Diffusion thermally activated

Atoms move by thermally activated diffusion from site to site. 

The diffusion coefficient corresponding to the measured values of /ch (D = kn/4nRn, is the reaction diameter, supposed to be equal to 2 A) equals 2.7 x 10 cm s at 4.2K and 1.9K. The self-diffusion in H2 crystals at 11-14 K is thermally activated with = 0.4 kcal/mol [Weinhaus and Meyer 1972]. At T < 11 K self-diffusion in the H2 crystal involves tunneling of a molecule from the lattice node to the vacancy, formation of the latter requiring 0.22 kcal/mol [Silvera 1980], so that the Arrhenius behavior is preserved. Were the mechanism of diffusion of the H atom the same, the diffusion coefficient at 1.9 K would be ten orders smaller than that at 4.2 K, while the measured values coincide. The diffusion coefficient of the D atoms in the D2 crystal is also the same for 1.9 and 4.2 K. It is 4 orders of magnitude smaller (3 x 10 cm /s) than the diffusion coefficient for H in H2 [Lee et al. 1987]. 

The attack of most glasses in water and acid is diffusion controlled and the thickness of the porous layer formed on the glass surface consequently depends on the square root of the time. There is ample evidence that the diffusion of alkali ions and basic oxides is thermally activated, suggesting that diffusion occurs either through small pores or through a compact body. The reacted zone is porous and can be further modified by attack and dissolution, if alkali is still present, or by further polymerisation. Consolidation of the structure generally requires thermal treatment. 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Temperature influences skin permeability in both physical and physiological ways. For instance, activation energies for diffusion of small nonelectrolytes across the stratum corneum have been shown to lie between 8 and 15 kcal/mole [4,32]. Thus thermal activation alone can double the rate skin permeability when there is a 10°C change in the surface temperature of the skin [33], Additionally, blood perfusion through the skin in terms of amount and closeness of approach to the skin s surface is regulated by its temperature and also by an individual s need to maintain the body s 37° C isothermal state. Since clearance of percuta-neously absorbed drug to the systemic circulation is sensitive to blood flow, a fluctuation in blood flow might be expected to alter the uptake of chemicals. No clear-cut evidence exists that this is so, however, which seems to teach us that even the reduced blood flow of chilled skin is adequate to efficiently clear compounds from the underside of the epidermis. 

Durable changes of the catalytic properties of supported platinum induced by microwave irradiation have been also recorded [29]. A drastic reduction of the time of activation (from 9 h to 10 min) was observed in the activation of NaY zeolite catalyst by microwave dehydration in comparison with conventional thermal activation [30]. The very efficient activation and regeneration of zeolites by microwave heating can be explained by the direct desorption of water molecules from zeolite by the electromagnetic field this process is independent of the temperature of the solid [31]. Interaction between the adsorbed molecules and the microwave field does not result simply in heating of the system. Desorption is much faster than in the conventional thermal process, because transport of water molecules from the inside of the zeolite pores is much faster than the usual diffusion process. 

As the pore size is reduced to 1 nm or less, gas permeation may exhibit a thermally activated diffusion phenomena. For example, in studies at Oak Ridge National Laboratory, for a certain proprietary membrane material and configuration, permeation of helium appeared to increase much faster than other gases resulting in an increase in Helium to C02 selectivity from 5 at 25°C to about 48.3 at 250°C (Bischoff and Judkins, 2006). Hydrothermal stability of this membrane in the presence of steam, however, was not reported. 

The concentration profile studies find that the hydrogen diffusion coefficient in a-Si H is thermally activated, as shown in Fig. 17 (Street et al., 1987). Over the temperature range of 130 to 300°C, the diffusion data is described by the Arhennius expression... 

If Dh is indeed time dependent as in eq. (5) it is not obvious that C(x, t) will follow an error function expression as in eq. (3) or that >H will be thermally activated as in eq. (4). We now show that eqs. (3) and (4) still apply with a time dependent diffusion coefficient, by making a coordinate transformation (Kakalios and Jackson, 1988). The one-dimensional diffusion equation... 

That is, for conditions where the diffusion distance is kept constant at various temperatures, D will have a weak temperature dependence, and Dh will be thermally activated. For constant diffusion distance, it is the time to diffuse a distance L that is thermally activated. 

Diffusion being a thermally activated process, the diffusion coefficient depends on the absolute temperature T according to an Arrhenius law... 

There is a thermally activated structural rearrangement of the protein such that channels appear and the quencher molecules are able to penetrate the protein—the penetration model.(67) This model distinguishes between external diffusion, kd(ext), and diffusion within the protein as follows ... 

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