Ideal random Copolymerization

A value of unity (or nearly unity) for the monomer reactivity ratio signifies that the rate of reaction of the growing chain radicals towards each of the monomers is the same, i.e., A ii ki2 and 22 - 21 and the copolymerization is entirely 

Equation (7.12) means that kiilk 2 and k2ilk22 will be simultaneously either greater or less than unity, or in other words, that both radicals prefer to react with the same monomer. All copolymers whose rir2 product equals, or nearly equals, 1 are therefore called ideal copolymers ox random copolymers. Ionic copolymerizations (Chapter 8) are usually characterized by the ideal type of behavior. 

The relative amounts of the two monomer units along the copolymer chain are thus determined not only by the relative concentrations of the monomer units in the feed but also by the relative reactivities of the two monomers. It is thus obvious that if r and r2 are widely different, while rir2 = 1, copolymers containing appreciable amounts of both Mi and M2 cannot be obtained. 

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This relationship allows ku/k12 = r1 and k22/k21 = r2 (the reactivity ratios) to be determined. Ideally random copolymerization (no specific interactions) gives rt r2 = 1 the extent to which rt r2 < 1 indicates the tendency of alternation. 

MS insertion. The values of ij x T2 are less than but near to unity in both temperatures, which suggests the nearly ideal random copolymerization reactions and very small probability to find two adjacent p-MS units in the polymer chain. In other words, the p-MS units shall be homogeneously distributed in the polymer chain. In catalyst II cases, the copolymerization reactions exhibit even higher rj (rj > 60), very strongly favorable for ethylene incorporation, and almost no possibility of p-MS consecutive insertion (r2 0). The less opened active site in Et(Ind)2ZrCl2 catalyst may sterically prohibit p-MS consecutive insertion. 

The product of the polymerization constants, riT2, is very frequently used as an index for evaluating the alternating tendency in binary copolymeriz-ation/" In fact, the reciprocal of the product rir2 is often called the alternation tendency index. The ideal (random) copolymerization condition exists for the case / i/ 2 = Where ri and r2 are very low and the rir2 product tends to zero the alternating tendency increases.The product r r2 can be zero in two cases—where one or both reactivity ratios are zero. Where r — 0, the copolymer chain is built of isolated Mi units separated by sequences of M2 monomer units. Strictly alternating copolymer would be obtained when both / i and V2 are zero. The second condition is often found for MA copolymerizations, as described in Chapter 10. Where ri > 1, the polymer is richer in Ml monomers than the monomer feed. For ri < 1, the opposite holds. 

Binary copolymerization resembles distillation of a bicomponent liquid mixture, with a reactivity ratio corresponding to the ratio of vapor pressures of the pure components in the latter case. The vapor-liquid composition curves of ideal binary mixtures have no inflection points and neither do the polymer-composition curves for random copolymerizations, in which/ r2 — 1 (Fig. 7-1). For this reason, such comonomer systems are sometimes called ideal. 

Sections of polymer chains must be capable of packing together in ordered periodic arrays for crystallization to occur. This requires that the macromolecules be fairly regular in structure. Random copolymerization will prevent crystallization. Thus, polyethylene would be an ideal elastomer except for the fact that its very regular and symmetrical geometry permits the chains to pack together closely and crystallize very quickly. To inhibit crystallization and confer elastomeric properties on this polymer, ethylene is commonly copolymerized with substantial proportions of another olefin or with vinyl acetate. 

Random copolymerization of MMA with other polar monomers proceeds in a living fashion with relative monomer reactivity ratios in the order BuA > MMA = EtMA > /-PrMA when mediated by 4(Sm Me)/THF [60, 89]. Block polymerization of MMA with other polar monomers as lactone yields ideal living copolymers (PDI = 1.11-1.34) under these conditions. Similarly, ABA triblock copolymers were obtained by sequential addition of MMA, BuA, and MMA [89]. AB block copolymers could be obtained by sequential addition of (L,L)-lactide and (D,D)-lactide (PDI = 1.38) as well as -caprolactone and (l,l)- lactide monomers (PDI = 1.36) in the presence of Y(OCH2CH2NMe2) [82]. 

