Cyclization, kinetic theory

In summary, a formulation of the equilibrium cyclization and ring opening rates of a polymer chain has been obtained using the one-dimensional representation of the potential. These, when combined with the steady-state rate of the Wilemski-Fixman-Doi theory, " give an appropriate description of the cyclization kinetics. 

Theoretical evidence [Hartree-Fock (RHF) calculations and density functional theory] has been obtained for a concerted mechanism of oxirane cleavage and A-ring formation in oxidosqualene cyclization. A common concerted mechanistic pathway has been demonstrated for the acid-catalysed cyclization of 5,6-unsaturated oxiranes in chemical and enzymic systems. For example, the conversion of (24) into (26) proceeds via (25) and not via a discrete carbocation (27). Kinetic studies and other evidence are presented for various systems. 

Furthermore, FO theory can only treat reactions under kinetic control. Reactions under thermodynamic control may give different results. Thus, calculations indicate that kinetic control favors 6-endo cyclization of 2-oxo-5-hexenyl radicals58 whereas thermodynamic control gives 5-exo cyclization.59... 

These and related phenomena can be explained in terms of the thermodynamic theory of macrocyclics distribution, formulated by Jacobson and Stockmayer9) and its kinetic extension 10). The Jacobson-Stockmayer theory, relating the distribution of cyclic oligomers to the conformational probability of ring closure, does not take into account kinetic limitations and has mostly been used as a convenient tool for studying the conformation of macromolecules in solution s). A number of papers appeared in which distribution of cyclic oligomers was studied with this aim and which ignored mechanistic and kinetic aspects of the cyclization processes. 

This apparent duality has led to certain misunderstanding and confusion and for the reader less acquainted with this field the relation between theoretical distribution predicted by Jacobson-Stockmayer theory and the distributions observed in real systems (frequently different from those predicted by the theory) could be not clear. Thus, in this section we describe the theories and then explain major experimental results in terms of the thermodynamics and kinetics of cyclization. 

We first present the thermodynamic theory of cyclization and then discuss possible deviations which prevent establishing thermodynamically controlled distributions and lead to kinetic control of cyclization. 

There has been a mechanistic investigation of the possible intermediates in the thermal C -C cyclization of enyne-carbodiimides [424]. Kinetic studies of enyne-carbodiimides with electron-withdrawing substituents gave a nonlinear Hammett correlation. This supported a concerted/nonpolar mechanism to produce a carbene intermediate. However, when electron-donating substituents were present, the results indicated a polar cyclization mechanism giving a carbene with zwitte-rionic character. Earlier, theoretical investigations by density functional theory (DFT) and NBO analysis had supported a diradical intermediate. 

The work of Stepto et al. [26-28] included two aspects, namely, the aforementioned experimental work and the theoretical work based on the so-called rate theory [27, 28]. The rate theory involves a set of kinetic differential equations, which are based on the time dependence of the concentrations of monomers and reaction products. In Stepto s approach the time dependence is converted into a dependence on the conversion. At first, the rate theory was elaborated for three-dimensional polycondensations excluding a significant influence of cyclization, and later, extended to two-dimensional polycondensations including cyclization. A detailed description of the complex equations is beyond the scope of this chapter, which is focused on the discussion of the consequences of Stepto s work. Three results are particularly important ... 

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