Sequence Distribution Analysis

These PMR findings prompted us to undertake a detailed sequence distribution analysis of poly(isobutylene-co- pinene). Sequence distributions can be expres d by the run number/ , i.e the average number of hetero-linkages per 100 consecutive monomer linkages in a copolymer chain (2i). 

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 

We have used a trial and error l st square method to select the best experimental value of R. The PMR spectra of a series of poly(isobutylene-co- )inene), containing from 59 to 97 weight% isobutylene, are shown in Fig. 4. The run numbers obtained from these spectra are listed in Table 2. 

Alternatively, run numbers of copolymers can also be calculated from reactivity ratios using Eq. (6) (21)  

PMR spectra of poly(isobutylene-co-p-pinenes). (Isobutylene contents shown in wt %) 

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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. 

Kennedy J.P., Chou T., Sequence distribution analysis of isobutylene-styrene and isobutylene-isoprene copolymers, J. Macromol. Sci. Chem., A10(7), 1976,1357-1369. 

Determination of the (micro)structure of polymers (branching, compositional analysis of copolymers and blends, comonomer ratios, sequence distributions, analysis of end-groups)... 

Copolymer sequence analysis follows the same procedure. A computer program (HIXCO.TRIAD) was previously written for the two-state B/B model-fitting of triad sequence distributions and applied to (unfractionated) propylene-butylene copolymers and... 

Applications of the method to the estimation of reactivity ratios from diad sequence data obtained by NMR indicates that sequence distribution is more informative than composition data. The analysis of the data reported by Yamashita et al. shows that the joint 95% probability region is dependent upon the error structure. Hence this information should be reported and integrated into the analysis of the data. Furthermore reporting only point estimates is generally insufficient and joint probability regions are required. 

The analysis of 1H NMR spectra of aliphatic and aromatic polyanhydrides has been reported by Ron et al. (1991), and McCann et al. (1999) and Shen et al. (2002), and 13C NMR has been reported by Heatley et al. (1998). In 1H NMR, the aliphatic protons have chemical shifts between 1 and 2 ppm, unless they are adjacent to electron withdrawing groups. Aliphatic protons appear at about 2.45 ppm when a to an anhydride bond and can be shifted even further when adjacent to ether oxygens. Aromatic protons typically appear with chemical shifts between 6.5 and 8.5 ppm and are also shifted up by association with anhydride bonds. The sequence distribution of copolymers can be assessed, for example in P(CPH-SA), by discerning the difference between protons adjacent to CPH-CPH bonds, CPH SA bonds, and SA-SA bonds (Shen et al., 2002). FTIR and 111 NMR spectra for many of the polymers mentioned in Section II can be found in their respective references. 

Staubli et al. (1991) offer an in depth analysis of the effects of sequence distribution on the Tg of poly(anhydride-co-imide)s and discuss the experimental results with respect to several applicable theoretical models... 

Thermogravimetric analysis In thermogravimetric analysis (TGA) a sensitive balance is used to follow the weight change of the sample as a function of temperature. Its applications include the assessment of thermal stability and decomposition temperature, extent of cure in condensation polymers, composition and some information on sequence distribution in copolymers, and composition of filled polymers, among many others. 

Nuclear magnetic resonance spectroscopy of dilute polymer solutions is utilized routinely for analysis of tacticlty, of copolymer sequence distribution, and of polymerization mechanisms. The dynamics of polymer motion in dilute solution has been investigated also by protoni - and by carbon-13 NMR spectroscopy. To a lesser extent the solvent dynamics in the presence of polymer has been studied.Little systematic work has been carried out on the dynamics of both solvent and polymer in the same systan. 

This highly sophisticated investigation has been superseded by C spectroscopy, which is mote sensitive to the stereochemical envirorunent and does not requite the preparation of deuterated polymers. C NMR analysis of steric purity and sequence distribution can, therefore, be directly carried out on commercially available polymers. Thus, any doubt regarding the previous conclusions about laboratory-produced polymers obtained under necessarily different... 

The determination of the microstructure of vinyl polymers is not merely a characterisation tool. Each polymer molecule is unique, and each polymer chain is a record of the history of its formation, including mis-insertions, rearrangements, the incorporation of co-monomers, and the mode of its termination. NMR analysis of polymers can therefore be used to provide detailed mechanistic and kinetic information. This approach has been applied particularly successfully to the microstructure, i. e. the sequence distribution of monomer insertions, of polypropylene, giving rise to a wealth of studies far too numerous to cover here. Progress in this area has recently been summarised in two excellent and very comprehensive review articles [122, 123[. Here we will cover only the most fundamental aspects of stereoselective polymerisations. 

