Barrier entropic

Flexible six- and eight-7t-electron systems would impose an entropic barrier to concerted 10-7i-electron concerted reactions. Most of the examples, as in the cases above, involve cyclic systems in which the two termini of the conjugated system are held close together. 

If we now assume that this surface at temperature T is in equilibrium with a gas then the adsorption rate equals the desorption rate. Since the atoms/molecules are physisorbed in a weak adsorption potential there are no barriers and the sticking coefficient (the probability that a molecule adsorbs) is unity. This is not entirely consistent since there is an entropic barrier to direct adsorption on a specific site from the gas phase. Nevertheless, a lower sticking probability does not change the overall characteristics of the model. Hence, at equilibrium we have... 

For concentrations between the Rouse and reptation regimes, D can depend more sensitively on N due to the entropic barrier mechanism [6, 64]. In this crossover region, D can be written as... 

The deposition of each stem of m repeat units can be treated [8,41] as a set of m equilibria. While this generalization appears to account for more local details, the general conclusions are the same as in the LH theory. In realistic situations, we expect nonsequential deposition of repeat units into various stems. These partially formed stems will then sort out through entropic barriers to attain the lamellar thickness. We remrn to this issue in Section VII. 

Fig. 21. Indirect carboxylate-zinc interactions through bridging hydroxyl groups (Fig. 20) orient the nucleophilic lone electron pair (stippled dumbbell) of zinc-bound solvent. This reduces the conformational disorder about the Zn -O axis, and thereby reduces the entropic barrier to catalysis (Merz, 1990).

Analysis of the activation parameters for the different encapsulated substrates reveals that the source of catalysis is more complex than simply a reduction of the entropy of activation, since different effects are observed for substrates 26,27,30. While the rate acceleration for the encapsulated 26 was exclusively due to lowering the entropic barrier, for 27 and 30 a decrease in the enthalpic barrier for rearrangement is observed in addition. It is possible that, for 27 and 30 binding into the narrow confines of the metal-ligand assembly induces some strain on the bound molecules, thereby raising their ground-state energies compared to those of the unbound... 

For these spin-forbidden transitions, with AS = 2, this assumption is very likely invalid and the process is nonadiabatic, i.e., k < 1. If it is assumed that the entire entropic barrier of the quintet-singlet transition is due to nonadiabaticity, a minimum value of k 10 4 is obtained. 

The assumption that the entropic barrier to the spin state transition is due entirely to spin-forbidden nonadiabaticity is equivalent to assuming that the transition state has the structure of the high-spin state. This is unlikely to be the case, and insofar as the assumption is invalid, the minimum value of k is increased. There is some evidence from the volume of activation for the spin state transition that the transition state lies well along the reaction coordinate between the low-spin and high-spin states. This novel experiment was accomplished independently by two groups with use of the photoperturbation technique with the sample subjected to variable pressure 44, 115). In the two cases reported, the volume of activation places the transition state about midway between the low-spin and high-spin states. If this is correct then there will be a considerable chemical contribution to the... 

In recent years, direct, time-resolved methods have been extensively employed to obtain absolute kinetic data for a wide variety of alkyl radical reactions in the liquid phase, and there is presently a considerable body of data available for alkene addition reactions of a wide variety of radical types [104]. For example, rates of alkene addition reactions of the nucleophilic ferf-butyl radical (with its high-lying SOMO) have been found to correlate with alkene electron affinities (EAs), which provide a measure of the alkene s LUMO energies [105,106]. The data indicate that the reactivity of such nucleophilic radicals is best understood as deriving from a dominant SOMO-LUMO interaction, leading to charge transfer interactions which stabilize the early transition state and lower both the enthalpic and entropic barriers to reaction, with consequent rate increase. A similar recent study of the methyl radical indicated that it also had nucleophilic character, but its nucleophilic behavior is weaker than that expressed by other alkyl radicals [107]. 

In the system with three CF2 groups, i.e. 22, the radical takes on perfluoroalkyl character and the impact on cyclization rate is magnified still further. The dominant factor which has been credited for giving rise to the high reactivities of perfluoro-n-alkyl radicals in their additions to alkenes, particularly to electron-rich alkenes, is their high electrophilicities. That is, charge transfer interactions, e.g. [(CF3CF2CF2) s (alkene)l5+]] stabilize an early transition state and lower both the enthalpic and entropic barriers to reaction. 

Cyclobutanes are usually more difficult than cyclopropanes to prepare by cyclization. Although their ring strain is as high as that of cyclopropanes, more bonds must assume a suitable conformation for cyclobutane formation, resulting in a higher entropic barrier (Table 9.1). 

Quantum mechanical calculations in the gas phase and DMSO solution at different temperatures can highlight the hazards of standard 0 K gas-phase calculations.259 For the Wittig reaction, a small barrier in the potential energy curve is transformed into a significant entropic barrier in the free energy profile, and the formally neutral oxaphosphetane intermediate is displaced in favour of the zwitterionic betaine in the presence of DMSO. 

The effects of the solvent and finite temperature (entropy) on the Wittig reaction have been studied by using DFT in combination with molecular dynamics and a continuum solvation model.62 The free energy profile has been found to have a significant entropic barrier to the addition step of the reaction where only a small barrier was present in the potential energy curve. 

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