Scrambling equilibria

One is generally interested in the enthalpies of scrambling reactions since these may be measured thermochemically and thus brought into relationship with equilibrium constants. Real scrambling equilibria, however, deviate more or less from the ideal random case. And, in order to be able to calculate enthalpies, it is assumed that for large values of the enthalpy, (JS)real (JS)rand. Accordingly, we may now estimate the enthalpy of a real scrambling reaction. 

Scrambling equilibria in mixtures of dimethyl selenide and dichloro-diselenide as well as dimethyl diselenide and dichloro diselenide have been investigated recently (103). The reactions observed at room temperature to occur in such mixtures are scrambling of methyl groups and chlorine atoms on selenium as well as condensation polymerization resulting from the elimination of methyl chloride. 

There are three important categories in the practical chemistry of scrambling equilibria (i) all-neso model systems, (ii) scrambling of bridging groups with each other and with monofunctional substituents and (iii) the scrambling of these between different central atoms. 

The families of a,o)-dimethoxyl poly(methylphosphonates) for which p 2, alkyl polyphosphates for which p = 2, sodium polyphosphates for which p = 3 and aliphatic hydrocarbons for which p % 2 are examples of systems for which more than (v — 1) equilibrium constants are needed to represent the scrambling equilibria involving the chain population (since p > 1). 

The electrochemistry of the above systems once again involves a two-electron process, involving two reversible one-electron steps. The difference in potential between these steps is given by AE°. This value is made up of a statistical component associated with a valence scrambling equilibrium as well as a component that reflects the electrostatic repulsion between the metal centers. 

They found that deuterium labeled 2-phenyl-5-methoxy-4-[(methoxy-d3)-carbonyl]oxazole (7) scrambled on heating to give a 1 1 equilibrium mixture of 7 and the corresponding rearranged ester 9 ... 

To the left of the peak where the tubules have shorter lengths, c, i is less than Cii so the net flux is from i-mers to (i — l)-mers. To the right of the peak, the distribution of polymer length falls off, and c, i is greater than Cj. Therefore, the net flux will be in the opposite direction. The combined action of these fluxes wiU result in the broadening of the peak distribution. Eventually, the peak will completely disappear due to the relationships among the concentrations of each polymer species. In this respect, the initial polymer-protomer equilibrium is maintained by the balanced rates of protomer addition and loss from polymer ends, and the protomers will scramble or diffuse from one polymer to another. Indeed, even after the polymer length redistribution reaches its thermo-... 

Thermal decomposition of a doubly labelled azidotriazole gave rise to the open-chain triazine (117) in which the labels were not scrambled. Laser flash photolysis of the triazole leads to (117) within 20 ns with no observable intermediate. Ab initio calculations indicate that a dynamic equilibrium between the open-chain triazine (117) and a cyctic nitrene (118), as originally proposed, is highly disfavoured. 

The thermodynamic stabilities of phenonium ions relative to the parent have been determined in the gas phase by measuring the position of the equilibrium between (46) and (47)7 The results followed a Yukawa-Tsuno relationship with a p value of -12.6 and an r+ value of 0.62, the general behaviour being more like benzenium ions than benzyl cations, with tt-delocalization less effective than in benzyl cations. A theoretical study of the elimination of molecular H2 from the benzenium ion C6H7+ shows that the barrier to this process appears to be very small.The gas-phase Friedel-Crafts alkylation reaction of CF3C6L6+ (L = H or D) with C2L4 is accompanied by isotopic scrambling, which has been used to elucidate the mechanism of this process. A theoretical calculation shows that the lifetime of triplet phenyl cation must be very short. ... 

The exchange in the alkoxyamine-based polymer occurs in a radical process that is tolerant of many functional groups. The exchange process is therefore applicable to polymers with various functional groups. TEMPO-based polyester 43 and polyurethane 44 were synthesized for studies of the scrambling of disparate polymers imder thermodynamic control (Fig. 8.11) [37], Two kinds of TEMPO-based polymers were mixed and heated in a closed system. After 24 hours when the crossover reaction achieved equilibrium, GPC and NMR analyses revealed that they were totally scrambled through bond recombination on the TEMPO units. 

The initially observed perturbation (or equilibrium isotope effect) will disappear as isotopic scrambling (or mixing) subsequently occurs. This is illustrated above for the malic enzyme note the initial displacement of the equilibrium toward malate, followed by readjustment of the system to its flnal equilibrium position. The magnitude of the initial perturbation provides information on the occurrence of kinetic isotope effects and the nature of the rate-limiting step in an enzymatic process. See also Kinetic Isotope Effect Solvent Isotope Effect... 

Readout of the ligand information by a substrate is achieved at the rates with which L and S associate and dissociate it is thus determined by the complexation dynamics. In a mixture of ligands Li, L2. .. L and substrates Si, S2. . - S , information readout may assume a relaxation behaviour towards the thermodynamically most stable state of the system. At the absolute zero temperature this state would contain only complementary LiSi, L2S2. .. L S pairs at any higher temperature this optimum complementarity state (with zero readout errors) will be scrambled into an equilibrium Boltzmann distribution, containing the corresponding readout errors (LWS , n n ), by the noise due to thermal agitation. 

The establishment of the equilibrium state is also confirmed by a scrambling experiment using the dimer 3 with one of the Cgo cages labeled by He encapsulation. As shown in Scheme 4, the HSVM treatment of unlabeled (empty) Cgo with labeled 3 for 30 min in the presence of KCN as a catalyst resulted in scrambling of labeled Cgo in both monomer and in dimer 3 in a ratio of 3 7, as examined by He NMR spectroscopy [23]. The structure of... 

Similarly, condensation of a mixture of CsHe and C3D6 with nickel vapor resulted in isotopic scrambling. The intraligand isomerizations may be explained in terms of a 1,3-hydrogen shift via a nf-allyl nickel hydride complex in equilibrium with a ir-propene complex, e.g.,... 

Our study of propene-J-13C, -2-13C, and -5-13C reacting on zeolite HZSM-5 clearly shows that the isopropyl cation is not formed in measurable concentration as a persistent species (45). Furthermore, there is no label scrambling of the 2 position, although 1,3-label scrambling is facile on the zeolite. This strongly argues against a free isopropyl cation—even as a transient intermediate At low temperature, the equilibrium structure of propene is a 77 complex 22 with the Brpnsted site. This mode of coordination... 

The "scrambling reaction of POCl3 with the crystalline P2Os-net-work provides an excellent example of the applicability of the Lp.g.f. approach (72). POCl3 causes a partial degradation of the network and the equilibrium state resembles exactly a threefunctional polycondensation. The ratio R = [C1]/[P] is known from the experiment and from stoichiometry one gets... 

The Ce isomer distribution—2-methylpentane (28%), 3-methylpentane (14%), and w-hexane (32%)—is very far from thermodynamic equilibrium, and the presence of these isomers indicates that both isopropyl cation 31 [Eq. (5.62)] and n-propyl cation 34 [Eq. (5.63)] are involved as intermediates [as shown by 13C(2)—13C(1) scrambling in the stable ion147]. 

Similar three-electron-bonded intermediates must also be formed in the well-known thiyl radical-induced scrambling of disulfides (Owen and Ellis 1973). Mechanistic details have been studied using the pulse radiolysis technique which allowed the identification the three-bonded intermediate and the determination of some equilibrium constants, but also gave evidence that this system may be more complex than described by reactions (42) and (43) (Boni-facic and Asmus 1984). 

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