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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 13 C 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]. Consider the description of the sequence distribution of isotactic and syndiotactic placements in the polymerization of a monosubstituted ethylene. The approach is general and can be applied with appropriate modi cation to the 1,4-polymerization of a 1,3-diene. Dyad tacticity is de ned as the fractions of pairs of adjacent repeating units that are isotactic or syndiotactic to one another. The isotactic and syndiotactic dyads (XV) are usually referred to as meso and racemic dyads. The horizontal line in XV represents a segment of the polymer

chain, and each vertical line represents the con guration at the stereocenter in a repeating unit. The fractions of isotactic and syndiotactic dyads are referred to as (m) and (r) or i

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1. two linearly separable classes in a onedimensional feature space;

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and s, respectively. Triad tacticity describes isotactic, syndiotactic, and heterotactic triads (XVI) whose fractions are designated as (mm), (rr), and (mr), or I, S, and H, respectively. These de nitions are clari ed by considering a portion of a polymer chain such as XVII. Chain segment XVII has a total of 9 repeating units but only 8 dyads and 7 triads. There are 6 meso dyads and 2 racemic dyads; m 3, r 1, There are 4 isotactic, 2 heterotactic, and 4 4 1 syndiotactic triads; mm 4, mr 2, rr 1. 7 7 7

m r 1 mm rr mr 1 8-10 8-11

m mm 0:5 mr r rr 0:5 mr 8-12 8-13

It is clear that a determination of any two triad fractions allows a complete de nition of both the triad and dyad structures of a polymer via Eqs. 8-10 through 8-13. An atactic polymer is one in which r m 0:5 and mm rr 0:25, mr 0:5 with a random distribution of dyads and triads. The (all-) isotactic polymer has m mm 1. The (all-) syndiotactic polymer is de ned by r rr 1. For random distribution with m 6 r 6 0:5 or mm 6 rr 6 0:25, one has different degrees of syndiotacticity or isotacticity. Isotacticity predominates when m > 0:5 and mm > 0:25 and syndiotacticity predominates when r > 0:5 and rr > 0:25. These polymers are random tactic polymers, containing random placement of isotactic and syndiotactic dyads and triads. When the distribution of dyads and triads is less than completely random, the polymer is a stereoblock polymer in which there are block (which may be short or long) of isotactic and syndiotactic dyads and triads. The advent of high-resolution 13 C NMR allows the determination of tetrad, pentad, and even higher sequence distributions in many polymers [Bovey, 1972; Bovey and Mirau, 1996; Farina, 1987]. The tetrad distribution consists of the isotactic sequence mmm, the syndiotactic sequence rrr, and the heterotactic sequences mmr, rmr, mrm, rrm. The sum of the tetrad fractions is unity, and the following relationships exist:

2. two linearly separable classes in a two-dimensional feature space;

mm mmm 0:5 mmr rr rrr 0:5 mrr mr mmr 2 rmr mrr 2 mrm 8-14 8-15 8-16

2

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

rrmm. The sum of the pentad sequences is unity, and the following relationships exist:

These experiments permit some simple qualitative assessments of the characteristics of the MLP model, and illustrate some aspects of its behavior. It is shown that:

mmmr 2 rmmr mmrm mmrr mrrr 2 mrrm rrmr rrmm mmm mmmm 0:5 mmmr mmr mmmr 2 rmmr mmrm mmrr rmr 0:5 mrmr 0:5 rmrr mrm 0:5 mrmr 0:5 mmrm rrm 2 mrrm mrrr mmrr rmrr rrr rrrr 0:5 mrrr 8-17 8-18 8-19 8-20 8-21 8-22 8-23 8-24

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