Triads

Figure C 1.2.10. Representative examples of fullerene based donor-bridge-acceptor dyads and triads.

Liddell P A, Kuciauskas D, Sumida J P, Nash B, Nguyen D, Moore A L, Moore T A and Gust D 1997 Photoinduced charge separation and charge recombination to a triplet state in a carotene-porphyrin-fullerene triad J. Am. Chem. Soc. 119 1400-5... 

When Mendeleef devised his periodic table the noble gases were unknown. Strictly, their properties indicate that they form a group beyond the halogens. Mendeleef had already used Group VIIl to describe his transitional triads and the noble gases were therefore placed in a new Group O. 

These observations suggest how the terminal mechanism can be proved to apply to a copolymerization reaction if experiments exist which permit the number of sequences of a particular length to be determined. If this is possible, we should count the number of Mi s (this is given by the copolymer composition) and the number of Mi Mi and Mi Mi Mi sequences. Specified sequences, of any definite composition, of two units are called dyads those of three units, triads those of four units, tetrads those of five units, pentads and so on. Next we examine the ratio NmjMi/Nmi nd NmjMiMi/NmiMi If these are the same, then the mechanism is shown to have terminal control if not, it may be penultimate control. To prove the penultimate model it would also be necessary to count the number of Mi tetrads. If the tetrad/triad ratio were the same as the triad/dyad ratio, the penultimate model is proved. 

The foregoing discussion has been conducted in terms of Mi sequences. Additional relationships of the sort we have been considering also exist for dyads, triads, and so forth, of different types of specific composition. Thus an ability to investigate microstructure experimentally allows some rather subtle mechanistic effects to be studied. In the next section we shall see how such information is obtained. 

The spectrum shown in Fig. 7.5 shows the appropriate portion of the spectrum for a copolymer prepared from a feedstock for which fj = 0.153 It turns out that each polyene produces a set of three bands The dyad is identified with the peaks at X = 298, 312, and 327 nm the triad, with X = 347 367, and 388 nm and the tetrad with X = 412 and 437 nm. Apparently one of the tetrad bands overlaps that of the triad and is not resolved. Likewise only one band (at 473 nm) is observed for the pentad. The identification ol these features can be confirmed with model compounds and the location and relative intensities of the peaks has been shown to be independent of copolymer composition. 

Once these features have been identified, the spectra can be interpreted in terms of the numbers of dyads, triads, tetrads, and pentads ( ) of the butadiene units and compared with predicted sequences of various lengths. Further con sideration of this system is left for Problems 4-6 at the end of the chapter... 

For the case of copolymers, suppose we consider the various triads of repeat units. There are six possibilities MjMjMj, M1M1M2, M2M1M2, M2 M2 M2, M2 M2 Ml, and Mi M2 Mi. These can be divided into two groups of three, depending on the identity of the central unit. Thus the center of a triad can be bracketed by two monomers identical to itself, different from itself, or by one of each. In each of these cases the central repeat unit is in a different environment, and a characteristic proton in that repeat unit will resonate at a different location, depending on the effect of that environment. 

Figure 7.6 Chemical shift (from hexamethyldisiloxane) for acrylonitrile-methyl methacrylate copolymers of the indicated methyl methacylate (Mj) content. Methoxyl resonances are labeled as to the triad source. [From R. Chujo, H. Ubara, and A. Nishioka, Polym. J. 3 670 (1972).]...

The same system of notation can be extended further by focusing attention on the backbone substituents rather than on the methylenes. Consider bracketing a center substituent with a pair of monomers in which the substituents have either the same or opposite configurations as the central substituent. Thus the two bracketing units are either m or r with respect to the central unit and the probabilities of the resulting triads are obtained from the probabilities of the respective m or r additions. The following possibilities exist ... 

An isotactic triad [XV] is generated by two successive meso additions XXX... 

The probability of the syndiotactic triad is given by p. , which becomes... 

These triads can also be bracketed by two more units to generate 10 different pentads following the pattern established in Table 7.8. It is left for the reader to verify this number by generating the various structures. 

The probabilities of the various dyad, triad, and other sequences that we have examined have all been described by a single probability parameter p. When we used the same kind of statistics for copolymers, we called the situation one of terminal control. We are considering similar statistics here, but the idea that the stereochemistry is controlled by the terminal unit is inappropriate. The active center of the chain end governs the chemistry of the addition, but not the stereochemistry. Neither the terminal unit nor any other repeat unit considered alone has any stereochemistry. Equations (7.62) and (7.63) merely state that an addition must be of one kind or another, but that the rates are not necessarily identical. 

