Triads distribution

As an example of the use of MIXCO.TRIAD, an analysis of comonomer triad distribution of several ethylene-propylene copolymer samples will be delineated. The theoretical triad Intensities corresponding to the 2-state B/B and 3-state B/B/B mixture models are given In Table VI. Abls, et al (19) had earlier published the HMR triad data on ethylene-propylene samples made through continuous polymerization with heterogeneous titanium catalysts. The data can be readily fitted to the two-state B/B model. The results for samples 2 and 5 are shown In Table VII. The mean deviation (R) between the observed and the calculated Intensities Is less than 1% absolute, and certainly less than the experimental error In the HMR Intensity determination. 

Table 2. Triad distribution of ethylene/1-hexene copolymer...

The characteristics of C NMR spectra for all copolymers were similar. The triad distributions for all copolymo" from NMR monomer insertion are shown in Table 2. Based on the triad distribution of ethylene/l-hex aae copolymers in Table 2, we found that microstructurc of copolymer obtainrai fiom aluminoxane system was slightly different in monomer incorporation, but found significantly when borated system was applied. We suspected that this difference was arising fiom the diffaences in bimetallic complex active species between [aluminoxane] [catalyst] and [Borate] [catalyst] which had the electronic and gMmetric effects fiom the sterric effect of larger molecule of borate compare to the aluminoxane on the behaviors of comonomer insertion in our systems. 

Figure 6. Comonomer triad distributions observed by 13C NMR analysis during the (n-Bu)3SnH reductions of TCH (----------) and PVC (------).

Figure 7. A comparison of the observed (symbols) and simulated (solid lines) comonomer triad distributions in (n-Bu)3SnH reduced TCH.

Table 2. Triad Distributions and Composite Rate Constants (K) for 30...

In contrast to the case of Cp2ZrX2/MAO giving atactic poly(alkene)s, Cp MCl2/MAO, M = Zr (139) and Hf (140), are the catalyst precursors of the syndiotactic polymerization of 1-butene and propylene [176]. Triad distribution indicated that this is chain-end controlled syndiospecific polymerization. The syndiospecificity is attributed to the increase of steric encumbrance around the metal center. Thus, Cp HfX2 is the most effective syndiospecific catalyst component in this system. 

Figure 3. Triad distribution in poly(iiiethyl methaciylate) as a function of p . Points at < O.S are obtained by radical polymerization, those at p > O.S by anionic polymerization (10). Copyright Academic Press.

The influence "of THF is shown in Figure 1, where the frequencies of the iso-, syndio- and hetero-tactic triads, i, s and h, of each sample can be read off along the appropriate median (e.g. the apex i corresponding to i = 1-0, the base opposite i corresponding to i = 0). The curve represents the Bernoullian triad distribution (h = 2i1/2s1 2). The black circles refer to samples prepared in toluene solution containing the optimum trace of THF (Xthf s . ) for initiation of isotactic growth centres. 

The steric triad distributions of polypropylene with structure (IS) are consistent with an enantiomorphic-site propagation model based on stereochemical control by the chirality of the active center on the catalyst 132,133). It should be noted that isotactic polypropylenes are formed along both propagation models, enantiomorphic-site control and chain-end control. 

Triad sequence assignments have been made for ethyl acrylate-centered triads. Apparent reactivity ratios have been calculated for the semi-batch copolymers using run number theory. A model has been developed to describe the power-feed systems and predict the triad distributions in the incremental and final copolymer using the experimentally determined r-j and r values. 

There is another way to confirm that the triad distribution cannot result from a random polymerization. The observed relative proportion of the triad structure in Figure Id is (l) (.93) (.26). The corresponding distribution for the triad structure for, 266 mole fraction VCI2 would be (l) (,36) (.13) Obviously, this comparison confirms from just a consideration of the triad distribution that the polymer does not conform to Bernoullian statistics. 

Although several techniques have been used to characterize stereosequence distribution, we suggest that the percent crystallinity and temperature of melting measurements are more generally applicable than any other technique presently available. Bovey and co-workers (7) showed how NMR measurements can be used to determine the triad distribution in polymers such as polymethyl methacrylate in which there is sufficient difference between the NMR spectra corresponding to syndiotactic, isotactic, and heterotactic triads to allow quantitative measurements to be made. This type of measurement unfortunately is restricted to few systems and would lead to a unique description of the stereostructure of the chain only when a model involving one or two probability parameters is applicable (See Appendix I). 

