Diffusivity rotational

Photoexcited fluorescence from spread monolayers may be studied [158,159] if the substance has both a strong absorption band and a high emission yield as in the case for chlorophyll [159]. Gaines and co-workers [160] have reported on the emission from monolayers of Ru(bipyridine)3, one of the pyridine ligands having attached C g aliphatic chains. Ruorescence depolarization provides information about the restriction of rotational diffusion of molecules in a monolayer [161], Combining pressure-area... 

Courtney S H, Kim S K, Canonica S and Fleming G R 1986 Rotational diffusion of stiibene in alkane and alcohol solutions J. Chem. See. Faraday Trans. 2 82 2065-72... 

We call the correlation time it is equal to 1/6 Dj, where Dj is the rotational diffusion coefficient. The correlation time increases with increasing molecular size and with increasing solvent viscosity, equation Bl.13.11 and equation B 1.13.12 describe the rotational Brownian motion of a rigid sphere in a continuous and isotropic medium. With the Lorentzian spectral densities of equation B 1.13.12. it is simple to calculate the relevant transition probabilities. In this way, we can use e.g. equation B 1.13.5 to obtain for a carbon-13... 

Three rotational diffusion coefficients, two polar angles 0 and T... 

Rotational diffusion coefficient, Dg, internal motion rate parameter, angle between the internal rotation axis and the internuclear axis... 

Isotropic rotational diffusion with one internal degree of freedom... 

Tao T 1969 Time-dependent fluorescence depolarization and Brownian rotational diffusion coefficients of macromolecules Biopolymers 8 609-32... 

Cross A J, Waldeck D H and Fleming G R 1983 Time resolved polarization spectroscopy level kinetics and rotational diffusion J. Chem. Phys. 78 6455-67... 

Ha T, Glass J, Enderle T, Chemla D S and Weiss S 1998 Hindered rotational diffusion and rotational ]umps of single molecules Phys. Rev. Lett. 80 2093-7... 

The full width at half height of these Lorentzian peaks is 4Drot- In this ease, one says that the individual peaks have been broadened via rotational diffusion. When the Doppler broadening ean not be negleeted relative to the eollisional broadening, the above integral... 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

This is obvious for the simplest case of nondeformable anisotropic particles. Even if such particles do not change the form, i.e. they are rigid, a new in principle effect in comparison to spherical particles, is their turn upon the flow of dispersion. For suspensions of anisodiametrical particles we can introduce a new characteristic time parameter Dr-1, equal to an inverse value of the coefficient of rotational diffusion and, correspondingly, a dimensionless parameter C = yDr 1. The value of Dr is expressed via the ratio of semiaxes of ellipsoid to the viscosity of a dispersion medium. 

A possible approach to interpretation of a low-frequency region of the G ( ) dependence of filled polymers is to compare it with a specific relaxation mechanism, which appears due to the presence of a filler in the melt. We have already spoken about two possible mechanisms — the first, associated with adsorption phenomena on a filler s surface and the second, determined by the possibility of rotational diffusion of anisodiametrical particles with characteristic time D 1. But even if these effects are not taken into account, the presence of a filler can be related with the appearance of a new characteristic time, Xf, common for any systems. It is expressed in the following way... 

Fig. 11a and b. Decay of the alignment echo height as a function of the mixing time x2 for different motional mechanisms, a Tetrahedral jumps as a model for conformational changes b Diffusive motion, the solid lines correspond to unrestricted rotational diffusion, the dashed lines to diffusion restricted to an angular region of 8°. Note the strong dependence of the decay curves on the evolution time t, in case of diffusive motion... 

Fig. 12a and b. Calculated 2H spin alignment spectra for diffusive motion, a unrestricted rotational diffusion for different mixing times x2 b diffusion restricted to angular regions as indicated for long mixing times t2... 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

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... 

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

In this case one determines the spectral intensity solely in the centre, not over the whole frequency range. Therefore the analysis often refers not to the spectrum as a whole, but to relaxation times Tg,i or and their dependence on rotational relaxation time tj [85]. This dependence contains much information and can be easier to interpret. It enables one to determine when free rotation turns into rotational diffusion. 

Consequently, the m-diffusion model does not extend to the domain where the Hubbard relation holds. Therefore, the J-diffusion model is the only realistic description of rotational diffusion within the framework of impact theory. 

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