Copolymerization monomer sequence distribution

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 implicit penultimate model was proposed for copolymerizations where the terminal model described the copolymer composition and monomer sequence distribution, but not the propagation rate and rate constant. There is no penultimate effect on the monomer reactivity ratios, which corresponds to... 

The examination of monomer sequence distributions by NMR is one of the most extensively used applications in materials science. When two (or more) dissimilar monomers A and B are copolymerized, a polymer is obtained with varying placements of A and B units along the backbone as shown in Fig. 10. It is important to know the relative distribution of monomer sequences, as these have an influence on the polymer s properties, and information about the distributions is valuable for studies of copolymerization mechanism. Initially, NMR was the only technique available to determine monomer sequences. 

In traditional treatments of copolymerization kinetics, tlie values of the ratios 6 a and i u are implicitly set equal to unity (Section 7.3.1.2.2). Since they contain no terms from cross propagation, these parameters have no direct influence on either the overall copolymer composition or the monomer sequence distribution they only influence the rate of polymerization. 

Cases have been reported where the application of the penultimate model provides a significantly better tit to experimental composition or monomer sequence distribution data. In these copolymerizations / AABi fDAD and/or "aba isba- I hese include many copolymerizations of MAH" " and... 

The NMR technique is also proving valuable, for example, in its application in assigning relative rates of attack in copolymerization. Moad et alM has shown that labelled monomer can be very useful in studying the NMR of polymers. NMR of PMMA prepared from MMA carbonyl- 3c has proved to be very convenient in the determination of the tacticity of homopolymers while NMR of copolymers prepared from labelled monomers can rapidly provide infomiation on monomer sequence distribution. 

Not only in the mathematical description of copolymer composition, but also in that of monomer sequence distribution, is it convenient to use so-called conditional probabilities. These conditional probabilities are defined as the chance that a certain event takes place out of aU possibilities at a certain stage. For the purpose of the copolymerization equations, conditional probabilities related to propagation only are considered. In case of the TM, an example of such a conditional probability is the chance that monomer 2 will add to a monomer 1 chain-end radical (P12). In terms of eqns [l]-[4], this probability is the rate of reaction [2] divided by the sum of the rates of reaaions [1] and [2]. The two relevant conditional probabilities are defined as in eqns [6] and [7] ... 

Works pertaining to studying the formation and properties of protein-like behavior included copolymers made by copolymerizing NIPAAm with hydrophilic monomers, including, methacrylic acid (MAA), acrylic acid (AA), and sodium styrene sulfate (NaSS). Inter- and intramolecular association was observed that was governed by the interplay between the solubility of the hydrophilic units and temperature-dependent solubility of NIPAAm. In most instances, the monomer sequence distribution in the resultant copolymer was not measured the presence of blockiness was inferred indirectly. 

Cals, R. E. and Stuk, G. J., Copolymerization of Acrylamide with Sulfur Dioxide. Determination of the Effect of Copol3nnerization Temperature on the Monomer Sequence Distribution by 13C N.M.R., Polym., 19 179 (1978). 

Tapered Block Copolymers. The alkyllithium-initiated copolymerizations of styrene with dienes, especially isoprene and butadiene, have been extensively investigated and illustrate the important aspects of anionic copolymerization. As shown in Table 15, monomer reactivity ratios for dienes copolymerizing with styrene in hydrocarbon solution range from approximately 8 to 17, while the corresponding monomer reactivity ratios for styrene vary from 0.04 to 0.25. Thus, butadiene and isoprene are preferentially incorporated into the copolymer initially. This type of copolymer composition is described as either a tapered block copolymer or a graded block copolymer. The monomer sequence distribution can be described by the structures below ... 

The copolymerizations between monoolefins and dienes have been considered to be of practical and theoretical importance. As reported in the literatures ethylene-butadiene and propylene-butadiene copolymers can be prepared with conventional Ziegler-Natta titanium-based or vanadium-based catalysts. The copolymer composition and monomer sequence distribution strongly depend on the catalyst system and polymerization conditions. Alternating copolymers were synthesized when the catalyst components were mixed at the... 

Explanations, other than the inadequacy of the terminal model, have been given to explain potential causes for deviation. Pichot et al. [30] offered several possible explanations for these discrepancies including 1) preferential solvation of one of the monomers in the polymer 2) AN existing as a dimer due to dipole-dipole interactions and 3) terminal radical interaction with the AN nitrile group. Harwood [64] presents evidence indicating that it is the monomer concentrations local to the active radical center that controls the copolymerization and backbone monomer sequence distribution rather than the average monomer concentrations in the reactor. Harwood calls this the bootstrap model because it is the nature of the polymer chain itself that controls the local monomer concentration near its active chain-end. 

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). 

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... 

The instantaneous composition of a copolymer X formed at a monomer mixture composition x coincides, provided the ideal model is applicable, with stationary vector ji of matrix Q with the elements (8). The mathematical apparatus of the theory of Markov chains permits immediately one to wright out of the expression for the probability of any sequence P Uk in macromolecules formed at given x. This provides an exhaustive solution to the problem of sequence distribution for copolymers synthesized at initial conversions p l when the monomer mixture composition x has had no time to deviate noticeably from its initial value x°. As for the high-conversion copolymerization products they evidently represent a mixture of Markovian copolymers prepared at different times, i.e. under different concentrations of monomers in the reaction system. Consequently, in order to calculate the probability of a certain sequence Uk, it is necessary to average its instantaneous value P Uk over all conversions p preceding the conversion p up to which the synthesis was conducted. 

---