Dyad distribution

The distribution of styrene crosslinks in cured unsaturated polyesters based on maleic anhydride, phthalic anhydride, propylene glycol and dipropylene glycol is found to be dependent on the molar ratio of styrene vs. maleic/fumaric unit. If the molar ratio is higher than 1, the dyad distribution is predominant lower molar ratios yield mostly styrene microdomains, i.e. n-ads with more than 2 styrene repeating units 232>. 

In case of poly(isobutylene-co-P-pinene) the characteristic resonances associated with the gem-dimethyl structures in Ae 6 = 0.8 to 1.1 range provide an ideal diagiK -tic tool for the analysis of dyad distributions. The relative proportion of resonances determined at 6 = 0.8,1.0 and 1.1 reflect the relative proportion of uncrowded, half-crowded and fuUy-crowded gem-dimethyl groups respectively. Thus... 

Shown below is a representative portion of a terpolymer chain derived from monomers A, B and C. The structural features of interest are the relative amounts A-, B- and C-monomer units the relative amounts of AA-, (BA+AB)-(CA+AC)-, BB-, (BC+CB)- and CC-pairs (dyad distributions) the relative amounts of groups of... 

Szwarc assumed that the dyad distribution in the copolymer corresponds to the distribution of the related active species. It follows that the ratio of concentrations of segments [0CH2CH20]/[0CH20] = q was equal to fraction fA, fB = (1 — e) and fc = fD = q (1 — q). Thus, according to Szwarc, the stationary monomer concentrations in contact with living polymers are as follows ... 

These authors have also studied by H-NMR spectroscopy the microstructure of THF-3,3-dimethyloxetane (DMO) copolymers at 0 °C and calculated the dyad distribution (cf. Sect. 15.1.2). 

Only one independent variable is necessary to describe the Bernoullian process in full since the sum of and is equal to unity. Dyad distribution data contain two independent observations which is sufficient to check for conformity to Bernoullian statistics, (Although there are three dyad types, the mole fraction of one of them is always defined by the mole fractions of the other two since the mole fraction of the total dyad is, of course, equal to one, i.e. there are only two independent observations.) However, a better test for conformity is found in a triad distribution since this contains five independent observations (there are six triads). 

As with the Bernoullian model, comparison between an observed and calculated sequence distribution is required to check for conformity to first-order Markov statistics. Obviously, with only two independent observations, a dyad distribution is insufficient for determining the two independent probabilities of the model. In contrast, a triad distribution provides five independent observations, so this can be used to check conformity to first-order Markov statistics. Trial values of the monomer addition probabilities can be obtained by taking appropriate combinations of the expressions shown in Table 2.3. For example, is given by... 

Poly (vinyl alcohol-co-vinyl acetate) polymers are surface active species which can be used to stabilise latex and oil in water dispersions. In order to understand the properties of these materials, it is necessary that their sequence distributions are well characterised. A number of NMR studies on the microstructure of PVA/PVAc copolymers have been made [51-53] (see also chapter 3). Moritani and Fujiwara [51], for example, have used proton and carbon-13 NMR spectroscopy to extract dyad distributions for a range of copolymers with different degrees of deacetylation. Samples were prepared using one of three routes direct saponification of PVAc alcoholyis of PVAc using sodium methoxide and reacetylation of PVA. From the polymer composition and the dyad distribution, the parameter rj was calculated for each polymer as follows ... 

Compositional features of the copolymers, such as monomer contents, dyad distributions, and monomer centered triad fractions were calculated from monomer feed compositions, conversions obtained in copolymerization experiments and reactivity ratios of 0.78 and 0.26 for aFS and MA, respectively, using methods and a computer program we have described previously. For ease of discussion, aFS will be represented by S and MA will be represented by M when dyads and triads are discussed subsequently. Monomer centered triad fractions, which represent the fraction of monomer units of a given type, eg. M, in a particular triad environment, eg. SMS, will be designated as Fxyz> where xyz is the triad sequence and y is the central monomer unit under consideration. 

The resonances of methylene carbons and of the methine carbons of MA units (6 =45-32 ppm are partially overlapped but are sufficiently well defined that assignments may be made based on dyad distributions and on MA-centered triad fractions calculated for the copolymers and on assignments made previously for polyMA and polyaFS The three sharp signals observed between 6(,=46-32 ppm in Figures 7A, 7B and 8A are attributed to methine carbons because the resonances of such carbons are narrower than those of methylene carbons in the spectra of polystyrene and poly(alkyl... 

The microstructural features of stereoregular copolymers prepared directly from monomers can be related to conditional monomer placement probabilities, which are, in turn, related to monomer reactivity ratios and monomer feed ratios. Thus, the conditional probability that an A unit follows a B unit in a copolymer chain, P(a/b), can be calculated from BA and BB dyad distributions or from the monomer reactivity ratio for B,r, and the ratio of, monomers A and B in the feed (A /B ), according to the following equations. 

Siiailarly, poly(2,3-dimethy 1-1,3-butadiene) prepared with a butyl lithium/hexane system was found to contain predominantly 1,4-cis and 1,4-trans units, arranged rcUidomly [l00,10ll. The methylene carbon and proton resonances were used to obtain dyad distributions in these studies, and the methyl proton resonances provided a measure of triad distributions. Although polymers prepared from 2,3-dimethyl-1,3-butadiene had about 7% 1,2-structure, these polymers were also fovind to have Bernoullian structures. 

