Molecules with Ring Motions

A nonlinear molecule consisting of N atoms can vibrate in 3N — 6 different ways, and a linear molecule can vibrate in 3N — 5 different ways. The number of ways in which a molecule can vibrate increases rapidly with the number of atoms a water molecule, with N = 3, can vibrate in 3 ways, but a benzene molecule, with N = 12, can vibrate in 30 different ways. Some of the vibrations of benzene correspond to expansion and contraction of the ring, others to its elongation, and still others to flexing and bending. Each way in which a molecule can vibrate is called a normal mode, and so we say that benzene has 30 normal modes of vibration. Each normal mode has a frequency that depends in a complicated way on the masses of the atoms that move during the vibration and the force constants associated with the motions involved (Fig. 2). 

Thermodynamic Considerations. Most polymerisations are characterised by a reduction in entropy as a large number of monomer molecules with the freedom to move in three dimensions are joined together and ultimately constrained to a linear ID polymer chain, where motion is much more restricted. Hence, for a ROP to be thermodynamically favourable under such circumstances, ring strain is usually needed to provide an enthalpic driving force, A/Zrop, that overcomes the unfavourable TAArop term that contributes to AGrop [eqn (8.1)]. 

In the case of discussed molecules, it means that for the nucleobase molecules populating zero vibrational level for every vibration, the planar or nearly planar geometry (Fig. 21.3) is the most probable. Molecules with considerably nonplanar conformation of pyrimidine ring will populate higher vibrational levels. Therefore, we can estimate a fraction of molecules with essentially nonplanar geometry based on population of vibrational levels characterized by number 1 and higher. Similar approach is used for analysis of structure and vibrational spectra of molecules with large amplitude motions [34]. 

We discussed the structure of the repeated ring operator in Section VII.D and pointed out that it contains a variety of dynamic events such as a series of correlated collisions identical to those that appear in the singlet theory via the operators and R. These operators represent the correlated collisions of a single solute molecule with the solvent and serve to renormalize the single-particle motion. Other events in R represent the coupling of the motion of the two solute molecules. In view of this, it is convenient to introduce the propagator for independent motion of the pair... 

The use of NMR spectroscopy for probing molecules adsorbed on alumina dispersions is briefly cited. Soderlind and Blum [66] used deuterium NMR to probe the dynamics and structure of a surfactant (an alkylbenzenesulfonate, SHBS) adsorbed onto alumina. The phenyl ring was deuterium-labeled, and from the analysis of the lineshapes of H spectra, valuable information on the degree of motional freedom in the adsorbed layer was obtained. As deuterium possesses a quadrupole moment, it is sensitive to the orientation of the molecule with respect to the external magnetic field. This sensitivity generates a quadrupolar splitting, which is defined as the separation between the two allowed transitions for the deuterium nucleus. In liquid systems, the quadrupole interaction is averaged out, but for static systems powder... 

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