Carbon diffusion, activation energies

FIGURE 9.14 Dependence of the diffusion activation energy of carbon dioxide, methane, and propane in organosihcon polymers on the kinetic diameter of the penetrant molecules (designations of polymers are the same as in Figure 9.9). (From analysis of results presented in Semenova, S.I., J. Membr. Sci., 231, 189, 2004. With permission.)... 

Fig. 8. Variation of activation energy with kinetic molecular diameter for diffusion in 4A 2eohte (A), 5A 2eohte (0)> carbon molecular sieve (MSC-5A) (A). Kinetic diameters are estimated from the van der Waals co-volumes. From ref. 7. To convert kj to kcal divide by 4.184.

Endotliermic Decompositions These decompositions are mostly reversible. The most investigated substances have been hydrates and hydroxides, which give off water, and carbonates, which give off CO9. Dehydration is analogous to evaporation, and its rate depends on the moisture content of the gas. Activation energies are nearly the same as reaction enthalpies. As the reaction proceeds in the particle, the rate of reaction is impeded hy resistance to diffusion of the water through the already formed product. A particular substance may have sever hydrates. Which one is present will depend on the... 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

The value of the activation energy approaches 50000 near the stoichiometric composition. This diffusion process therefore approximates to the selfdiffusion of metals at stoichiometty where the vacancy concentration on the carbon sub-lattice is small. 

It has been shown that it is favorable for surface carbon to go into the first subsurface layer of cobalt.71 Diffusion to octahedral sites of the first subsurface layer is thermodynamically preferred by 50 to 120 kJ/mol and the corresponding activation energy is low. Theoretical calculations on the conversion of surface carbidic to subsurface carbon on Co (0001) found that the electron withdrawing power, and therefore the poisoning effect on potential CO adsorption, is maximal for subsurface carbon.41 Metal dx/ orbitals are less likely to accept electrons from the CO 5a orbital, and thus metal-CO bonding will weaken. The dxz orbital will in turn be less able to back-donate into the CO 2n orbital, resulting in additional... 

Diffusion of dioxygen occurs 102 105 times more slowly with the diffusion coefficient D 10 7 10 10 cm2 s 1 Carbon-centered atom of P changes its orbital hybridization in this reaction and changes the C—C bond angles from 120° to 109°. Since P is macroradical and is surrounded by segments of macromolecules, this process occurs with an activation energy Solubility of dioxygen in the amorphous phase of polymer is about 3 x 10 4-2 x 10 3 mol L 1 atm-1... 

Based on the experimental data and some speculations on detailed elementary steps taking place over the catalyst, one can propose the dynamic model. The model discriminates between adsorption of carbon monoxide on catalyst inert sites as well as on oxidized and reduced catalyst active sites. Apart from that, the diffusion of the subsurface species in the catalyst and the reoxidation of reduced catalyst sites by subsurface lattice oxygen species is considered in the model. The model allows us to calculate activation energies of all elementary steps considered, as well as the bulk... 

In many cases, redox reactions that are favorable from a thermodynamic point of view may not actually take place sometimes, the activation energy barriers for such reactions are too high to allow fast transformation, according to the preferred thermodynamic considerations. For example, the complete oxidation of any organic molecule to carbon dioxide and water is thermodynamically favorable. However, such oxidation is not favorable kinetically, which implies that organic molecules— including all forms of living species—are not oxidized immediately this fact explains the ability to sustain life. The reason for this difference between kinetic and thermodynamic considerations, for redox reactions, is partly because redox reactions are relatively slow compared to other reactions and partly due to the fact that, in many cases, reactions are poorly coupled because of slow species diffusion... 

In Figure 18.2 we present the diffusion coefficient of carbon in iron as a function of the inverse of the temperature (1/7). It is evident that the logarithm of D is directly proportional to l/T, as expected in view of Eq. (18.3). This type of temperature dependence is indeed typical of activation-energy-driven processes, in general. This is discussed below. For the sake of illustration, we present in Table 18.1 a few actual values of E and D. 

Figure 4.41 Variation with temperature of the diffusivity for carbon in BCC-Fe (a — Fe). Activation energy is in units of J/mol. Reprinted, by permission, from D. R. Gaskell, An Introduction to Transport Phenomena in Materials Engineering, p. 519. Copyright 1992 by Macmillan Publishing Co.

An observation of motion of single atoms and single atomic clusters with STEM was reported by Isaacson et al,192 They observed atomic jumps of single uranium atoms on a very thin carbon film of —15 A thickness or less. Coupled motion of two to three atoms could also be seen. As the temperature of the thin film could not be controlled, no Arrhenius plot could be obtained. Instead, the Debye frequency , kTIh, was used to calculate the activation energy of surface diffusion, as is also sometimes done in field ion microscopy. That the atomic jumps were not induced by electron bombardment was checked by observing the atomic hopping frequencies as a function of the electron beam intensity. 

Reactions of the hydronium ion with porous active carbon have been investigated in aqueous systems. Hydronium-ion activity, specific-anion concentration, and carbon dosage have been among the major variables studied. Rates of reaction have been found to be limited by pore diffusion, as partially verified by activation energies of —(2 to 3) kcal. per mole-deg. The results can be interpreted partly in terms of a reaction of the hydronium ion and dissolved oxygen with a surface benzpyran (chromene) group to produce hydrogen peroxide and a surface benzopyrylium (carbonium) ion with a sorbed anion, and partly in terms of physical sorption of the acid on the carbon surface. 

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