Anisotropy of diffusion

S. Hess, D. Frenkel and M. P. Allen, On the anisotropy of diffusion in nematic liquid crystals - test of a modified affine transformation model via molecular dynamics. Mol. Phys., 74 (1991) 765-774. 

Fig. 7.20 Anisotropy of diffusion amplitudes A,- for a cylindrical molecule (a) and a simple technique for measurements of anisotropy of diffusion coefficients for a dye dissolved in a...

In a liquid crystal, the anisotropy of diffusion results in an anisotropy of mobility and, consequently, conductivity. The corresponding tensor for a uniaxial phase has a standard form ... 

In the case of composite laminates, new problems linked to the anisotropy of diffusion paths, the eventual role of interfacial diffusion and the role of pre-existing or swelling-induced damage appeared in the mid-1970s. The interest was mainly focused on the effect of humidity on carbon fibre/amine crosslinked epoxy composites of aeronautical interest. For the pioneers of this research (Shen and Springer, 1976), the determination of diffusion kinetic laws appeared as the key objective. Various studies revealed that, in certain cases, diffusion in composites caimot be modelled by a simple Pick s law and that Langmuir s equation is more appropriate. Carter and Kibler (1978) proposed a method for the parameter identification. At the end of the 1970s, the kinetic analysis of water diffusion into composites became a worldwide research objective. Related experimental results can be summarized as follows. 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

That not only an increased interaction energy at the traps can be responsible for a template-controlled growth but also an anisotropy of the surface diffusion... 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

The overall tumbling of a protein molecule in solution is the dominant source of NH-bond reorientations with respect to the laboratory frame, and hence is the major contribution to 15N relaxation. Adequate treatment of this motion and its separation from the local motion is therefore critical for accurate analysis of protein dynamics in solution [46]. This task is not trivial because (i) the overall and internal dynamics could be coupled (e. g. in the presence of significant segmental motion), and (ii) the anisotropy of the overall rotational diffusion, reflecting the shape of the molecule, which in general case deviates from a perfect sphere, significantly complicates the analysis. Here we assume that the overall and local motions are independent of each other, and thus we will focus on the effect of the rotational overall anisotropy. 

The anisotropy of the overall tumbling will result in the dependence of spin-relaxation properties of a given 15N nucleus on the orientation of the NH-bond in the molecule. This orientational dependence is caused by differences in the apparent tumbling rates sensed by various internuclear vectors in an anisotropically tumbling molecule. Assume we have a molecule with the principal components of the overall rotational diffusion tensor Dx, Dy, and l)z (x, y, and z denote the principal axes of the diffusion tensor), and let Dx< Dy< Dz. 

It should be mentioned that rotational anisotropy of the molecule will result in an increase in the R2 values for NH vectors having particular orientation with respect to the diffusion tensor frame [46]. This increase could be misinterpreted as conformational exchange contributions, and, vice versa, small values of Rex, usually of the order or 1 s 1 or less, could be mistaken for the manifestation of the rotational anisotropy. Therefore, identification of residues subjected to conformational exchange is critical for accurate analysis of relaxation data. Additional approaches are necessary to distinguish between the two effects. As suggested earlier [27] (see also Ref. [26]), a comparison between R2 and the cross-correlation rate r]xy could serve this purpose, as tjxy contains practically the same combination of spec-... 

Fluorescence polarization 1) steady state 2) time-resolved emission anisotropy rotational diffusion of the whole probe simple technique but Perrin s Law often not valid sophisticated technique but very powerful also provides order parameters... 

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