Tacticity sequence statistics

Table 1.8 Tacticity sequence probabilities expressed in terms of propagation probabilities for Bernoullian and first-order Markov statistics the parameters u and v are defined in the text...

As an example of the statistical analysis of a tacticity sequence distribution. Table 1.9 gives the experimental distribution for poly(vinyl chloride) derived from Figure 1.19, together with the distribution calculated for Bernoullian statistics with P = 0.456. The agreement is within experimental error up to tetrads. A Bernoullian sequence distribution and a preference for syndio-... 

From appropriate ratios of these sequence lengths, what conclusions can be drawn concerning terminal versus penultimate control of addition The following are experimental tacticity fractions of polymers prepared from different monomers and with various catalysts. On the basis of Fig. 7.9, decide whether these preparations are adequately described (remember to make some allowance for experimental error) by a single parameter p or whether some other type of statistical description is required ... 

The mechanism of B polymerization is summarized in Scheme 4,9. 1,2-, and cis- and trews-1,4-butadiene units may be discriminated by IR, Raman, or H or nC MMR speclroseopy.1 92 94 PB comprises predominantly 1,4-rra//.v-units. A typical composition formed by radical polymerization is 57.3 23.7 19.0 for trans-1,4- c7a -1,4- 1,2-. While the ratio of 1,2- to 1,4-units shows only a small temperature dependence, the effect on the cis-trans ratio appears substantial. Sato et al9J have determined dyad sequences by solution, 3C NMR and found that the distribution of isomeric structures and tacticity is adequately described by Bernoullian statistics. Kawahara et al.94 determined the microslructure (ratio // measurements directly on PB latexes and obtained similar data to that obtained by solution I3C NMR. They94 also characterized crosslinked PB. 

Nuclear Magnetic Resonance. The successful study of polymers in solution by high resolution NMR spectroscopy started with the pioneering work on the sequence structure of poly methyl methacrylate in 1960. Since then, an ever-increasing number of investigations have been carried out ranging from the elucidation of the statistics of homopolymer and copolymer structure to the study of conformation, relaxation and adsorption properties of polymers. The aspects of sequence length determination and tacticity have received considerable attention (Klesper 84, for example, reports more than 500 entries). Therefore, a detailed review will not be attempted. (For a detailed description of the NMR Theory and statistics of polymer structure, see Bovey 59, Randall 23, and Klesper 84). 

The structures of stereoregular and tactic polymers described above are ideal. Real polymers are always irregular they do not have perfect steric or tactic structures. Thus, the mean sequence and composition of steric and configurational diads, triads, etc. must be given by suitable statistical parameters, in analogy to the case for constitutional diads, triads, etc. 

Two matrices that describe conformations that alternate in sequence are used to specify conformation in tactic vinyl polymers. Tacticity introduces asymmetric elements into the chain. One convention used in specifying chain asymmetry consists of distinguishing between right handed chains termed d and left handed or 1 chains. This convention, admittedly arbitrary, is borrowed from the field of optical activity. For a tactic polymer with a threefold potential (Figure 2.13), the statistical weight matrix for a d placement between neighboring bonds is... 

The use of statistical models to interpret (and to rationalize) NMR tacticity and sequence data is well established (97,98). In this volume the enantiomorphic-site model has been used by Segre et al. in their studies of polypropylene at high fields (55). A two-site model has been en loyed by Shimozawa et al. to observe the effects of internal donors m propylene polymerization (56). Other models for polyolefins have been reported in the literature, e.g., the multi-site model (99), the dual catalytic-site/chain-end model (100), the perturbed model (101), the consecutive two-site model (102), the four-component model (103), and the chain end model (104). 

By determining which statistical model is followed in a polymerization, such as Bemoullian, or Markov, or other, it should be possible to understand better the mechanism of steric control. Thus the Bernoulli model describes those reactions in which the chain ends determine the steric arrangement. These are polymerizations that are carried out under conditions that yield mostly atactic polymers. The high isotactic sequences follow the enantiomorphic site model and the high syndio-tactic ones usually follow the Markov models. 