Infrared spectroscopy has been used for quantitatively measuring the amounts of 1,2-, 3,4-, cis-1,4-, and trans-1,4-polymers in the polymerization of 1,3-dienes its use for analysis of isotactic and syndiotactic polymer structures is very limited [Coleman et al., 1978 Tosi and Ciampelli, 1973]. Nuclear magnetic resonance spectroscopy is the most powerful tool for detecting both types of stereoisomerism in polymers. High-resolution proton NMR and especially 13C NMR allow one to obtain considerable detail about the sequence distribution of stereoisomeric units within the polymer chain [Bovey, 1972, 1982 Bovey and Mirau, 1996 Tonelli, 1989 Zambelli and Gatti, 1978],... 

Statistical analysis of the stereochemical sequence distributions (Table 8-3 and Sec. 8-16) also supports the enantiomorphic site control model. 

The polymer chain end control model is supported by the observation that highly syndiotactic polypropene is obtained only at low temperatures (about —78°C). Syndiotacticity is significantly decreased by raising the temperature to —40°C [Boor, 1979]. The polymer is atactic when polymerization is carried out above 0°C. 13C NMR analysis of the stereoerrors and stereochemical sequence distributions (Table 8-3 and Sec. 8-16) also support the polymer chain end control model [Zambelli et al., 2001], Analysis of propene-ethylene copolymers of low ethylene content produced by vanadium initiators indicates that a syndiotactic block formed after an ethylene unit enters the polymer chain is just as likely to start with an S- placement as with an R-placement of the first propene unit in that block [Bovey et al., 1974 Zambelli et al., 1971, 1978, 1979]. Stereocontrol is not exerted by chiral sites as in isotactic placement, which favors only one type of placement (either S- or R-, depending on the chirality of the active site). Stereocontrol is exerted by the chain end. An ethylene terminal unit has no preference for either placement, since there are no differences in repulsive interactions. 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

Mean-square unperturbed dimensions a and their temperature coefficient, d tin 0) I d T, are calculated for ethylene-propylene copolymers by means of the RIS theory. Conformational energies required in the analysis are shown to be readily obtained from previous analyses of PE and PP, without additional approximations. Results thus calculated are reported as a function of chemical composition, chemical sequence distribution, and stereochemical composition of the PP sequences. Calculations of 0 / nP- are earned out using ( ) r r2 = 0.01, 1.0, 10.0, and 100.0, (ii) p, = 0.95, 0.50, and 0.05, liii) bond length of 153 pm and bond angles of 112°for all skeletal bonds, iv) = 0 and 10°, and (v) statistical weight factors appropriate for temperatures of 248, 298, and 348 K. Matrices used are ... 

From the analysis of 13C NMR spectra of polypropylenes, Doi96) found that the sequence distribution of inverted propylene units follows first-order Markov statistics. Table 4 lists the two reactivity ratios rQ and rt, for the polymerization of propylene with the soluble catalysts composed of VC14 and alkylaluminums at — 78 °C ... 

We explain these results based upon the specific arrangement of monomers in the oligomer chain. The exact sequence of monomers will affect their solubility in supercritical COy, therefore, one expects to see more than one envelope for tne MMA oligomers which possess two BA units. In contrast, soft ionization mass spectrometry will not distinguish such isomers. Soft ionization mass spectrometric analysis preceded by SFC separation should yield molecular weight and sequence distribution data on copolymers. 

Carbon-13 nuclear magnetic resonance was used to determine the molecular structure of four copolymers of vinyl chloride and vinylidene chloride. The spectra were used to determine both monomer composition and sequence distribution. Good agreement was found between the chlorine analysis determined from wet analysis and the chlorine analysis determined by the C nmr method. The number average sequence length for vinylidene chloride measured from the spectra fit first order Markovian statistics rather than Bernoullian. The chemical shifts in these copolymers as well as their changes in areas as a function of monomer composition enable these copolymers to serve as model... 

The determination of percentage of styrene and butadiene isomer distribution in copolymers is an extension of the methods for the analysis of polybutadiene. The styrene band at 700 cm 1 is largely independent of the sequence distribution and therefore useful in styrene content determination [76]. A series of bands in the IR spectrum of crystalline isotactic polystyrene at 758, 783, 898, 920, 1053, 1084, 1194, 1261, 1297, 1312 cm"1 have been attributed to the helical structure [77]. The absorption bands for butadiene in SBR are similar to BR structures (Table 3.2a). 

Propylene content in EPM rubber can be determined with the help of IR spectra. A propylene band near 1155 cm 1 has been widely used [79] for EPM analysis, frequently in combination with the polyethylene band at 721 cm"1. Tacticity is important in EPM rubber, and the bands at 1229 and 1252 cm"1 are characteristic of syndiotactic and isotactic structures, respectively, (both bands are present in atactic polypropylene as well). Polymer structure may vary in the relative tactic placement of adjacent head to tail propylene units and in the sequence distribution of base units along the chain. Some of them can be identified [80] by infrared spectra, such as isolated or head to tail propylene units ... 

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