Binary copolymerization

Notice that Eqs. (56) and (95) are equivalent, with the only difference that Eq. (95) uses pseudo-kinetic constants in place of the actual kinetic constants found in Eq. (56). The beauty of this modeling approach is that it is not necessary to develop new equations for copolymerization (binary or higher) the equations developed for homopolymerization, including the moment equations, are equally applicable to copolymerization, provided that pseudo-kinetic constants are used to replace the actual polymerization kinetic constants. 

The values of these ratios change appreciably by passing from the heterogeneous (suspension) to the homogeneous (DMF) system. In the case of copolymerization in suspension in the presence of the K2S208—AgN03 oxidation-reduction system at 30—40 °C, the ratios were found to be ry = 0,77 0,2 and r2 = 1,09 0,04, whereas in the case of the copolymerization in solution they are = 0,52 and r2 = 1,7. The difference in these values seems to be the result of the different solubility of the monomers in water and of the different rate of diffusion of the monomers to the surface of the precipitated copolymer20. From this it follows that 4 is the more reactive monomer in this binary system. 

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. 

It is a characteristic feature of this copolymerization, as in general of binary systems in which one of the monomers is a diene, that with the progress of the reaction a secondary crosslinking process becomes possible. 

Labeled initiators have been used in evaluating the relative reactivity of a wide range of monomers towards initiating radicals.159 The method involves determination of the relative concentrations of the end groups fanned by addition to two monomers (e.g. 119 and 120) in a binary copolymer formed with use of a labeled initiator. For example, when AlBMe-a-13C is used to initiate copolymerization of MMA and VAc (Scheme 3.99),157 the simple relationship (eq. 14) gives the relative rate constants for addition to the two monomers. Copolymerizations studied in this way arc summarized in Tabic 3.13. 

Tire simplest model for describing binary copolyinerization of two monomers, Ma and Mr, is the terminal model. The model has been applied to a vast number of systems and, in most cases, appears to give an adequate description of the overall copolymer composition at least for low conversions. The limitations of the terminal model generally only become obvious when attempting to describe the monomer sequence distribution or the polymerization kinetics. Even though the terminal model does not always provide an accurate description of the copolymerization process, it remains useful for making qualitative predictions, as a starting point for parameter estimation and it is simple to apply. 

Cases have been reported where the application of the penultimate model provides a significantly better fit to experimental composition or monomer sequence distribution data. In these copolymerizations raab "bab and/or C BA rBBA- These include many copolymerizations of AN, 4 26 B,"7 MAH28" 5 and VC.30 In these cases, there is no doubt that the penultimate model (or some scheme other than the terminal model) is required. These systems arc said to show an explicit penultimate effect. In binary copolynierizations where the explicit penultimate model applies there may be between zero and three azeotropic compositions depending on the values of the reactivity ratios.31... 

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 ... 

Extensive work on radical copolymerization has shown that the composition in a binary copolymer, consisting of monomers Mi and M2, is determined by four rate constants ky for a propagating chain ending with adding to monomer Mj. 

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. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

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. 

Recently, Teymour and coworkers developed an interesting computational technique called the digital encoding for copolymerization compositional modeling [20,21], Their method uses symbolic binary arithmetic to represent the architecture of a copolymer chain. Here, each binary number describes the exact monomer sequence on a specific polymer chain, and its decimal equivalent is a unique identifier for this chain. Teymour et al. claim that the... 

The rate of copolymerization in a binary system depends not only on the rates of the four propagation steps but also on the rates of initiation and termination reactions. To simplify matters the rate of initiation may be made independent of the monomer composition by choosing an initiator which releases primary radicals that combine efficiently with either monomer. The spontaneous decomposition rate of the initiator should be substantially independent of the reaction medium, as otherwise the rate of initiation may vary with the monomer composition. 2-Azo-bis-isobutyronitrile meets these requirements satisfactorily. The rate Ri of initiation of chain radicals of both types Ml and M2 is then fixed and equal to 2//Cd[7], or twice the rate of decomposition of the initiator I if the efficiency / is equal to unity (see Chap. IV). The relative proportion of the two types of chain radicals created at the initiation step is of no real importance, for they wall be converted one into the other by the two cross-propagation reactions of the set (1). Melville, Noble, and Watson presented the first complete theory of copolymerization suitable for handling the problem of the rate. The theory was reduced to a more concise form by Walling, whose procedure is followed here. 

