Copolymerization reactivity ratios for

Herfert and co-workers resolved the copolymerization reactivity ratios for two bridged metallocenes at the second-Order Markov level (140), as shown in Table 3. The data demonstrate bridged metallocenes are somewhat sensitive to... 

Table 5. Free-Radical Copolymerization Reactivity Ratios for the Monomer Pairs...

Use of the modified copolymerization reactivity ratios for the quantitative description of the system where the CTC is considered to copolymerize with the neutral monomer does not serve to prove the concept that the CTC acts as an independent monomer and controls propagation. The method serves only as a mathematical model to describe the initial and final state of the system. Also, the concept is useful to assign a reactivity to the CTC, which is assumed to be an active species. However, whenever the equimolar ratio of donor monomer-MA is distributed in the polymer a dominant role cannot be envisioned for the CTC in the propagation step. 

Acrylamide copolymerizes with many vinyl comonomers readily. The copolymerization parameters ia the Alfrey-Price scheme are Q = 0.23 and e = 0.54 (74). The effect of temperature on reactivity ratios is small (75). Solvents can produce apparent reactivity ratio differences ia copolymerizations of acrylamide with polar monomers (76). Copolymers obtained from acrylamide and weak acids such as acryUc acid have compositions that are sensitive to polymerization pH. Reactivity ratios for acrylamide and many comonomers can be found ia reference 77. Reactivity ratios of acrylamide with commercially important cationic monomers are given ia Table 3. 

An example of a commercial semibatch polymerization process is the early Union Carbide process for Dynel, one of the first flame-retardant modacryhc fibers (23,24). Dynel, a staple fiber that was wet spun from acetone, was introduced in 1951. The polymer is made up of 40% acrylonitrile and 60% vinyl chloride. The reactivity ratios for this monomer pair are 3.7 and 0.074 for acrylonitrile and vinyl chloride in solution at 60°C. Thus acrylonitrile is much more reactive than vinyl chloride in this copolymerization. In addition, vinyl chloride is a strong chain-transfer agent. To make the Dynel composition of 60% vinyl chloride, the monomer composition must be maintained at 82% vinyl chloride. Since acrylonitrile is consumed much more rapidly than vinyl chloride, if no control is exercised over the monomer composition, the acrylonitrile content of the monomer decreases to approximately 1% after only 25% conversion. The low acrylonitrile content of the monomer required for this process introduces yet another problem. That is, with an acrylonitrile weight fraction of only 0.18 in the unreacted monomer mixture, the low concentration of acrylonitrile becomes a rate-limiting reaction step. Therefore, the overall rate of chain growth is low and under normal conditions, with chain transfer and radical recombination, the molecular weight of the polymer is very low. 

GopolymeriZation Initiators. The copolymerization of styrene and dienes in hydrocarbon solution with alkyUithium initiators produces a tapered block copolymer stmcture because of the large differences in monomer reactivity ratios for styrene (r < 0.1) and dienes (r > 10) (1,33,34). In order to obtain random copolymers of styrene and dienes, it is necessary to either add small amounts of a Lewis base such as tetrahydrofuran or an alkaU metal alkoxide (MtOR, where Mt = Na, K, Rb, or Cs). In contrast to Lewis bases which promote formation of undesirable vinyl microstmcture in diene polymerizations (57), the addition of small amounts of an alkaU metal alkoxide such as potassium amyloxide ([ROK]/[Li] = 0.08) is sufficient to promote random copolymerization of styrene and diene without producing significant increases in the amount of vinyl microstmcture (58,59). 

Table 2 shows characteristic reactivity ratios for selected free-radical, ionic, and coordination copolymerizations. The reactivity ratios predict only tendencies some copolymerization, and hence some modification of physical properties, can occur even if and/or T2 are somewhat unfavorable. For example, despite their dissimilar reactivity ratios, ethylene and propylene can be copolymerized to a useful elastomeric product by adjusting the monomer feed or by usiag a catalyst that iacreases the reactivity of propylene relative to ethylene. 