If the enthalpies of the cross-propagation steps are more negative than those of the homo-propagation steps, then copolymerization will be enhanced (the overall —AH, is higher). When the opposite is true, copolymerization will be hampered. For identical enthalpies and entropies of homo- and cross-propagations, there still remains the term ASmix, which for ideally random copolymers (ASmix 8 J mol-1 xdeg-1) reduces the equilibrium concentration of each comonomer by a factor of two. In such cases a = (3 = 1/2. 

The observed monomer reactivity ratios of different monomer pairs vary widely but can be divided into a rather small number of classes. A useful classification (Rudin, 1982 Odian, 1991) is based on the product of ri and T2, such as rir2 0 (with n 1, T2 1), rir2 1,0 < r r2 < 1, and > 1 (with n > 1, T2 > 1), representing, respectively, alternating, random (or ideal), random-alternating, and block copolymerizations. 

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. 

At the other end of the commonly encountered range we find the product rjr2 1. As noted above, this limit corresponds to ideal copolymerization and means the two monomers have the same relative tendency to add to both radicals. Thus if rj = 10, monomer 1 is 10 times as likely to add to Mj- than monomer 2. At the same time r2 = 0.1, which also means that monomer 1 is 10 times as likely to add to M2 than monomer 2. In this case the radicals exert the same influence, so the monomers add at random in a proportion governed by the specific values of the r s. 

Preference for reaction with the unlike monomer occurs when ri is less than 1. When r and T2 are approximately equal to 1, the conditions are said to be ideal, with a random (not alternating) copolymer produced, in accordance with the Wall equation. Thus, a random copolymer (ideal copolymer) would be produced when chlorotrifluoroethylene is copolymerized with tetrafluoroethylene (Table 7.1). 

As previously noticed, butyl rubber (HR), poly(methylpropene-co-2-methyl-1,3-butadiene), is a random copolymer of isobutene and 0.7-2.2 mol% of isoprene. The industrial slurry process used all over the world consists in a low-temperature copolymerization initiated by A1C13 in meth-ylchloride. In contrast to 1,3-butadiene, isoprene copolymerizes readily with the more reactive isobutene. Reactivity ratios of the pair isobutene-isoprene, ri = 2.5 0.5 and r2 = 0.4 0.1, measured at the conditions of industrial process [10], show that the copolymerization behaves ideally (ri-r2 = 1), and, at the used low concentration of isoprene, isolated units of this latter comonomer are randomly distributed along the chain with 90% M-p-aiw-enchainment [52,53] ... 

When ri = l,r2 = 1, and r r2 = 1, the copolymerization is said to be ideal each radical shows the same preference for one of the monomers. The sequence of monomers in the copolymer is completely random, and the polymer composition is the same as the comonomer feed. A plot of mole percent of Mi in the copolymer against mole percent of Mi in the corresponding feed will give a straight line with zero intercept. 

It is evident that for ideal copolymerization, each radical displays the same preference for adding one monomer over the other. Also, the end group on the growing chain does not influence the rate of addition. For the ideal copolymer, the probability of the occurrence of an M] unit immediately following an M2 unit is the same as locating an M, unit after another Mj unit. Therefore, the sequence of monomer units in an ideal copolymer is necessarily random. 

Case 1 rj > 1 and rj < 1 or r, < 1 and rj > 1. In this case, one of the monomers is more reactive than the other toward the propagating species. Consequently, the copolymer will contain a greater proportion of the more reactive monomer in the random sequence of monomer units. An important practical consequence of ideal copolymerization is that increasing difliculty is experienced in the production of copolymers with significant quantities of both monomers as the (fiflerence in reactivities of the two monomers increases. 

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