Monomer reactivity ratio radical chain copolymerization

Copolymerization. Acrylic and methacrylic acids readily copolymerize free radically with many vinyl monomers. This versatility results from a combination of their highly reactive double bonds and their miscibility with a wide variety of water- and solvent-soluble monomers. Reactivity ratios derived from copolymerizations with many monomers are tabulated in many books on polymerization, for example in Wiley s Polymer Handbook (14) (see also Wiley s Database of Polymer Properties). Q and e values are parameters that may be established for a monomer based on a large number of reactivity ratios with other monomers. These parameters are associated with interactions between the monomer and the growing chain via resonance (Q) and polar effects (e). 

Copolymerization Equation-Monomer Reactivity Ratios. During the copolymerization of two comonomers (A and B), the chain can grow by the occurence of the four following reactions that differ from one another by the nature of the free radical and the inserted monomer ... 

For any specific type of initiation (i.e., radical, cationic, or anionic) the monomer reactivity ratios and therefore the copolymer composition equation are independent of many reaction parameters. Since termination and initiation rate constants are not involved, the copolymer composition is independent of differences in the rates of initiation and termination or of the absence or presence of inhibitors or chain-transfer agents. Under a wide range of conditions the copolymer composition is independent of the degree of polymerization. The only limitation on this generalization is that the copolymer be a high polymer. Further, the particular initiation system used in a radical copolymerization has no effect on copolymer composition. The same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysis of initiators such as AIBN or peroxides, redox, photolysis, or radiolysis. Solvent effects on copolymer composition are found in some radical copolymerizations (Sec. 6-3a). Ionic copolymerizations usually show significant effects of solvent as well as counterion on copolymer composition (Sec. 6-4). 

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. 

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. kn ki2 and 22 — A 2i and the copolymerization is entirely random. In other words, both propagating species and M2 have little or no preference for adding either monomer. The copolymer composition is the same as the comonomer feed with a completely random placement of the two monomers along the copolymer chain. Such behavior is referred to as Bemoullian. Free-radical copolymerization of ethylene and vinyl acetate and that of isoprene and butadiene are examples of such a system, but this is not a common case. Random monomer distributions are obtained more generally in a situation where both types of radicals have exactly the same preference for the same type of monomer as represented by the relationship... 

When one reactivity ratio is greater than unity and the other is less than unity, either propagating species will prefer to add monomers of the first type. Relatively long sequences of this monomer will thus be formed if the reactivity ratios differ sufficiently. A special situation arises when ri 1 and T2 1 or vice versa. In this case, the product composition will tend toward that of the homopolymer of the more reactive monomer. Such reactivity ratios refiect the existence of an impractical copolymerization. An example of this type of behavior is the radical chain polymerization of styrene-vinyl acetate system, where monomer reactivity ratios of 55 and 0.01 are observed. The large differences between the monomer reactivity ratios imparts a tendency toward consecutive homopolymerization of the two monomers. For example, when ri 1 and T2 1, both and... 

Recently, the Research Group on NMR, SPSJ, assessed reliability of copolymer analysis by NMR using three samples of radically prepared copolymers of MMA and acrylonitrile with different compositions. 1H and 13C NMR spectra of the copolymers were collected from 46 NMR spectrometers (90 500 MHz) and the composition and sequence distribution were determined.232 Table 14 summarizes the monomer reactivity ratios determined by 13C NMR analysis. The large difference between rxx and r2X indicates the presence of a penultimate effect in this radical copolymerization, as previously reported.233 The values of riy, especially rxx, depended on the comonomer feed ratio, suggesting higher order of neighbouring unit effect on the reactivity of chain-end radicals. 

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... 

Random copolymers of styrene/isoprene and styrene/acrylonitrile have been prepared by stable free radical polymerization. By varying the comonomer mole fractions over the range 0.1-0.9 in low conversion SFRP reactions it has been demonstrated that the incorporation of the two monomers in the copolymer is analogous to that found in conventional free radical copolymerizations. The composition and microstructure of random copolymers prepared by SFRP are not significantly different from those of copolymers synthesized conventionally. These two observations support the conclusion that the presence of nitroxide in the SFR process does not influence the monomer reactivity ratios or the stereoselectivity of the propagating radical chain. Rather, the SFR propagation mechanism is essentially the same as that of the conventional free radical copolymerization process. 

