Copolymerization reactivity ratios from composition

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... 

Figure 5.4. Kellen-Ttidos plot for calculation of reactivity ratios from composition of monomer mixture, R, and composition of copolymer, E Copolymerization of methacrylic acid with methyl methacrylate in the presence of PEG 20,000. Reprinted from S.PolowinskijEnr.PoZym.t/., 19,679 (1983) with kind permission from Elsevier Science Ltd.

Attempts to obtain simple reactivity ratios from composition data by various techniquesled to the conclusion that the kinetics of the styrene-MA copolymerization do not follow the classical scheme of Mayo-Lewis and/or Alfrey-Goldfinger. All systems gave rise to Fineman-Ross and... 

Numerous reports are available [19,229-248] on the development and analysis of the different procedures of estimating the reactivity ratio from the experimental data obtained over a wide range of conversions. These procedures employ different modifications of the integrated form of the copolymerization equation. For example, intersection [19,229,231,235], (KT) [236,240], (YBR) [235], and other [242] linear least-squares procedures have been developed for the treatment of initial polymer composition data. Naturally, the application of the non-linear procedures allows one to obtain more accurate estimates of the reactivity ratios. However, majority of the calculation procedures suffers from the fact that the measurement errors of the independent variable (the monomer feed composition) are not considered. This simplification can lead in certain cases to significant errors in the estimated kinetic parameters [239]. Special methods [238, 239, 241, 247] were developed to avoid these difficulties. One of them called error-in-variables method (EVM) [239, 241, 247] seems to be the best. EVM implies a statistical approach to the general problem of estimating parameters in mathematical models when the errors in all measured variables are taken into account. Though this method requires more information than do ordinary non-linear least-squares procedures, it provides more reliable estimates of rt and r2 as well as their confidence limits. 

The uncertainties and poor j eement in determinations of ethylene/ propene reactivity ratios from monomer and polymer composition [m = (Mj/Mj) monomer p = (Mi/M2) polymer] and the copolymerization equation p = (1 + rjm)/(l + rj/m) give particular interest to approaches based on the analysis of monomer unit distributions in the copolymer. 

The monomer reactivity ratios r and r2 can be determined from the experimental conversion-composition data of binary copolymerization using both the instantaneous and integrated binary copolymer composition equations, described previously. However, in the former case, it is essential to restrict the conversion to low values (ca. < 5%) in order to ensure that the feed composition remains essentially unchanged. Various methods have been used to obtain monomer reactivity ratios from the instantaneous copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or (7.17)] are mentioned in the following paragraphs. Two of the simpler methods involve plotting of r versus r2 or F versus f. ... 

Perfluoro-2-methylene-l,3-dioxolane monomers can be copolymerized with each other to modify the physical properties of the polymers. The refractive index and Tg depend on the copolymer composition. The copolymers are readily prepared in solution and in bulk. For example, the copolymerization reactivity ratios of monomers A and C (Figure 4.10) are = 0.97 and - 0.85 [35]. The data show that this copolymerization yields nearly ideal random copolymers. Figure 4.11 shows the change in Tg as a function of the copolymer composition. The copolymers have only one T, which increases from 110 to 165 C as the mole fraction of monomer A increases. The copolymer films prepared by casting are flexible and tough and have a high optical transparency. 

The reactivity ratios of a copolymerization system are the fundamental parameters in terms of which the system is described. Since the copolymer composition equation relates the compositions of the product and the feedstock, it is clear that values of r can be evaluated from experimental data in which the corresponding compositions are measured. We shall consider this evaluation procedure in Sec. 7.7, where it will be found that this approach is not as free of ambiguity as might be desired. For now we shall simply assume that we know the desired r values for a system in fact, extensive tabulations of such values exist. An especially convenient source of this information is the Polymer Handbook (Ref. 4). Table 7.1 lists some typical r values at 60°C. 

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. 

