Reactivity ratio number

The reactivity ratios are proportional to the product of two exponential numbers. 

In the most common production method, the semibatch process, about 10% of the preemulsified monomer is added to the deionised water in the reactor. A shot of initiator is added to the reactor to create the seed. Some manufacturers use master batches of seed to avoid variation in this step. Having set the number of particles in the pot, the remaining monomer and, in some cases, additional initiator are added over time. Typical feed times ate 1—4 h. Lengthening the feeds tempers heat generation and provides for uniform comonomer sequence distributions (67). Sometimes skewed monomer feeds are used to offset differences in monomer reactivity ratios. In some cases a second monomer charge is made to produce core—shell latices. At the end of the process pH adjustments are often made. The product is then pumped to a prefilter tank, filtered, and pumped to a post-filter tank where additional processing can occur. When the feed rate of monomer during semibatch production is very low, the reactor is said to be monomer starved. Under these... 

In this copolymerization, the reactivity ratios are such that there is a tendency for S and the acrylic monomers to alternate in the chain. This, in combination with the above-mentioned specificity in the initiation and termination steps, causes chains with an odd number of units to dominate over those with an even number of units. 

The effects of solvent on radical copolymerization are mentioned in a number of reviews.69 72 97,98 For copolymerizations involving monomers that arc ionizablc or form hydrogen bonds (AM, MAM, HEA, HEMA, MAA, etc.) solvent effects on reactivity ratios can be dramatic. Some data for MAA-MMA copolymerization are shown in Table 8.4.w... 

The present results show that the first step of the interaction between olefins and Bt2 is the formation of CTCs, whose Kf are highly sensitive to structural effects. Both Kf ratios and reactivity ratios of olefins are scarcely affected by the solvent. An increase by two in number of alkyl substituents on the double bond increases both Kf and kobsd roughly by a factor of 103. Therefore, at variance with the expectation for an AdgCl mechanism, substituent effects are not much more influential on k tsd than on Kf. This suggests that the rates of CTC ionization be actually reduced by reversal. 

Mayo-Lewis Binary Copolymeriration Model. In this exeimple we consider the Mayo-Lewis model for describing binary copolymerization. The procedure for estimating the kinetic parameters expressed as reactivity ratios from composition data is discussed in detail in our earlier paper (1 ). Here diad fractions, which are the relative numbers of MjMj, MiMj, M Mj and MjMj sequences as measured by NMR are used. NMR, while extremely useful, cannot distinguish between MiM and M Mi sequences and... 

Our theoretical studies [38] showed that the hyperbranched polymers generated from an SCVP possess a very wide MWD which depends on the reactivity ratio of propagating and initiating groups, r=kjk. For r=l, the polydispersity index where P is the number-average degree of polymerization. 

Hence by assigning two parameters, a Q and an c, to each of a set of monomers, it should be possible according to this scheme to compute reactivity ratios ri and V2 for any pair. In consideration of the number of monomer pairs which may be selected from n monomers—about n /2—the advantages of such a scheme over copolymerization experiments on each pair are obvious. Price has assigned approximate values to Q and e for 31 monomers, based on copolymerization of 64 pairs. The latitude of uncertainty is unfortunately large assignment of more accurate values is hampered by lack of better experimental data. Approximate agreement between observed and predicted reactivity ratios is indicated, however. 

High-resolution nuclear magnetic resonance spectroscopy, especially 13C NMR, is a powerful tool for analysis of copolymer microstructure [Bailey and Henrichs, 1978 Bovey, 1972 Cheng, 1995, 1997a Randall, 1977, 1989 Randall and Ruff, 1988], The predicted sequence length distributions have been verihed in a number of comonomer systems. Copolymer microstructure also gives an alternate method for evaluation of monomer reactivity ratios [Randall, 1977]. The method follows that described in Sec. 8-16 for stereochemical microstructure. For example, for the terminal model, the mathematical equations from Sec. 8-16a-2 apply except that Pmm, Pmr, Pm and Prr are replaced by p, pi2, p2j, and p22. 

