Relative extent of reaction

The complexity of this relation depends on the reaction orders involved. Generally, one finds that it is not easy to arrive at expressions for the time dependence of the various species concentrations. However, it is often possible to obtain relations for the relative extents of reaction that are useful for design purposes. In Chapter 9 we will see the implications of such relations in the selection of reactor type and modes of contacting. 

Even after the poisoning effectiveness of an amine is optimized by redistribution treatments, a considerable fraction of the amine can remain coordinatively bound to Lewis acid sites that are inactive for skeletal rearrangements of hydrocarbons. However, advantage can be taken of the fact that the relative extent of reaction of an amine with Lewis and... 

Using/= 3 gives the relative extent of reaction for the trifunctional Bethe lattice. 

Correlation of weight-average molar mass and relative extent of reaction for trifunctionally branched polyurethanes. Data from M. Adam et at., J. Phys. France 1809(1987). 

At relative extent of reaction = 1, the gel fraction is of order unity Pgei 1, and most of the chains are attached to the gel. The percolation transition is almost complete, with very small sol fraction left Psol [Pg.237]

The dependence of the overlap parameter on relative extent of reaction is sketched in Fig. 6.30. Equation (6.140) describes the decrease in overlap as the gel point is approached until P = 1 at the Ginzburg point. The characteristic polymers and the network strands above the gel point are just at their overlap concentration inside the critical region (where P— 1). Beyond the Ginzburg point on the gel side of the gel point, the overlap of network strands starts to increase again at and builds as the correlation length (and hence the network strand length) decreases. Notice that the overlap parameter is symmetric around the gel point. 

Dependence of the overlap parameter P on relative extent of reaction e. 

The extent of reaction p can, in principle, be measured by molecular spectroscopy methods such as FTIR and NMR. Howevei, these methods always have some small relative error (typically of order a few percent). Since the same error has to apply to any determination of the extent of reaction at the gel point p, the relative error in the relative extent of reaction e = p — Pc)IPc diverges at the gel point. As a result, plots such as Fig. 6.34,... 

Consider a gelation process stopped at relative extent of reaction... 

Recall from Chapter 6, the relative extent of reaction e, which describes the proximity to the gel point for gels in the gelation regime. At the gel point = 0 and the gelation regime ends at e 1, where the gel fraction is approximately unity. The gel fraction grows above the gel point with exponent j3 [Pgei see Eq. (6.99)]. The number of monomers in the characteristic branched polymer decreases beyond the gel point with exponent — 1/cr A see Eq. (6.95)]. Hence, Eq. (7.93) expects the... 

Table 4-3 Relative Extent of Reaction for [Fe(n)/HOOH]2+-Induced...

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