Conventional reactivity ratios

One of the factors which can affect the sequence distribution of copolymers of this type is the value of the apparent reactivity ratios, n and r2. The fact that these ratios are apparent is important since the conversions obtained in these polymerizations at any point in time are considerably higher than those at which conventional reactivity ratio calculations should be applicable (T 6). Nonetheless, under otherwise similar conditions, changes in the apparent reactivity ratios may provide some information about the different systems. 

The copolymerization of TXN and St was analysed in a number of papers 150,151 in terms of conventional reactivity ratios without paying attention to the proper characterization of copolymers and other factors discussed in this volume (cf. Chap. 15). Some additional information comes from the studies of similar systems, i.e. DXL-St copolymerization 152). Also in this case product characterization mainly involved solubility studies, although Yamashita et al. claimed that 1H-NMR spectra confirmed that the product is indeed a true copolymer. This claim was based on a rather limited analysis of H-NMR spectra, however, and was not confirmed by analysis of spectra of related models. Copolymerization conditions were as follows [DXL]0 = 0.7 - 3.7 mol l [St]0 = 4.5 — 2.7 mol l-1, [BF3 OEt2] = 2,5 10-2 mol 1 1, 25 °C, in toluene. After 2-8hrs, from 2% to 9% product with fr ] = 0.12 — 0.32 dl g-1 (viscosity determination conditions not specified) was obtained. 

There is also some evidence that the ionic liquid medium affects polymer structure. Biedron and Kubisa150 reported that the tacticity of PMA prepared in the chiral ionic liquid 19 is different from that prepared in conventional solvent. It is also reported that reactivity ratios for MMA-S copolymcrization in the ionic liquid IS161 differ from those observed for bulk copolymerization. 

Although, there are reports on differences in reactivity ratios observed for conventional radical eopolymeri/.ation v.y living radical copolymeri/.alion (ATRP"75 276 546 >l8 or RAK D48), most research suggests that reactivity ratios are identical31 8 549 and any discrepancies in composition should be attributed to other factors. 

In comparing observed reactivity ratios between various polymerization systems, it is important to take into account the possible effect of molecular weight on copolymer composition.3475 19 In conventional radical eopolymeri/.ation, the specificity shown in the initiation and termination steps can have a significant effect on the composition of low molecular weight copolymers (usually <10 units). These effects are discussed in Section 7.4.5. In a living polymerization molecular weights are low at low conversion and increase with conversion. In these... 

One might also anticipate that the influence of bootstrap effects (Section 8.3.1.2) would be quite different in living and non-living processes. 68 A comprehensive study of reactivity ratios in living and conventional radical polymerization may provide a test of the various hypotheses for the origin of this effect. 

The sterically unencumbered catalyst active site allows the copolymerization of a wide variety of olefins with ethylene. Conventional heterogeneous Ziegler/Natta catalysts as well as most metallocene catalysts are much more reactive to ethylene than higher olefins. With constrained geometry catalysts, a-olefins such as propylene, butene, hexene, and octene are readily incorporated in large amounts. The kinetic reactivity ratio, rl, is approximately... 

While conventional studies of over-all rates of co-oxidation may (4, 33) [with an occasional exception (33)] or may not (21) be capable of detecting small difference in termination constants, the discussion below shows that there are enough unknowns in co-oxidation rate studies that the careful rate measurements at the IFP are inadequate for measuring reactivity ratios (r values). Thus, from 12 pairs of r values determined... 

As mentioned in Chapter 2, if two comonomers are not connected with the template by covalent bonds, reactivity ratios can be calculated on the basis similar to the conventional copolymerization. The only difference is that reactivity ratios ri and T2 for both monomers depend on the concentration of the template. In order to compare experimental data with these considerations, copolymerization of methacrylic acid with styrene was carried out in the presence of PEG (mol. wt. 20,000) as the template. The reactivity ratios rf and r2 can be calculated according to the Kellen-Tiidos method. The results are shown in the Figure 5.4. According to this method, a proper functions of monomer mixture composition, R, and copolymer composition, E, were plotted ... 

