications. Francium, the elusive element 87, has only fleeting existence in nature due to its very short radioactive half-life, and this delayed its discovery until 1939. 

Theoretical calculations on model PCET systems have assisted in the interpretation of experimental data and have provided insight into the underlying fundamental principles of PCET reactions. The theoretical framework described in this chapter enables the prediction of experimentally testable trends in rates and kinetic isotope effects. The interplay between experiment and theory will be vital to further progress in the field. 

Mechanistic interpretations of the copper-catalyzed aromatic nucleophilic substitution reactions remain unsettled even after half-a-century of debate [19, 20]. Possible pathways involve an S Ar reaction mediated by copper complexation to the pi-system (Scheme 4a), an electron transfer reaction followed by halide dissociation (Scheme 4b), four-centered c-bond metathesis reaction (Scheme 4c) and Cu(l) oxidative addition to the Ar-X bond, followed by the nucleophile exchange and reductive elimination in the resulting Cu(lll) system (Scheme 4d). There is presently a considerable body of experimental and theoretical data for and against each of the proposed mechanisms [21]. While the mechanistic studies were mostly related to the formation of C-C, C-O and C-N bonds, it is likely that the copper-catalyzed halogen exchange reactions follow a similar trend. 

In the following, we will present jellium-related theoretical approaches (specifically the shell-correction method (SCM) and variants thereof) appropriate for describing shell effects, energetics and decay pathways of metal-cluster fragmentation processes (both the monomer/dimer dissociation and fission), which were inspired by the many similarities with the physics of shell effects in atomic nuclei (Section 4.2). In Section 4.3, we will compare the experimental trends with the resulting theoretical SCM interpretations, and in addition we will discuss theoretical results from first-principles MD simulations (Section 4.3.3.1). Section 4.4 will discuss some of the latest insights concerning the importance of electronic-entropy and finite-temperature effects. Finally, Section 4.5 will provide a summary. 

A theoretical treatment of aqueous two-phase extraction at the isoelectric point is presented. We extend the constant pressure solution theory of Hill to the prediction of the chemical potential of a species in a system containing soivent, two polymers and protein. The theory leads to an osmotic virial-type expansion and gives a fundamentai interpretation of the osmotic viriai coefficients in terms of forces between species. The expansion is identical to the Edmunds-Ogston-type expression oniy when certain assumptions are made — one of which is that the solvent is non-interacting. The coefficients are calculated using simple excluded volume models for polymer-protein interactions and are then inserted into the expansion to predict isoelectric partition coefficients. The results are compared with trends observed experimentally for protein partition coefficients as functions of protein and polymer molecular weights. 

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