Cage combination efficiency

These equations [(3)-(5)] are simply implied by composite mechanisms, such as Scheme 1, but have not received much previous attention. They express the curvature in Eyring (ln(k/T) vs 1/T) treatments of observed rate constants for two step mechanisms where neither step is clearly rate determining. For the cage pair case, this includes the domain where the cage combination efficiency is from 10 to 90 percent (0.1 < F(,(T) < 0.9). A notational clarification, which is required by this curvature, is to introduce the apparent activation parameters (AH t PP t PP) that would be obtained from the ln(2k obs/T) versus 1/T linearized fit. As we will show, the apparent activation parameters must be kept distinct from the AH and AS of equations (3) and (4). The latter... 

Quantum yields for adduct 63 and total product (63-65) formation from the reaction of - -t with several tertiary amines are summarized in Table 12. Quantum yields measured at 1.0 M amine concentration are lower than the values extrapolated to infinite amine concentration due to incomplete quenching of It. Extrapolated total quantum yields range from 0.07 to 0.33, providing a lower limit for the efficiency of the proton transfer step, kh> in Fig. 11. The other reaction products, 1,2-diphenylethane (64) and 1,2,3,4-tetraphenylbenzene (65), are formed mainly via in-cage radical pair disproportionation and out of cage combination, respectively. The relative importance of radical pair combination, disproportionation, and cage escape is dependent... 

Thus the relative photoinitiating efficiencies of benzophenone derivatives may be influenced by whether or not their photoexcited states are quenched by monomer, and the fraction of in-cage combination of the radicals formed by hydrogen abstraction, as wdl as the stents to which the respective semi-pinacol radicals terminate polymer chains. At elevated tmiperatures, differences in the initiating abilities of the semi-pinacol radicals must also be considered. 

The combination efficiencies, predicted for the collisional case by the RBM, can be converted to the simple chemical models (Scheme 1) through the effective local concentration of the initial pair and the observed diffusive time constants. The k jp of Scheme 2 is thus given as 3D/do. The Fc(T) and F p(T) values of Table I yield the corresponding k, p and k, values at each temperature. The corresponding activation parameters for diffusive separation and combination of the collisional cage pairs are summarized in Table II. 

The Halpern procedure becomes less accurate when the fractional cage efficiency is not so close to one. A system with the activation parameters of Figure 6, except for a reduction of AH (i, models a more fluid solvent. Diffusive escape becomes faster, relative to cage combination, and this leads to reduced values of F (T). A reduction of the value of AH to 2.6 kcal/mole gives Fq(T) as 0.2 at the mean of the temperature range that would apply to a AH app value of 30.6 kcal/mole. The Halpern procedure leads to an estimated 28 kcal/mole for the BDE in this case, somewhat less than the actual 30 kcal/mole value. The value of Fq(T), the... 

This allows the basic parameters of the model to be expressed as three distinct radii, that for the cage (p), that for the normalization (r ) and that for diffusive separation (b). One might hope that a single value of p and r would suffice for a given cage pair source in every solvent. However, consideration of the Noyes model indicates this cannot be the case. The physical basis here is the distance which a pair separates during the short time while the relative velocity vectors of the cage partners are oriented towards separation. This relative velocity orientation is intrinsic to the initiation event. Variations in combination efficiency with solvent fluidity, in Noyes model, are ascribed entirely to these small initial... 

The most popiilar form of motor speed control for adjustable-speed pumping is the voltage-controlled pulse-width-modulated (PWM) frequency synthesizer and AC squirrel-cage induction motor combination. The flexibility of apphcation of the PWM motor drive and its 90 percent- - electric efficiency along with the proven ruggedness of the traditional AC induction motor makes this combination popular. 

The macrocyclic receptors 32 [43] and 33 [44] combining two calix[4]arene motifs within the molecule were designed for anion recognition. While 32 creates 1 1 complexes with several anions (halides, HSOj, H2POj), compound 33 is too rigid to efficiently complex halides or benzoate. By contrast, similar cage molecule 34 with the ureido bridges showed complexation ability towards chloride or benzoate. 

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