Also copolymers with non-conventional structure can be obtained by copolymerization in the presence of templates interacting with comonomers. Average length of sequences of units is in such products higher. Changing the template concentration we can influence the reactivity ratios of monomers and the structure of the product. 

It was demonstrated that MACROMER will copolymerize with conventional monomers in a predictable manner as determined by the relative reactivity ratios. The copolymer equation ... 

Thus, the analysis of the reactivity ratios of the primary and secondary amino groups indicates that for conventional curing agents this cannot be regarded as a serious factor affecting the network topology. 

The initiation step could also be positively affected by the above-mentioned transport properties, as the efficiency factor f assumes higher values with respect to conventional liquid solvents due to the diminished solvent cage effect One further advantage is constituted by the tunability of the compressibility-dependent properties such as density, dielectric constant, heat capacity, and viscosity, all of which offer additional possibilities to modify the performances of the polymerization process. This aspect could be particularly relevant in the case of copolymerization reactions, where the reactivity ratios of the two monomers, and ultimately the final composition of the copolymer, could be controlled by modifying the pressure of the reaction system. 

The S-PIB macromonomer was copolymerized by radical copolymerization with MMA and S, and the reactivity ratio of the small comonomer was calculated by a modified copolymer equation [85]. With MMA, rMMA=0.5 was obtained, i.e., close to that reported for conventional S/MMA system. With S however, rs= 2.1 was determined which suggested that the reactivity of S-PIB is lower than that of S, possibly due to steric interference. 

Since water is the byproduct, and also has an undesired inhibitory effect on catalyst activity, it must be separated efficiently from the reaction mixture. To achieve this, both conventional reactive distillation and reactive membrane separation are considered as process alternatives. In the latter process, a Knudsen-membrane is applied. Consequently, the mass transfer matrix [/c] has a diagonal structure and the diagonal elements are the Knudsen-selectivities - that is, the square-roots of the ratios of the molecular weights Mr. 

For the following reasons Mayo s conventional method for determining reactivity ratios (15) fails in copolymerizations of trioxane (9), and if the reactivity ratios were known, the same reasons would prevent calculation of copolymer compositions ... 

These equilibria also strongly affect copolymerization. Monomer reactivity ratios in controlled/living systems should be identical to those in conventional cationic copolymerizations, if the comonomers react exclusively with carbocationic species. The equilibrium between active and... 

These predictions are essentially confirmed by experience. Most free-radical reactivity ratios are measured by convention at temperatures near 60°C, and the effect of changes in conditions in the range 0-90" C is usually assumed to be negligible, compared to the experimental difficulties in detecting the elTects of slight variations in r or f2. 

Note also that although a conventional high conversion vinyl copolymer may exhibit a wide range of compositions (depending on the reactivity ratios of the comonomers and the monomer feed composition), there are generally so many mutually miscible intermediate compositions that the extremes can be expected to blend well with the rest of the mixture. 

Recent investigations [259] have indicated that the polymerization is not conventional free radical in character but is likely to be coordinated anionic. In support of this view are the reactivity ratio coefficients in copolymerization of vinyl chloride with vinyl acetate and methyl methacrylate, which are different from those found with free radical initiators. 

These are simply the equations of Alfrey and Price (1 j, which relate monomer reactivity ratios to Q and e values, and in which the reasonable values of 2 = and 2 = 1 re substituted, with the convention that the reference standard, ethylene, is monomer 2. In Equation 6 it is seen that the Qi value is simply a ratio of propagation rate constants unmodified by the presence of differences in e values, as is the case in the styrene-based scheme. This would seem to be a more desirable type of parameter to deal with, simply because its meaning is perfectly straightforward. 

One potential problem with conventional free-radical copolymerization is that the reactivity ratios of the two monomers tend to be different from one another [6]. On one hand this leads to non-random sequences of the monomers on a single chain (usually the product of the reactivity ratios is less than one so that there is a tendency to form alternating sequences) and, on the other, to substantial composition drift if the polymerization is carried out in bulk to high conversions. Random copolymers with a range of compositions as a result of composition drift may however be useful in practice, allowing a compositionally graded interface to be formed. 

