Cage factor

In principle, the cage factor can be estimated from stationary (F ) or time-resolved (Fcab) experiments. As will be shown later, only Fcab represents the actual fraction of... 

Implicit in the form of Equation 13.4 are the assumptions that AA, AB and BB are the only products, that they are always obtained 1 2 1 ratios of from out-of-cage combinations, and that exclusive formation of AB signihes complete in-cage reaction of the radical pairs. The limitations of Equation 13.4, particularly when applied to the evaluation of the cage factor in constrained or microphase-compartmentalized media, have been discussed recently. In symmetrically substituted compounds where the geminate radicals produced upon lysis have the same structures, the addition of radical scavengers or time-resolved detection of the radicals is needed for the estimation of FoAB-... 

With 30-70 wt% PVC, the kinetic curves show an initial sharp decrease followed by a slow component that satisfactorily obeys a second-order rate law (Fig. 13.6). Levin et al. proposed that the initial change in the absorption corresponds to the in-cage combination of the radicals pairs, while the slow component represents the combination of the radicals that have diffused into the (polymer) bulk. Interestingly, at >70 wt% PVC, only the fast in-cage combination of the geminate radical pairs can be observed. From the relative amplitudes of the fast and slow components of the kinetic curves, approximated values for the cage factor Fcab were calculated. Fcab increase from zero in films with <30 wt% PVC to near unity (>0.95) in films with >70 wt % PVC. 

Consider the difficult case of self-diffusion in a hard-sphere fluid. It is useful to define the caging factor x as < / p(0) >/8/iBMkT and a shielding factor S by = (S/2)(Jm- Then Eq. (3.7) can be rearranged to give the self-diffusion coefficient... 

The quantities g(Rp), fV(0), and W (oo) are all equilibrium properties which are readily evaluated for a given liquid density from the radial distribution function using the formulas derived in Section II. The caging factor is more difficult to evaluate. For each impact there is a contribution to < / p(0) > of... 

Density Transition State Rr/R, Stability Factors F(0) F(oo) Contact Factor 9(Rp) Attempt Factor U Cage Factor Z Diffusion CoelKcient D/De ... 

Figure 9. Frequency dependence of the cage factor x( ), the barrier crossing flux Jj(co), and the hydrodynamic contribution to friction versus reduced frequency co in units of...

FIG. 29-1 Motor prices in dollars per horsepower for 1800 rev/min sqnirrel-cage induction motors from 3 to 10,000 hp. Dripproof and TEFC motors shown from 3 to 400 horsepower have 1.15 service factor for other motors above 250 horsepower, the service factor is 1.0. The basis of these data is July, 1994. To convert dollars per horsepower to dollars per kilowatt, multiply by 1.340 to convert horsepower to kilowatts, multiply by 0.746. 

Dynamic information such as reorientational correlation functions and diffusion constants for the ions can readily be obtained. Collective properties such as viscosity can also be calculated in principle, but it is difficult to obtain accurate results in reasonable simulation times. Single-particle properties such as diffusion constants can be determined more easily from simulations. Figure 4.3-4 shows the mean square displacements of cations and anions in dimethylimidazolium chloride at 400 K. The rapid rise at short times is due to rattling of the ions in the cages of neighbors. The amplitude of this motion is about 0.5 A. After a few picoseconds the mean square displacement in all three directions is a linear function of time and the slope of this portion of the curve gives the diffusion constant. These diffusion constants are about a factor of 10 lower than those in normal molecular liquids at room temperature. 

Can use squirrel cage induction motors with minimal derating. Good power factor (with most designs). Speed increase possible... 

According to cq. 1, the term/should take into account all side reactions that lead to loss of initiator or initiator-derived radicals. These include cage reaction of the initiator-derived radicals (3.2.8), primary radical termination (3.2.9) and transfer to initiator (3.2.10). The relative importance of these processes depends on monomer concentration, medium viscosity and many other factors. Thus/is not a constant and typically decreases with conversion (see 3.3.1.1.3 and 3.3.2.1.3). 

Thus, the size and the reactivity of the initiator-derived radicals and the medium viscosity (or microviscosity) are important factors in determining the initiator efficiency. Thus, the extent of the cage reaction is likely to increase with... 

In other cases, the cage reaction may simply lead to reformation of the initiator. This process is known as cage return and is important during the decomposition of BPO (Section 3.3.2.1.1) and DTBP (Section 3.3.2.4). Cage return lowers the rate of radical generation but does not directly yield byproducts. It is one factor contributing to the solvent and viscosity dependence of kA and can lead to a reduced at high conversion. 

There have been numerous studies on the kinetics of decomposition of A IRK. AIBMe and other dialkyldiazenes.46 Solvent effects on are small by conventional standards but, nonetheless, significant. Data for AIBMe is presented in Table 3.3. The data come from a variety of sources and can be seen to increase in the series where the solvent is aliphatic < ester (including MMA) < aromatic (including styrene) < alcohol. There is a factor of two difference between kA in methanol and k< in ethyl acetate. The value of kA for AIBN is also reported to be higher in aromatic than in hydrocarbon solvents and to increase with the dielectric constant of the medium.31 79 80 Tlic kA of AIBMe and AIBN show no direct correlation with solvent viscosity (see also 3.3.1.1.3), which is consistent with the reaction being irreversible (Le. no cage return). 

While the rate of azo-compound decomposition shows only a small dependence on solvent viscosity, the amount of cage reaction (and hence f) varies dramatically with the viscosity of the reaction medium and hence with factors that determine the viscosity (conversion, temperature, solvent, etc.) 1... 

A slow rate of p-scission also means that the main cage recombination process will be cage return to reform the peroxydicarbonate. Dialkyl peroxides are typically not found amongst the products of peroxydicarbonate decomposition. In these circumstances, cage recombination is unlikely to be a factor in reducing initiator efficiency. 

Fig. 5.3. Now the reaction rate is determined by AGcage and Ag age, but AGcage is almost entirely determined by simple concentration factors. Thus a comparison of Ag age and Agfat allows one to explore fundamental catalytic aspects, including real entropic effects, without preoccupation with the rather trivial effective concentration effect, associated with bringing the reactants to the same cage.

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