Correspondence induced

Correspondingly inducing a fall in temperature produces the reverse effects to that caused by rise in temperature in each case. 

I hc dispersion forces, however, possess different properties. As London has pointed out, if several molecules interact simultaneously with one another, each molecule will introduce into the other molecules a scries of coordinated periodic dipoles, which are in phase with the exciting dipoles. Each molecule thus produces a number of induced periodic dipoles each of which is always oriented so that it is attracted to the corresponding inducing molecule. The resulting simultaneous interaction of several molecules leads to the additive superposition of the forces of attraction of individual pairs of molecules. Thus, for example, if we have three molecules, the dispersion energy will be... 

In the presence of gross errors in positions given by a set T, the corresponding induced bias in variable i is... 

Microfluidics, Fig. 5 Control of the positions of the particle and corresponding induced vortices using different DC electric fields perpendicular to El. The new configuration of electric fields boosts the mixing process. The red lines inside the microchamber represent the streamlines of the flow field. The color bar shows the... 

Perhaps the simplest situation of an abstract simplicial complex derived from combinatorial data is that of a flag complex. For a graph G and a subset S CV (G) of its vertices, we let G[[Pg.129]

In physical chemistry, the van der Waals force (or van der Waals interaction), named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules (or between parts of the same molecule) other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral molecules. The term includes the force between two permanent dipoles (Keesom force), the force between a permanent dipole and a corresponding induced dipole (Debye force) and the force between two instantaneously induced dipoles (London dispersion force) It is also sometimes used loosely as a s5monym for the totality of intermo-... 

Fig. 22-1 (a) Darkly shaded regions denote nonuniformities which scatter incident light power into bound modes and radiation. The profile of the perturbed fiber is n x,y,z). (b) Darkly shaded regions denote corresponding induced currents with distribution J(x,y,z) within the unperturbed fiber of profile n(x,y). 

In the case when the compound reacting with the optically active molecule also possesses one or more electronic transitions the evidence of the chemical interaction can become indiscutable. The very existence of an association submits the electronic transitions of the compound to the dissymmetry of the chiral molecule. They become optically active and, consequently, detectable by the intermediary of the corresponding induced COTTON effects. Figure 9 shows the induction of optical activity in the d-d transition of the Cuii ion complexed with the optically active ligand N-tosyl L-alanine(YI) in aqueous solution at pH 10 [18]. 

The average cloud is spherically synnnetric with respect to the nucleus, but at any instant of time there may be a polarization of charge givmg rise to an instantaneous dipole moment. This instantaneous dipole induces a corresponding instantaneous dipole in the other atom and there is an interaction between the instantaneous dipoles. The dipole of either atom averages to zero over time, but the interaction energy does not because the instantaneous and induced dipoles are correlated and... 

One aspect that reflects the electronic configuration of fullerenes relates to the electrochemically induced reduction and oxidation processes in solution. In good agreement with the tlireefold degenerate LUMO, the redox chemistry of [60]fullerene, investigated primarily with cyclic voltammetry and Osteryoung square wave voltammetry, unravels six reversible, one-electron reduction steps with potentials that are equally separated from each other. The separation between any two successive reduction steps is -450 50 mV. The low reduction potential (only -0.44 V versus SCE) of the process, that corresponds to the generation of the rt-radical anion 131,109,110,111 and 1121, deserves special attention. 

Of course, these shortcomings of the Wakao-Smith flux relations induced by the use of equations (8.7) and (8.8) can be removed by replacing these with the corresponding dusty gas model equations, whose validity is not restricted to isobaric systems. However, since the influence of a strongly bidisperse pore size distribution can now be accounted for more simply within the class of smooth field models proposed by Feng and Stewart [49], it is hardly worthwhile pursuing this."... 

Comparison of the water-induced acceleration of the reaction of 2.4a with the corresponding effect on 2.4g is interesting, since 2.4g contains an ionic group remote from the reaction centre. The question arises whether this group has an influence on the acceleration of the Diels-Alder reaction by water. Comparison of the data in Table 2.1 demonstrates that this is not the case. The acceleration upon going from ethanol to water amounts a factor 105 ( 10) for 2.4a versus 110 ( 11) for 2.4g. Apparently, the introduction of a hydrophilic group remote from the reaction centre has no effect on the aqueous acceleration of the Diels-Alder reaction. 

The rate of the Lewis-acid catalysed Diels-Alder reaction in water has been compared to that in other solvents. The results demonstrate that the expected beneficial effect of water on the Lewis-acid catalysed reaction is indeed present. However, the water-induced acceleration of the Lewis-add catalysed reaction is not as pronounced as the corresponding effect on the uncatalysed reaction. The two effects that underlie the beneficial influence of water on the uncatalysed Diels-Alder reaction, enforced hydrophobic interactions and enhanced hydrogen bonding of water to the carbonyl moiety of 1 in the activated complex, are likely to be diminished in the Lewis-acid catalysed process. Upon coordination of the Lewis-acid catalyst to the carbonyl group of the dienophile, the catalyst takes over from the hydrogen bonds an important part of the activating influence. Also the influence of enforced hydrophobic interactions is expected to be significantly reduced in the Lewis-acid catalysed Diels-Alder reaction. Obviously, the presence of the hydrophilic Lewis-acid diminished the nonpolar character of 1 in the initial state. 

The catalysed reaction was considered to arise from the heterolysis of dinitrogen pentoxide induced by aggregates of molecules of nitric acid, to yield nitronium ions and nitrate ions. The reaction is autocatalytic because water produced in the nitration reacts with the pentoxide to form nitric acid. This explanation of the mechanism is supported by the fact that carbon tetrachloride is not a polar solvent, and in it molecules of nitric acid may form clusters rather than be solvated by the solvent ( 2.2). The observation that increasing the temperature, which will tend to break up the clusters, diminishes the importance of the catalysed reaction relative to that of the uncatalysed one is also consistent with this explanation. The effect of temperature is reminiscent of the corresponding effect on nitration in solutions of nitric acid in carbon tetrachloride ( 3.2) in which, for the same reason, an increase in the temperature decreases the rate. 

It has already been noted that, as well as alkylbenzenes, a wide range of other aromatic compounds has been nitrated with nitronium salts. In particular the case of nitrobenzene has been examined kinetically. Results are collected in table 4.4. The reaction was kinetically of the first order in the concentration of the aromatic and of the nitronium salt. There is agreement between the results for those cases in which the solvent induces the ionization of nitric acid to nitronium ion, and the corresponding results for solutions of preformed nitronium salts in the same solvent. 

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