Kinetic analyses were done for several copper-catalyzed copolymerizations of MMA/nBMA,263 nBA/ styrene,264 266 and nBA/MMA.267 All these studies show that there were no significant differences in reactivity ratio as well as in monomer sequence between the copper-catalyzed and conventional radical polymerizations. Only a difference was observed in the copolymerizations between MMA and ometh-acryloyl-PMMA macromonomers where the reactivity of the latter is higher in the metal-catalyzed polymerizations.267 However, this can be ascribed not to the different nature of the propagating species but to the difference in the time scale of monomer addition or other factors. Simulation has also been applied for the copolymerization study.268... 

A mixture of two monomers that can be homopo-lymerized by a metal catalyst can be copolymerized as in conventional radical systems. In fact, various pairs of methacrylates, acrylates, and styrenes have been copolymerized by the metal catalysts in random or statistical fashion, and the copolymerizations appear to also have the characteristics of a living process. The monomer reactivity ratio and sequence distributions of the comonomer units, as discussed already, seem very similar to those in the conventional free radical systems, although the detailed analysis should be awaited as described above. Apart from the mechanistic study (section II.F.3), the metal-catalyzed systems afford random or statistical copolymers of controlled molecular weights and sharp MWDs, where, because of the living nature, there are almost no differences in composition distribution in each copolymer chain in a single sample, in sharp contrast to conventional random copolymers, in which there is a considerable compositional distribution from chain to chain. Figure 26 shows the random copolymers thus prepared by the metal-catalyzed living radical polymerizations. 

The copolymerization of MMA with nBA was also studied using different catalytic systems. The calculated reactivity ratios were close to those for a conventional radical polymerization and similar for different Cu-based catalytic systems (bpy, PMDETA, and Me6TREN) [92]. The distribution of triads and the polymer stereochemistry was as in any other free radical system [93]. 

Sawamoto et aL used the RuCl2(PPh3)3/Al(OzPr)3 catalyst to prepare St/MMA copolymers [126]. They found that the polymerization proceeded well using 1-phenylethyl bromide as the initiator and that the composition of the copolymer matched the comonomer feed composition, or behaved azeotropically [126]. The polymers were well-defined, with predictable molecular weights and relatively low polydispersities (Mw/Mn<1.5). The reactivity ratios were similar to those determined from conventional free radical processes. Later work used a NiBr2(n-Bu3P)2 catalyst system for the ATRP of a 50/50 mixture of MMA/MA and MMA/nBA [127]. The results indicated that the copolymerization was controlled with copolymer Mn=ll,800 (Mw/Mn=1.47) and 12,500 (Mw/Mn=1.47),respectively. 

MMA/BA CuBr/bpy. TREN and PMDETA Similar reactivity ratios to conventional RP, similar sequences and tacticity Ziegler and Matyjaszewski [92],Madru-ga et al. [93]... 

The controlled growth is even more important for pDMS MMs, which are less compatible with pMMA. Thus, co-methacryloyl pDMS MMs in ATRP had reactivity ratios much closer to MMA than in a conventional process under similar conditions (rPDMS=0.82 vs 0.34) [320]. The reactivity ratios depend on many factors, which include not only the polymerization mechanism but also the reaction temperature, as presented in Table 11 and Fig. 41 [139,320]. 

The conventional [Eq. (7.77)] and simplified [eq. (7.81)] terpolymeriza-tion equations can be used to predict the composition of a terpolymer from the reactivity ratios in the two-component systems M1/M2, M1/M3, and Ms/Ms- The compositions calculated by either of the terpolymerization equations show good agreement with the experimentally observed compositions. Neither equation is found superior to the other in predicting terpolymer compositions. Both equations have been successfully extended to multicomponent copolymerizations of four or more monomers [30,31]. 

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