Sequences copolymerization

Polymerization, block This term has been applied to both bulk polymerization (casting of polymerizing syrup) and sequence copolymerization (block copolymerization). It is only this latter that is recognized by lUPAC as true copolymerization. Confusion may be avoided to some extent by the use of the prefix co which implies the polymerization of more than one monomer. 

It is apparent from items (l)-(3) above that linear copolymers-even those with the same proportions of different kinds of repeat units-can be very different in structure and properties. In classifying a copolymer as random, alternating, or block, it should be realized that we are describing the average character of the molecule accidental variations from the basic patterns may be present. In Chap. 7 we shall see how an experimental investigation of the sequence of repeat units in a copolymer is a valuable tool for understanding copolymerization reactions. This type of information along with other details of structure are collectively known as the microstructure of a polymer. 

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

These observations suggest how the terminal mechanism can be proved to apply to a copolymerization reaction if experiments exist which permit the number of sequences of a particular length to be determined. If this is possible, we should count the number of Mi s (this is given by the copolymer composition) and the number of Mi Mi and Mi Mi Mi sequences. Specified sequences, of any definite composition, of two units are called dyads those of three units, triads those of four units, tetrads those of five units, pentads and so on. Next we examine the ratio NmjMi/Nmi nd NmjMiMi/NmiMi If these are the same, then the mechanism is shown to have terminal control if not, it may be penultimate control. To prove the penultimate model it would also be necessary to count the number of Mi tetrads. If the tetrad/triad ratio were the same as the triad/dyad ratio, the penultimate model is proved. 

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 first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

Regular copolymer—These copolymers have an ordered sequence in the distribution of monomers. These are produced by controlled feeding of the monomers during copolymerization. 

Alternating copolymer—In these copolymers, the monomers are arranged in an alternate sequence. Alternating copolymers are produced by special copolymerization processes. 

Currently, more SBR is produced by copolymerizing the two monomers with anionic or coordination catalysts. The formed copolymer has better mechanical properties and a narrower molecular weight distribution. A random copolymer with ordered sequence can also be made in solution using butyllithium, provided that the two monomers are charged slowly. Block copolymers of butadiene and styrene may be produced in solution using coordination or anionic catalysts. Butadiene polymerizes first until it is consumed, then styrene starts to polymerize. SBR produced by coordinaton catalysts has better tensile strength than that produced by free radical initiators. 

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 ... 

Copolymerizations are processes that lead to the formation of polymer chains containing two or more discrete types of monomer unit. Several classes of copolymer that differ in sequence distribution and/or architecture will be... 

Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

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... 

Methods for evaluation of reactivity ratios comprise a significant proportion of the literature on copolymerization. There are two basic types of information that can be analyzed to yield reactivity ratios. These are (a) copolymer composition/convcrsion data (Section 7.3.3.1) and (b) the monomer sequence distribution (Section 7.3.3.2). The methods used to analyze these data are summarized in the following sections. 

The solvent in a bulk copolymerization comprises the monomers. The nature of the solvent will necessarily change with conversion from monomers to a mixture of monomers and polymers, and, in most cases, the ratio of monomers in the feed will also vary with conversion. For S-AN copolymerization, since the reactivity ratios are different in toluene and in acetonitrile, we should anticipate that the reactivity ratios are different in bulk copolymerizations when the monomer mix is either mostly AN or mostly S. This calls into question the usual method of measuring reactivity ratios by examining the copolymer composition for various monomer feed compositions at very low monomer conversion. We can note that reactivity ratios can be estimated for a single monomer feed composition by analyzing the monomer sequence distribution. Analysis of the dependence of reactivity ratios determined in this manner of monomer feed ratio should therefore provide evidence for solvent effects. These considerations should not be ignored in solution polymerization either. 

Harwood112 proposed that the solvent need not directly affect monomer reactivity, rather it may influence the way the polymer chain is solvated. Evidence for the proposal was the finding for certain copolymerizations, while the terminal model reactivity ratios appear solvent dependent, copolymers of the same overall composition had the same monomer sequence distribution. This was explained in... 

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

The propagating species involved in the polymerization of cyclic formal seem to resemble carbocations, and random copolymers are formed in the copolymerization of cyclic formals with styrene. For the copolymerization of DOL with styrene, the DOL-St cross-sequence was estimated, by NMR or by chemical methods, from the decrease of the formal unit in the copolymer and the formation of nearly random copolymer was confirmed132. ... 

The effect of a catalyst is important in cationic copolymerizations. Epoxides and /3-lactones form random copolymers only with trialkyl aluminum catalysts. Unusual sequence distributions were observed in the cationic copolymerization of epoxides or lactones using Lewis acids175-177) have been attributed to the di-... 

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... 

In their paper Hill and coworkers discriminate between alternative copolymerization models by fitting the models to composition data and then predicting sequence distributions based on the fitted models. Measured and fitted sequence distributions are then compared. A better approach taken here is to fit the models to the sequence distribution data directly. 

Perret, R., and Skoulios, A., Synthese et caracterisation de copolymeres sequences polyoxyethylene/poly-e-caprolactone. 

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... 

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