Most of the largest differences between observed and calculated r values in Table VI occur for cumene combinations. Such discrepancies are inevitable if cumene tends to alternate with butadiene and Tetralin but not with styrene. (This distinction could be partly experimental error, which tends to be greatest in combinations of the least reactive hydrocarbon—cumene—with the other hydrocarbons.) These alternation tendencies are measured by the products of the reactivity ratios, the last number in each group of three in Table VI, 1 corresponding to no effect and 0 to inability of one or both peroxy radicals to react with the hydrocarbon from which it is derived. If we take cumene to be 1/40 as reactive as butadiene (instead of 1/30, as in the table), agreement is better for the two styrene-cumene reactivity ratios and poorer for the other cumene ratios. If instead we take cumene to be 1/20 as reactive as butadiene, agreement is much better for the butadiene-cumene and Tetralin-cumene... 

First number in each set is reactivity ratio for peroxide radical of hydrocarbon at top... 

Figure 18 shows the relationship between the degree of coordination (x in 17), ie. the number of positive charges on a polymer chain, and the reactivity ratio (fcpyp/fcpy) for the reaction with Fe(II)-edta2 79). The reactivity ratio increases with x value. Hence, the PVP complex with a higher degree of coordination is considered to have a stronger electrostatic domain because it has more positive charges on the PVP chain. The reactivity ratios ( Qpvp/fcpy) for the partially quaternized PVP(QPVP)-Co(III) complexes 19 are also plotted in Fig. 18. The reactivity ratio...

The reactivity ratios may be evaluated by performing a series of low-conversion copolymerizations at different, monomer-feed ratios, isolating the copolymer, and determining its composition. A number of mathematical analyses have been proposed in order to provide, from the experimental data, correct values for the two unknown reactivity ratios. There is some difference of opinion as to the best method for obtaining values having quantifiable errors.84,64" However, several of... 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

A number of reactivity ratios have been determined from initial copolymer composition data. These are recorded in Table 2. In view of the difficulties associated with their determination and uncertainty whether the copolymer composition equation is accurate under all conditions, they should be considered as of unknown accuracy. 

Harwood (17) has described a technique using run number theory to calculate reactivity ratios based on sequence distribution. The run number, R, which characterizes a particular copolymer may be calculated as follows ... 

An equation can be derived which relates run number, and feed composition to reactivity ratios ... 

A method for calculating apparent reactivity ratios based on run number theory has been applied to "starved-feed" styrene/ ethyl acrylate systems. The reactivity ratios found are in agreement with those determined from solution polymerization data. The further confirmation of the observed agreement between reactivity ratios determined at low conversions and those determined by run number theory in "starved-feed" high conversion copolymerization requires the analysis of other comonomer pairs. 

Triad sequence assignments have been made for ethyl acrylate-centered triads. Apparent reactivity ratios have been calculated for the semi-batch copolymers using run number theory. A model has been developed to describe the power-feed systems and predict the triad distributions in the incremental and final copolymer using the experimentally determined r-j and r values. 

It was found that the reactivity ratios of the copolymerization system greatly influences the number of the arms of the star polymer. 

The relative reactivity of the macromonomer in copolymerization with a common comonomer, A, can be assessed by l/rA=kAB/kAA> i-e-> the rate constant of propagation of macromonomer B relative to that of the monomer A toward a common poly-A radical. In summarizing a number of monomer reactivity ratios in solution copolymerization systems reported so far [3,31,40], it appears reasonable to say that the reactivities of macromonomers are similar to those of the corresponding small monomers, i.e., they are largely determined by the nature of their polymerizing end-group, i.e., essentially by their chemical reactivity. 

In the predominating reactions, the number of different types of monomer units and their sequences are determined by their relative molecular reactivities for the macrocellulosic radicals and the monomer reactivity ratios. These types of reactions are useful in that less reactive monomers can be included in copolymers to add selected organochemical and macromelecular properties to the modified cellulosic products. In cases where vinyl monomers have been reacted to form oligomers, these reactions are useful in increasing the reactivity of oligomers with macrocellulosic radicals (29, 30, 31). 

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