Lebedev model

Nikonenko, V., Lebedev, K., Manzanares, J.A., and Pourcelly, G. 2003. Modeling the transport of carbonic acid anions through anion-exchange membranes. Electrochim. Acta 48, 3639-3650. 

The model of Lebedev assumes that the chemical reaction of A and B begins only when they are in some active volume, v, given by 7X3 where X is the permanent crystal lattice parameter and 7 is a coefficient which depends on the nature of the matrix and which usually differs little from unity. Initially, no more than one particle is located in the cell. The particles can transfer from one cell to another with an average frequency, km, so that the diffusion coefficient Def = km /6X2. Particles appearing in the active volume, v, are in thermal equilibrium with the surrounding medium for a period l/ftm during which the probability of reaction is proportional to k, the rate coefficient of the unimolecular conversion (A. . . B) - AB. The probability of the reaction occurring in the cell is... 

The rate of radical decay has been studied by many workers but there is important disagreement between their data. These are given in Table 13. More recently, the rate of radical decay between 40 and 90°C was discussed according to the model of Lebedev [217] (section 3.2.1a). The initial radical concentration after irradiation at 20°C corresponds to the plateau of radical concentration versus dose curve. In the range 70—90°C, an activation energy of 53 kcal mole-1 was found. 

The Schlumberger version of SLDM code (called MAXANIS) was developed to model the diffusion problem at the time and frequency domains. MAXANIS uses staggered Lebedev grid and can calculate electromagnetic field in 3D anisotropic models containing blocks inclined in arbitrary directions. The code includes zero frequency solution as a limiting case. 

On the other hand, it is also quite important to study reaction kinetics in nitrogen plasmas to understand quantitative amount of various excited species including reactive radicals. Many theoretical models have been proposed to describe the number densities of excited states in the plasmas. Excellent models involve simultaneous solvers of the Boltzmann equation to determine the electron energy distribution function (EEDF) and the vibrational distribution function (VDF) of nitrogen molecules in the electronic ground state. Consequently, we have found noteworthy characteristics of the number densities of excited species including dissociated atoms in plasmas as functions of plasma parameters such as electron density, reduced electric field, and electron temperature (Guerra et al, 2004 Shakhatov Lebedev, 2008). 

Numerical studies on number densities of various excited states in the Nj plasma have eagerly been carried out all over the world (Guerra et al., 2004 Shakhatov Lebedev, 2008). We also make a numerical code to calculate number densities as functions of the following parameters gas temperature Tsr electron density Ne, total discharge pressure P, and reduced electric field E/N as a rather simplified model (Akatsuka et al., 2008 Ichikawa et al., 2010). 

Several cerium(IV) complexes of various bidentate and tetradentate hydroxypyrodinonate (HOPO) complexes have been studied as model compounds for plutonium(IV) complexes (Xu et al., 2000). Bidentate HOPO monoanions are isolelectronic with catecholate dianions and they display a similar complex formation behavior towards cerium(IV) ions. However, HOPO ligands are more acidic and form stable complexes with cerium(IV) at lower pH values than catechol. The tetradentate ligands form more stable complexes than the corresponding bidentate ligands. New types of chelators for cerium(IV) and pluto-nium(IV) are the 2,3-dihydroxyterephthalamides (Gramer and Raymond, 2004 Xu et al., 2004). Some authors have made comparisons between the coordination chemistry and the redox behavior of cerium and berkelium (Lebedev et al., 1975 Milyukova et al., 1980 Yakovlev et al., 1982). 

Figure 6.34 shows a comparison of calculated compressional velocities with experimental data from measurements on granite of different grain sizes (Lebedev et al., 1974a,b). Forward-calculated curves cover the experimental data and indicate also for this model that textural properties are connected with the aspect ratio as model input. 

---