Rotation Brownian motion

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... 

Woessner D E 1962 Nuclear spin relaxation in ellipsoids undergoing rotational Brownian motion J. Chem. Rhys. 37 647-54... 

Zatsepin V. M. Time correlation functions of one-dimensional rotational Brownian motion in n-fold periodical potential. Theor. and Math. Phys. 

McConnell J. Rotational Brownian Motion and Dielectric Theory. (Academic Press, New York) (1980). 

If excited molecules can rotate during the excited-state lifetime, the emitted fluorescence is partially (or totally) depolarized (Figure 5.9). The preferred orientation of emitting molecules resulting from photoselection at time zero is indeed gradually affected as a function of time by the rotational Brownian motions. From the extent of fluorescence depolarization, we can obtain information on the molecular motions, which depend on the size and the shape of molecules, and on the fluidity of their microenvironment. 

Weber G. (1953) Rotational Brownian Motions and Polarization of the Fluorescence of Solutions, Adv. Protein Chem. 8, 415-459. 

G. Weber, Rotational Brownian motion and polarization of the fluorescence of solutions,... 

Rotational Brownian Motion and Polarization of the Fluorescence of Solutions Gregorio Weber... 

The time scale over which a chemical reaction occurs is 1/k, where k i is the observed pseudo first-order reaction rate. The time scale over which a molecule re-orients is Trot, which is, according to the simple Debye model of rotational Brownian motion... 

Exercise. Rotational Brownian motion of a dipole in an external time-dependent field has been described by ... 

During the first diffusional step in which the molecule executes a kind of translational and rotational Brownian motion in the soft-fluctuating force field of its neighbors, its direction cosines are represented as... 

Here (Oe and co are delivered by the corresponding Langevin equations of the theory of the rotational Brownian motion. In order to obtain these equations, one must include in the dynamic equations (4.308) and (4.310) the random thermal torques. We do that in the following way ... 

The torque —TJn In W, which is exerted on the particle body on the part of the surrounding liquid and causes the rotational Brownian motion of the particle. 

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... 

However, for nonspherical particles, rotational Brownian motion effects already arise at 0(0). In the case of ellipsoidal particles, such calculations have a long history, dating back to early polymer-solution rheologists such as Simha and Kirkwood. Some of the history of early incorrect attempts to include such rotary Brownian effects is documented by Haber and Brenner (1984) in a paper addressed to calculating the 0(0) coefficient and normal stress coefficients for general triaxiai ellipsoidal particles in the case where the rotary Brownian motion is dominant over the shear (small rotary Peclet numbers)—a problem first resolved by Rallison (1978). 

Here, V, the volume of the spherical molecule, t] is the viscosity of the solution, k is the Boltzmann constant, and T is the thermodynamic temperature. This equation is based on the theory of rotational Brownian motion of rigid spheres in a viscous fluid. 

The classical oscillator model was found to be particularly useful in the description of the relationships of the polarization of the luminescence and its dependence on rotational Brownian motion and other factors for small molecules ... 

The simplest case of the rotational Brownian motion of a spherical partice or a rigid dumbell in a viscous medium is given by ... 

Although the relation between fluorescence depolarmtion and rotational Brownian motion was first identified by Perrin and the development of the theoret-... 

On binding of an antigen to an antibody there will be a reduction or a restriction in the rotational Brownian motion of the fluorescent label. This will cause considerable polarization of the fluorescence along or perpendicular to the optical axis of the excitation polarizer, depending upon whether the fluorescence transition moment of the molecule is oriented closer to 0 or 90° to the transition moment associated with the absorption band excited. Let us first consider the case where the transition moments for excitation and fluorescence are parallel (or nearly so). 

Debye extended the foregoing arguments in order to establish the Smoluchowski equation [Eq. (5)] for the rotational Brownian motion of a dipolar particle about a... 

Thus the Debye equation [Eq. (1)] may be satisfactorily explained in terms of the thermal fluctuations of an assembly of dipoles embedded in a heat bath giving rise to rotational Brownian motion described by the Fokker-Planck or Langevin equations. The advantage of a formulation in terms of the Brownian motion is that the kinetic equations of that theory may be used to extend the Debye calculation to more complicated situations [8] involving the inertial effects of the molecules and interactions between the molecules. Moreover, the microscopic mechanisms underlying the Debye behavior may be clearly understood in terms of the diffusion limit of a discrete time random walk on the surface of the unit sphere. 

It is of importance that for one-dimensional rotational Brownian motion in a potential, i and i,- defined by Eq. (151) may be expressed in closed form for an arbitrary potential V0([Pg.329]

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