Reorganization dynamics first order

Dynamics of typical reorganizing systems that have been investigated using NMR line shape analysis include first-order degenerate processes such as degenerate bond rotations (equation 1), first-order interconversions where A and B are different species (equation 2), bimolecular group transfer (equation 3) and mutual exchange (equation 4). 

Each density matrix equation 16 is written for a single chemical species. The term responsible for dynamic effects is Ee given in equation 21 for the latter species undergoing a single reorganization process with pseudo-first-order rate constant k1 and e(ae) denotes the density matrix after a particular reorganization process has taken place. 

We have shown how organolithium compounds adopt a variety of structures which differ in state of aggregation and degree of solvation. These species interconvert rapidly at equilibrium by different mechanisms, such as intermolecular C—Li exchange ligand transfer and dissociation-recombination processes as well as first-order reorganizations such as inversion and rotation. Dynamics of many of these processes have been determined by our methods of NMR line shape analysis. 

The main utility of recent molecular dynamics calculations has been first to determine if the assumption of quadratic free energy curves holds and second, to calculate the reorganization free energy in order to test Eqs. (24) and (25). In principle, a molecular dynamic simulation of the free... 

An example of typical ESR spectra, measured in the first derivative mode, is shown in Fig. 12. Just like NMR, ESR can be used to detect phase transitions and to study the orientation and dynamics of liquid crystals. The spectra shown in Fig. 12, for example, are from a study comparing the dynamics of the spin label at the end of the polymer chain and the freely dissolved spin probe in a liquid-crystalline polyether by continuous wave ESR (Fig. 12) and 2D Fourier transform ESR experiments [137]. The end label showed smaller ordering and larger reorientational rates than the dissolved spin probe. Furthermore, it was demonstrated that the advanced 2D FT ESR experiments (see below) on the end-labeled polymer chain could not be explained by the conventional Brownian model of reorientation, although this model could explain the ID spectra. This led to the development of a new motional model of a slowly relaxing local structure, which enabled differentiation between the local internal modes experienced by the end label and the collective reorganization of the polymer molecules around the label. The latter was shown to be slower by two orders of magnitude. 

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