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For the more complex situation with other b-hydride transfers, additional terms would be needed to account for those reactions. An alternate approach is to use Eq. 8-50 with ks and ktr;M rede ned as composite rate constants for the sum of all b-hydride transfers. The derivations of Eqs. 8-48 through 8-50 assume that transfer to hydrogen does not involve adsorption of hydrogen at the active sites prior to transfer. If hydrogen competes with monomer and the group I III metal component for adsorption at the active sites, the treatment described above requires modi cation of A and M and the introduction of H2 . 8-4i-4 Values of Kinetic Parameters



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Is the excel format 2007+? You are going to need to look into automation by using Excel interop:

So substituting (9.86), (9.88), and (9.89) in the first boundary condition in (9.68) yields (9.90) As z and ft t\ z are two orthogonal and thus independent directions, it follows that the first boundary condition in (9.68) is equivalent to

Evaluation of the various kinetic parameters requires a determination of the active-site concentration. [C*] is usually determined from experiments in which the active sites are

(9.91)





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quenched (made inactive) with CH3 O3 H, 14 CO, or 14 CO2 [Jaber and Fink, 1989; Mejzlik et al, 1986, 1988; Tait and Watkins, 1989; Vozka and Mejzlik, 1990] Other methods include the use of number-average molecular weight (combined with polymer yield) and 14 C-labeled group I III metal component Each of the techniques has limitations that require care if reliable results are to be obtained For example, quenching with CH3 O3 H gives high values for [C*] since the polymer chains terminated by chain transfer to the group I III metal component are reactive toward methanol Values of [C*] obtained at different conversions need to be extrapolated to zero conversion Literature values of the active-site concentrations range from tenths or hundredths of a percent to tens of percents of the transition metal concentration [Lieberman and Barbe, 1988; Tait and Watkins, 1989].

11 12

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The boundary condition (9.68) for the magnetic field yields ft {z t\ (Vu)}ls = 0, because ft {V t\ ['\7 t\ (vz)]} Is = O. Now as u is constant overthe cavity walls (Le., uls = 0), the gradient of u over the walls can only point in the direction of ft, so this boundary condition is trivially satisfied.

Much of this is indicative of the range of activity of different initiators, especially when comparing older initiators to the recent high-mileage initiators However, some of the variation is due to the problems inherent in measurement of [C*] Literature values of kp and other rate constants also show a considerable range Both rate and molecular weight data are often interpreted in terms of multicenter models, in which the initiator contains both selective (either iso- or syndioselective) and nonselective (aselective) active sites [Chien and Hu, 1987; Kissin, 2001a, 2002; Liu et al, 2001b] Table 8-4 shows various kinetic parameters in propene polymerization (065 M in n-heptane) using a TiCl4 /Al(C2 H5 )3 initiator ([Ti] 00001 M) supported on MgCl2 with ethyl benzoate and methyl-p-toluate as internal and external Lewis bases.

For a given frequency w = ck, describing the electromagnetic radiation field by two scalar potentials, we can reduce the general three-dimensional problem of finding the natural modes of an open cavity to two scalar problems [84]: 1. Solving the Helmholtz equation (9.92)

The concentrations of isoselective and aselective active sites were obtained by a combination of quenching experiments for the total concentration of active sites and ESR (as well as isotactic index) measurements for the isoselective active sites The amounts of isoselective and aselective active sites as percentages of total titanium are expressed by (C*)I and (C*)A , respectively kpI and kpA represent the propagation rate constants for isoselective and aselective active sites, respectively The external base is critical to achieving a highly isoselective polymerization With an internal base but no external base, isoselective polymerization is favored over aselective by a factor of 21 because (C*)I =(C*)A favors aselective polymerization by a factor of 4, while kpI /kpA favors isoselective polymerization by a factor of 83.

(9.93)

With both internal and external bases present, the concentration of aselective active sites decreases, as does their reactivity while there is negligible effect on the isoselective sites Isoselective polymerization.

TABLE 8-4 Kinetic Parameters in Polymerization of Propene by MgCl2 /TiCl4 /Al(C2 H5 )3 at 50 Ca Kinetic Parameterb (C*)I [C*]I (C*)A kpI kpA Isotactic index c ktr;A c ktr;M c ks

over the cavity walls and Sommerfeld's radiation condition (9.63) at infinity, which amounts to 15 e ikr lim u(r) = g((},cjJ)-. (9.94)

Internal Base Only 6.0 6:0 10 6 24 138 16.6 68.2 4:0 10 4 9:1 10 3 8:2 10 3

(9.95)

Internal and External Bases 2.3 2:3 10 6 2.4 133 5.1 96.0 1:2 10 4 7:2 10 3 9:7 10 3

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What do you mean with: "it is not possible to use Excel Interop any more"? Office 2013 still have Interop library and it works perfectly fine under .












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