Pentad distribution

This amorphous polypropylene, therefore, has a tendency toward short blocks of meso and racemic sequences. This structural conclusion is not readily apparent from a simple inspection of the pentad distribution although the dominant pentads are mmmm, mmmr, rrrr, rrrm and mmrr as indicated by the above formula for the average configurational structure. 

The pentad distribution consists of the isotactic sequence mmmm, the syndiotactic sequence rrrr, and the heterotactic sequences rmmr, mmrm, mmrr, rmrm, rmrr, mrrm,... 

The steric pentad distributions of the polypropylene with structure (14) are in accord with the symmetric Bemoullian statistical model (Eq. 30) based on stereochemical control by the last propylene unit of a growing chain end. 

Steric defects in isotactic polypropylene, which involve the appearance of isolated r diads or pairs of r diads, may be considered on a pentad level (Figures 3.45a and b respectively). The 13C NMR signals associated with occasional stereoerrors in the propylene isotactic polymers produced by chiral metallocene-based catalysts (pairs of r diads) indicate that the polymerisation stereochemistry is governed by the enantiomorphism of catalytic sites an error pentad distribution close to mmmr.mmrr.mmrm-.mrrm = 2 2 0 1 is observed... 

Figure 3.45 Typical steric defects (pentad distribution of stereoerrors) in a (mainly) isotactic poly(a-olefin) chain (a) isolated r diad, characteristic of chain end stereocontrol (b) pair of r diads, characteristic of enantiomorphic site stereocontrol during the propagation...

Chain end stereocontrol, which gives rise to single-inversion pentads, mmrm and mmmr, as main error signals in 13C NMR spectra, is characteristic of propylene polymerisation with the Cp2TiPli2— [A Me) ] catalyst at lowered temperature (leading to stereoblock polypropylene) in this case an error pentad distribution is observed close to mmmr mmrr mmrm mrrm= 1 0 1 0 (Figure 3.35a) [1,30]. 

As shown in Figure 23, PP is no longer able to crystallize when the stereoregularity of the chains is reduced below a threshold value (below about 70% m diad, or 40% mmmm pentad content for iPP, or below about 60% rrrr pentad content for sPP), and it becomes amorphous (amPP). When statistical randomness in the sequence of chirotopic methynes in the polymer chain is reached, the polymer is called atactic (aPP). In this case the pentad distribution is perfectly random Bcrnoullian mmmm mmmr rmmr mmrr (rmrr+ mrmm) mrmr rrrr rrrm mrrm 1 2 1 2 4 2 1 2 1. 

The tacticity (pentad distribution) of the product polymer was analyzed by NMR (data not shown). The tacticity was virtually the same with and without the catalyst (T1 and 2,4,6-Me), meaning that the propagating species is a free radical. These results strongly indicate the existence of RT. 

The correct pentad distribution for a perfectly hemiisotactic polymer is the following [mmmm] [mmmr [rmmr [mmrf [rrrf [mrrr]. [mrrm] = 3 2 1 4 3 2 1. 

From Energy Differences to Pentad Distributions 1464 Systematic and Independent Prediction of Pentad 1465 Distributions... 

Considering each insertion as an independent event (which implies enantiomorphic site control, i.e., the chirality of the catalyst is the dominating factor for stereocontrol). Hart and Rappe then calculated the intensities for the mmmm pentad by multiplication of the individual probabilities. The calculated intensities were in excellent agreement with those from NMR data for a series of substituted ethylene-bridged, C2-symmetric zirconocenes. The use of this new and more quantitative approach to analysis of the relationship between the molecular structure of the catalyst and the polymer microstructure was, however, restricted to comparison of intensities for the mmmm pentad. Application to error pentads or prediction of pentad distributions for new or modified catalysts was not attempted. 

Table 3. Calculated (Observed) Pentad Distributions (%) of Polypropene Obtained from Pol5mierization Using Catalysts 1—3...

