Copolymer reactivity ratios

The parameters rj and T2 are the vehicles by which the nature of the reactants enter the copolymer composition equation. We shall call these radical reactivity ratios, although similarly defined ratios also describe copolymerizations that involve ionic intermediates. There are several important things to note about radical reactivity ratios ... 

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. 

Table 7.1 Values of Reactivity Ratios ri and T2 and the Product ri T2 for a Few Copolymers at 60°C...

Equations (7.40) and (7.41) suggest a second method, in addition to the copolymer composition equation, for the experimental determination of reactivity ratios. If the average sequence length can be determined for a feedstock of known composition, then rj and r2 can be evaluated. We shall return to this possibility in the next section. In anticipation of applying this idea, let us review the assumptions and limitation to which Eqs. (7.40) and (7.41) are subject ... 

As we have already seen, it is the reactivity ratios of a particular copolymer system that determines both the composition and microstructure of the polymer. Thus it is important to have reliable values for these parameters. At the same time it suggests that experimental studies of composition and microstructure can be used to evaluate the various r s. 

Evaluation of reactivity ratios from the copolymer composition equation requires only composition data—that is, analytical chemistry-and has been the method most widely used to evaluate rj and t2. As noted in the last section, this method assumes terminal control and seeks the best fit of the data to that model. It offers no means for testing the model and, as we shall see, is subject to enough uncertainty to make even self-consistency difficult to achieve. 

The data in Table 7.6 list the mole fraction of methyl acrylate in the feedstock and in the copolymer for the methyl acrylate (Mi)-vinyl chloride (M2) system. Use Eq. (7.54) as the basis for the graphical determination of the reactivity ratios which describe this system. 

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. 

Copolymers of acrylamide and acryloyloxyethyltrimethylammonium chloride have become increasingly preferred due to the favorable reactivity ratios between these two monomers, which result ia copolymers with a uniform composition. 

For a growing radical chain that has monomer 1 at its radical end, its rate constant for combination with monomer 1 is designated and with monomer 2, Similady, for a chain with monomer 2 at its growing end, the rate constant for combination with monomer 2 is / 22 with monomer 1, The reactivity ratios may be calculated from Price-Alfrey and e values, which are given in Table 8 for the more important acryUc esters (87). The sequence distributions of numerous acryUc copolymers have been determined experimentally utilizing nmr techniques (88,89). Several review articles discuss copolymerization (84,85). 

Acrylonitrile copolymeri2es readily with many electron-donor monomers other than styrene. Hundreds of acrylonitrile copolymers have been reported, and a comprehensive listing of reactivity ratios for acrylonitrile copolymeri2ations is readily available (34,102). Copolymeri2ation mitigates the undesirable properties of acrylonitrile homopolymer, such as poor thermal stabiUty and poor processabiUty. At the same time, desirable attributes such as rigidity, chemical resistance, and excellent barrier properties are iacorporated iato melt-processable resias. 

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). 

Copolymers. Although many copolymers of ethylene can be made, only a few have been commercially produced. These commercially important copolymers are Hsted in Table 4, along with their respective reactivity coefficient (see Co polymers. The basic equation governing the composition of the copolymer is as follows, where and M2 are the monomer feed compositions, and r2 ate the reactivity ratios (6). 

Copolymers of diallyl itaconate [2767-99-9] with AJ-vinylpyrrolidinone and styrene have been proposed as oxygen-permeable contact lenses (qv) (77). Reactivity ratios have been studied ia the copolymerization of diallyl tartrate (78). A lens of a high refractive iadex n- = 1.63) and a heat distortion above 280°C has been reported for diallyl 2,6-naphthalene dicarboxylate [51223-57-5] (79). Diallyl chlorendate [3232-62-0] polymerized ia the presence of di-/-butyl peroxide gives a lens with a refractive iadex of n = 1.57 (80). Hardness as high as Rockwell 150 is obtained by polymerization of triaHyl trimeUitate [2694-54-4] initiated by benzoyl peroxide (81). 

GopolymeriZation. The importance of VDC as a monomer results from its abiHty to copolymerize with other vinyl monomers. Its Rvalue equals 0.22 and its e value equals 0.36. It most easily copolymerizes with acrylates, but it also reacts, more slowly, with other monomers, eg, styrene, that form highly resonance-stabiHzed radicals. Reactivity ratios (r and r, with various monomers are Hsted in Table 2. Many other copolymers have been prepared from monomers for which the reactivity ratios are not known. The commercially important copolymers include those with vinyl chloride (VC),... 

During copolymerization, one monomer may add to the copolymer more rapidly than the other. Except for the unusual case of equal reactivity ratios, batch reactions carried to completion yield polymers of broad composition distribution. More often than not, this is an undesirable result. 

Vinyhdene chloride copolymerizes randomly with methyl acrylate and nearly so with other acrylates. Very severe composition drift occurs, however, in copolymerizations with vinyl chloride or methacrylates. Several methods have been developed to produce homogeneous copolymers regardless of the reactivity ratio (43). These methods are appHcable mainly to emulsion and suspension processes where adequate stirring can be maintained. Copolymerization rates of VDC with small amounts of a second monomer are normally lower than its rate of homopolymerization. The kinetics of the copolymerization of VDC and VC have been studied (45—48). 

