Diffusion rotational/translational

The above experimental results largely relate to spectroscopic techniques, which do not give direct information about the spatial scale of the molecular motions. The size of the spatial heterogeneities is estimated by indirect methods such as sensitivity of the dynamics to the probe size or from the differences between translational and rotational diffusion coefficients (rotation-translation paradox). It might be expected that the additional spatial information provided by neutron scattering could help to discriminate between the two scenarios proposed. 

In view of these results for binary glasses composed of molecules with different masses respectively different Tg, one may speculate that the isotropic reorientation of the small molecules results from translational diffusion in an essentially rigid glassy matrix formed by the large molecules, i.e., the diffusional process may be probed by 2H NMR via rotational-translational coupling.183 Finally, we note that the stimulated-echo technique was also applied to study the main relaxation in... 

What type of diffusion takes place within the system (rotational, translation, or both) ... 

Diffusion is the random movement of a particle because of an exchange of thermal energy with its environment. Membrane lipids and proteins participate in highly anisotropic translational and rotational diffusion motion. Translational diffusion in the plane of the membrane is described by the mean square lateral displacement after a time At (r ) = TD At. Lipid lateral diffusion coefficients in fluid phase bilayers are typically in the range Dj 10 to 10 cm /s (3). 

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. 

The characteristic parameters generally considered are the temperature and electron density which are of primary importance under equilibrium coiulitions For example, with a D.C. plasma generator, two different zones have been pointed out in a nitrogen plasma jet at atmospheric pressure The first zone is such that 10 < n < lO cm and 9000 K < T < 15000 K, and the different criteria show that LTE is achieved. The second zone has a low electronic density 10 < n, < < 10 cm , a quite low temperature 3000 K < T < 7000 K, and uilibrium is not realized, due in part to diffusion. Nevertheless in both cases, the relaxation times of rotation-rotation, and rotation-translation exchanges are sufficiently low to consider the rotational and the translational temperatures to be equal, b) Spectroscopic measurement methods... 

As noted above, from [r], via Eq. (1.30), we can determine Vh and therefore the viscometric hydrodynamic radius, RH,r]- It is also possible to determine a frictional hydrodynamic radius, RH,f, from sedimentation or translational diffusion experiments, using Stokes law. Since the kinematics of viscosity measurement involves rotation of the macromolecule whereas that in sedimentation or diffusion involves translation, Rh - and Rhj may, in principle, differ numerically. In fact, they... 

Differences between the two methods exist with regard to particle property and type of quantity DUM only evaluates the translational diffusion (xh,t) and probes number frequencies, whereas DLS is also sensitive to the diffusive rotation (xh app) and yields intensity weighted distribution functions. Furthermore, the methods usually differ in sample size Typical sample concentrations in DLS are in the range of 0.01 vol%. These are, for instance, 50,000 particles a 100 nm in a measurement volume of 10 pm, which are all observed in the order of minutes (Willemse et al. 1997), whereas with DUM, the total number of traced particles is smaller by factor 10-100, with an observation time in the order of seconds for each. Last but not least, DLS allows for a temporal resolution in the range from ns to ms, whereas DUM is subject to video processing, typically with 30 frames per second, and is, therefore, not sensitive to very fast relaxation processes (like gradient diffusion). 

The complex dynamics of liquid crystals is characterized by a superposition of local and collective motions, comprising internal isomerization, overall rotational diffusion (rotation of the molecule about the long axis and reorientation of this axis) and translational diffusion, and collective order fluctuations. Different NMR techniques are designed to follow these motions and to differentiate the various motional modes on the basis of their timescale. 

Dielectric constant Rotational diffusion coefficient Translational diffusion coefficient Mean value in the moment-ratio notation Electric field of light Electric field Geometric term in OPC Conductivity... 

First, the plane n(x,y) coincides with the diffuser mean plane of G, IT (x ,y ). When G is translated a distance x and rotated an angle Aa respect to the y axis of Il (x ,y ), we ob-a null movement of the speckle pattern on a circumference of center C and radius R ... 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

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