Cross over ratio

For polyisoprenyllithium anions, it was also observed that increased linking efficiency was achieved at higher DVB/RLi ratios, Figure 10. In comparison, the polyisoprenyllithium anions link more efficiently than polybutadienyllithium. Also, in contrast to polybutadienyllithium anions, polyisoprene star formation does not result in coupled dimer at the lower DVB/RLi ratios. This is perhaps reflected in the faster cross-over rate from the polydienyllithium anion to the vinylbenzylanion (reaction... 

In several cases the melt viscosity of a series of lightly-branched polymers has been determined as a function of MW, and compared with that of linear polymers, and it has been found or may be deduced from the published data that there is a cross-over molecular weight, below which the branched polymer is less viscous, but above which it more viscous, than the linear polymer of equal MW. This behaviour is observed with some comb-shaped polystyrenes (35) and poly(vinyl acetate)s (59, 89), star polybutadienes (57, 58, 123), and randomly-branched polyethylenes (56,61). Jackson has found (141) that if the ratio ZJZC of the number of chain atoms at the cross-over point, Zx, to the number at the kink in the log 0 — logM curve, Zc, [as given in Ref. (52)], is plotted against nb, the number of branches, a reasonable straight line is obtained, as in Fig. 5.1. 

A-Dialkylaminomethylbenzotriazoles usually exist in the crystalline state solely as the N(l) isomers, but in solution they form equilibrium mixtures of the N(l) (209, 210) and N(2) (211) isomers <75JCS(Pl)l 181, 87JCS(Pi)2673). The N(l) and N(2) isomers are of nearly equal stability in nonpolar solvents and in the gas phase (2 1 ratio on statistical grounds). Polar solvents favor the 1- and 3-substituted forms over the 2-substituted, and conversely substituents at positions four and seven favor the 2-substituted form. The interconversion of these N(l) and N(2) isomers proceeds intermolecularly, as demonstrated by cross-over experiments, by a dissociation-recombination mechanism involving the formation of intermediate iminium cations and the benzotriazole anion. 

The open-loop Bode diagram for all the components in the control loop, excepting the controller, is plotted and the cross-over frequency determined. If the total open-loop amplitude ratio at Bode criterion, the gain of a proportional controller which would cause the system to be on the verge of instability will be ... 

Figure 11.6A illustrates the effect of a change in the ratio of ki/k2 for the imidazole-catalysed hydrolysis of 4-nitrophenyl acetate. When the pH is changed from 5 to 6, the maximal concentration of the intermediate increases. The pH profile in Fig. 11.6B provides a graphic illustration of the range of pH within which an intermediate can be detected this is between the cross-over pH values of about 5 and 10 for these conditions. The range illustrated is for 0.1 M imidazole and could be extended because k is dependent on the concentration of imidazole whereas k2 is not. 

There thenfollowed reports by Katz [13] and Grubbs [14] and their co-workers on studies that aimed to simplify and confirm the analysis. The key remaining issue was whether a modified pairwise mechanism, in which another alkene can coordinate to the metal and equilibrate with the product prior to product displacement, would also explain the appearance of the anomalous cross-over products early in the reaction evolution. However, a statistical kinetic analysis showed that for a 1 1 mixture of equally reactive alkenes, the kinetic ratio of cross-metathesis should be 1 1.6 1 for the pairwise mechanism and 1 2 1 for the Chauvin mechanism. Any equilibration (substrate or product) would, of course, cause an approach towards a statistical distribution (1 2 1) and thus allow no distinction between the mechanisms. 

In these calculations, you will be converting either from moles of the given substance to grams of the unknown or from grams of the given substance to moles of the unknown. Either way, you will need to use the mole ratio as the mechanism for crossing over from one substance to the next. Other than the step with the mole ratio, these calculations are the same as the calculations from earlier in the chapter that converted mass to moles or moles to mass for a single substance. We ll use the same equation from the sample problem to continue with this example. 

After the crossing over step, you may need to reduce the subscripts to their lowest terms. For example, Mg202 becomes MgO. Be202 becomes BeO. Remember, formulas for ionic compounds represent ratios of ions. 

Thus, how should block copolymers between styrene and a vinyl ether be prepared Starting with styrene or with a vinyl ether In the former system, the propagating styryl cation is intrinsically more reactive but present at much lower concentration. A rough estimate of the ratio of cation reactivities is = 103 but the ratio of carbocations concentrations is = I0 S. Thus, the ratio of apparent rate constants of addition is 10-2. Macromolecular species derived from styrene should add to a standard alkene one hundred times slower than those derived from vinyl ethers. Thus, one cross-over reaction St - VE will be accompanied by =100 homopropagation steps VE - VE. Therefore, in addition to a small amount of block copolymer, a mixture of two homopolymers will be formed. Blocking efficiency should be very low, accordingly. 

The first prediction from Equation j is that the O3 decay is first-order for fc3 [O3] > fc4[NH3] and3/2-orderfor fc3[03] < k4[NH3]. We have observed both rate laws and found that the cross-over occurs for [NH3]/[03] 100 consequently, 3/ 4 should be 100. The rate constants 3 and 4 have been measured. We believe the best value (9) for ks to be 5.2 X 10 M sec" at 30°C. The two most reliable results for fc4 are given by Albers et al. (10) and Kurylo et al. (iJ). Both of their Arrhenius expressions give the same value of 7.0 X lO M" sec" for 4 at 30 °C. The ratio of these reported rate constants is 75, which supports our conclusion. 

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