Analogy between activated diffusion

We noted the analogy between reaction-diffusion systems and thermodynamic cooperative systems. However, the former differ essentially from the latter in that each local subsystem can operate in far-from-equilibrium situations so that it may already represent a very active functional unit. It is this difference that makes reaction-diffusion media capable of exhibiting the wealth of self-organization phenomena including turbulence never met in equilibrium or near-equilib-rium cooperative systems. In this book, we will concentrate on the fields of oscillatory units which are coupled through diffusion or some other interactions. For a variety of other aspects of reaction-diffusion systems, one may refer to Fife s book (1979a). 

Quantum chemists have developed considerable experience over the years in inventing new molecules by quantum chemical methods, which in some cases have been subsequently characterized by experimentalists (see, for example, Refs. 3 and 4). The general philosophy is to explore the Periodic Table and to attempt to understand the analogies between the behavior of different elements. It is known that for first row atoms chemical bonding usually follows the octet rule. In transition metals, this rule is replaced by the 18-electron rule. Upon going to lanthanides and actinides, the valence f shells are expected to play a role. In lanthanide chemistry, the 4f shell is contracted and usually does not directly participate in the chemical bonding. In actinide chemistry, on the other hand, the 5f shell is more diffuse and participates actively in the bonding. 

In this section the analogy between heat and mass transfer is introduced and used to solve problems. The specific estimation relationships for permeants in polymers are discussed in Section 4.2 with the emphasis placed on gas-polymer systems. This section provides the necessary formulas for a first approximation of the diffusivity, solubility, and permeability, and their dependence on temperature. Non-Fickian transport, which is frequently present in high activity permeants in glassy polymers, is introduced in Section 4.3. Convective mass transfer coefficients are discussed in Section 4.4, and the analogies between mass and heat transfer are used to solve problems involving convective mass transfer. Finally, in Section 4.5 the solution to Design Problem III is presented. 

Preparations whose active substance is imbedded between polymeric foils, have recently obtained some importance in their technical application. Such deposit systems may be inserted into cavities of the body e.g. into the uterus or below the palpebra (119). The active substance then slowly diffuses through the foil so that its concentration and duration of activity can be regulated by the type and thickness of the membrane (120). An essential advantage of this procedure lies in the possibility to remove easily, at any time, the deposit system at the end or to interrupt the treatment. With analogous implantations this is only possible by an operative treatment. 

Simulations of C NMR lineshapes have shown that experimental spectra that appear to result from a superposition of two different lines (cf. Fig. 15) can be explained by the above-mentioned molecular jump model. Analogous conclusions were drawn from macroscopic sorption kinetic data (82). From the experimental C NMR lineshapes, a mean residence time tj of 20 and 150 p-s for a concentration of six molecules per u.c. at 250 and 200 K, respectively, was derived. Provided that these jumps detected in C NMR spectroscopy are accompanied by a translational motion of the molecules, it is possible to derive self-diffusivities D from the mean residence times. Assuming the diffusion path of a migrating molecule as a sum of individual activated jumps, for isotropic systems the relation (P) = 6Dtj is valid, where (P) denotes the mean square jump length. Following experimental and theoretical studies on the preferential sorption sites of benzene molecules in the MFI framework (83-90), in our estimate the mean distance between adjacent sorption sites is assumed to be 1 nm. 

We assume that relation between the activation energy for diffusion of oxygen in silicon nanoparticle (Dj) and in bulk silicon (E ) by analogy with [1] reads... 

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