Crossover ratio

Not all adsorption beds will develop stable MTZs. One requirement for stability (i.e., the MTZ reaches a limiting size) is that the equilibrium line must be favorable. In the case of a single adsorbate isothermally removed from a non-adsorbable component, the curve of loading as a function of composition must be concave downward in the region of loading below the stoichiometric point to be favorable. This effect is described in more detail in Section 7.9. In non-isothermal adsorption it is possible for the temperature effects to cause a favorable isotherm to become an unfavorable equilibrium line. This was discussed previously in the context of the crossover ratio R. 

During ad.sorption mo.st of the heat is generated in the MTZ. When the heat capacity of the gas stream is high reiative to that of the bed, the gas will carry the heat forward ahead of the MTZ. This effect can be quantified by use of a crossover ratio, R, defined by the following equation (Keiieretal. i987) ... 

When R = 1 the thermal wave progresses through the bed more or less at the same speed as the mass transfer zone. Hence, virtually all the heat released on adsorption can be expected to be retained in the MTZ and the isothermal assumption should not be made unless either the heat of adsorption is low and/or the concentration of the adsorbable component is low. When R is very much less than unity the thermal wave lags behind the MTZ and hence the heat of adsorption can be retained in the equilibrium portion of the bed (that is, from the entrance up to Le shown in Figure 5.6 (b)). Retention of the heat of adsorption in this way is beneficial to the subsequent desorption step (Garg and Ausikaitis 1983). When R is very much greater than unity the heat is easily removed from the MTZ and it is safe to invoke the isothermal assumption. Further discussion on the crossover ratio is given in Section 7.5.3. 

Hthiated 4-substituted-2-methylthia2oles (171) at -78 C (Scheme 80). Crossover experiments at—78 and 25°C using thiazoles bearing different substituents (R = Me, Ph) proved that at low temperature the lithioderivatives (172 and 173) do not exchange H/Li and that the product ratios (175/176) observed are the result of independent metala-tion of the 2-methyl and the C-5 positions in a kinetically controlled process (444). At elevated temperatures the thermodynamic acidities prevail and the resonance stabilized benzyl-type anion (Scheme 81) becomes more abundant, so that in fine the kinetic lithio derivative is 173, whereas the thermodynamic derivative is 172. 

If TI T2, with both values less than unity, the copolymer starts out richer in monomer 1 than the feed mixture and then crosses the 45° line, and is richer in component 2 beyond this crossover point. At the crossover point the copolymer and feed mixture have the same composition. The monomer ratio at this point is conveniently solved from Eq. (7,15) ... 

The exact mechanism has still not been completely worked out. Opinions have been expressed that it is completely intermolecular, completely intramolecular, and partially inter- and intramolecular. " One way to decide between inter- and intramolecular processes is to run the reaction of the phenolic ester in the presence of another aromatic compound, say, toluene. If some of the toluene is acylated, the reaction must be, at least in part, interraolecular. If the toluene is not acylated, the presumption is that the reaction is intramolecular, though this is not certain, for it may be that the toluene is not attacked because it is less active than the other. A number of such experiments (called crossover experiments) have been carried out sometimes crossover products have been found and sometimes not. As in 11-14, an initial complex (40) is formed between the substrate and the catalyst, so that a catalyst/substrate molar ratio of at least 1 1 is required. 

This accounts for the considerable discrepancy between the alkene Z/E ratio found on work-up and the initial oxaphosphetan ais/trans ratio. By approaching the problem from the starting point of the diastereomeric phosphonium salts (19) and (20), deprotonation studies and crossover experiments showed that the retro-Wittig reaction was only detectable with the erythreo isomer (19) via the cis-oxaphosphetan (17). Furthermore, it was shown that under lithium-salt-free conditions, mixtures of (19) and (20) exhibited stereochemical drift because of a synergistic effect (of undefined mechanism) between the oxaphosphetans (17) and (18) during their decomposition to alkenes. 

The slow diffusion coefficient is measurable only at high enough polyelectrolyte concentrations. The value of c at which the slow mode appears is higher if Cj is higher. When the ratio X = c/cg is about 1, the onset of the slow mode and the crossover between the smaller Df for A, < 1 and higher Df for A > 1 occur. Dj depends [33] on c strongly. 

Thus, the synthesis of a styrene-methyl methacrylate block polymer requires that styrene be the first monomer. Further, it is useful to decrease the nucleophilicity of polystyryl carbanions by adding a small amount of 1,1-diphenylethene to minimize attack at the ester function of MMA [Quirk et al., 2000]. Block copolymers of styrene with isoprene or 1,3-butadiene require no specific sequencing since crossover occurs either way. Block copolymers of MMA with isoprene or 1,3-butadiene require that the diene be the first monomer. The length of each segment in a block copolymer is controlled by the ratio of each monomer to initiator. The properties of the block copolymer vary with the block lengths of the different monomers. 

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