Reactivity ratios definition

Bajoras and Makuska investigated the effect of hydrogen bonding complexes on the reactivities of (meth)acrylic and isotonic acids in a binary mixture of dimethyl sulfoxide and water using IR spectroscopy (Bajoras and Makuska, 1986). They demonstrated that by altering the solvent composition it was possible to carry out copolymerization in the azeotropic which resulted in the production of homogeneous copolymers of definite compositions at high conversions. Furthermore, it was shown that water solvent fraction determines the rate of copolymerization and the reactivity ratios of the comonomers. This in turn determines the copolymer composition. 

Reactivity Ratios and Relative Rates of Oxidation. Table VI summarizes reactivity ratios for all combinations of butadiene, styrene, Tetralin, and cumene reported here and by Hendry (12) for butadiene. The underscored r values in the table are calculated from the base point in the same column (1.00) and the reciprocals (because of the definition of r in Equation 2) of the relative reactivities of the hydrocarbons toward an average R02 radical, B S T C = 1.0 2.2 4.5 5 30 (all underscored values in the butadiene column). The calculated and experimental values always agree within 50%, and in seven out of 12 systems, within 15%. Thus, among these four hydrocarbons a change of R— in RC>2 affects relative reactivities by less (often much less) than 50%. 

Get the heck out of here, you might say, how did you get that Figure it out But, this relationship is certainly correct. Just use Equations 6-10 and 6-51, substitute into Equation 6-53 and you will get the definition of x (Equation 6-45). Going back to the expression in Equation 6-53 and substituting for the conditional probabilities (Equations 648 to 6-50), we then obtain an expression for in terms of the reactivity ratios and the molar feed ratio (Equation 6-54) ... 

The reactivity ratios, although numerically different for the Ziegler and free radical catalysts, do show the same orders of monomer reactivity, vinyl acetate being less reactive and methyl methacrylate much more reactive than vinyl chloride. With the rather wide scatter in literature values for reactivity ratios — particularly with coordination systems — the data on VC/MM A cannot be regarded as completely indicative of a non-radical reaction however, the very low value of rj in the VA/VC system is more definitive. 

To solve these equations and eliminate the reactive intermediates, we note the stationary-state approximation and the definition of the reactivity ratios r and r2 above. Then... 

By definition, T] and r2 represent the relative preference of a given radical that is adding its own monomer to the other monomer. The physieal significance of Equation 8.9 ean be illustrated by eonsidering the product of the reactivity ratios. 

Each of the four propagation reactions has its own rate constant [ky], where subscript i refers to the nature of the propagating radical chain-end and subscript j denotes the nature of the adding monomer. In the mathematical description of copolymer composition as a function of comonomer feed composition, the individual propagation rate constants are not used. Instead, it is common practice to use so-called reactivity ratios. These reactivity ratios are defined as the ratio between the rate constant for homopropagation and that for aosspropagation. The definition of reactivity ratios is mathematically represented as shown in eqn [5] ... 

Similar to the TM, reartivity ratios are also defined for the case of the PUM. Instead of two reactivity ratios as is the case for the TM, four reactivity ratios are required for the PUM in order to describe copolymer composition and monomer sequence distribution. In the literature, two ways of representing these reactivity ratios are encoimtered, that is, on one hand r,- and rf, and, on the other hand, ru and rji. Preference is given to the latter notation, since it provides a more transparent comparison to the notation of the TM. The definition of the reactivity ratios is shown in eqn [24] ... 

FIGURE 12.6 Definition of the reactivity ratios rj and r2 for ethylene/propylene copolymerization (E = ethylene = monomer 1 P = propylene = monomer 2 R = rate of indicated insertion process). 

The symbols for the monomer reactivity ratios are often abbreviated to rj, rj , r2 and r, respectively (see monomer reactivity ratios for the definitions of r and r2 ignoring the penultimate-unit effect). 

Note 3. The present definition ignores the penultimate-unit effect. For the definition of monomer reactivity ratios accounting for the penultimate-unit effect, see Note 3 of chain-end reactivity ratios. 

Equation (9.23) is to be compared with the Feng and Stewart relations (9.4) which describe the fluxes in the same system under non-reactive conditions, The factor (BA coth BA - 1) has the form sketched in Figure 9.2. From the definition of B given by equation (9.19) it is seen chat 9- 0 as and each tend to zero, their ratio remaining equal to Che... 

If, for the purpose of comparison of substrate reactivities, we use the method of competitive reactions we are faced with the problem of whether the reactivities in a certain series of reactants (i.e. selectivities) should be characterized by the ratio of their rates measured separately [relations (12) and (13)], or whether they should be expressed by the rates measured during simultaneous transformation of two compounds which thus compete in adsorption for the free surface of the catalyst [relations (14) and (15)]. How these two definitions of reactivity may differ from one another will be shown later by the example of competitive hydrogenation of alkylphenols (Section IV.E, p. 42). This may also be demonstrated by the classical example of hydrogenation of aromatic hydrocarbons on Raney nickel (48). In this case, the constants obtained by separate measurements of reaction rates for individual compounds lead to the reactivity order which is different from the order found on the basis of factor S, determined by the method of competitive reactions (Table II). Other examples of the change of reactivity, which may even result in the selective reaction of a strongly adsorbed reactant in competitive reactions (49, 50) have already been discussed (see p. 12). 

The only physical difference is that here the current, I, is not directly measurable and thus the dimensionless current density, J, is not directly computable. This difficulty can, however, be overcome if the ratio of the reactivities, A, of normally adsorbed and backspillover oxygen is known (e.g. from electrochemical promotion experiments, where A, as already noted, also expresses the Faradaic efficiency). Thus in this case upon combining the definition of A with equation (11.23) one obtains the following expression for J ... 

Definition of a method for obtaining samples for a source of kinetic data on this reactive extmsion must take several factors into account o Extremely small initiator to polymer ratios are involved, o The rate of dispersion of the initiator and the degree of dispersion obtained is likely itiq>ortant to both the homogeneity of the product and the efficiency of the initiator. 

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