Reactivity, ratio

Reactivity ratios of a number of activated acrylates and methacrylates with different structural monomers are given in Table 2. Polymer compositions produced at low conversions from equimolar monomer fe compositions are also indicated in the Table. These values are back calculated from the reactivity ratios, and are hence equivalent to experimental data. The actual copolymeriz-ability patterns of three comonomer pairs are also shown in Fig. 4. These results show that, among the various monomer pairs, AOTcp with styrene, and AOTcp with 7V-vinylpyrrolidone, produce azotropic copolymers at about equimolar monomer feed compositions. The relatively small reactivity ratios of these two monomer pairs indicate that their equimolar copolymerization produces approximately alternating, rather than random or block, copolymers. 

Copolymerization of AOCp with N-vinylpyrrolidone was found to be complicated because of the low solubility of the resulting copolymers. This problem is thought to arise from strong interchain H-bonding between the two comonomer units. However, the copolymerization experiments could be carried out satisfactorily by using H-bond breaking solvents such as dimethylform-amide (DMF) or dimethylsulfoxide (DMSO). 

TaUe 2. Copolymerization reactivity ratios (r, and r,) of activated (meth)acrylates (M,) and structural monomers (M,) 

Activated monomer Comonomer If tg Mf incorporation into polymer 10% Mf 50% M, in feed in feed Ref. 

Af-vinylpyrrolidone (—) [44], and 2-carboxyphenyl acrylate (AOCp) with styrene -----[45]. The solid line repre- 

The reactivity ratios, r, = knlkl2 and r2 = kjk2l, are extremely important quantities, expressing the relative preference of the radical species for the monomers. If r, is greater than 1, for example, it means that a chain with a terminal radical of type 1 would rather add another monomer of type 1 than a monomer of type 2. Furthermore, the reactivity ratios are the only two independent rate variables that we need to know or measure, as opposed to the four individual rate constants. 

We ll discuss the measurement of reactivity ratios shortly. First, we ll have a look at what types of copolymers we would expect to get for certain limiting values of the reactivity ratios and then have an initial look at the problem of composition drift. 

When we first introduced the rate constants, we took a quick look at what types of copolymers we would expect to get under certain limiting conditions. It s useful to repeat this exercise in terms of the reactivity ratios, going into a little more detail for certain limiting cases. This time, however, you should figure it out for yourself first  

then kn must equal zero. Similarly, if r2 = then k2l must equal zero. Accordingly, chain radicals with a terminal group of type I will only add monomers of type 1, while Mj chain radicals will show equivalent discrimination, only wishing to add monomers of their own type. Hence, only homopolymers are produced. 

and r2 are both large, but not infinite, then block or blocky copolymers wili be produced, perhaps with some homopolymer, depending on how large the reactivity ratios are and the relative concentration of the monomers in the feed. 

It can be seen that the monomer-polymer composition for terpolymerization in a CSTR will depend on the valnes of reactivity ratios. Consider the expression derived for monomer-polymer composition during copolymerization in a CSTR. Equation (10.12) rewritten in terms of monomer 1 composition only is 

For the special case when the reactivity ratio rj2= 1, Equation (10.26) becomes 

FIGURE 10.3 Copolymer composition versus monomer composition in a CSTR for diethyl fumarate acrylonitrile system. 

Example 10.1 Discuss the Monomer-Copolymer Composition Curve for the System Methacrylonitrile-Styrene Formed in a CSTR 

Example 10.2 Discuss the Terpolymer Composition Curves for the Termonomer Systems Acrylonitrile-Styrene-Alphamethyl-Styrene by Free Radical Polymerization in a CSTR 

As has been shown above, the C02-induced reduction in kp,app amounts up to about 40%. It is interesting to see whether reactivity ratios, which determine copolymer composition, may also be affected by the addition of SCCO2. Special attention has been paid to copolymerization of such monomer pairs for which homopolymerization kp,app values are affected by CO2 in different ways, such as styrene-(meth)acrylate systems. In addition, acrylate-(meth)acrylate copolymerization systems were studied. 

According to the terminal model, the composition of binary copolymers is determined by the reactivity ratios r and by the composition of the monomer mixture via Eq. (4) [33]  

In a reaction of two monomers, designated as Mi and Ma, four distinct reactions can be written as follows  

The ratios of 11/ 12 and k22/k2i are called monomer reactivity ratios. They can be written as follows  

The relationship can be express in terms of the ratio of the monomers, [Mi]/[M2] that end up in the formed polymer, R  

These reactivity ratios represent the relative rates of reactions of polymer radicals with their own monomers vs. that with the comonomers. When ri 1, the radical Mi is reacting with monomer Ml faster than it is with the comonomer M2. On the other hand, when ri 1, the opposite is true. Based on the r values, the composition of the copolymers can be calculated from a copolymerization equation [52] shown below  

If and r2 values are equal to or approach zero, each polymer radical reacts preferentially with the other monomer. This results in an alternating copolymer, regardless of the composition of the monomer mixture. That is, however, a limiting case. In the majority of instances, r x V2 is greater than zero and less than one. When the polymer radicals react preferentially with their own monomer, and r x r2 1, then mainly a mixture of homopolymers forms and only some copolymerization takes place. 

Reactivity of vinyl monomers is very often determined experimentally by studying copolymerizations. Values of many free-radical reactivity ratios have been tabulated for many different monomer pairs, 

The ratio ri can be considered as the tendency of monomer Mi to react with itself (i.e. form a homopolymer) or to react with another monomer type present (i.e. to form a copolymer). 

