Binary Copolymerizations

Since Bartlett and Nozaki originated the concept that a CTC could play an important role in alternating copolymerizations, numerous studies have been conducted to substantiate this concept. Iwatsuki and coworkers, from their many studies on vinyl ether-MA 

The work of several authors tends to support the concept that the magnitude of the equilibrium constant K) for the CTC can be considered as a measure of alternating copolymerizability. Kokubo et found that the mean rates of spontaneous copolymerization (%/min) for 1,2-dimethoxyethylene, 2-chloroethyl vinyl ether, and p-dioxene with MA, under comparable conditions, were 0.092, 0.089, and 0.006, respectively. This agrees with the order of the K values for these three charge-transfer complexes (see table in Appendix to this chapter). 

Hallensleben s work with n-butyl (NBVE), isobutyl (IBVE), and tert-butyl vinyl ether (TBVE) copolymerization with MA shows the same effect. The copolymerization rates follow the order TBVE IBVE NVBE, with corresponding K values (table in appendix to this chapter) of 2.12, 1.11, and 0.56 liter mole  

01 B p-Dioxene-MA Alternating copolymerization with free-radical initiators 

0 C Chloroethyl vinyl ether-MA Dimethoxyethylene-MA Spontaneous alternating copolymerization near room temperature K decreases with solvent polarity) 

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The complexity of the terpolymer composition equation (eq. 36) can be reduced to eq. 41 through the use of a modified steady slate assumption (eqs. 38-40), However, while these equations apply to component binary copolymerizations it is not clear that they should apply to terpolymerization even though they appear to work well. It can be noted that when applying the Q-e scheme a terpolymer equation of this form is implied. 

Azeotropic compositions are rare for terpolymerization and Ham 14 has shown that it follows from the simplified eqs. 38-40 that ternary azeotropes should not exist. Nonetheless, a few systems for which a ternary azeotrope exists have now been described (this is perhaps a proof of the limitations of the simplified equations) and equations for predicting whether an azeotropic composition will exist for copolymerizations of three or more monomers have been formulated.20113 This work also shows that a ternary azeotrope can, in principle, exist even in circumstances where there is no azeotropic composition for any of the three possible binary copolymerizations of tire monomers involved. 

The instantaneous rate of monomer consumption in binary copolymerization is then given by eq. 62 ... 

Even when only the terminal monomer unit is considered, radical-radical termination in binary copolymerization involves at least seven separate reactions (Scheme 7.12). There are two homoterminalion processes and one cross termination process to consider. In the case of cross termination, there arc two pathways for disproportionation. There are then at least three pieces of information to be gained ... 

Another important consequence of the limitations concerning cross-addition is that anionic polymerization is not suited for the synthesis of random copolymers. If a mixture of two anionically polymerizable monomers is reacted with an initiator, the most electrophilic monomer will polymerize while the other is left almost untouched 30). In other words, a general feature of anionic binary copolymerization is that one of the reactivity ratios is extremely high while the other is close to zero. 

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... 

The residual monomers mi, m2 for binary copolymerizations can be calculated from the integrated form of the Skeist (5) equation, which defines Xi as in Equation (10) rather than Equation (9), viz. 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

Rigorous kinetic analysis has shown [41] that the products of binary copolymerization, formed under the conditions of constant concentrations of monomers, may be described by the extended Markov chain with four states Sa, if to label monomeric units conventionally coloring them in red and black. Unit Ma is presumed to be black when the corresponding monomer Ma adds to the radical as the first monomer of the complex. In other cases, when monomer Ma adds individually or as the second monomer of the complex, the unit Ma is assumed to be red. As a result the state of a monomeric unit is characterized by two attributes, one of which is its type (a=l,2) while the second one is its color (r,b). For example, we shall speak about the unit being in the state Sx provided it is of the first type and red-colored, i.e. Mrx. The other states Sa are determined in a similar manner ... 

The values of K and (3(K > 0 and 0 < P < 1) were calculated for each monomer pair from the logarithmic plot of the ratio of the monomers in the monomer feed [MJ/[M2] to the comonomer units in the copolymer using a modified equation of binary copolymerization ... 

In some cases, the reactivity of the growing chain end depends on the nature of the last but one monomer unit. So, eight propagation constants have to be considered. This so-called penultimate effect can be the reason why the binary copolymerization cannot be described precisely enough by Eq. 3.18. 

In copolymerizations of three monomers there are nine growing steps to be taken into account. From these, six reactivity ratios can be derived. They are difficult to obtain from terpolymerizations and are therefore taken from binary copolymerizations. 

In binary copolymerizations, therefore, four propagation reactions, having four rate constants, are considered. 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

A comparison of the three binary copolymerizations of 1,6-anhydro-/S-D-gluco-, -galacto-, and -manno-pyranose derivatives gives some insight into the mechanism of copolymerization, if it is assumed on this evidence that the per-p-xylyl and perbenzyl derivatives can be used interchangeably.107... 

It should be emphasized that copolymerizations that conform to the premises of binary-copolymerization theory produce copolymers of well defined structure. The kinetics of the competitive propagation-reactions determine not only the copolymer composition but also the sequence distribution. The mathematical procedures needed for calculating number-average sequence-lengths of mers, and sequence length-distributions of mers, are well known and have been... 

