Rotational diffusion effects

The techniques described under Photon Correlation exploit the correlation between the photons emitted by single molecules and by a small number of molecules. Picosecond photon correlation techniques investigate effects driven by the absorption of a single photon of the excitation light. The effects investigated by FCS are driven by Brownian motion, rotation, diffusion effects, intersystem crossing, or conformational changes. Because of these random and essentially sample-internal stimulation mechanisms, correlation techniques do not necessarily depend on a pulsed laser. 

Another, yet unexplored, problem is the extent to which the autocorrelation function and the obtained diffusion characteristics are affected by the rotational diffusion of the particles. Intuitively, one can expect that the rotational diffusion effectively speeds up the decay of the autocorrelation function and hence shorter diffusion times should be observed. This is shown in Fig. 31. The one-label, no rotation data points are the same as in Fig. 30 and serve as a reference. The other data points show the same system in which the rotation of the diffusing particle is switched on. As could be expected, when the relative size of the particle is small as compared to the dimensions of the active volume, the rotation has little effect. However, when the particle dimensions are comparable to those of the active volume, the apparent diffusion time... 

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... 

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. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

The effective diffusivities determined from limiting-current measurements appear at first applicable only to the particular flow cell in which they were measured. However, it can be argued plausibly that, for example, rotating-disk effective diffusivities are also applicable to laminar forced-convection mass transfer in general, provided the same bulk electrolyte composition is used (H8). Furthermore, the effective diffusivities characteristic for laminar free convection at vertical or inclined electrodes are presumably not significantly different from the forced-convection diffusivities. 

Measurements of rotating-disk effective diffusivities (H7, S8)forCu2+ ion (see Section I V,C) indicate that a greater increase in surface area takes place when the limiting current is generated by linear potential decrease than... 

Key Words Carbon-13 spin relaxation, T, Measurements, Nuclear Overhauser effect, Rotation-diffusion tensor, HOESY experiments... 

Fortunately, in the case of a rotational diffusion tensor with axial symmetry (such molecules are denoted "symmetric top"), some simplification occurs. Let us introduce new notations D// = Dz and D = Dx = Dy. Furthermore, we shall define effective correlation times ... 

The fluoresence lifetimes calculated for TIN in low viscosity alcohols are approximately proportional to the solvent viscosity (12) which suggests that in these solvents there is a non-radiative process related to. the rotational diffusion mobility of the TIN molecule. The observed extent of the quenching, however, is significantly greater than that expected due to viscosity effects alone and cannot be explained by a collisionally-induced, Stern-Volmer type process involving methanol molecules (25.) as the appropriate plot is non-linear. 

The overall tumbling of a protein molecule in solution is the dominant source of NH-bond reorientations with respect to the laboratory frame, and hence is the major contribution to 15N relaxation. Adequate treatment of this motion and its separation from the local motion is therefore critical for accurate analysis of protein dynamics in solution [46]. This task is not trivial because (i) the overall and internal dynamics could be coupled (e. g. in the presence of significant segmental motion), and (ii) the anisotropy of the overall rotational diffusion, reflecting the shape of the molecule, which in general case deviates from a perfect sphere, significantly complicates the analysis. Here we assume that the overall and local motions are independent of each other, and thus we will focus on the effect of the rotational overall anisotropy. 

R. M. Levy and R. P. Sheridan, Combined effect of restricted rotational diffusion plus jumps on nuclear magnetic resonance and fluorescence probes of aromatic ring motions in proteins, Biophys. J. 41, 217-221 (1983). 

The second piece of evidence in distinguishing rods in a magnetic field to those out of the magnetic field was the rotational diffusion coefficient of the rod. It was the rotational diffusion coefficient that revealed the effect that an applied magnetic field had on a nanorod moving non-Brownian outside a field (2000 ° /s) and in it (70 ° /s). 

Alternatively, in order to take into account the effects of rotational diffusion of a water molecule around the metal-oxygen axis, a rotational correlation time for the metal-H vector was considered as an additional parameter besides the longer overall reorientational time 82). 

Selected entries from Methods in Enzymology [vol, page(s)] Additive properties of polarization, 246, 286 angle-resolved, assessment of peroxidation effects on membranes, 233, 274-275, 281-283, 287-288 binding isotherm construction, 246, 287-288 effect of inner filter effects, 246, 288 incoherent systems, 246, 263-264 orientational averaging, 246, 265, 269-270 Perrin equation, 246, 284-285 polarization of emission, 246, 284 rotational diffusion, 246, 9, 260 time-resolved, assessment of peroxidation effects on membranes, 233, 274, 283-285, 285-287. 

In addition to the above effects, the intermolecular interaction may affect polymer dynamics through the thermodynamic force. This force makes chains align parallel with each other, and retards the chain rotational diffusion. This slowing down in the isotropic solution is referred to as the pretransition effect. The thermodynamic force also governs the unique rheological behavior of liquid-crystalline solutions as will be explained in Sect. 9. For rodlike polymer solutions, Doi [100] treated the thermodynamic force effects by adding a self-consistent mean field or a molecular field Vscf (a) to the external field potential h in Eq. (40b). Using the second virial approximation (cf. Sect. 2), he formulated Vscf(a), as follows [4] ... 

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