Table 6.6 Comparison of theoretical and experimental triad distributions in copolymer of styrene Mt with methyl methacrylate M2 prepared in bulk copolymerization (T = 60 °C) at conversions p = 0.03 -0.05 [281]...

Table 6.8 Parameters (2.4) of the penultimate model (2.3) describing copolymerization of styrene M, with acrylonitrile M2 in toluene solution at T = 60 °C. The values of reactivity ratios were obtained [283] from the data on copolymer composition (I) and triad distribution (II)...

Since considerations of sequence distributions can be used to derive the simple copolymer equation, it is not surprising that measured values of triad distributions in binary copolymers [by H or C NMR analyses] can be inserted into the copolymer equation to calculate reactivity ratios [19]. 

Solution NMR is widely used in polymer processing for the qualitative and quantitative analyses of tacti-city, end-groups, degradation products, chain defects, and monomer sequence distribution.A typical application is in the characterization of monomer sequence distribution by quantitative NMR spec-troscopy. For example. Fig. 7 shows a typical NMR spectrum of ethylene-co-l-butene. From the relative peak areas, it is possible to determine the fractions of the two monomers, their reactivity ratios, the triad distribution, and the blockiness or randomness of the monomer distributions. All of these structure factors play an important role in the polymer s physical and mechanical properties. 

The triad distribution in the copolymer was found to be bernoullian and is accounted for by a one-parameter model therefore, chain end control of the stereochemistry was assumed [80]. For the systems based on bipyridine, no influence of the counter-ion on the stereochemistry of the produced copolymers was found however, the catalytic activity was highest with the weakest coordinating anion [81]. Bis-chelated complexes of 2,2 -bipyridine or 1,10-phenanthroline [ Pd(N-N)2 X2 ] were efficient catalyst precursors, particularly when used in 2,2,2-tri-fluoroethanol as the solvent [82] under these conditions stabilization of the catalytic system by an oxidant is unnecessary, and very high molecular weights were obtained [83]. 

Carbon 13 nuclear magnetic resonance can be used quantitatively in analyses of polymers to measure conveniently comonomer concentrations, average sequence lengths, run numbers and comonomer triad distributions. 

The integrated areas from the 13c NMR spectrum in Figures 3 and 5 lead to the following results for the triad distribution ... 

A triad distribution is useful because it gives the relative concentrations of each of the possible connecting sequences. With this information, the comonomer concentrations, number average sequence... 

The development of the concepts of run number, average sequence lengths and triad distributions would be of little more than academic interest if they could not be usefully applied. The concept of run number is most valuable in a consideration of the effect of comonomer content versus branch length in affecting polyethylene density. The following section utilizes the run number in a correlation with a number of polyethylene physical properties. 

Table I. Triad Distribution in 60 mol % Hydrolyzed Poly(AAm-PAAm-BisAAm) Gel from NMR...

As mentioned earlier, these sequence distributions can be used to derive the copolymer composition equation. Furthermore, employing experimental triad distribution data, one can also calculate the reactivity ratios [119]. The measurement of triad and dyad sequences is largely accomplished via and NMR spectroscopy. 

Ross, J.F., Copolymerization Kinetic Constants and Their Prediction from Dyad/ Triad Distributions,/. Macromol. Sci.-CHEM, A21, 453 (1984). 

The same procedure can be applied to different copolymerization models, for example, PUM, and different types of data sets, for example, triad distributions as a function of monomer feed composition. Both will lead to more complex mathematical... 

Figure 14 STY-centered triad distribution in STY-MAnh copolymers synthesized in butanone ( ), l l,IM-dimethylformamide (DMF) (o) and toluene (A). MSM, SSM+MSS and SSS are STY-Centered triads with two, one and zero MAnh neighboring monomer residues, respectively. Reprinted from Klumperman, B. Vonk, G. Eur. Polym. J. 1994, 30,955-960. ...

The apparent reactivity ratios that govern the copolymerization in the solvents were determined and are significantly different. Nevertheless, the triad distribution as a funrtion of copolymer composition shows that within experimental error, one set of curves describes all three situations. This again is clear evidence that solvents do not affect the tme monomer reactivity ratios, but only the monomer partitioning. In the derivations by Klumperman and O Driscoll it is clearly shown that these partitioning effects cancel from the sequence distribution versus copolymer composition equations. 

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). 

Expressions for the mole fractions of longer sequences can be built up in a similar fashion. Expressions for first-order Markov dyad and triad distributions are given in Table 2.3, and can be compared with the analogous expressions for stereochemical sequence distributions in chapter 1. 

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... 

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