VEs do not readily enter into copolymerization by simple cationic polymerization techniques instead, they can be mixed randomly or in blocks with the aid of living polymerization methods. This is on account of the differences in reactivity, resulting in significant rate differentials. Consequendy, reactivity ratios must be taken into account if random copolymers, instead of mixtures of homopolymers, are to be obtained by standard cationic polymeriza tion (50,51). Table 5 illustrates this situation for butyl vinyl ether (BVE) copolymerized with other VEs. The rate constants of polymerization (kp) can differ by one or two orders of magnitude, resulting in homopolymerization of each monomer or incorporation of the faster monomer, followed by the slower (assuming no chain transfer). 

The Q and e values of VP are 0.088 and —1.62, respectively (125). This indicates resonance interaction of the double bond of the vinyl group with the electrons of the lactam nitrogen, whence the electronegative nature. With high e+ monomers such as maleic anhydride, VP forms alternating copolymers, much as expected (126). With other monomers between these Q and e extremes a wide variety of possibiHties exist. Table 14 Hsts reactivity ratios for important comonomers. 

Although reactivity ratios indicate that VP is the more reactive monomer, reaction conditions such as solvent polarity, initiator type, percent conversion, and molecular weight of the growing radical can alter these ratios (138). Therefore, depending on polymerization conditions, copolymers produced by one manufacturer may not be identical to those of another, especially if the end use appHcation of the resin is sensitive to monomer sequence distribution and MWD. 

The combined values of the reactivity ratios (ie, r. r ) yield important clues regarding the composition of the copolymer. Reactivity ratio combinations are generally classified in five categories (15) designated Types 1—V in the discussion. I... 

Fig. 1. Copolymer composition as a function of monomer feed ratio for various reactivity ratio combiaations, designated I—V and explained ia the text...

Epichlorohydrin Elastomers without AGE. Polymerization on a commercial scale is done as either a solution or slurry process at 40—130°C in an aromatic, ahphatic, or ether solvent. Typical solvents are toluene, benzene, heptane, and diethyl ether. Trialkylaluniinum-water and triaLkylaluminum—water—acetylacetone catalysts are employed. A cationic, coordination mechanism is proposed for chain propagation. The product is isolated by steam coagulation. Polymerization is done as a continuous process in which the solvent, catalyst, and monomer are fed to a back-mixed reactor. Pinal product composition of ECH—EO is determined by careful control of the unreacted, or background, monomer in the reactor. In the manufacture of copolymers, the relative reactivity ratios must be considered. The reactivity ratio of EO to ECH has been estimated to be approximately 7 (35—37). 

AGE-Gontaining Elastomers. The manufacturing process for ECH—AGE, ECH—EO—AGE, ECH—PO—AGE, and PO—AGE is similar to that described for the ECH and ECH—EO elastomers. Solution polymerization is carried out in aromatic solvents. Slurry systems have been reported for PO—AGE (39,40). When monomer reactivity ratios are compared, AGE (and PO) are approximately 1.5 times more reactive than ECH. Since ECH is slightly less reactive than PO and AGE and considerably less reactive than EO, background monomer concentration must be controlled in ECH—AGE, ECH—EO—AGE, and ECH—PO—AGE synthesis in order to obtain a uniform product of the desired monomer composition. This is not necessary for the PO—AGE elastomer, as a copolymer of the same composition as the monomer charge is produced. AGE content of all these polymers is fairly low, less than 10%. Methods of molecular weight control, antioxidant addition, and product work-up are similar to those used for the ECH polymers described. 

In contrast to ionic chain polymerizations, free radical polymerizations offer a facile route to copolymers ([9] p. 459). The ability of monomers to undergo copolymerization is described by the reactivity ratios, which have been tabulated for many monomer systems for a tabulation of reactivity ratios, see Section 11/154 in Brandrup and Immergut [14]. These tabulations must be used with care, however, as reactivity ratios are not always calculated in an optimum manner [15]. Systems in which one reactivity ratio is much greater than one (1) and the other is much less than one indicate poor copolymerization. Such systems form a mixture of homopolymers rather than a copolymer. Uncontrolled phase separation may take place, and mechanical properties can suffer. An important ramification of the ease of forming copolymers will be discussed in Section 3.1. 

The influence of radiation dose on the polymer composition and the swelling degree of (pAM-DAEA-HCl) are shown in Table 3. The results show that the percent of acrylamide in the copolymer is higher than that of the amine. This can be attributed to smaller reactivity ratios of monomers of diallylammonium salts relative to acryl-... 

Kunitake, Yamaguchi and Aso149 studied the copolymerization of 2-furaldehyde with olefins and vinyl ethers using BF3 Et20 in methylene chloride or toluene at —78 °C. No copolymers were obtained with olefins, but p-tolyl vinyl ether or 2,3-dihydropyran gave polyethers. With the former co-monomer the values of the reactivity ratios were rx = 0.15 0.15 and r2 = 0.25 0.05 (Mj = 2-furaldehyde). 

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 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. 

Thus, the terminal model allows the copolymer composition for a given monomer feed to be predicted from just two parameters the reactivity ratios rAB and rBA- Some values of terminal model reactivity ratios for common monomer pairs are given in Table 7.1. Values for other monomers can be found in data... 

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