Rotational relaxation processes

Characteristic time of the a-process Rotational relaxation time in the Allegra model Characteristic time of /1-relaxation... 

Depending on the method of pumping, the population of may be achieved by — Sq or S2 — Sq absorption processes, labelled 1 and 2 in Figure 9.18, or both. Following either process collisional relaxation to the lower vibrational levels of is rapid by process 3 or 4 for example the vibrational-rotational relaxation of process 3 takes of the order of 10 ps. Following relaxation the distribution among the levels of is that corresponding to thermal equilibrium, that is, there is a Boltzmann population (Equation 2.11). 

The perturbation theory presented in Chapter 2 implies that orientational relaxation is slower than rotational relaxation and considers the angular displacement during a free rotation to be a small parameter. Considering J(t) as a random time-dependent perturbation, it describes the orientational relaxation as a molecular response to it. Frequent and small chaotic turns constitute the rotational diffusion which is shown to be an equivalent representation of the process. The turns may proceed via free paths or via sudden jumps from one orientation to another. The phenomenological picture of rotational diffusion is compatible with both... 

Vibrational broadening in [162] was taken into account under the conventional assumption that contributions of vibrational dephasing and rotational relaxation to contour width are additive as in Eq. (3.49). This approximation provides the largest error at low densities, when the contour is significantly asymmetric and the perturbation theory does not work. In the frame of impact theory these relaxation processes may be separated more correctly under assumption of their statistical independence. Inclusion of dephasing causes appearance of a factor... 

As the process of rotational relaxation is close to a correlated one (y 1) for both gases, according to (3.74) the aE cross-section is twice as large as oj. This result agrees with experiment and it appears that quasi-classical impact theory may be applied to description of rotational relaxation in moderately dense gases. 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

Only the radically symmetric (s-wave or 1 = 0) solution is of interest since rotational relaxation has been assumed to be very much more rapid than the processes of molecular diffusion or exciton transfer. The solution of eqn. (78) subject to the boundary conditions (68) and (69), in the steady-state where dp/dt = 0, leads to the density [129,140]... 

An interesting development in molecular rotational relaxation has been the microwave double-resonance method176-178. The technique permits the exploration of the fine detail of the processes which occur in collisions of polyatomic molecules, and results for a number of symmetric tops have been reported. For example, Oka has described experiments on NH3 in which inversion doublets for selected J values were pumped by high microwave power. Pumping disturbs the population of the inversion doublet, and also that of other doublets which are populated from the original pair by collision processes. By absorption measurements of other inversion doublets with steady state irradiation, Oka has shown that in NH3/NH3 collisions, transitions which are allowed by the electric dipole selection rules (A/ = 0, 1, + - —) are preferred. Oka s analysis indicates that relaxation is most favourable in collision with molecules having similar J values, which are termed rotational resonances (R-R transfer). For example the process... 

It has been postulated that methyl group relaxation times reflect energy differences between preferred conformations and the transition state for rotation. (32) Decreasing the number of diaxial 1,3-steric interactions lowers the energy of the preferred conformation but increases the energy of activation for the rotational process. Rotation rates are decreased but the efficiency of the relaxation process is enhanced, i.e. 71, is decreased. In Fig. 3 are shown the Tx data for a related series of steroids of interest to us. As can be seen, loss of 1,3-diaxial interactions does markedly reduce methyl Tx values. This is particularly evident for the change to an a/B-cis ring fusion as in compound [11]. 

The fluorescence spectrum is found to be markedly non-Boltz-mann and sharply peaked at the directly excited level throughout the laser pulse. This is due to two effects the competition between electronic quenching and rotational relaxation processes (4) and the short length of the laser pulse. Because the pulse is so short, steady state is not established throughout the upper rotational levels. The peaks of the fluorescence pulses from levels which are not directly excited by the laser lag the laser pulse peaks by one to four nanoseconds, depending on the energy gap between the given level and the directly excited level. 

The extremely fast quenching of C-0 An. by C-O is probably rotational relaxation of the highfy rotationaily excited C O photofragment. The slower process for C Oo some unknown combination of vibrational and electronic quenching and reaction. Likewise, contributions of vibrational and electronic relaxation to the observed quenching by Ar, 0-, and N2 are not determined. 

The first two of these processes, rotational and vibrational relaxation, do not usually cause a loss of fluorescence. The molecule is still in an electronically excited state and can radiate but at different wavelengths from the initial state. It is therefore possible to observe these relaxation processes by using some method to disperse or select the wavelength of the fluorescence. 

For the determination of product vibrational and rotational distributions, we must consider the time for vibrational or rotational relaxation by gas-phase collisions. This is not as strongly dependent on the nature of the products as it is for electronic quenching. Rotational relaxation is a much more efficient process than vibrational relaxation, requiring typically less than one hundred collisions to rotationally relax a molecule compared with several thousand collisions to bring about vibrational relaxation [76]. Thus, primary product vibrational energy distributions may be determined at pressures greater than 10-4 Torr, whilst much lower pressures are required to observe unrelaxed rotational state distributions. 

The second technique (method I of ref. 264) is to measure the relaxation. Here the infrared emission is observed from different points downstream from where the reagents are mixed in a fast-flow system. Even at the shortest times, rotational relaxation is complete, but the relaxation of the vibrational states can be followed and the distributions extrapolated back to yield a set of Rv. Pacey and Polanyi [265] have found small, but significant, differences between the Rv derived from a simple extrapolation and those determined using an analysis that allowed for the concurrent processes of reaction, diffusion, flow, radiation, and deactivation. Using a large-capacity sorption... 

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