Methyl-2-furaldehyde gave a similar overall behaviour, but a penultimate effect was observed in its copolymerization with isopropenylbenzene whereby two molecules of the aldehyde could add together if the penultimate unit in the growing chain was from the olefin. This was borne out by the copolymers composition and spectra. The values of the reactivity ratios showed this interesting behaviour rx = 1.0 0.1, r2 = 0.0 0.1. An apparent paradox occurred the aldehyde, which could not homo-polymerize, had equal probability of homo- and copolymerization and the olefin, which homopolymerized readily, could only alternate. The structure arising from this situation was close to a regular sequence of the type ... 

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. 

The solvent in a bulk copolymerization comprises the monomers. The nature of the solvent will necessarily change with conversion from monomers to a mixture of monomers and polymers, and, in most cases, the ratio of monomers in the feed will also vary with conversion. For S-AN copolymerization, since the reactivity ratios are different in toluene and in acetonitrile, we should anticipate that the reactivity ratios are different in bulk copolymerizations when the monomer mix is either mostly AN or mostly S. This calls into question the usual method of measuring reactivity ratios by examining the copolymer composition for various monomer feed compositions at very low monomer conversion. We can note that reactivity ratios can be estimated for a single monomer feed composition by analyzing the monomer sequence distribution. Analysis of the dependence of reactivity ratios determined in this manner of monomer feed ratio should therefore provide evidence for solvent effects. These considerations should not be ignored in solution polymerization either. 

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. 

For copolymerizations proceeding by the activated monomer mechanism (e.g., cyclic ethers, lactams, /V-carboxy-a-amino acid anhydrides), the actual monomers are the activated monomers. The concentrations of the two activated monomers (e.g., the lactam anions in anionic lactam copolymerization) may be different from the comonomer feed. Calculations of monomer reactivity ratios using the feed composition will then be incorrect. 

The dependence of the composition of the copolymer on the proportions of the monomers in the initial mixture can be portrayed graphically in a so-called copolymerization diagram (Fig. 3.4). The mole fraction of one of the two monomeric units in the resulting copolymer is plotted against the mole fraction of this monomer in the original reaction mixture the curve can also be calculated from the reactivity ratios by means of Eq. 3.18. 

As can be seen from Fig. 3.4, it is very rare for the polymer composition to correspond to that of the monomer mixture. For this reason the composition of the monomer mixture, and hence also that of the resulting polymer, generally changes as the copolymerization proceeds. Therefore, for the determination of the reactivity ratios one must work at the lowest possible conversion. In practical situations where, for various reasons, one is forced to polymerize to higher conversions, this leads to a chemical non-uniformity of the copolymers in addition to the usual non-uniformity of molecular weights. 

The determination of the reactivity ratios requires a knowledge of the composition of the copolymers made from particular monomer mixtures numerous analytical methods are available (see Sect. 2.3.2). In principle, it is possible to calculate and r2, using Eq. 3.18, from the composition of only two copolymers that have been obtained from two different mixtures of the two monomers M and M2. However, it is more precise to determine the composition of the copolymers from several monomer mixtures and to calculate, for each individual experiment, values of r2 that would correspond to arbitrarily chosen values of r from the rearranged copolymerization equation ... 

The polymerization of a mixture of more than one monomer leads to copolymers if two monomers are involved and to terpolymers in the case of three monomers. At low conversions, the composition of the polymer that forms from just two monomers depends on the reactivity of the free radical formed from one monomer toward the other monomer or the free radical chain of the second monomer as well as toward its own monomer and its free radical chain. As the process continues, the monomer composition changes continually and the nature of the monomer distribution in the polymer chains changes. It is beyond the scope of this laboratory manual to discuss the complexity of reactivity ratios in copolymerization. It should be pointed out that the formation of terpolymers is even more complex from the theoretical standpoint. This does not mean that such terpolymers cannot be prepared and applied to practical situations. In fact, Experiment 5 is an example of the preparation of a terpolymer latex that has been suggested for use as an exterior protective coating. 

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