Self-diffusion anisotropy

C. Filipoi, D.E. Demco, X. Zhu, R. Vinokur, O. Conradi, R. Fechete, M. MoeUer, Water self-diffusion anisotropy and electrical conductivity of perfluorosulfonic acid/ SiOa composite proton exchange membranes, Chem. Phys. Lett. 554 (2012) 143—149. 

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... 

Self-diffusion along the boundary in Exercise 9.6 is highly anisotropic because diffusion along the tilt axis (parallel to the dislocations) is much greater than diffusion transverse to it (i.e., perpendicular to the dislocations but still in the boundary plane). Find an expression for the anisotropy factor,... 

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

Porion, P., Rodts, S., Al-Mukhtar, M., Faugere, A.M. and Delville, A. (2001) Anisotropy of the Solvent Self-Diffusion Tensor as a Probe of Nematic Ordering within Dispersions of Nanocomposites. Physical Review Letters 87, 208302-208700... 

The results of estimation of coefficient of self-diffusion due to simulation for macromolecules with different lengths are shown in Fig. 12. The introduction of local anisotropy practically does not affect the coefficient of diffusion below the transition point M, the position of which depends on the coefficient of local anisotropy. For strongly entangled systems (M > M ), the value of the index —2 in the reptation law is connected only with the fact of confinement of macromolecule, and does not depend on the value of the coefficient of local anisotropy. At the particular value ae = 0.3, the simulation reproduces the results of the conventional reptation-tube model (see equation (5.21)) and corresponds to the typical empirical situation (M = 10Me). 

Very recently, detailed further analyses of the translation and reorientation dynamics of SCW have been reported showing consistency with our results in the limit of very low-density supercritical states for water [47], The dynamical behavior of SCW in this study is also compared to that of supercritical benzene showing that the density dependence of the self-diffusion coefficient and rotational dynamics of SCW is smaller than that of supercritical benzene because SCW is capable of maintaining stronger degrees of structural correlations and orientational anisotropy than benzene, which tends to lose intermolecular correlations at a much faster rate upon decreasing density [47],... 

The spatially distributed PGSE experiment provides a nice means of demonstrating diffusion anisotropy. The intensity of the image pixel depends on the local gradient g and the self-diffusion tensor as... 

This result is in agreement with recent PFG NMR measurements with oriented ZSM-5 crystals, where the mean self-diffusivity of methane averaged over the straight and sinusoidal channels (i.e., in the x, y plane) has been found to be larger by a factor of 3-5 than the self-diffusivity in the c direction, perpendicular to those 42,43). For the self-diffusion of methane in ZSM-5/silicalite-I, the MD simulations were in very satisfactory agreement with the experimental PFG NMR and QENS self-diffusion data (cf. Refs. 34-38). Furthermore, the degree of a mass transport anisotropy in the MFI framework as predicted by MD simulations (34-38) is compatible with the experimental findings (42,43,49). 

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. 

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

Recent single-crystal studies reveal the surface-structure sensitivity and anisotropy of self-diffusion (70, 71]. Depending on the structure of the crystal face, diffusion coefficients may vary by orders of magnitude. This is shown for rhodium adatom diffusion on various rhodium crystal faces in Figure 4.14. Diffusion rates parallel to steps are greater than diffusion rates perpendicular to them. 

E. Preuss, N. Freyer, and H.P. Bonzel. Surface Self-Diffusion on Pt(IIO) Directional Dependence and Influence of Surface-Energy Anisotropy. Appl. Phys. /141 137 (1986). 

Ramseier [/. AppL Phys. 38, 2553 (1967)] found an anisotropy of 12% for the self-diffusion coefficients of tritium in ice, but the same activation energy, in the directions parallel and perpendicular to the c-axis. His numerical results are in substantial agreement with those given in Table Vll. He favors a vacancy mechanism with entire H2O molecules diffusing. 

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. 

Gornyy and Al tovsky (1970), Spedding and Shiba (1972) determined the anisotropy of self-diffusion in single crystals of Y and Er, respectively. Selfdiffusion in Y seems to be strongly anisotropic to contrast to the results in Er (table 12.1). Further work, particularly in the hep phas es of the heavy rare earth metals, should elucidate this problem. 

M. Klein, J.-C. Perrin, S. Leclerc, L. Guendouz, J. DiUet, O. Lottin, Anisotropy of water self-diffusion in a NAPION membrane under traction. Macromolecules 46 (2013) 9259-9269. 

Self-diffusion coefficients were measured simultaneously in single crystals of MgSi03 perovskite under lower mantle conditions. No anisotropy in the diffusion... 

The experimental values of an average coefficient of self-diffusion, D) = ( ) H- 2D ) and the anisotropy for p-azoxyanisole (see Table 11... 

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