A mechanism in which the stereochemistry of the growing chain does exert an influence on the addition might exist, but at least two repeat units in the chain are required to define any such stereochemistry. Therefore this possibility is equivalent to the penultimate mechanism in copolymers. In this case the addition would be described in terms of conditional probabilities, just as Eq. (7.49) does for copolymers. Thus the probability of an isotactic triad controlled by the stereochemistry of the growing chain would be represented by the reaction... 

Use zero-order Markov statistics to evaluate the probability of isotactic, syndio-tactic, and heterotactic triads for the series of p values spaced at intervals of... 

The probabilities give the fractions of the three different types of triads in the polymer. 

If the fractions of triads could be measured, they either would or would not lie on a single vertical line in Fig. 7.9. If they did occur at a single value of p, this would not only give the value of p (which could be obtained from the fraction of one kind of triad), but would also prove the statistics assumed. If the fractions were not consistent with a single p value, higher-order Markov statistics are indicated. 

Figure 7.9 Fractions of iso, syndio, and hetero triads as a function of p, calculated assuming zero-order Markov (Bernoulli) statistics in Example 7.7.

To investigate the triads by NMR, the resonances associated with the chain substituent are examined, since structures [XV] -[XVII] show that it is these that experience different environments in the various triads. If dyad information is sufficient, the resonances of the methylenes in the chain backbone are measured. Structures [XIII] and [XIV] show that these serve as probes of the environment in dyads. 

The area under one of the methyl peaks is proportional to the concentration of the corresponding triad. 

Table 7.9 lists the estimated fractions of dyads of types m and r and the fractions of triads of types i, s, and h. These fractions represent the area under a specific peak (or four peaks in the case of the meso dyads) divided by the total area under all of the peaks in either the dyad or triad category. As expected for the sample labeled isotactic, 89% of the triads are of type i and 87% of the dyads are of type m. Likewise, in the sample labeled syndiotactic, 68% of the triads are s and 83% of the dyads are r. 

Table 7.9 The Fractions of Meso and Racemic Dyads and Iso, Syndio, and Hetero Triads for the Data in Fig. 7.10...

The number of iso triads in a sequence of nj iso repeat units is nj - l,and the number of syndio triads in a sequence of n syndio repeat units is n - 1. We can verify these relationships by examining a specific chain segment [XVIII] ... 

In this example both the iso and syndio sequences consist of eight repeat units, with seven triads in each. The repeat unit marked is counted as part of each type of triad, but is itself the center of a hetero triad. 

With these definitions in mind, we can immediately write expressions for the ratio of the total number p of iso triads to the total number of syndio triads ... 

Use the dyad and triad fractions in Table 7.9 to calculate the average lengths of isotactic and syndiotactic sequences for the polymers of Fig. 7.10. Comment on the results. 

Since the total numbers of dyads and triads always occur as ratios in Eqs. (7.73) and (7.74), both the numerators and denominators of these ratios can be divided by the total number of dyads or triads to convert these total numbers into fractions That is, p-Jp = Pi/Ps- Thus the fractions in Table 7.9... 

This type of analysis adds nothing new to the picture already presented by the dyad and triad probabilities. It is somewhat easier to visualize an average sequence, however, although it must be remembered that the latter implies... 

As apparent from structure [XVIII], a hetero triad occurs at each interface between iso and syndio triads. The total number of hetero triads, therefore, equals the total number of sequences of all other types = SNnj +... 

In Figure 1, the pairs (or triad) of phases that form ia the various multiphase regions of the diagram are illustrated by the corresponding test-tube samples. Except ia rare cases, the densities of oleic phases are less than the densities of conjugate microemulsions and the densities of microemulsions are less than the densities of conjugate aqueous phases. Thus, for samples whose compositions He within the oleic phase-microemulsion biaodal, the upper phase (ie, layer) is an oleic phase and the lower layer is a microemulsion. For compositions within the aqueous phase-microemulsion biaodal, the upper layer is a microemulsion and the lower layer is an aqueous phase. When a sample forms two layers, but the amphiphile concentration is too low for formation of a middle phase, neither layer is a microemulsion. Instead the upper layer is an oleic phase ("oil") and the lower layer is an aqueous phase ("water"). 

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