At low temperatures, the calculated pentad distributions for 1 and 2 are in excellent agreement with experiment, with overall RMS deviations at 10 °C amounting to 1.6 and 1.2 percentage points, respectively. The theoretical pentad distribution for 1 reflects slightly less syndiospecificity than found in analysis of the NMR spectrum, whereas 2 along with the related, sterically more encumbered catalyst 8, is predicted to be somewhat too isospecific. The... 

For 3, the predicted pentad distribution is inaccurate (RMS deviations above 5 percentage points) even at low temperatures. This catalyst is normally referred to as hemiisospecific, although the low intensities observed for the rrrr pentad suggest that weakly isospecific perhaps is a better term. With one olefin coordination site being ideally enantio-... 

Thus, for prime examples of catalysts of significant isospecific or syndiospecific character, it seems to be possible to calculate the pentad distribution independently with very good accuracy at low temperatures using a relatively simple molecular mechanics approach. For catalysts with weak enantioselectivities, small errors in the calculated selectivity may lead to marked errors in the predicted pentad distribution. 

Catalysts 4—6 (with a Me. Et and Pr substituent, respectively) are hemiisospecific, and low enantio-selectivity for the (S) complexes have been reported in previous calculations. As noted above for compound 3. accurate estimates of the pentad distribution are hard to obtain for catalysts displaying low enantioselectivity (Table 2). 

Whereas the calculated pentad distribution for the ethyl-substituted catalyst 5 is in excellent agreement with experiment at low temperatures (RMS deviation of <1 percentage point at 10 °C), the methyl and isopropyl-substituted catalysts are predicted to be too syndiospecific and too isospecific, respectively (Table... 

Careful comparison of calculated and observed pentad distributions at a range of different temperatures thus indicates that back-skip is important for explaining the stereospecificity of 4—6 above 30—50 °C, but is unnecessary for explaining the observed isospecificity of 7. 

Statistical modeling of pentad distributions of polypropenes prepared with these catalyst systems can be satisfactorily done using a two-site modeF - based on a mixing of a chain-end-controlled site (to model the atactic blocks) and an enantiomorphic site (for isotactic blocks). ... 

The same is true for re-re and si-si options. The statistical modeling of experimental pentad distribution can be performed by considering a first-order Markovian model. The insertion probability for a si... 

The resulting probability expressions for pentad distribution are collected in Table 12. 

The resulting isotactic Bernoullian model (this is a true Bernoullian model, as the chain end effect is neglected) gives the calculated pentad distribution reported in Table 13. Each pentad contains two symmetric contributions for example, the mmmm pentad derives from the two possibilities... 

This model can be applied to evaluate the pentad distribution from NMR spectra of metallocene-based isotactic polypropenes in which overlapping with peaks from end group or regioirregular units (2.1 and 3.1) occurs. In this case only the peaks of mmmm, mmmr, mmrr, and mrrm pentads can be obtained from direct spectrum integration. Furthermore. the mmmr peak overlaps with the mmmm base, and the mmrr has to be correct by subtracting the contribution from the 2,1-erythro unit. The total pentad distribution is calculated under the hypothesis that the polymerization statistic follows a pure enantiomorphic site control, using the expressions reported in Table 13 as follows ... 

The parameter /j(re re) represents the isospecific propagation at this site (two successive reinsertions), while p re si) is the probability of error correction after a stereoerror. This model is called the asym metric Markovian model and the mathematical expressions for pentad distribution are collected in Table 14. 

In this case the probability of insertion of a monomer with a given enantioface at site 1 is equal to the probability of insertion of a monomer with the opposite enantioface at site 2. This probability is indicated with the parameter a. The resulting expressions for pentad distribution for the syndiotactic Bernoullian model are reported in Table 15. 

Table 15. Calculated Pentad Distribution with the Syndiotactic Bernoullian Model...

This fact can be included in the model considering the probability of site isomerization pbs, in the expressions for pentad distribution. The final result is shown in Table 16. 

To evaluate the sequence (pentad) distribution we obtaine the two matrixes Am and Ar defined as... 

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