Sector method

The rate of initiation was measured directly and radical lifetimes were determined using the rotating sector method. The following results were obtained.f... 

Even though the rates of initiation span almost a 10-fold range, the values of k, show a standard deviation of only 4%, which is excellent in view of experimental errors. Note that the rotating sector method can be used in high-pressure experiments and other unusual situations, a characteristic it shares with many optical methods in chemistry. 

The lifetime of polystyrene radicals at 50 C was measuredt by the rotating sector method as a function of the extent of conversion to polymer. The following results were obtained ... 

From this we can see that knowledge of k f and Rf in a conventional polymerization process readily yields a value of the ratio kp fkt. In order to obtain a value for kf wc require further information on kv. Analysis of / , data obtained under non-steady state conditions (when there is no continuous source of initiator radicals) yields the ratio kvlkx. Various non-stcady state methods have been developed including the rotating sector method, spatially intermittent polymerization and pulsed laser polymerization (PLP). The classical approach for deriving the individual values of kp and kt by combining values for kp kx. with kp/k, obtained in separate experiments can, however, be problematical because the values of kx are strongly dependent on the polymerization conditions (Section... 

A superficially related dependence of on the medium has been observed by Norrish and Smith working with methyl methacrylate, and by Burnett and Melville with vinyl acetate. Rates in poor solvents are high, and determination of by the rotating sector method reveals what appears to be a decrease in kt in the poor solvents. This apparent decrease in kt accounts for the increased rate of polymerization. Actually, precipitation of the polymer seems to be responsible for the effect. The growing radicals become imbedded in precipitated droplets, presumably of very small size. The termination reaction is suppressed owing to isolation of the chain radical in one droplet from that in another. This gel effect is fairly common in systems yield-... 

Few kinetic studies of reactions of alkyl radicals with tin hydrides other than Bu3SnH have been reported. Studies of the reactions of the tert-butyl radical with Me3SnH and Ph3SnH were performed by the rotating sector method,80 but an error in absolute values exists in that method as judged by differences in rate constants for reactions of Bu3SnH with alkyl radicals... 

Measurements of kp were performed by the rotating sector method and its variations until the late 1980s [Flory, 1953 Odian, 1991 Walling, 1957]. In the late 1980s advances in pulsed laser technology and size exclusion chromatography resulted in the development of a technique called pulsed laser polymerization-size exclusion chromatography (PLP-SEC) [Beuermann and Buback, 2002 Beuermann et al., 1997, 2000 Buback et al., 1986, 1992,... 

The rotating sector method requires the introduction of the parameter is, defined as the average lifetime of a growing radical under steady-state conditions. The radical lifetime is given by the steady-state radical concentration divided by its steady-state rate of disappearance ... 

The ratio kp/k, can be obtained from Eq. 3-157 from xs and the rate of polymerization under steady-state conditions. (The subscript s in Eq. 3-157 and subsequent equations in this section refers to steady-state values the absence of s denotes non-steady-state values.) The individual rate constants kp and k, can be determined by combining kpjk, with kpjit, 1 obtained from Eq. 3-25. Thus, the objective of the rotating sector method is the measurement of xs. 

The PLP-SEC method, like the rotating sector method, involves a non-steady-state photopolymerization [Beuermann, 2002 Beuermann and Buback, 2002 Komherr et al., 2003 Nikitin et al., 2002], Under pulsed laser irradiation, primary radicals are formed in very short times ( 10 ns pulse width) compared to the cycle time ( 1 s). The laser pulse width is also very short compared to both the lifetimes of propagating radicals and the times for conversion of primary radicals to propagating radicals. The PLP-SEC method for measuring kp requires that reaction conditions be chosen so that no significant chain transfer is present. The first laser pulse generates an almost instantaneous burst of primary radicals at high... 

This difficulty has now been overcome. Howard, Schwalm, and Ingold (24) show that the rate constant for reaction of any alkylperoxy radical with any hydrocarbon can be determined (by the sector method) by carrying out the autoxidation of the hydrocarbon in the presence of >0.1 M hydroperoxide corresponding to the chosen radical. All the absolute propagation and termination constants for the co-oxidation of cumene and Tetralin were thus determined. Our Tetralin-cumene work suggests that their results agree well with the best we have been able to get... 

Only ratios of rate constants of autoxidation can be determined by ordinary steady-state velocity measurements. Non-steady state methods, notably the sector method, have been used to evaluate the individual or absolute rate constants. We have devised a method for measuring the change in rate of autoxidation under non-stationary conditions directly, by means of sensitive manometric apparatus, and for deriving individual rate constants from these measurements. 

One of the early specialized techniques used for the study of radical reactions was the rotating sector method. The use of this technique (Fig. 6) for determining reaction kinetics was demonstrated by Melville for the gas phase polymerization of methyl methacrylate, and later by Bartlett and Swain for the liquid phase reaction, and by Carlsson and Ingold for tin hydride reductions. ... 

Optical cells can also be used to investigate the kinetics of radical polymerization reactions under high pressure by means of the rotating sector method. Again, the apparatus is presented in Chapter 4.3.4. An example of the method for the evaluation of individual rate constants in radical polymerization of ethylene is given below. 

The rotating-sector method was applied to determine the individual rate constants of chain propagation and chain termination of the radical polymerization of ethylene [23,24]. The photo-initiator was diphenyldisulfide. First, the overall rate of polymerization was measured under steady illumination at pressures of 50 - 175 MPa and 132 - 199°C (Fig. 3.3-9). It increases first steeply and then less steeply with increasing pressure. At 175 MPa the rate of polymerization is ten times higher than at the low pressure of 50 MPa. 

Tedder and Walton (964) report a combination rate constant of 5.3 x 10 11 cm3 molcc 1 see -1 by a rotating-sector method... 

The rotating sector method has proved to be of immense value for certain types of work. It has been used to study chain reactions, in which chain termination steps depend on a different power of the radical concentration from the chain propagating steps. It has also been used to obtain the absolute rates of certain... 

The rotating sector method has also been used to investigate the second order decomposition of biacetyl at room temperature at 4358 A... 

The principle of the rotating sector method has been described many times and we will not discuss it in detail133. Briefly it is as follows (see also Chapter 1, Volume 1). 

A recent numerical development is the introduction of the slow or smooth variable discretization (SVD) technique [101-103]. In the diabatic-by-sector method, the basis functions to expand the total wavefunction are fixed within each sector. In the SVD method, the hyperangular basis functions are constructed using the discrete variable representation (DVR) [104], The requirement is only that the total wavefunction be smooth in the adiabatic parameter p. By expanding the hyperradial wavefunctions using DVR basis functions, a new set of hyperangular basis functions are determined and they... 

Hammond and coworkers (147,349,374) have developed a rotating sector method to measure by ESR the bimolecular decay of radicals produced by photolysis. Calvin and coworkers (148) have also studied the kinetics of ESR signal decay by intermittent UV-irradiation of charge-transfer complexes. A CAT was used by both groups to... 

The only investigations specifically of the termination process appear to be those of McDowell and Sharpies [62]. By combining measurements of the rate of initiation in alcohol retarded systems with determinations of the chain length by the rotating sector method, a value ot defined by... 

The rate coefficients and the Arrhenius parameters of the propagation reaction (20) were determined also by the rotating sector method Since the assign-... 

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