Examples of Nonequivalence

There are instances where some or all parts of the concept of equal reactivity of functional groups are invalid [Kronstadt et al., 1978 Lovering and Laidler, 1962], The assumption of equal reactivities of all functional groups in a polyfunctional monomer may often be incorrect. The same is true for the assumption that the reactivity of a functional group is 

Polymerization of terephthalic acid with 4,6-diamino-l,3-benzenediol via oxazole formation (Eq. 2-219) proceeds with a sharp and continuous decrease in reaction rate with increasing polymer molecular weight [Cotts and Berry, 1981]. Reaction becomes progressively more diffusion-controlled with increasing molecular size due to the increasing rigid-rod structure of the growing polymer. 

Trifunctional monomers constitute an important class of monomers. One often encounters such reactants in which the various functional groups have different reactivities. Thus, the polyesterification of glycerol (VII) with phthalic anhydride proceeds with incomplete 

Kinetic analysis of a step polymerization becomes complicated when all functional groups in a reactant do not have the same reactivity. Consider the polymerization of A—A with B—B where the reactivities of the two functional groups in the B—B reactant are initially of different reactivities and, further, the reactivities of B and B each change on reaction of the other group. Even if the reactivities of the two functional groups in the A—A reactant are the same and independent of whether either group has reacted, the polymerization still involves four different rate constants. Any specific-sized polymer species larger than dimer is formed by two simultaneous routes. For example, the trimer A—AB—B A—A is formed by 

The two routes (one is Eqs. 2-37b and 2-37c the other is Eqs. 2-37a and 2-37d) together constitute a complex reaction system that consists simultaneously of competitive, consecutive and competitive, parallel reactions. 

2-2d Nonequivalence of Functional Groups in Polyfunctional Reagents 2-2d-1 Examples of Nonequivalence 

4-tolylene diisocyanate several factors cause the reactivities of the two fimctional groups to differ. These can be discussed by considering the data in Table 2-3 on the reactivities of various isocyanate groups compared to that in phenyl isocyanate toward reaction with 

TABLE 2-3 Reactivity of Isocyanate Group with -C4H90H  

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These three unique binding sites represent the second example of nonequivalence in the reovirus core structure. While site iii is partially similar to site ii, sites i and ii are entirely different both in terms of the secondary structure and the pattern of charged/hydrophobic/polar residues that the XI surface presents to g2. a2-i lies over the middle of a XI-A molecule, and a2-ii bridges from the middle of a Xl-B across to the carboxy-terminal part of a Xl-B from another decamer. a2-iii lies on the XI shell directly on an icosahedral 2-fold axis in one of two equally-likely, two-fold related orientations. Consequently, a2-iii has not been built into the 3.6A electron density maps, and instead a a2-ii model has been docked onto that site. It is clear, however, that the various versions of a2 differ only at the interface with the XI surface. The differences between a2-i and ii are subtle, and the most drastic change is an unravelled helix (residues 39-46) in cj2-ii with respect to a2-i. 

Scheme 1.2 Examples of nonequivalency of a-substituents in lithium enolates 4 and 5, rhodium enolate 6, and palladium enolate 7.

A nice example of this teclmique is the detennination of vibrational predissociation lifetimes of (HF)2 [55]. The HF dimer has a nonlinear hydrogen bonded structure, with nonequivalent FIF subunits. There is one free FIF stretch (v ), and one bound FIF stretch (V2), which rapidly interconvert. The vibrational predissociation lifetime was measured to be 24 ns when excitmg the free FIF stretch, but only 1 ns when exciting the bound FIF stretch. This makes sense, as one would expect the bound FIF vibration to be most strongly coupled to the weak intenuolecular bond. 

The problem of which the example in Sec. 2 represents a very special case can be stated as follows Given the collection of figures [ ], the permutation group H and the content (k,H,m), determine the number of nonequivalent configurations of content (k,Jl,m) with... 

As an example of the prevalence of high-symmetry structures we can take the closest packings of spheres only in the cubic and the hexagonal closest-packing of spheres are all atoms symmetry equivalent in other stacking variants of closest-packings several nonequivalent atomic positions are present, and these packings only seldom occur. 

In the above examples two NMR signals will be observed because they have two sets of nonequivalent one with methyl protons and the other marked with b. 

