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Fig. 6-9 Sequence-length distribution for an ideal copolymerization with r1 5, r2 0:2 and f1 f2 . N 1 x is represented by ; N 2 x , by - - -. The plots for N 2 x are shown slightly to the left of the actual sequence length. After Vollmert (transl. Immergut) [1973] (by permission of Springer-Verlag New York, Inc., New York).
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p11 p12 p22 p21 0:50. Although the most plentiful sequence is M1 at 50%, there are considerable amounts of other sequences: 25%, 12.5%, 6.25%, 3.13%, 1.56%, and 0.78%, respectively, of dyad, triad, tetrad, pentad, hexad, and heptad sequences. The distribution of M2 sequences is exactly the same as for M1 sequences. For a feed composition other than equimolar, the distribution becomes narrower for the monomer present in lower amount and broader for the monomer in larger amount a general phenomenon observed for all sequence length distributions. It is clear that the copolymer, with an overall composition of F1 F2 0:50, has a microstructure that is very different from that of a perfectly alternating copolymer. The sequence length distribution for an ideal copolymerization with r1 5, r2 0:2 for an equimolar feed composition is shown in Fig. 6-9. This copolymerization has p11 * * p21 0:8333 and p12 p22 0:1667. Both M1 and M2 propagating centers have a 5 : 1 tendency to add M1 over M2, but M1 pentad sequences are not the most plentiful, although they are among the most plentiful. The most plentiful sequence is M1 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 M1 sequences. There are smaller amounts of longer sequences: 3.2% of 10-unit, 1.3% of 15-unit, and 0.4% of 20-unit M1 sequences. The sequence length distribution is much narrower for the less reactive M2 monomer. Single M1 units are by far the most plentiful (83.3%) with 13.9% dyads, 2.3% triads, and 0.39% tetrads. An alternating copolymerization with r1 r2 0:1 and f1 f2 has the sequence length distribution shown in Fig. 6-10 (p11 p22 0:0910; p12 p21 0:9090). The sequence
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Fig. 6-10 Sequence length distribution for an alternating copolymerization with r1 r2 0:1 and f1 f2 . After Vollmert (transl. Immergut) [1973] (by permission of Springer-Verlag New York, Inc., New York).
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length distributions for both monomer units are identical. The single M1 and single M2 sequences are overwhelmingly the most plentiful the M1M2 makes up 90.9% of the copolymer structure. There are 8.3% and 0.75%, respectively, of dyad and triad sequences of both M1 and M2. Compare this distribution with that in Fig. 6-8 for the ideal copolymer having the identical overall composition. The large difference in the distributions for the two copolymers clearly indicates the difference between alternating and ideal behavior. High-resolution nuclear magnetic resonance spectroscopy, especially 13C NMR, is a powerful tool for analysis of copolymer microstructure [Bailey and Henrichs, 1978; Bovey, 1972; Cheng, 1995, 1997a; Randall, 1977, 1989; Randall and Ruff, 1988]. The predicted sequence length distributions have been veri ed in a number of comonomer systems. Copolymer microstructure also gives an alternate method for evaluation of monomer reactivity ratios [Randall, 1977]. The method follows that described in Sec. 8-16 for stereochemical microstructure. For example, for the terminal model, the mathematical equations from Sec. 8-16a-2 apply except that Pmm , Pmr , Prm and Prr are replaced by p11, p12 , p21 , and p22 . 6-2g-2 Copolymer Compositions of Different Molecules
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A second uncertainty concerning copolymer composition is the distribution of composition from one copolymer molecule to another in a sample produced at any given degree of conversion [Cheng, 1997b; Galvan and Tirrell, 1986; Tacx et al., 1988]. Stockmayer [1945] indicated that the distribution of copolymer composition due to statistical uctuations generally follows a very sharp Gaussian curve. Although the distribution is wider for Aspx pdf417 integrationon .net
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