Reactivity ratios for the copolymerization of AN with 7 in methanol at 60 °C, proved to be equal to rx AN= 3,6 0,2 and r%n = 0 0,06, i.e., AN is a much more active component in this binary system. The low reactivity of the vinyl double bond in 7 is explained by the specific effect of the sulfonyl group on its polarity26. In addition to that, the radical formed from 7 does not seem to be stabilized by the sulfonyl group and readily takes part in the chain transfer reaction and chain termination. As a result of this, the rate of copolymerization reaction and the molecular mass of the copolymers decrease with increasing content of 7 in the initial mixture. 

Reactivity ratios for the copolymerization of AN and DM WS in DMSO were found to be rj =0,53 and r2=0,036, and in water r1=0,56 and r2=0,25. The higher reactivity of DM VPS in the copolymerization with AN in aqueous medium, as compared with its reactivity in DMSO, can be explained by a higher degree of dissociation of DMVPS in aqueous medium. This fact also produces a considerable effect on the character of the distribution of monomeric units within the copolymers, which manifests itself in the change of their solubility in water. Copolymers containing 30% of monomeric units AN obtained from a 90 10 mixture of AN and DMVPS in DMSO, irrespective of the level of conversion, are completely soluble in water, whereas copolymers of the same composition, but obtained in aqueous medium with a yield 40%, are insoluble in water. 

Whether a given species functions as an inhibitor, a retarder, a transfer agent or a comonomer in polymerization is dependent on the monomcr(s) and the reaction conditions. For example, oxygen acts as an inhibitor in many polymerizations yet it readily copolymerizes with S, Reactivity ratios for VAc-S... 

Certain monomers may act as inhibitors in some circumstances. Reactivity ratios for VAc-S copolymerization (r< 0.02, rVu -2.3) and rates of cross propagation are such that small amounts of S are an effective inhibitor of VAc polymerization. The propagating chain with a terminal VAc is very active towards S and adds even when S is present in small amounts. The propagating radical with S adds to VAc only slowly. Other vinyl aromatics also inhibit VAc polymerization.174... 

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. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Ra, Ra symbol of a-type radical or ion and its concentration kap constant of propagation reaction between Ra and M klap constant of termination reaction between Ra and R rap> rfia reactivity ratios for binary free-radical copolymerization of monomers Ma and M ... 

Reactivity ratios for 1-hexene (M ) with 5-methyl-1,4-hexadiene CM2) copolymerization at 30 c in hexane solvent using a Et2AlCl/6-TiCl3 AA catalyst system (Al/Ti atomic ratio s 1.5) were determined. The compositions of copolymers were measured by 300 MHz 1H-NMR spectroscopy. The reactivity ratios, calculated by the Tidwell-Mortimer method, were 1.1 + 0.2 for each of the two monomers. 

We also investigated the copolymerizations of 1-hexene with 4-methyl-l-hexene and of 4-methyl-l-hexene with 5-methyl-l-hexene by the aforementioned techniques (33). The monomer reactivity ratios for these two pairs are shown in Table VII. 

The monomer reactivity ratios for many of the most common monomers in radical copolymerization are shown in Table 6-2. These data are useful for a study of the relation between structure and reactivity in radical addition reactions. The reactivity of a monomer toward a radical depends on the reactivities of both the monomer and the radical. The relative reactivities of monomers and their corresponding radicals can be obtained from an analysis of the monomer reactivity ratios [Walling, 1957]. The reactivity of a monomer can be seen by considering the inverse of the monomer reactivity ratio (1 jf). The inverse of the monomer reactivity ratio gives the ratio of the rate of reaction of a radical with another monomer to its rate of reaction with its own monomer... 

