Linear surface adsorption-desorption reactions

Examples with the linear surface adsorption-desorption reactions... 

In the case of the full 2D problem with linear surface adsorption-desorption reactions (1), (2), (131) and (132), we present two tests. 

Linear surface adsorption-desorption reactions. Case A2 with the times of flow t — 100, 211 and 350 s... 

Figure 3 Comparison between the volume concentrations (1/H) c dz and for the linear surface adsorption-desorption reactions, Case A2, obtained using our effective problem (eff), average of the section of the concentration from the original problem (pbreeB) and the concentration coming from the simple average (moy) at time, t = 100 s.

Table 5 Full linear surface adsorption-desorption problem parameter values at the Case A2 diffusive transport with surface reaction...

Currently, there are numerous empirical functions of the adsorption-desorption reactions kinetics proposed for various specific conditions. As a rule, the adsorption rate is considered to be a linear function of the number of active centres on the surface of the mineral. The simplest is the single-reaction model, which assumes that the exchange is caused by the interaction of a single component i with active centres of a single type surface, is subject to the first order reactions and its rate may be presented by the following equation... 

TPD Temperature programmed desorption After pre-adsorption of gases on a surface, the desorption and/or reaction products are measured while the temperature Increases linearly with time. Coverages, kinetic parameters, reaction mechanism... 

The rate coefficients of reactions (15)-(27) were taken from the results of ab initio calculations. Reactions (28) and (29) describe the process of surface dehydroxylation/hydroxylation. We used a value of 1013 sec-1 as an estimation of the preexponential factor (this value corresponds to the characteristic frequency of internal vibrations of the reaction center) for the desorption reaction. To describe the experimental dependence of the growth rate vs. temperature adequately, we considered that the water adsorption energy is a linear function of the hydroxylation degree / ... 

The first boundary condition is equivalent to the well-known Levich approach (ca=1 for according to which, it is supposed that the concentration values vary only within a very thin concentration layer while it is supposed to keep its bulk value elsewhere [9], Eq. (3b) has been proposed by Coutelieris et al. [8] in order to ensure the continuity of the concentration upon the outer boundary of the cell for any Peclet number. Furthermore, eq. (3c) and (3d) express the axial symmetry that has been assumed for the problem. The boundary condition (3e) can be considered as a significant improvement of Levich approach, where instantaneous adsorption on the solid-fluid interface cA(ri=Tia,ff)=0) is also assumed for any angular position 0. In particular, eq. (3e) describes a typical adsorption, order reaction and desorption mechanism for the component A upon the solid surface [12,16] where ks is the rate of the heterogeneous reaction upon the surface and the concentration of component A upon the solid surface, c,is, is calculated by solving the non linear equation... 

In Step 1, the hydrated metal ions lose one H2O molecule and form an intermediate complex with a surface site. The fast relaxation associated with Step 1 was ascribed to simultaneous adsorption/desorption of the metal ions on a major portion of the 7-AI2O3 surface sites. In the second step a metal ion-surface complex is formed that results in the release of a proton. This slow relaxation was attributed to the adsorption/desorption of metal ions on the remaining, multiple type sites of the 7-AI2O3 surface that comprise a small fraction of the total surface sites. Yasunaga and Ikeda (1986) characterized the first type of surface sites as strong sites and the multiple type sites as weak sites. Linearized rate equations relating reciprocal relaxation times to the intrinsic rate constants were developed and validated for the two-step reaction mechani.sm. A plot of the linearized equation for Step 2 (the faster... 

Cyclic voltammetry is a widely used electrochemical technique, which allows the investigation of the transient reactions occurring on the electrode surface when the potential applied to the electrode is varied linearly and repetitively at a constant sweep rate between two given suitable limits. The steady-state current-potential curves or voltammograms provide direct information as to the adsorption-desorption processes and allow estimating the catalytic properties of the electrode surface. 

To calculate thermodynamic equilibrium in multicomponent systems, the so-called optimization method and the non-linear equation method are used, both discussed in [69]. In practice, however, kinetic problems have also to be considered. A heterogeneous process consists of various occurrences such as diffusion of the starting materials to the surface, adsorption of these materials there, chemical reactions at the surface, desorption of the by-products from the surface and their diffusion away. These single occurrences are sequential and the slowest one determines the rate of the whole process. Temperature has to be considered. At lower substrate temperatures surface processes are often rate controlling. According to the Arrhenius equation, the rate is exponentially dependent on temperature ... 

Surface reaction mechanisms include adsorption, desorption, surface nucleation, polynucleation, mononucleation and ion exchange reaction. The dependencies of amounts of precipitate and solution composition on time are different for each mechanism. For example, linear, exponential and logarithmic rate equations are established for volume diffusion, polynuclear growth and spiral growth, respectively. 

The adsorption/desorption rate constants were experimentally measured using a chromatographic technique W and the surface reaction rate constants were obtained independently from a non-linear regression of the data from the steady state runs. The set of coupled hyperbolic partial differential equations (l)-(4) were solved numerically by the method of characteristics. The high degree of coupling in the different characteristic directions required that an iterative method be used for the numerical solution. ... 

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