In many binary copolymerizations, there is a pronounced tendency for the two types of monomer unit to alternate along the copolymer chain. In extreme cases, there is almost perfect alteration, notably for pairs of monomers, e.g, maleic anhydride and stilbene, which do not polymerize on their own. Ternary copolymenzations are of practical importance die kinetic treatments developed for binary copolymerizations can be extended to diese systems. 

When propylene unit inversion is present, the polymerization of propylene can be represented as a binary copolymerization involving the following four steps. 

A terpolymer has been prepared from cyclopentene, sulfur dioxide, and acrylonitrile by Y. Yamashita and co-workers. The mechanism was recognized as a binary copolymerization between a cyclopentene/S02 complex and free acrylonitrile. 

Spontaneous copolymerization of cyclopentene (CPT) with sulfur dioxide (SOt) suggests the participation of a charge transfer complex in the initiation and propagation step of the copolymerization. The ESR spectrum together with chain transfer and kinetic studies showed the presence of long lived SOg radical. Terpolymerization with acrylonitrile (AN) was analyzed as a binary copolymerization between CPT-SOt complex and free AN, and the dilution effect proved this mechanism. Moderately high polymers showed enhanced thermal stability, corresponding to the increase of AN content in the terpolymer. 

Considering the terpolymerization of CPT-SO2-AN system as a binary copolymerization of CPT-SO2 complex and free acrylonitrile, the copolymerization equation can be derived as follows, assuming a fast equilibrium. 

Binary copolymerization of the CPT-AN system was carried out at 40°C using AIBN as initiator. From the Finemann-Ross plot of the copolymer composition and monomer feed ratios, the monomer reactivity ratios were determined. (CPT) = 0, r2 (AN) = 1.97. The increase of the relative reactivity of CPT by forming a complex with SC is calculated as follows. 

The scope of the spontaneous copolymerization of P(III) monomers has been extended to copolymerizations with more sophisticated regulations of the arrangements of monomeric units in copolymers. They include a 2 1 sequence-ordered binary copolymerization of 43 with 46 (Eq. (27))30) and 1 1 1 sequence-ordered terpolymerizations of 54/acrylate 47jCQ2 (Eq. (28)) 39) and 48/49139 (Eq. (29))40 ... 

Fig. 11. Diagrams of the composition of the terpolymerizations of TECQ, TCNQ, and St, and of TMCQ, TCNQ, and St as binary copolymerizations between TECQ and St and between TMCQ and St, respectively. The lines are calculated using r Kj/Kj) = 15 10 and r2(K2/Ki) = 0.5 0.3 for the terpolymerization of the TECQ-TCNQ-St system ( ), and r](K,/K2) = 7 + 3 and r2(K2/Kj) = 0.7 0.3 for the terpolymerization of the TMCQ-TCNQ-St systrm (O), respectively...

A generalization of the theory of the binary copolymerization for multicomponent systems in the case of the terminal model (2.8) is not difficult since the copolymer microstructure is still described by the Markov chain with states S corresponding to the monomer units Mj. The number m of their types determines the order of... 

For the quantitative description of the sequence distribution in the multicomponent copolymers the statistical characteristics similar to the ones applied for the description of the binary copolymerization products were used [45, 104-110]. In their well-known paper [45] Alfrey and Goldfinger stated an exponential character of the run distribution f (n) for length n with copolymerization of any number m of monomer types. Besides this distribution and its statistical moments [104-107] other parameters as alternation degree were introduced [108,107], which equals the overall fraction of all heterotriads P(M Mj) (i 4= j), and also the parameter with the similar meaning called alternating order [109]. Tosi [110] suggested to use informational entropy as a quantitative measure of the randomness of the multicomponent copolymers ... 

The conditions of the existence of such bimodal distributions are well-known for the binary copolymerization [169-171], since in this case the differential equation proposed by Skeist [12] for the determination of the composition distribution has an explicit solution. Indeed when m = 2, the only one independent equation of the two equations (5.2) has a simple solution [169, 170, 172] ... 

In Refs. [173-176] it was suggested to use the weight composition distributions instead of the molar ones and the results of their numerical calculation for some systems were reported The authors of Ref. [177] carried out a thorough theoretical study of the composition distribution and derived an equation for it without the Skeist formula. They, as the authors of Ref. [178], proposed to use dispersion of the distribution (5.3) as a quantitative measure of the degree of the composition inhomogeneity of the binary copolymers and calculated its value for some systems. Elsewhere [179-185] for this purpose there were used other parameters of the composition distribution. In particular the discussion of the different theoretical aspects of the binary copolymerization is reported in a number of reviews by Soviet authors [186-189], By means of numerical calculations there were analyzed [190-192] the limits of the validity of the traditional assumption which allows to ignore the instantaneous component of composition distribution of the copolymers produced at high conversions. 

In the case of the binary copolymerization described by the terminal model (2.1) there are the following types of phase portraits ... 

The above results in the case of the binary copolymerization can be easily obtained from the analysis of the expression (5.4). However, for the copolymerization of more than two monomers such an analysis is not possible since the proper explicit solution of Eqs. (5.2) is not available yet. The traditional methods of dynamic systems theory are considered the most effective for establishing the common qualitative peculiarities of the trajectory behavior [204-205]. 

The most thorough topological classification of the dynamic behavior of the copolymerization systems suppose to make them out by their kinds, each of them is determined by the types of all SPs as well as by manifolds separating their basins (regions of their attraction). Every kind is characterized by the type of its phase portrait. The case of the binary copolymerization obviously is trivial since each of the types (5.8) consists of only one genus which in its turn includes a single kind. 

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