Ra, Ra symbol of a-type radical or ion and its concentration kap constant of propagation reaction between Ra and M klap constant of termination reaction between Ra and R rap> rfia reactivity ratios for binary free-radical copolymerization of monomers Ma and M ... 

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 ... 

Binary free-radical copolymerizations of organotin derivatives of unsaturated acids (tri-n-butylstannyl methacrylate, bis-triethylstannyl maleate (TESM) and P-phenyl-tri-n-butylstannyl methacrylate (PBSM)) with certain vinyl monomers such as styrene (St) 87) and vinyl chloride (VC) have been studied 24,25,92). 

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 ... 

Bajoras and Makuska investigated the effect of hydrogen bonding complexes on the reactivities of (meth)acrylic and isotonic acids in a binary mixture of dimethyl sulfoxide and water using IR spectroscopy (Bajoras and Makuska, 1986). They demonstrated that by altering the solvent composition it was possible to carry out copolymerization in the azeotropic which resulted in the production of homogeneous copolymers of definite compositions at high conversions. Furthermore, it was shown that water solvent fraction determines the rate of copolymerization and the reactivity ratios of the comonomers. This in turn determines the copolymer composition. 

Examples considered in this paper deal with binary heteropolymers prepared by the method of chemical modification of homopolymers and by the free-radical copolymerization of a mixture of two monomers, Mi and M2. The products of each of these processes is a mixture of an enormous... 

This technology was extended to the preparation of chiral capillary columns [ 138 -141 ]. For example, enantioselective columns were prepared using a simple copolymerization of mixtures of O-[2-(methacryloyloxy)ethylcarbamoyl]-10,11-dihydro quinidine, ethylene dimethacrylate, and 2-hydroxyethyl methacrylate in the presence of mixture of cyclohexanol and 1-dodecanol as porogenic solvents. The porous properties of the monolithic columns can easily be controlled through changes in the composition of this binary solvent. Very high column efficiencies of 250,000 plates/m and good selectivities were achieved for the separations of numerous enantiomers [140]. 

In one approach, polymethacrylate-type monoliths have been fabricated by copolymerization of the chiral monomer 0-9-[2-(methacryloyloxy)ethylcarbamoyl]-10,11-dihydroquinidine 1 or 0-9-(tert-butylcarbamoyl)-ll-[2-(methacryloyloxy) ethylthio]-10,ll-dihydroquinine 2 (see Figure 1.34a), the comonomer 2-hydroxyethylmethacrylate (HEMA), the crosslinker ethylenedimethacrylate (EDMA) in presence of the binary porogenic solvent mixture cyclohexanol and 1-dodecanol, directly in a single step within fused-silica capillaries. Initiation of the polymerization by either thermal treatment or UV irradiation yielded microglobular polymer morphologies, such as those well known from their corresponding nonchiral... 

Lu and coworkers have synthesized a related bifunctional cobalt(lll) salen catalyst similar to that seen in Fig. 11 that contains an attached quaternary ammonium salt (Fig. 13) [36]. This catalyst was found to be very effective at copolymerizing propylene oxide and CO2. For example, in a reaction carried out at 90°C and 2.5 MPa pressure, a high molecular weight poly(propylene carbonate) = 59,000 and PDI = 1.22) was obtained with only 6% propylene carbonate byproduct. For a polymerization process performed under these reaction conditions for 0.5 h, a TOF (turnover frequency) of 5,160 h was reported. For comparative purposes, the best TOF observed for a binary catalyst system of (salen)CoX (where X is 2,4-dinitrophenolate) onium salt or base for the copolymerization of propylene oxide and CO2 at 25°C was 400-500 h for a process performed at 1.5 MPa pressure [21, 37]. On the other hand, employing catalysts of the type shown in Fig. 12, TOFs as high as 13,000 h with >99% selectivity for copolymers withMn 170,000 were obtained at 75°C and 2.0 MPa pressure [35]. The cobalt catalyst in Fig. 13 has also been shown to be effective for selective copolymer formation from styrene oxide and carbon dioxide [38]. 

Lu X-B, Wang Y (2004) Highly active, binary catalyst systems for the alternating copolymerization of CO2 and epoxides under mild conditions. Angew Chem Int Ed 43 3574—3577... 

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. 

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