Various attempts have been made to place the radical-monomer reaction on a quantitative basis in terms of correlating structure with reactivity. Success in this area would give a better understanding of copolymerization behavior and allow the prediction of the monomer reactivity ratios for comonomer pairs that have not yet been copolymerized. A useful correlation is the Q-e scheme of Alfrey and Price [1947], who proposed that the rate constant for a radical-monomer reaction, for example, for the reaction of Mp radical with M2 monomer, be written as... 

The patterns of reactivity scheme is a more advanced treatment of copolymerization behavior. It follows the general form of the Q-e scheme but does not assume that the same intrinsic reactivity or polarity factors apply both to a monomer and its corresponding radical [Bamford and Jenkins, 1965 Jenkins, 1999, 2000 Jenkins and Jenkins, 1999]. The monomer reactivity ratio for monomer 1 is expressed in terms of four parameters... 

The reactivity ris is the monomer reactivity ratio for copolymerization of monomer 1 with styrene. Since styrene has very little polar character, ris measures the intrinsic reactivity of Mi- radical. The polarity of Mi- radical % is obtained from... 

The values of v and u for a monomer are obtained from monomer reactivity ratios for copolymerization of that monomer with a series of reference monomers. A plot of the data according to Eq. 6-60a as [log r 2 — log ns] versus 71] yields a straight line whose slope is u2 and intercept on the y-axis is —v2. 

Consider the following monomer reactivity ratios for the copolymerization of various pairs of monomers ... 

Some ROPs proceed with the simultaneous operation of two different mechanisms, for example, NCA copolymerizations initiated by some secondary amines proceed with both the amine and activated monomer mechanisms. The monomer reactivity ratios for any comonomer pair are unlikely to be the same for the two different propagations. Any experimentally determined r values are each composites of two different r values. 

Statistical copolymerization occurs among ethylene and various a-olefins [Baldwin and Ver Strate, 1972 Cooper, 1976 Pasquon et al., 1967 Randall, 1978]. The reactivities of monomers in copolymerization generally parallel their homopolymerization behavior ethylene > propene > 1-butene > 1-hexene [Soga et al., 1989]. Table 8-7 shows monomer reactivity ratios for several comonomer pairs. 

In the literature one can find extensive compilations of reactivity ratios for numerous monomer pairs. For evaluation of the copolymerization experiments and for calculating the reactivity ratios, there is now extensive software available. 

Table 5.2 Reactivity ratios for copolymerization of p-cresyl formaldehyde oligomers with methacrylic groups (10) and styrene (2). [Reproduced from S. Polowinski, Polimery, 39, 419 (1994), with kind permission from 1. Ch. P.]...

GPC is a promising method for examination of template polymerization, especially copolymerization. Copolymerization of methacrylic acid with methyl methacrylate in the presence of polyCdimethylaminoethyl methacrylate) can be selected as an example of GPC application for examination of template processes. The process was carried out in tetrahydrofurane as solvent at 65°C. After proper time of polymerization, the samples were cooled, diluted by THF, filtered, and injected to GPC columns. Two detectors on line UV and differential refractometer, DRI, were applied. UV detector was used to measure concentration of two monomers, while the template was recorded by DRI detector (Figure 11.3) The decrease in concentration ofboth monomers can be measured separately. It was found that a big difference in the rate of polymerization between template process and blank polymerization exists. The rate measured separately for methacrylic acid (decrease of concentration of methacrylic acid in monomers mixture) was much higher in the template process. Furthermore, the ratio ofboth monomers changes in a different manner. Reactivity ratios for both monomers can be computed. Decrease in concentration during the process is shown in Figure 11.4. 

The radical reaction mechanism was confirmed by polymerizing a mixture of styrene and methyl methacrylate. The ratio of the monomers in the copolymer (1.15) was nearly equal to the value (1.05) calculated from the reactivity ratio for radical copolymerization and differed considerably from the value of 10.5 for the cationic copolymerization and from the value 0.15 for anionic copolymerization (78). 

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