Fractional cage efficiency

AS obs) with those for the elementary processes of Scheme 1. The fractional cage efficiency factor [Fq(T)] is temperature dependent to the extent that k /k j is temperature dependent. ... 

The variables of equation (9) are the ratio (K) of the initial separation distance (d j) to the sum of the hard sphere collision radii (s), the ratio (L) of the proportionality constant for the combination reaction (k ) to the second order rate constant for pair diffusion (k(j2) ind the ratio (r) of the time elapsed since pair formation to the diffusive time constant (s /D). The fractional cage efficiency is the complement to the pair... 

The relationships corresponding to equations (l)-(5) above are as follows The obse ed rate constants (kjfobs) and activation parameters (AH xfobs AS -pfobs) for disappearance of R by reaction with T depend on the second order rate constant for diffusive collision to form the cage pair (k pj), equation 12) and the fractional cage efficiency (Fjc equation 11). The latter is determined by the first order rate constants for the chemical reaction (kjc) and diffusive (re)separation (kj j) of the T/R collisional cage pair. The associated activation parameters are given by equations (13) and (14). 

In cases where the fractional cage efficiency is this low (< 0.1), equation (14) can be replaced with the more intuitive approximate form shown as equation (14a). This equation together with the value of AS xD used to obtain the value of AS xc... 

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... 

In some texts the initiator efficiency (/) is defined simply in terms of the yield of initiator-derived radicals (the fraction of radicals I- that undergo cage escape - Section 3.2.8). This number will always be larger than that obtained by application of eq. 1. 

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 initiator radicals initially formed in solution are held together briefly in a cage of solvent molecules. This cage effect causes radical molecules to recombine and slows down their diffusion through the solvent. Therefore, the rate of initiation (R.) depends on the rate of decomposition of the initiator (k ) and on the fraction e of the initiator radicals that escape the solvent cage affecting the efficiency of the chain initiation reaction (20). 

Nonexcited Permanent-Magnet Motors. Permanent-magnet motors have permanent magnets embedded in a squirrel-cage-type rotor (Fig. 5.113). They produce fixed poles that lock into step with the armature field. Because of its relatively high efficiency and power factor, this motor is popular in the fractional- and lower-integral-horsepower range. 

Note 2 In some texts, the initiator efficiency is defined as the fraction of radicals that escapes the cage (see cage effect). 

Quantitative data obtained at 45°C by these authors indicate clearly that termination (by coupling or disproportionation) is not very efficient since a significant fraction of alkoxy radicals (typically 35-40%) escape from the cage to initiate new oxidation radical chains. 

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