Diffusion, anomalous translational

Sitnitsky et al developed a model-free theoretical framework for a phenomenological description of spin-lattice relaxation by anomalous translational diffusion in inhomogeneous systems based on the fractional diffusion equation. The dependence of the spin-lattice relaxation time on the size of the pores in... 

The conditions on the phase diagram for which this anomalous behavior occurs has been termed water s structurally anomalous region. Inspection of the order map (Figure 4) reveals a dome of structural anomalies within the temperature-density plane, bounded by loci of maximum tetrahedral order (at low densities) and minimum translational order (at high densities) as shown in Figure 5. Also marked on Figure 5 are regions of diffusive anomalies,... 

It has been assumed in Equation (6) that the tracer can freely access all void space, be it infra- or interparticle. Note that if a barrier to this exchange exists instead, the possibility of the onset of anomalous diffusion should be considered.42 In this case, the molecular displacement does not increase linearly as a function of the echo time, due to the physical threshold, which translates in an apparent reduction of the diffusion coefficients (till vanishing) for increasing A. Thus, the independence of De on the echo time must be controlled in order not to produce erratic experimental values. 

Since translational diffusion process is sensitive to the microscopic structure in the solution, understanding the diffusion provides an important insight into the structure as well as the intermolecular interaction. Therefore, dynamics of molecules in solution have been one of the main topics in physical chemistry for a long time. 1 Recently we have studied the diffusion process of transient radicals in solution by the TG method aiming to understand the microscopic structure around the chemically active molecules. This kind of study will be also important in a view of chemical reaction because movement of radicals plays an essential role in the reactions. Here we present anomalous diffusion of the radicals created by the photoinduced hydrogen abstraction reaction. The origin of the anomality is discussed based on the measurments of the solvent, solute size, and temperature dependences. 

Fig. 12. Translational diffusion coefficients of protein 4 determined at different scattering angles (6) are plotted against their corresponding K2 values where K = (4irn/ ) sin (0/2). This anomalous behavior is due to sample heterogeneity. From Ahmed et al. (1975), reproduced with permission.

Anomalous rotational diffusion in a potential may be treated by using the fractional equivalent of the diffusion equation in a potential [7], This diffusion equation allows one to include explicitly in Frohlich s model as generalized to fractional dynamics (i) the influence of the dissipative coupling to the heat bath on the Arrhenius (overbarrier) process and (ii) the influence of the fast (high-frequency) intrawell relaxation modes on the relaxation process. The fractional translational diffusion in a potential is discussed in detail in Refs. 7 and 31. Here, just as the fractional translational diffusion treated in Refs. 7 and 31, we consider fractional rotational subdiffusion (0rotation about fixed axis in a potential Vo(< >)- We suppose that a uniform field Fi (having been applied to the assembly of dipoles at a time t = oo so that equilibrium conditions prevail by the time t = 0) is switched off at t = 0. In addition, we suppose that the field is weak (i.e., pFj linear response condition). 

The fit to an Eigen equation of the proton transfer step to the carbon base (CN") indicates that the 2 step is not rate limiting and the cyanide ion behaves as if it were a heteroatom base. The anomalously large values of the rate constants for oxonium and hydroxide ions are consistent with their faster diffusion rates resulting from Grotthus translational-type effects. 

There are several practical difficulties in translating incremental outgassing data into diffusion coefficients (Farley 2000). The most commonly used computational models require that the distribution of diffusant be uniform within the diffusion domain. This assumption is violated in many samples by the a-ejection effect and by He diffusion in nature, both of which act to round the concentration profile at the grain surface. As a consequence, the initial rate of He release from a sample is anomalously retarded relative to later release. Fortunately this effect can be identified and greatly reduced by incremental outgassing schedules that involve cycling from low to high temperatures and back (Farley 2000). 

In addition, protein motion reduces the retardation of the water dynamics, because the dimension of the water translational space is increased and at the same time the decay of the orientational correlation is accelerated. In spite of this accelerated dynamics, hydration water diffusion remains anomalous for a thermalized protein. 

The anomalous reflections reported for the benzyl ester are described as lying on diffuse hyperbolas at 16 A and 8 A. We interpret these reflections as resulting from the presence of the 11-residue 3-tum helix, for which the value 16.8 A for co would be predicted, on the assumption that the residue distance is the same as in the methyl ester, 1.53 A. This corresponds to 5.60 A per turn Bamford, Hanby, and Happey suggested 5.76 A or a somewhat smaller value for the translation along the fiber axis, and we have found the data to correspond to 3 X 5.76 = 17.3 A, or 1.57 A per residue. The increase of 0.04 A over the methyl ester may well be due to van der Waals repulsion of the side chains. 

The molecular properties relating to the anomalous solubihty of p-CDs were studied by NMR spectroscopy and MDS on a-, p- and y-CD. The trajectories, translational diffusion constants, spatial distribution functions and time correlation functions were calculated. Differences in solubility could be explained by the different hydration shells around the CD s and the differing flexibiUty in the macrocyclic ring motions. 

To a first (rather crude) approximation these contributions are independent - the translational contribution is like that of a monatomic gas, and the other contributions correspond to the transport of molecular internal energy by a diffusion mechanism. Approximations of this sort actually predate the more elaborate kinetic-theory treatments based on an extended Boltzmann-like equation, and are often accurate to about a 10% level, with the notable exception of strongly polar gases, which have anomalously low thermal conductivities. In this approximation X can be calculated from t, D and the specific heat of the gas. 

Noticeable deviations of (r )(t) from the equation (25) are seen at low hydrations, where effective value of a continuously decreases at t < 10 ps. These deviations should be attributed to the water molecules, which are strongly bound to lysozyme surfaces (there is about 36 water molecules, having two or more hydrogen bonds with lysozyme molecule [635, 636]). The total MSD of such water molecules quickly achieves saturation during their rather long residence times. So, the simulations indicate the presence of two main classes of water molecules with respect to the translational motion molecules with short residence times, which show anomalous diffusion due to the spatial disorder already at the short times, and molecules with long residence times, which remain bound to some centers on lysozyme surface during hundreds of picoseconds. 

In case of anomalous diffusion, diffusion rates depend on time or spatial scale considered. A quantitative analysis of the hydration dependence of the water translational mobility may be done in different ways. One may compare the MSD r ) at some chosen time t or, alternatively, compare the times t that yield the same value of (r ). Besides, one may characterize water mobility by the time-dependent effective diffusion coefficient... 

Change of the fitting parameters in equation (26) with hydration is shown in Fig. 123. The exponent of a of anomalous diffusion of ions demonstrates sigmoid-like behavior with hydration. An inflection point of this dependence, which indicates transition between two regimes, is remarkably close to the percolation threshold of water at F = 15.5. Below and above this hydration level, different temporal/spatial disorder is probed by Na+ ions in the hydration shell of DNA. When the hydration shell is dispersed in a large number of small clusters below the percolation threshold, a is low (at about 0.65). When the hydrogen-bonded network of water exists above the percolation threshold, a approaches 0.80. So, spanning water network smooths a DNA surface for translational motion of ions. 

Field-gradient NMR diffusometry is suitable for recording translational displacement properties by self-diffusion. This in particular refers to the anomalous segment displacement regime. Center-of-mass diffusion is also accessible this way but must be handled with some care because of the experimental limitation of the maximum diffusion time. Furthermore the in-... 

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