Temperature reduction generally provides a severalfold enhancement of nonequivalence magnitude (15,16,19). Cocaine (3) at 20°C shows methylphenylcarbinol-induced nonequivalence in Hj and Hj, and in the A-methyl and 0-methyl resonances of 0.14, 0.03, 0.01, and 0.05 ppm, respectively (15). On lowering the temperature to -40°C, these differences increase to 0.47, 0.06, 0.12, and 0.17 ppm. Only the nonequivalence for Hs changes in sense (zero nonequivalence is observed for H5 at 0°C). Although the increase in nonequivalence magnitude with a reduction of temperature can be attributed in some cases to an increase in the equilibrium constants for CSA-solute association, such enhancement is observed even when the CSA is present in such excess as to cause essentially complete solvation of the enantiomeric solutes (doubtless 3 is such an example). Here, temperature reduction must also increase the intrinsic spectral differ-... 

Very recently (51), nonequivalence has been found in a variety of additional monobasic solutes whose configurational analysis was thought earlier to lie outside the scope of the CSA technique. 2-Butanol, for example, when dissolved in benzene saturated with TFAE, shows nonequivalence in both methyl resonances. A variety of other chiral and prochiral compounds such as 2-propanol, methyl 2-propyl sulfide, 2-aminobutane, and 2-methyl-1-butanol show nonequivalence for their enantiotopic methyl groups under these conditions. The magnitudes of nonequivalence in these instances are small (0.02-0.03 ppm) but, as illustrated in Figure 4 for enriched 2-butanol,... 

Granot and Reuben report an example of an aqueous chiral shift reagent. In water, several proton resonances of norepinephrine exhibit nonequivalence in the presence of cobaltous adenosine-5 -triphosphate (101). 

What happens for a nonracemic mixture of enantiomers Is it possible to calculate the values of the chiral properties of the solution from knowledge of the properties of the enantiopure compound In principle, yes, on the condition that there is no autoassociation or aggregation in solution. Then, the observed properties will be simply the weighted combination of the properties of two enantiomers. A nice example of where this normal law may be broken was discovered by Horeau in 1967 it is the nonequivalence between enantiomeric excess (ee) and optical purity (op, with op = [a]exi/[ ]max) for 2,2-methylethyl-succinic acid. In chloroform op is inferior to ee, while in methanol op = ee. This was explained by the formation of diastereomeric aggregates in chloroform, while the solvation by methanol suppresses the autoassociation. 

All nuclear multiplet structures due to coupling of nonequivalent nuclei are, as noted earlier, subject to effects on line shapes by chemical or positional exchange. For those multiplet structures arising from coupling of nuclei, one of which has a nonzero nuclear quadrupole moment, effects of quadrupole relaxation must be considered. For example, if a proton or fluorine atom is bonded to a nitrogen nucleus (I = 1), a triplet resonance will be expected in the proton or fluorine spectrum. For observation of this fine structure it is necessary that the lifetimes of the nuclear spin states of nitrogen (m = 1, 0, —1) be greater than the inverse frequency separation between multiplet components, i.e., t > l/ANx (106). The lifetimes of N14 spin states can become comparable to or less than 1 /A as a result of quadrupole relaxation. When the N14 spin-state lifetimes are comparable... 

Examples of kinetic analysis of NMR spectra in the transition between slow and fast exchange (on the NMR time scale) are somewhat limited. Treatment of fluorine exchange in sulfur tetrafluoride is selected here because this exchange process exemplifies the type of kinetic process ideally suited to NMR study. The fluorine atoms of the two nonequivalent environments in this molecule of C2v symmetry give rise to two triplets under conditions of very slow exchange at temperatures below —85° (at 40 Mc/sec). 

Protons that are chemically equivalent but magnetically nonequivalent are indicated by, for example, A A. The examples of such systems given below illustrate the medtod. This system for designating spin systems is merely a labeling device. The appearance of actual spectra will depend on die magnitude of die various J values. Nevertheless this is a convenient and common way of categorizing coupled proton systems. 

Some other typical examples of 1,2,4-trioxolanes with nonequivalent peroxidic oxygen atoms are shown in Figure 3 <1995LA1571>. 

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