The value of ri and rj indicates the composition and structural type (i.e. random or block) of the copolymer being produced. 

A value of r, = 1 indicates that ki,i and ki,2 are of similar magnitude and there is an even chance of M, or M2 adding to the propagating chain if the propagating radical is M,. 

= r2 or r, rj = 1 then both -Ml and -Ml radical types show a similar preference for adding Mi and Mj monomer units. 

In this case the resulting copolymer will be of a random distribution and the copolymer composition will directly reflect the starting monomer composition. 

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Copolymerization involves the reaction of at least two different monomers A and B. In the case of chain copolymerization, the reactivity ratios and are important, aiid rg = / bb BA di re /cy die... 

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 reciprocal of a radical reactivity ratio is sometimes used to quantitatively express the reactivity of monomer M2 by comparing its rate of addition to radical Mi - relative to the rate of Mi adding to Mi-. 

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...

Any discussion based on reactivity ratios is kinetic in origin and therefore reflects the mechanism or, more specifically, the transition state of a reaction The transition state for the addition of a vinyl monomer to a growing radical involves the formation of a partial bond between the two species, with a corre sponding reduction of the double-bond character of the vinyl group in the monomer ... 

The temperature dependence of the reactivity ratio rj also involves the Ell Ej2 difference through the Arrhenius equation hence... 

The reactivity ratios are proportional to the product of two exponential numbers. 

It is proposed to polymerize the vinyl group of the hemin molecule with other vinyl comonomers to prepare model compounds to be used in hemoglobin research. Considering hemin and styrene to be species 1 and 2, respectively, use the resonance concept to rank the reactivity ratios rj and X2. 

Another troublesome aspect of the reactivity ratios is the fact that they must be determined and reported as a pair. It would clearly simplify things if it were possible to specify one or two general parameters for each monomer which would correctly represent its contribution to all reactivity ratios. Combined with the analogous parameters for its comonomer, the values rj and t2 could then be evaluated. This situation parallels the standard potential of electrochemical cells which we are able to describe as the sum of potential contributions from each of the electrodes that comprise the cell. With x possible electrodes, there are x(x - l)/2 possible electrode combinations. If x = 50, there are 1225 possible cells, but these can be described by only 50 electrode potentials. A dramatic data reduction is accomplished by this device. Precisely the same proliferation of combinations exists for monomer combinations. It would simplify things if a method were available for data reduction such as that used in electrochemistry. 

There are no inherent restrictions on Q and e hence the individual reactivity ratios can take on a wide range of values. 

Alfrey assigned styrene an e value of-1.0, but this was revised to the present value, which gives better agreement with experimental reactivity ratios. 

Reactivity ratios for the 7V-vinylphthalimide (molecule 1)-styrene (molecule 2) system were measured, and foundt to be ri = 0.075 and I2 = 8.3. Use these values to estimate values of Q and e for 7V-vinylphthalimide then estimate the parameters rj and 12 for system in which molecule 2 is vinyl acetate. 

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. 

Microstructure studies, by contrast, offer both a means to evaluate the reactivity ratios and also to test the model. The capability to investigate this type of structural detail was virtually nonexistent until the advent of modern instrumentation and even now is limited to sequences of modest length. 

In this section we shall use the evaluation of reactivity ratios as the unifying theme the experimental methods constitute the new material introduced. 

Each of these last forms weigh the errors in various data points differently, so some may be more suitable than others, depending on the precision of the data. Ideally all should yield the same values of the reactivity ratios. 

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. 

In spite of the compounding of errors to which it is subject, the foregoing method was the best procedure for measuring reactivity ratios until the analysis of microstructure became feasible. Let us now consider this development. 

To the extent that the data allow, suggest where these substituents might be positioned in Table 7.3. The following reactivity ratios describe the polymerization of acrylonitrile (Ml) with the monomers listed ... 

Chain-Growth Associative Thickeners. Preparation of hydrophobically modified, water-soluble polymer in aqueous media by a chain-growth mechanism presents a unique challenge in that the hydrophobically modified monomers are surface active and form micelles (50). Although the initiation and propagation occurs primarily in the aqueous phase, when the propagating radical enters the micelle the hydrophobically modified monomers then polymerize in blocks. In addition, the hydrophobically modified monomer possesses a different reactivity ratio (42) than the unmodified monomer, and the composition of the polymer chain therefore varies considerably with conversion (57). The most extensively studied monomer of this class has been acrylamide, but there have been others such as the modification of PVAlc. Pyridine (58) was one of the first chain-growth polymers to be hydrophobically modified. This modification is a post-polymerization alkylation reaction and produces a random distribution of hydrophobic units. 

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. 

The (smaller)/ (larger) values Hsted in Table 7 correspond to the reactivity ratios for monomer 1, r, and monomer 2, r. These are defined as... 

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). 

The early kinetic models for copolymerization, Mayo s terminal mechanism (41) and Alfrey s penultimate model (42), did not adequately predict the behavior of SAN systems. Copolymerizations in DMF and toluene indicated that both penultimate and antepenultimate effects had to be considered (43,44). The resulting reactivity model is somewhat compHcated, since there are eight reactivity ratios to consider. 

An emulsion model that assumes the locus of reaction to be inside the particles and considers the partition of AN between the aqueous and oil phases has been developed (50). The model predicts copolymerization results very well when bulk reactivity ratios of 0.32 and 0.12 for styrene and acrylonitrile, respectively, ate used. 

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. 

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. 

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