Obviously, because of the difference in the reactivity of styrene and DVB, the networks prepared by free radical copolymerization do not relate to such an ideal system with uniform distribution of DVB units and constant chain lengths between the junction points. Also, it was not possible to eliminate this serious defect by an anionic copolymerization of the comonomers. The anionic copolymerization has often been initiated by n- or sec-hutyl lithium [110-112]. Under such conditions, styrene is consumed faster than p-DVB, the monomer reactivity ratios being ri = 1.5S and r2 = 0.32. Therefore, DVB-enriched domains wUl form toward the end of the anionic process. On the other hand, the styrene—m-isomer reactivity ratio (r = 0.65 and r2 = 1.20) points to the local incorporation of m-DVB crosslinks into the initially formed copolymer [113, 114]. In addition, the anionic process is also accompanied by intramolecular cycUzation, similar to radical styrene DVB copolymerization [115,116]. 

The initiating radicals derived from AIBN, AZE and APE can be regarded as models for the growing radicals of MAN, MMA and STY, respectively in each case, the model radical has a hydrogen atom in place of a polymer chain. In the absence of effects of non-terminal groups, it would be expected that the ratio of the rate constants (k >/kM")foT the reactions of two monomers with, say, the Me2C(CN) radical, would be close to that for their reactions with the polyMAN radical, as deduced from studies of copolymerizations and values of monomer reactivity ratios. 

Copolymerization. In free-radical copolymerization (qv), the composition of the copolymer is controlled by the comonomer reactivity ratios (23). The monomer reactivity ratio is defined as the quotient of the rate constants for chain homopropagation to the rate constant for chain cross-propagation. 

Table D Typical Free-Radical Chain-Copolymerization Reactivity Ratios of Some Selected Monomers at Different Temperatures...

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). 

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. 

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. 

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... 

Monomers not amenable to direct homopolymerization using a particular reagent can sometimes be copolymcrizcd. For example, NMP often fails with methacrylates (e.g. MMA, BMA), yet copolymerizalions of these monomers with S are possible even when the monomer mix is predominantly composed of the methacrylate monomer,15j This is attributed to the facility of cross propagation and the relatively low steady state concentration of propagating radicals with a terminal MMA (Section 7.4.3.1). MMA can also be copolymerized with S or acrylates at low temperature (60 C).111 Under these conditions, only deactivation of propagating radicals with a terminal MMA unit is reversible, deactivation of chains with a terminal S or acrylate unit is irreversible. Molecular weights should then be controlled by the reactivity ratios and the comonomer concentration rather than by the nitroxide/alkoxyamine concentration. 

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. 

The reactivity ratios, rA and rB, express the relative preference of a growing chain for one of the two monomers. In free-radical copolymerizations they are roughly independent of solvent, initiator, and temperature. In ionic copolymerization, however, they depend strongly on the counterion and the solvent. 

An alternative rationale for the unusual RLi (hydrocarbon) copolymerization of butadiene and styrene has been presented by O Driscoll and Kuntz (71). Rather than invoking selective solvation, these workers stated that classical copolymerization kinetics is sufficient to explain this copolymerization. They adapted the copolymer-composition equation, originally derived from steady-state assumptions for free-radical copolymerizations, to the anionic copolymerization of butadiene and styrene. Equation (20) describes the relationship between the instantaneous copolymer composition c/[M,]/rf[M2] with the concentrations of the two monomers in the feed, M, and M2, and the reactivity ratios, rt, r2, of the monomers. The rx and r2 values are measures of the preference of the growing chain ends for like or unlike monomers. 

The reactivity ratios for pairs of given monomers can be very different for the different types of chain-growth copolymerization free-radical, anionic, cationic, and coordination copolymerization. Although the copolymer equation is valid for each of them, the copolymer composition can depend strongly on the mode of initiation (see Figure 10.8). 

The simple copolymer model, with two reactivity ratios for a binary comonomer reaction, explains copolymer composition data for many systems. It appears to be inadequate, however, for prediction of copolymerization rates. (The details of various models that have been advanced for this purpose are omitted here, in view of their limited success.) Copolymerization rates have been rationalized as a function of feed composition by invoking more complicated models in which the reactivity of a macroradical is assumed to depend not Just on the terminal monmomer unit but on the two last monomers in the radical-ended chain. This is the penultimate model, which is mentioned in the next Section. 

The simple copolymer model is a first-order Markov chain in which the probability of reaction of a given monomer and a macroradical depends only on the terminal unit in the radical. This involves consideration of four propagation rate constants in binary copolymerizations, Eqs. (7-2)-(7-4). The mechanism can be extended by including a penultimate unit effect in the macroradical. This involves eight rate constants. A third-order case includes antepenultimate units and 16 rate coefficients. A true test of this model is not provided by fitting experimental and predicted copolymer compositions, since a match must be obtained sooner or later if the number of data points is not saturated by the adjustable reactivity ratios. 

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. 

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