Rigidity conditions

Glass and Glassed Steel Glass is an inorganic product of fusion which is cooled to a rigid condition without ciystaUizing. With unique... 

Thus, thioarylation may be facilitated electrochemically. The conventional nucleophilic substitution of the phenylthio gronp for bromine in 4-bromobenzophenone requires extremely rigid conditions. When a difference in electric potentials is set up, the reaction proceeds readily and gives products in a high yield (80%). It is sufficient to set up only the potential difference necessary to ensure the formation of the substrate anion-radical (with the potential and current strictly controlled). The chemical reaction takes place in the bulk of solution and yields 4-(phenylthio)benzophenone (Pinson and Saveant 1974) (Scheme 5.1). 

As it was mentioned in Section 2.1.1, the concentration oscillations could be simulated quite well by a set of even two ordinary differential equations of the first order but paying the price of giving up the rigid condition imposed on interpretation of mechanisms of chemical reactions namely that they are based on mono- and bimolecular stages only (remember the Hanusse theorem [19]) An example of what Smoes [7] called the heuristic-topological model is the well-known Brusselator [2], Its scheme was discussed in Section 2.1.1 see equations (2.1.33) to (2.1.35). 

This statement comes from analytical and topological studies [4], Unlike the Lotka-Volterra model where due to the dependence of the reaction rate K(t) on concentrations NA and NB, the nature of the critical point varied, in the Lotka model the concentration motion is always decaying. Autowave regimes in the Lotka model can arise under quite rigid conditions. It is easy to show that not any time dependence of K(t) emerging due to the correlation motion is able to lead to the principally new results. For example, the reaction rate of the A + B -> 0 reaction considered in Chapter 6 was also time dependent, K(t) oc t1 d/4 but its monotonous change accompanied by a strong decay in the concentration motion has resulted only in a monotonous variation of the quasi-steady solutions of (8.3.20) and (8.3.21) jVa(t) (3/K(t) and N, (t) p/f3 = const. 

The global structure of IET formalism is similar to that of DET. The integral kinetic equations substitute for their differential analogs. The kernels of these equations are defined by the transfer rates and pair distribution functions. The auxiliary equations for these functions are also similar but not identical to those in DET. In the next section we will see that the integral theory may sometimes be reduced to the differential one, albeit under rigid conditions and with some losses. 

The experimental registration of delayed fluorescence is problematic because of the very rigid conditions for its observation. According to Eqs. (3.402) and (3.397), the number of second-time excited molecules does not exceed k x [A (0)]2 = jNq, where y k t (v /0cp)2. Hence, the amplitude of the... 

In the framework of the approximation given by the rigidity condition, a simple power law relation can be derived for the dependency of the small strain modulus G 0 of the composite on filler concentration . It is obtained,... 

The cycloaddition reaction proceeds under more rigid conditions and takes more time than a direct template condensation on the iron(II) ion. This can be explained by the fact that the overall mechanism of clathrochelate synthesis involves an intermediate tris-complex formation step. It is evident that macrocyclic square-planar iron(II) bis-dioximates are relatively kinetically stable, and the... 

The dye introduced into reaction mass at the stage of polymer synthesis is in much more rigid conditions. At this time this dye is exposed to the action of monomers which, as a rule, are more reactive that the polymer. 

Reaction of ethers with CBT under more rigid conditions yields the products of oxidation and hetarylation. At room temperature CBT reacts with diethyl ether to form 1-ethoxyethylbenzotriazole (—5%) together with the chlorination products. In the reaction with tetrahydrofuran l-(2-tetrahydrofuryl)benzotriazole is formed [69JCS(C)1474] (Scheme 55). 

Thiophenol is oxidized with DCT or TBT to diphenyl disulfide. The latter reacts with DCT under more rigid conditions to give benzyl chloride. DCT oxidizes dibenzyl sulfide in methanol to dibenzyl sulfoxide (69ZC325) (Scheme 120). 

There are a few more sulfur-oxygen linked radicals which have been characterized by pulse radiolysis and may reasonably be addressed as S.. O bonded species. They all require very rigid conditions for their stabilization and depend on the steric forces which hold the two interacting atoms in close... 

Indeed, the fluoroalcohol 339 is treated with an acid under more rigid conditions to form a mixture of isomeric alcohols differing in the fluorine configuration at C. ... 

---