Brownian diffusion rotational

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

Four different models for the molecular dynamics have been tested to simulate the experimental spectra. Brownian rotational diffusion and jump type diffusion [134, 135] have been used for this analysis, both in their pure forms and in two mixed models. Brownian rotational diffusion is characterized by the rotational diffusion constant D and jump type motion by a residence time t. The motions have been assumed to be isotropic. In the moderate jump model [135], both Brownian and jump type contributions to the motion are eou-pled via the condition Dx=. ... 

Above 100 K, motional effects on spectrum become pronounced with increasing temperature and, above 230 K, the spectra consist of essentially an isotropic and equally spaced hyperfine triplet, but with different relative intensities. The line shape simulations were carried out by adopting a Brownian rotational diffusion model in order to evaluate the associated (average) rotational correlation time, and its degree of anisotropy, = zpy, /... 

Figure 2. Theoretical spectra of NO2 anisotropically rotating about its x axis (b), y axis (c), and z axis (d). The spectra were calculated for Brownian rotational diffusion model by using R// = 5.27 X 10 sec- Rj = 5.27 x 10 sec and T2 =3.0 G. For isotropic rotation (a), R// = Rj = 1.67 X 10 sec l and T2 l=3.0 G were used. The rotational diffusion values used through (a) to (d) correspond to a constant value of r =l x 10 sec v, 9 167 GHz...

HPhe polarization of fluorescence technique employing dye-macromolecule x conjugates is a sensitive hydrodynamic method for studying the structure and interactions of proteins 19, 20, 41, 54, 65) and synthetic polypeptides 26, 30, 31, 49)- The relationship describing the dependence of polarization of fluorescence upon the Brownian rotational diffusion of the macromolecule was developed by Perrin 50) and extended by Weber 65) in the form of the equations (for excitation with natural light) ... 

Aragon, SR and Pecora, R, Fluorescence correlation spectroscopy and Brownian rotational diffusion. Biopolymers 14 (1975) 119-138. 

In a macroscopically disordered system such as a microcrystalline powder or a glassy frozen solution, all possible orientations p occur with weighting factors sin p. The EPR spectrum of such a disordered system depends on whether reorientation by rotational diffusion is very slow, moderate, or very fast on the EPR timescale. In the following we assume isotropic Brownian rotational diffusion with an isotropic value Riso of the diffusion tensor and a transverse relaxation time of 150 ns. 

The EPRLL programs also allow for non-Brownian rotational diffusion, which implies a discrete, step motion of the spin probe. Two limiting models are available (i) jump diffusion, and (2) approximate free diffusion. In currently available implementations of the SEE fine shape calculation, non-Brownian models may not be used with an orienting potential, and only with the assumption of an axially symmetric diffusion tensor. For these reasons, and since Brownian motion is usually an... 

In nitroxide free radicals characterized by a hyperfine tensor. A, and g-tensor, g, the interaction between the magnetic moment of an unpaired electron and the magnetic moment of nitrogen nucleus is highly anisotropic. The anisotropy determines the line shape of electron spin resonance (ESR) spectrum of completely immobilized nitrox-ides (Fig. 1), and can be completely averaged out for fast thermal Brownian rotational diffusion in low-viscous media. For the " N nucleus with 7=1 and no other interacting nuclei in the nitroxide, three equidistant lines of equal intensities and widths should be observed in ESR spectra in such media. In fact, even in media of... 

The anisotropy of the g and hyperfine tensor leads to a dependence of the spectral line shape of nitroxides on the reorientation rate in soft matter or liquid solution. In the simplest case, nitroxide motion can be considered as isotropic Brownian rotational diffusion and can then be characterized by a single rotational correlation time Zr. To understand Zr, one can consider the reorientation of the molecular z axis caused by stochastic molecular motion. With the angle 0 between the orientation of this axis at zero time and the orientation at time t, the correlation fimction (cos0) exhibits exponential decay with time constant (the brackets () denote the average over a large ensemble of nitroxide molecules). Starting from the rigid limit, exemplified by a solid sample at very low... 

While slow tumbling spectra are best simulated to extract rotational correlation times, fast tumbling spectra can be quantified via relative fine widths T2,r or amplitudes hi of the three fines using Kivelson fine width theory. As three lines define two independent amplitude ratios, the imderlying assumption of isotropic Brownian rotational diffusion can be tested. For spin labels in polymers or sirrfactant spin probes nitroxide motion is usually not isotropic In favorable cases, more detailed models of the motion can be obtained by the microscopic order macroscopic disorder (MOMD) or slowly relaxing local stracture (SRLS) models. ... 

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... 

When the regular motion is simply uniform rotation of the absorption and emission dipoles with angular velocity to around the helix axis, one has p(t) - p(0) = cot. For the corresponding random motion, one might have m)2> = 2Dt, where D is the effective diffusion coefficient for Brownian rotation of the transition dipole around the helix axis. When these expressions are incorporated in Eqs. (4.31) and (4.24), the latter becomes a generalization of a relation recently derived using a more cumbersome approach/104-1... 

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). 

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

Chapter 8 by W. T. Coffey, Y. P. Kalmykov, and S. V. Titov, entitled Fractional Rotational Diffusion and Anomalous Dielectric Relaxation in Dipole Systems, provides an introduction to the theory of fractional rotational Brownian motion and microscopic models for dielectric relaxation in disordered systems. The authors indicate how anomalous relaxation has its origins in anomalous diffusion and that a physical explanation of anomalous diffusion may be given via the continuous time random walk model. It is demonstrated how this model may be used to justify the fractional diffusion equation. In particular, the Debye theory of dielectric relaxation of an assembly of polar molecules is reformulated using a fractional noninertial Fokker-Planck equation for the purpose of extending that theory to explain anomalous dielectric relaxation. Thus, the authors show how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended via the continuous-time random walk to yield the empirical Cole-Cole, Cole-Davidson, and Havriliak-Negami equations of anomalous dielectric relaxation from a microscopic model based on a... 

Frictional electrification, 183-184 Frictional resistance, 50 Friedlander, S. K, 312, 316 Fuchs, N. A., 61 and brownian rotation, 138 and coagulation, 313-314 and diffusion charging, 188 and diffusion and collisions, 304 and equilibrium charge distributions, 204-205... 

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