Gas-phase relaxation

NMR Relaxation Behavior of Perfluorinated Gases 3.5.3.1 Introduction to Gas Phase Relaxation... 

Fig. 12. Vertical ionisation energies, Fermi (E.) and vacuum levels (V. L.) for gaseous (1), condensed and chemisorbed phases of (a) benzene, (b) acetylene and (c) ethylene, all plotted relative to cr-orbital ionisation potentials (I. P.) for the gas phase. Relaxation shifts are given by the vacuum level shifts while bonding shifts are given by relevant jr-orbital shifts. [Reproduced with permission from J. E. Demuth and D. E. Eastman, Phys. Rev. Letters 32, 1123 (1974)]...

Comparing FTMS with Fourier transform nuclear magnetic resonance (FTNMR), we first notice how the frequency range to be covered here is very large. Second, relaxation in NMR is invariably linked with the interaction among liquid-phase or solid-phase molecules. In the gas phase, relaxation depends on the vacuum and on the stability of the ions being observed. If the vacuum is not sufficient, collisions slow the ions and their movement becomes incoherent. The observation of an ion is also limited to its lifetime. 

For a comparison of these theoretical results with experiment one needs to deal with the troublesome two-body rate ko, which in V-T transfer is extremely sensitive to potential parameters. We choose to eliminate kg by relying on gas-phase relaxation measurements, which is not too restrictive as the most interesting exjjeriments, from a theoretical point of view, are those that measure the density dep>endence of the relaxation time. 

Since the absolute value of the vibrational energy relaxation rate is very difficult to calculate precisely, even in the gas phase, it is preferable, for comparison with experiment, to eliminate this variable using measured gas-phase relaxation rates. 

In the low density gas where interactions are binary, the inverse relaxation time is proportional to density, allowing the definition of a gas-phase relaxation rate constant /Cg = (P i) for sufficiently small density. This linear law... 

Nevertheless, for energy relaxation, exjyerimental similarities between matrix and liquid (or gas) phase relaxation have been noticed. Thus, for example, the semiempirical Legay s law correlating log( l/T,) to J (the nearest rotational quantum number to resonance) for hydrides in matrices is actually contained in gas-phase calculations, which explain in particular why deuterated compounds relax more slowly, as observed in all phases. 

One of the earliest properties of xenon studied by NMR was the gas-phase relaxation, which had been investigated in a detail as early as 1961. Xenon was observed to have a T relaxation time that is inversely dependent on the pressure, indicating the presence of a strong spin-rotation interaction. " Detailed studies of xenon relaxation in the presence of paramagnetic gases has been studied in detail by the Jamesons. 

Chann et examined the gas-phase relaxation of xenon at densities below 14amagat using a number of different gas mixtures. They concluded that the spin-rotation interaction is responsible for relaxation at low densities and determined a relaxation rate of the form... 

Within physical chemistry, the long-lasting interest in IR spectroscopy lies in structural and dynamical characterization. Fligh resolution vibration-rotation spectroscopy in the gas phase reveals bond lengths, bond angles, molecular symmetry and force constants. Time-resolved IR spectroscopy characterizes reaction kinetics, vibrational lifetimes and relaxation processes. 

Perturbation or relaxation techniques are applied to chemical reaction systems with a well-defined equilibrium. An instantaneous change of one or several state fiinctions causes the system to relax into its new equilibrium [29]. In gas-phase kmetics, the perturbations typically exploit the temperature (r-jump) and pressure (P-jump) dependence of chemical equilibria [6]. The relaxation kinetics are monitored by spectroscopic methods. 

A general limitation of the relaxation teclmiques with small perturbations from equilibrium discussed in the previous section arises from the restriction to systems starting at or near equilibrium under the conditions used. This limitation is overcome by teclmiques with large perturbations. The most important representative of this class of relaxation techniques in gas-phase kinetics is the shock-tube method, which achieves J-jumps of some 1000 K (accompanied by corresponding P-jumps) [30, and 53]. Shock hibes are particularly... 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

Suvernev A. A., Temkin S. I. Spin-rotational NMR-relaxation of spherical molecules in gas phase, Chem. Phys. Lett. 154, 49-55 (1989). 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

It has been shown that photoexcitation of the guanine-cytosine (G-C) base pair leads to proton transfer [231], Watson-Crick (WC) base pairs have excited state lifetimes much shorter than other non-WC base pairs indicating once again that the natural occurring WC base pairs are more photostable than other alternative configurations [115, 118, 232-235], Much work has been done in the gas phase where many different base pair isomers exist. The ultrafast relaxation of the WC base pair has also been confirmed in solution using fluorescence up-conversion measurements [117]. 

Cheremisinoff and Davis (1979) relaxed these two assumptions by using a correlation developed by Cohen and Hanratty (1968) for the interfacial shear stress, using von Karman s and Deissler s eddy viscosity expressions for solving the liquid-phase momentum equations while still using the hydraulic diameter concept for the gas phase. They assumed, however, that the velocity profile is a function only of the radius, r, or the normal distance from the wall, y, and that the shear stress is constant, t = tw. ... 

Droplet suspensions (gas-liquid, two-component system) Since the inertia of a liquid suspended in the gas phase is higher than the inertia of the gas, the time for the displacement of liquid under the pressure waves should be considered. Temkin (1966) proposed a model to account for the response of suspension with pressure and temperature changes by considering the suspensions to move with the pressure waves according to the Stokes s law. The oscillatory state equation is thereby approximated by a steady-state equation with the oscillatory terms neglected, which is valid if the ratio of the relaxation time to the wave period is small, or... 

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