Diffusion long range

A quantitative analysis [34], based on the adsorption isotherms and the intercrystalline porosity, yielded the remarkable result that a satisfactory fit between the experimental data and the estimates of Aong-range = Pinter Anter following Eqs. (3.1.11) and (3.1.12) only lead to coinciding results for tortuosity factors a differing under the conditions of Knudsen diffusion (low temperatures) and bulk-diffusion (high temperatures) by a factor of at least 3. Similar results have recently been obtained by dynamic Monte Carlo simulations [39—41]. 

The situation is completely different for mass transfer within the pore network of monolithic compounds. Here mass transfer can occur both on the pore surface or in the pore volume and molecular exchange between these two states of mobility can occur anywhere within the pore system, being completely uncorrelated with the respective diffusion paths. As a consequence, Eq. (3.1.11) is applicable, without any restrictions, to describing long-range diffusion in the pore space. Equation (3.1.14) is thus obtained, 

The experimental arrangement chosen in these studies allows the diffusion processes in the region of the adsorption hysteresis to be followed. Adsorption hysteresis is the phenomenon of history-dependent adsorption and describes the effect that, in addition to the pressure, the concentration also depends on whether the given pressure has been attained from lower values (i.e., on the adsorption branch ) or from higher values (the desorption branch ) [54]. Irrespective of its 

27 (squares) and 0 = 0.18 (triangles). The solid lines show the fits to the experimental data using the Arrhenius relationship D oc exp(—Ed/RT) with the activation energies for diffusion ED indicated in the figure. 

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While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

The propagator is often Gaussian (including the present cases of intracrystalline and long-range diffusion)... 

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

As shown by DFTB and CPMD simulations, the principal features of the transport mechanism are rotational diffusion of the protonic defect and proton transfer toward a neighboring oxide ion. That is, only the proton shows long-range diffusion, whereas the oxygens reside in their crystallographic positions. Both experiments " " and quantum-MD simulations, have revealed that rotational diffu-... 

Long-range, diffusion-limited, spontaneous phase domains separation initiated by delocalized concentration fluctuations occurring in an unstable region of a mixture bounded by a spinodal curve. 

Figure 18.7 Interfaces resulting from two types of continuous transformation, (a) Initial structure consisting of randomly mixed alloy, (b) After spinodal decomposition. Regions of B-rich and B-lean phases separated by diffuse interfaces formed as a result of long-range diffusion, (c) After an ordering transformation. Equivalent ordering variants (domains) separated by two antiphase boundaries (APBs). The APBs result from A and B atomic rearrangement onto different sublattices in each domain.

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