Similarly, one can speak about mean sequence-length and its dispersity in statistical copolymers, about mean tacticity and its dispersity in the stereoiegular polymers, and so on. 

A welcome textbook on the determination of polymer sequence structure using n.m.r. has been published. The book describes in detail the statistical treatment of both tacticity and copolymer composition, and also provides a sensible discussion of the experimental conditions necessary for accurate quantitative analysis. The numerous examples given involve almost exclusively vinyl polymerizations. Two reviews, by Bovey, and Katritzky and Weiss, of the subject have appeared, that by the latter being a useful elementary review suitable for undergraduate use. More general reviews of the application of n.m.r. to structural determination have appeared in Japanese, English, and Russian with an English... 

Shulz and collaborators in their kinetic polymerizations done anionically in with cumylcesium initiators. Their main concern was to determine the statistics which best described the tactic addition of monomer. By NMR analysis of sequence lengths they concluded that the system obeyed Markovian rather than Bernoulli an statistics. ... 

With simple homopolymers this is sufficient for the purpose, but with copolymers, including stereocopolymers which arise in any monomer %quence where tactic placements are possible, the chain statistics cannot be developed by operation with U alone. Here, the copolymer sequence, even if stereoisomeric, has to be generated using Monte Cario methods and a generator matrix G. The final result of such calculations provides a dipole moment ratio o/(nm) (where n is the number of skeletal bonds carrying dipole moments m) or (wdiere z is the degree... 

The single parameter of Bernoulli statistics can be simply determined from one-unit sequences that is, from the tacticity of a stereopolymer (or the composition of a copolymer). To determine the two parameters of first-order Markov statistics, the populations of all three two-unit sequences must be known (use can be made of the necessary relations. Table 3). To verify whether the proposed order is actually valid, the populations of sequences longer by one unit must be checked by experiment (e.g., Bernoulli statistics is established by a check on the two-unit populations, etc.). 

As a technique for the analysis of sequence distribution in copolymers, high-resolution NMR spectroscopy is particularly useful when the spectral resolution is sufficient to resolve the resonances of the specific sequences. A number of copolymer structural problems can be elucidated by using NMR spectroscopy. The composition of the copolymer can be quantitatively determined. The detection of compositional dyads can be used to determine the distribution of composition, that is, whether the sample is a mixture of homopolymers, a block copolymer, an alternating copolymer, or a random copolymer (see Chapter 1). If resonances are resolved due of the triad sequences of the copolymer, sequence distributions can be determined, and the mechanism of the copolymerization can be tested in terms of Bemoullian, first-order Markov, second-order Markov, or non-Markovian statistics. In rare circumstances, the tactic nature of the copolymer can be determined if distinguishable syndio- and isotactic n-ad resonances are resolved. Such an analysis has been carried out for copolymers of methyl methacrylate-methacrylic acid, for which the a-CHs resonances of all 20 triads have been assigned and have been used to determine the cotacticity of the copolymer [22]. 

In statistical copolymers a total of 20 configurational sequences occur i.e., for the MMA-centred triads, the following 10 tacticity coefficients and sequences are possible (1 - < mm) Pmmm, and (1 - for the MMM sequence,... 

For a complete description of the monomer sequence distribution and relative stereochemical configuration of monomer sequences, at least in terms of N- and M-centred triads, it is necessary to take into consideration as many as 10 different triads with a central N unit, which may be magnetically distinguishable as is shown in the scheme of Figure 7.22. Since both monomeric repeating units have a quaternary pseudoasymmetric carbon, from a stereochemical point of view 10 triads with a central M unit sensitive to tacticity must also be considered. The statistical analysis of the monomer sequence distribution and of the stereochemical configuration of the copolymer sequences was carried under the following assumptions with respect to the chemical composition of copolymer sequences, it was assumed that... 

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