Intermolecular relaxation processes

The importance of intermolecular relaxation processes (Hertz, 1967) in the interpretation of proton-relaxation data necessitates a rather deep understanding of the mechanics of liquids. Thus the H nucleus, although most extensively used in work concerned with chemical shifts and spin coupling constants, was not really taken as a probe for the molecular dynamics of complex organic molecules. It is only very recently that there has been a significant increase in literature on 7", for protons in organic molecules (Hall and Preston, 1974) stimulated most likely by 13C relaxation work. The nC nucleus, however, developed to be the abundant nucleus of relaxation experiments for three main reasons ... 

Consider a closed system characterized by a constant temperature T. The system is prepared in such a way that molecules in energy levels are distributed in departure from their equilibrium distribution. Transitions of molecules among energy levels take place by collisional excitation or deexcitation. The redistribution of molecular population is described by the rate equation or the Pauli master equation. The values for the microscopic transition probability kfj for transition from ith level toyth level are, in principle, calculable from quantum theory of collisions. Let the set of numbers vr be vibrational quantum numbers of the reactant molecule and vp be those of the product molecule. The collisional transitions or intermolecular relaxation processes will be described by ... 

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

A detailed description of the laser-excited vibrational fluorescence method and further results on relaxation processes in methane, including V - R transfer, have been given in reference In this paper, too, a comparison is made between the experimentally obtained F - F rates and calculations for the repulsive intermolecular potential responsible for these transitions. 

The electronic states of the medium must be far enough removed from those of the solute in which the electronic relaxation processes are occurring. For example, in pure crystals the intermolecular coupling does appear to influence the radiationless processes.42"43... 

The DS method occupies a special place among the numerous modern methods used for physical and chemical analysis of materials because it enables investigation of relaxation processes in an extremely wide range of characteristic times (105—10 13 s). Although the method does not possess the selectivity of NMR or ESR, it offers important and sometimes unique information about the dynamic and structural properties of substances. DS is especially sensitive to intermolecular interactions, and therefore cooperative processes may be monitored. It provides a link between the properties of the bulk and individual constituents of a complex material (see Fig. 1). 

The kinetic equations serve as a bridge between the microscopic domain and the behavior of macroscopic irreversible processes through the description of hydrodynamics in terms of intermolecular collisions. Hydrodynamics can specify a large number of nonequilibrium states by a small number of reproducible properties such as the mass, density, velocity, and energy density of a fluid conserved during the collision of molecules. Therefore, the hydrodynamic equations can describe a wide range of relaxation processes of nonequilibrium states to equilibrium state. We call such processes decay processes represented by phenomenological equations, such as Fourier s law of heat conduction. The decay rates are determined by the transport coefficients. Reliable transport coefficients provide microscopic and macroscopic information, and validate the results of molecular dynamics. 

Since the pulse time is so short (see Sec. 3.6.2.2.3) one can coherently excite many vibrational modes at a time and monitor relaxation processes in real time. The first reported femtosecond time-resolved CARS experiments (Leonhardt et al., 1987 Zinth et al., 1988) showed beautiful beating patterns and fast decays of the coherent signal for several molecular liquids. The existence of an intermolecular coherence transfer effect was suggested from the analysis of the beating patterns (Rosker et al., 1986). Subsequent studies by Okamoto and Yoshihara (1990) include the vibrational dephasing of the 992 cm benzene mode. A fast dephasing process was found that is possibly related to... 

K and from 50 to 10 000 Hz, and a semicircle was found, which indicates a single relaxation process. Another increment of xm" and xm is found below 6 K, and this type of increment is also found in other systems [107-109], It is suggested that intermolecular interactions in such low temperature regions may give rise to the phenomena. 

As will become obvious, after considering the different relaxation mechanisms, the intramolecular relaxation is more easily related to properties of individual molecules, whereas the intermolecular relaxation requires reference to a relative motion and collective processes for a proper description. 

The theoretical analysis of the relationship between small-scale relaxation processes in polymers PL reveals just these processes) and the intra- or intermolecular inter-actions shows that these processes are sensitive to various changes in the number (probability of formation) of intra- or interchain contacts in polymer solutions. The experimental data reveal that the intramolecular mobility (IMM) of the polymer in solution is highly susceptible to various conformational transformations of macro-molecules and to changes in the intermolecular interactions in complex multicom-... 

N relaxation in nitrobenzene has been studied at 14 and 32 MHz at temperatures between —10 and 60°C. (204) At low frequencies spin rotation interactions dominate and at lower temperatures intermolecular dipole-dipole interactions become important. However, at 32 MHz the predominant relaxation process is due to chemical shift anisotropy. (204)... 

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