Translational diffusional motions

Diffusional motion. Many rotational and translational diffusion processes for hydrocarbons within zeolites fall within the time scale that is measurable by quasielastic neutron scattering (QENS). Measurements of methane in zeolite 5A (24) yielded a diffusion coefficient, D= 6 x lO" cm at 300K, in agreement with measurements by pulsed-field gradient nmr. Measurements of the EISF are reported to be consistent with fast reorientations about the unique axis for benzene in ZSM-5 (54) and mordenite (26). and with 180 rotations of ethylene about the normal to the molecular plane in sodium zeolite X (55). Similar measurements on methanol in ZSM-5 were interpreted as consistent with two types of methanol species (56). 

In one method, the "cage" effect, or the percentage of an initial number of geminately produced radical pairs which react with each other within the "cage" in which they were born together, has been employed to examine the translational diffusion of radicals adsorbed on the external and internal surfaces of zeolites. In a second method, the formation and the structures of isomers from a geminate radical pair have been employed to examine the rotational and diffusional motion of radical pairs generated on a zeolite surface. 

In simulations of protein-protein interactions, where the proteins are treated as rigid bodies, only two solute particles are considered. Translational motion is then simulated for one of the proteins relative to the position of the other protein, which is kept fixed (Fig. 16). The displacement of the moving protein is then given by Eq. (11), with D replaced by the relative translation diffusional constant. Usually the effects of hydro-dynamic interactions are not considered but can be treated by using tensors for the diffusion coefficient instead of scalars. 

It is customary to describe the reorlentational kinetics by a time reflecting the rate at which the CF decays to its long time limit. In the case of a purely diffusional motion the best choice is the relaxation time T which appears in the onent of the equation 19 and 21 for the translational and the rotational CF s. For CF s which are not exponential we define a correlation time X as the area under the normalized CF ... 

Numerical simulations of the coarsening of several particles are now possible, allowing the particles to change shape due to diffusional interparticle transport in a manner consistent with the local interphase boundary curvatures [17]. These studies display interparticle translational motions that are a significant phenomenon at high volume fractions of the coarsening phase. 

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... 

The application of relaxation time measurements to study segmental motion (in polymers) as well as diffusional chain motion is very well documented but is still a subject of study, particularly using the frequency dependence of relaxation times to test the detailed predictions of models (McBriety and Packer 1993). The anisotropy of reorientation can also be studied conveniently, and recent interest in motion of molecules on surfaces (e.g. water on porous silica) has been investigated with great sueeess (Gladden 1993). Since the dipolar interaction is usually both intermolecular and intramolecular, the relaxation of spin- /2 nuclei (e.g. H) in the same molecule as a quadrupolar nucleus (e.g. H) can permit a complete study of reorientation and translation at a microscopic level (Schmidt-Rohr and Spiess 1994). 

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. Andrec et al. used a Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data. Sturz and Dolle examined the reorientational motion of toluene in neat liquid by using relaxation measurements. The relaxation rates were analyzed by rotational diffusion models. Chen et al measured self-diffusion coefficients for fluid hydrogen and fluid deuterium at pressures up to 200 MPa and in the temperature range 171-372 K by the spin echo method. The diffusion coefficients D were described by the rough sphere (RHS) model invoking the rotation translational coupling parameter A = 1. 

Quasielastic scattering is a very low energy inelastic process. The term is usually taken to mean a broadening of the elastic line and is most commonly the result of diffusional (translational or rotational) motion of atoms. (It can also be caused by the randon fluctuations of unpaired electronic spins of... 

Intcrmolecular dipole-dipole relaxation depends on the correlation time for translational motion rather than rotational motion. Intermolecular dipole-dipole interactions arise from the fluctuations which are caused by the random translational motions of neighboring nuclei. The equations describing the relaxation processes are similar to those used to describe the intramolecular motions, except is replaced by t, the translation correlation time. The correlation times are expressed in terms of diffusional coefficients (D), and t, the rotational correlation time and the translational correlation time for Brownian motion, are given by the Debye-Stokes-Einstein theory ... 

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