Suzuki and coworkers [102] investigated the structures of poly(1-phenylbutadienes) prepared by anionic or coordinated polymerization. The polymers contained predominantly 1,4-enchainments of the 1-phenylbutadiene inits and dyad distributions were measvirable from the olefinic carbon resonances. A predominantly trans-1,4-polymer was isomerized to yield a l,4-cis/l,4-trans copolymer in which the cis and trans units were distributed randomly along the polymer chain. The polymers obtained by anionic polymerization also had random structures. 

Several procedures are available for preparing polybutadienes that contain equal amounts of 1,4-cis and 1,2- units [104,105]. The structures of these equibinary" polymers have been investigated extensively by cmr spectroscopy [21,22,106,107]. The olefinic carbons of the 1,4-cis units are particularly useful for determining cis unit centered triad distributions, and some of the aliphatic carbon resonances have provided measures of dyad distributions. The... 

Kricheldorf and Schilling [109-110] for example, have shown that the carbonyl carbon resonances of L-alanine-L-phenylalanine copolymers can provide a measure of dyad distributions. Four carbonyl carbon... 

Thus, when sequential polymerization of q clic acetals was performed by introducing DXP into a solution of living polyDXL or vice versa, the copolymer isolated after longer reaction times showed DXL-DXL/DXL-DXP/DXP-DXP dyad distribution (determined by NMR) in ratios of 1 2 1, characteristic of random copolymers. When copolymerization was terminated after shorter reaction times, the proportion of heterodyads was lower, but at no stage of copolymerization could pure block copolymer be isolated. 

The monomer sequence distribution of Bd-Ip copolymer was determined by NMR spectrometry (Xie and Xiao, 1982). The dyad distribution and number average sequence length of these copolymers were quantitatively determined. The results show that the sequence distribution of monomer units in copolymers... 

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. 

NMR spectroscopy has made possible the characterization of copolymers in terms of their monomer sequence distribution. The area has been reviewed by Randall,100 Bovey,139 Tonelli,101 Hatada140 and others. Information on monomer sequence distribution is substantially more powerful than simple composition data with respect to model discrimination,25,49 Although many authors have used the distribution of triad fractions to confirm the adequacy or otherwise of various models, only a few25 58,141 have used dyad or triad fractions to calculate reactivity ratios directly. 

Unit distribution in the substituted PMMA (35) was investigated by two independant methods a) Direct analysis of copolymer microstructure by H-NHR at 250 MHz the NMR spectrum (pyridine solution at 80°C) are sufficiently well resolved to allow a quantitative analysis of unit distribution, in terms of A centered triads and isolated B units in ABA triads, b) UV studies of the ionization and of the intramolecular cyclization of the B B and B B dyads in protic basic media (Na0H-H 0 O.IN, NaOMe-MeOH O.IN) in such a medium the partially ionized copolymer chains are the site of a complex series of consecutive intramolecular reactions we have completely elucidated (35). The first step is of interest with respect to B unit distribution ... 

When measuring vinyl polymer tactlclty, one prefers the longest complete n-ad distribution available as well as the translated simplest comonomer distribution, possibly m versus r. An alternative exists to the m versus r distribution In the form of number average or mean sequence lengths. If any vinyl homopolymer Is viewed conceptually as a copolymer of meso and racemic dyads, mean sequence lengths can be determined for continuous runs of both meso and racemic configurations (32), that Is,... 

As was true in the case of mean sequence lengths for meso and racemic dyads, the necessary relationships can be used to develop corresponding equations for any particular n-ad distribution. A favorable point concerning the concept of "like" configurations is that it attaches a physical significance to the racemic distribution. 

If, instead, the dyad probability depends on the nature (m or r) of the preceding dyad, the distribution follows a first-order Markov process, with two independent statistical parameters and Pr , (the probability that after a m dyad a r dyad follows and vice versa, respectively). The corresponding equations are listed in Table 4, column 3. They correspond to those of a nonideal copolymerization and are reduced to the previous case when p + p = 1 ... 

More complex schemes have been proposed, such as second-order Markov chains with four independent parameters (corresponding to a copolymerization with penultimate effect, that is, an effect of the penultimate member of the growing chain), the nonsymmetric Bernoulli or Markov chains, or even non-Maikov models a few of these will be examined in a later section. Verification of these models calls for the knowledge of the distribution of sequences that become longer, the more complex the proposed mechanism. Considering only Bernoulli and Markov processes it may be said that at the dyad level all models fit the experimental data and hence none can be verified at the triad level the Bernoulli process can be verified or rejected, while all Markov processes fit at the tetrad level the validity of a first-order Markov chain can be confirmed, at the pentad level that of a second-order Maikov chain, and so on (10). 

The Suter-Flory model was successfully used to interpret the results of the epimerization reaction carried out on propylene oligomers (204) and on polypropylene itself (106, 205). In both cases a slight prevalence of the r dyad over the m (52/48) is observed. The epimerized polypropylene has a microstmcmre almost coincident with a Bernoulli distribution and represents the polymer sample closest to an ideal atactic polymer so far obtained. 

The sequence length distribution for an ideal copolymerization with r = 5, r2 = 0.2 for an equimolar feed composition is shown in Fig. 6-9. This copolymerization has pn — p2 0.8333 andp 2— p22 — 0.1667. Both M and M propagating centers have a 5 1 tendency to add Mi over M2, but Mi pentad sequences are not the most plentiful, although they are among the most plentiful. The most plentiful sequence is Mi at 16.7% with 14.0%, 11.6%, 9.7%, 8.1%, 6.7%, 5.6%, and 4.7%, respectively, of dyad, triad, tetrad, pentad, hexad, heptad, and octad Mi sequences. There are smaller amounts of longer sequences 3.2% of... 

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