Rationalisation

In both these NDT application fields, new construction and maintenance, these tendencies can lead to rationalisation, with cost reduction as a result, maintaining existing safety levels. 

It can be readily confirmed thaf by decreases as the number of bonds N increases and/or llieir length (r ) decreases. This relationship between the bond strength and the number of neighbours provides a useful way to rationalise the structure of solids. Thus the high coordination of metals suggests that it is more effective for them to form more bonds, even though each individual bond is weakened as a consequence. Materials such as silicon achieve the balance for an infermediate number of neighbours and molecular solids have the smallest atomic coordination numbers. 

The first use of QSARs to rationalise biological activity is usually attributed to Hansc [Hansch 1969]. He developed equations which related biological activity to a molecmle electronic characteristics and hydrophobicity. For example ... 

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

In summary, it seems that for most Diels-Alder reactions secondary orbital interactions afford a satisfactory rationalisation of the endo-exo selectivity. However, since the endo-exo ratio is determined by small differences in transition state energies, the influence of other interactions, most often steric in origin and different for each particular reaction, is likely to be felt. The compact character of the Diels-Alder activated complex (the activation volume of the retro Diels-Alder reaction is negative) will attenuate these eflfects. The ideas of Sustmann" and Mattay ° provide an attractive alternative explanation, but, at the moment, lack the proper experimental foundation. 

Despite the availability of relevant mechanistic parameters in the form of the rate constants and binding constants in Table 3.2, rationalisation of the observed enantioselectivities is still rather complicated and therefore some additional information has been gathered. 

Another consequence of the above analysis is, that the surprising inefficiency of micellar aggregates to catalyse Diels-Alder reactions can now be rationalised. Obviously, micelles are able to bind diene and dienophile efficiently but in different parts of the micelle. The reactions seems to take place at the surface of the micelle in a rather aqueous environment, where the concentration of diene is low. 

A principal aim of the discussion thus far has been to set out a theoretical framework within which it is possible to rationalise the effects of surface roughness on adhesion. It may be useful to summarise this framework before examining practical examples taken from the literature. 

Impact strength also increases as the notch depth is decreased. The variation of impact strength with notch depth and radius may be rationalised for some materials by use of the linear elastic stress concentration expression. 

In recent years impact testing of plastics has been rationalised to a certain extent by the use of fracture mechanics. The most successful results have been achieved by assuming that LEFM assumptions (bulk linear elastic behaviour and presence of sharp notch) apply during the Izod and Charpy testing of a plastic. 

Pick, D.. (1993). War Machine The Rationalisation of Slaughter in the Modern Age. New Haven, CT Yale University Press. 

To balance equations 10.2 and 10.3 in terms of electrical charge it has been necessary to add four electrons to the right-hand side of equation 10.2 and to the left-hand-side of equation 10.3. However, simple addition and rationalisation of equations 10.2 and 10.3 yields equation 10.1. 

It then follows that at low bromine concentrations this latter process is less likely, consequently the kinetic order is reduced. More ionic media will facilitate equilibrium (137) without the need for intervention of equilibrium (139) and vice versa, so that the observed variation in the kinetic order with this condition then follows. The absence of high kinetic orders in molecular chlorination also becomes rationalised since the C1J ion is not as stable as BrJ. 

The reaction was also found to be inhibited by addition of dioxan and tetra-hydropyran, the rate decrease being proportional to the ether concentration. The results were rationalised by the assumption that 2 1 and 1 1 phenol ether complexes were formed, respectively. The inhibition was attributed to participation of the hydroxyl group in solvation of the halogen atom of the alkyl halide, though this seems much less likely than a straightforward modification of the electron-supplying effect of the substituent3 54. 

Though the kinetic results above can be rationalised by reasonable premises, one experimental observation is markedly at variance and this is that the percentage of orr/io-benzoylation of toluene is constant under all conditions clearly there is still much to be understood about the role of the catalyst in these reactions. 

The detritiation of [3H]-2,4,6-trimethoxybenzene by aqueous perchloric acid was also studied, the second-order rate coefficients (107/c2) being determined as 5.44, 62.0, and 190 at 0, 24.6, and 36.8 °C, respectively, whilst with phosphate buffers, values were 3.75, 13.8, and 42.1 at 24.6, 39.9, and 55.4 °C, respectively. The summarised kinetic parameters for these studies are given in Table 134, and notable among the values are the more negative entropies of activation obtained in catalysis by the more negative acids. This has been rationalised in terms of proton transfer... 

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