Longe-range translational diffusion

Translational self-diffusion and rotation of the water molecules. Since the above two models fail to explain the data, one may think of a model which combines both, and which is certainly more realistic. We h ve2tr e< such a possibility with p = 0.95 and D 1.6 x 10 cm /s. This last value is the long range self-diffusion coefficient of water in this membrane, measured by radioactive tracers. We found that no fit is possible with these values whatever D is chosen. As for the preceeding section, we find that the fiE improves considerably if we take either p or Dt as parameters. With Dt fixed, we should increase p to 3 A, as above, and with p fixed, we should increase D to 10 cm /s. These results suggest that one should think of a model which contains these two features. The simplest one is a model where the water molecules, more precisely the protons, are restricted to diffuse (diffusion goejjficient D) in a sphere of radius a, where we expect D 10 cm and a 3 S. 

For translational long-range jump diffusion of a lattice gas the stochastic theory (random walk, Markov process and master equation) [30] eventually yields the result that Gg(r,t) can be identified with the solution (for a point-like source) of the macroscopic diffusion equation, which is identical to Pick s second law of diffusion but with the tracer (self diffusion) coefficient D instead of the chemical or Fick s diffusion coefficient. 

The last but not the least advantage of neutron spectroscopy is its ability to measure long-range translational motions over short distances, of the order of a few unit cells. Therefore diffusion coefficient measurements are free of spurious effects due to defects in the crystals. 

In contrast to crystalline solids characterized by translational symmetry, the vibrational properties of liquid or amorphous materials are not easily described. There is no firm theoretical interpretation of the heat capacity of liquids and glasses since these non-crystalline states lack a periodic lattice. While this lack of long-range order distinguishes liquids from solids, short-range order, on the other hand, distinguishes a liquid from a gas. Overall, the vibrational density of state of a liquid or a glass is more diffuse, but is still expected to show the main characteristics of the vibrational density of states of a crystalline compound. 

The fluidity of LB monolayers on solid supports was characterized by measuring the long-range (> 10 xm) translational diffusion of dissolved fluorescent lipids using fluorescence pattern photobleaching recovery (FPPR). In this technique, an area of the membrane is illuminated with a spatially striped intensity. After irreversibly photobleaching, fluorescence recovery occurs, as unbleached molecules from nonilluminated stripes move into the illuminated stripes . In fluid-like LB films, translational diffusion coefficients... 

Here V(<(), t) = pF(t) cos 4> is the potential arising from an external applied electric field F(f). Here, just as with the translational diffusion equation treated in Ref. 7, we consider subdiffusion, 0 < ct < 1 phenomena only. Here, the internal field effects are ignored, which means that the effects of long-range torques due to the interaction between the average moments and the Maxwell fields are not taken into account. Such effects may be discounted for dilute systems in first approximation. Thus, the results obtained here are relevant to situations where dipole-dipole interactions have been eliminated by extrapolation of data to infinite dilution. 

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