Rotational diffusion mutual

Use of the G.L.E. can lead to other refinements to the rotational diffusion model for example, Keyes (10) has noted that mutual rotational diffusion, where the relative reorientation of pairs of molecules is analyzed, can also be modelled in this way, with results obtainable not only for the simple linear diffusers treated earlier by Keyes and Kivelson (8), but for the as3mimetric diffuser as well. 

Its experimental confirmation provides information about the free rotation time tj. However, this is very difficult to do in the Debye case. From one side the density must be high enough to reach the perturbation theory (rotational diffusion) region where i rotational relaxation which is valid at k < 1. The two conditions are mutually contradictory. The validity condition of perturbation theory... 

The haphazard rotational motions of molecules or one or more segments of a molecule. This diffusional process strongly influences the mutual orientation of molecules (particularly large ones) as they encounter each other and proceed to form complexes. Rotational diffusion can be characterized by one or more relaxation times, t, describing the motion of a molecule or segment of volume, V, in a medium of viscosity, 17, as shown in the following equation ... 

When the reactants A and B are not spherically symmetric, their mutual reactivity depends on their orientation. Sole and Stockmayer [256] and Schmitz and Schurr [257] have modified the diffusion equation to include rotational diffusion of both reactants. By defining a reference axis in either species, the probability that a B reactant is a distance r away from A at time t, at an orientation (0, 0) with respect to the laboratory axis, and such that A and B are oriented at angles (0A, 0A) and (0B, 0b), respectively, is p(r,0,0 0a,0a> 0b,0b)- It satisfies the expression... 

The rotational effect on the correction term for diffusion-limited rate coefficients is shown as the intercepts on the ordinate of Fig. 17. Here, B is a small particle and only A can be re-oriented. As the size of A decreases, it can re-orient more quickly, but the mutual diffusion coefficient decreases till rA = rB. Hence, the very fact that the correction term increases with increase of rA shows that rotational diffusion is very important. 

Let us now briefly review the essential features of the efiect under consideration. Without an applied external fidd we have a random distribution of molecular axes as well as a certain state of chemical equilibrium regarding the mutual interconversion of Ai and Ag. Application of an external field determines some preferential orientation of the molecular dipoles of Ag. The system tends to establish this as rapidly as possible. Usually, this is achieved by means of rotational diffusion. In principle, however, the chemical process provides an alternative means of orienting dipoles without actually rotating them. The equilibrium constant jST(0) of those molecules which have an angle 0 with regard to the applied field will be changed according to... 

The available results present something of a problem for explanation in terms of rotational diffusion models, even after recognizing that two distinct species with similar static properties and molecular sizes but different relaxation rates can relax at nearly the same rate in an environment with a common (i.e., mutual) viscosity, as Kivelson has pointed out to the writer (91). Such conditions are not met in some of the available examples. Ones from very recent work are for mixtures of methanol, ethanol, and 2-propanol with added water up to 0.5 mole fraction for the first two and at 0.15 for the last by Bertolini, Cassettori, and Salvetti (92) at frequencies from 470 MHz to 3.75 GHz. They found essentially single Debye relaxations in all cases, with indications of slight broadening at -43 0. 

Let us now consider the contribution of diffusion to the maximum rates of homogeneous reactions involving associations as a first step in the interactions of proteins with both small and large substrates. In the present context association to form a specific complex does not include any covalent bond formation. Three events are involved in the approach to equilibrium collision, alignment to correct mutual orientation and for some processes separation after the event. These events depend on translational diffusion for approach and separation and on rotational diffusion for alignment. Earlier in this section the diffusion constant was defined using the principle of random Brownian motion and this will now be used in equations which have been derived to evaluate maximum collision rates. 

The list of experimentally accessible properties of colloid solutions is the same as the list of accessible properties of polymer solutions. There are measurements of single-particle diffusion, mutual diffusion and associated relaxation spectra, rotational diffusion (though determined by optical means, not dielectric relaxation), viscosity, and viscoelastic properties (though the number of viscoelastic studies of colloidal fluids is quite limited). One certainly could study sedimentation in or electrophoresis through nondilute colloidal fluids, but such measurements do not appear to have been made. Colloidal particles are rigid, so internal motions within a particle are not hkely to be significant the surface area of colloids, even in a concentrated suspension, is quite small relative to the surface area of an equal weight of dissolved random-coil chains, so it seems unlikely that colloidal particles have the major effect on solvent dynamics that is obtained by dissolved polymer molecules. 

These reactants possess anisotropic reactivity the reaction occurs at a certain mutual orientation, which does not take place at each collision. In the first approximation, these reactants can be considered as spheres each of which has a small reaction spot. The reaction occurs when the spheres collide by their spots. The reaction occurs without an activation energy. The size of the spot in the form of a circumference on the sphere-reactant can be characterized by the angle q, the relative surface area of the spot on the sphere is equal to sin (0/2), and the probability of collision with the favorable mutual orientation of two identical particles is sin (0/2). This is the geometric steric factor = sin (0/2) or - sin (0A/2)sin (0B/2) if the sizes of the spots differ for A and B. After collision the particle-reactants exist near each other for some time and turn relatively to each other. The rate of turn of the particles depends, naturally, on viscosity because the coefficient of rotational diffusion depends on viscosity... 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

From the photochemical viewpoint considerable interest attaches to the photodecomposition of formaldehyde into CHO + H. Evidence of isotope exchange (Klein and Schoen, 1956, 1958) suggests that dissociation occurs at 3650 A even though the rotational lines are not noticeably diffuse above 3000 A. These observations are not mutually inconsistent, however, for the probability of the radiationless transition leading to... 

In the time window between the absorption and emission of a photon, a number of molecular processes can occur. They concern either (a) the fluorophore itself (its rotational and translational diffusion, conformational changes, transition between electronic states differing in dipole moment) or (b) molecules in its immediate vicinity (reorganization of the solvent shell, diffusion of quenchers, etc.). All these processes influence the fluorescence properties (position and shape of the emission band, quantum yield, decay time, etc.). In most cases, both the fluorophore and the surrounding molecules participate in the process and fluorescence characteristics are in fact influenced by their mutual interactions. Figure 3 shows a survey of important... 

AcAc, acetylacetonate EPR, electron paramagnetic resonance DPM, dipivaloylmethane Tc, Correlation time for molecular tumbling A/x, concentration of spins X (per unit volume) D, mutual translational self-diffusion coefficient of the molecules containing A and X a, distance of closest approach of A and X ye, magnetogyric ratio for the electron C, spin-rotation interaction constant (assumed to be isotropic) Ashielding anisotropy <7 <7j ) coo, Debye frequency 0d, the corresponding Debye temperature Fa, spin-phonon coupling constant. 

Quasi-elastic light scattering (QELS) Measures translational, rotational, self, and mutual diffusion coefficients Experimental artifacts observed at low concentration Protein interactions can interfere at high concentratian... 

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