Diad/triad relationships

The next step is to consider a simple copolymerization of A and B units and then write probability expressions for the monomers, diads, triads, etc., and show how these are interrelated. After a while, the number of such equations looks dauntingly large, but the relationships axe actually pretty simple and easy to work out. Let s start with the obvious if there are just A and B units in the chain then the probability of finding an A, p A, is simply the number of A s divided by the total number of A s and B s (Figure 6-16). Similarly for which leads to... 

Relationships independent of the polymerization mechanism must exist between the various 7-ads since each of the 7-ads, from triads onward, consists of two or more diads. The relationships between the fractional compositions of diads and triads are... 

From the relationships derived (10), the six possible ratios of rate constants for a Markov first-order polymerization can be calculated from the corresponding diad and triad fractions via ... 

Then starting from reversibility relationships for triads you can relate diad information to these conditional probabilities, as shown in Equations 7-29. 

Figure 15-3, Relationship between triad fractions and the syndiotactic diad fraction. The lines give the theoretical relationship for an enantiomorphic catalyst with placements independent of the previously occurring placement the circles give the experimental results for the polymerization of methyl vinyl ether with Ab(S04)3/H2S04 in toluene. (From data of T. Higashimura, Y. Ohsumi, K. Kuroda, and S. Okamura.).

Isotactic triads can only be formed on an isotactic diad with a probability of Pifi. The relationships between diads and triads... 

The only exception to the A and B sequence numbers not being the same is for very low molecular weight copolymers. Any particular sequence begins and ends with the opposite unit and the only time that this is not true is for the end units of the copolymer chain, where each end unit is only a part of a diad. If one counts from the second unit of a copolymer chain to the next to last unit of any copolymer chain, the number of A sequences will always equal the number of B sequences. Consequently, a necessary relationship (4,14) for these triads is ... 

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