Adsorption Temkin type

Figure 13.5 Adsorption-desorption of ammonia at 280 " C on a model V2O5—WO3/TiO2 catalyst Dashed lines, inlet NH3 concentration triangles, outlet NH3 concentration solid lines, model fit with Temkin-type coverage dependence. Adapted from ref. [3].

Based on literature indications (Lietti et al., 1997, 2000) and supported by preliminary fits of the experimental data, a non-activated NH3 adsorption process and Temkin-type NH3 desorption kinetics have been assumed, i.e. 

Other modeling efforts include soil acidification models of the macroscopic type that account for the process of S04 sorption in different ways. These approaches, which assume equilibrium conditions to prevail, include the adsorption isotherm, solubility product, and anion exchange. Prenzel (1994) discussed the various limitations of the above approaches in their capability to account for changes in pH. Recently, Fumoto and Sverdrup (2000) used a constant capacitance approach to describe the pH dependency of S04 sorption isotherms in an andisol. Other modeling efforts of S04 isotherms were reported by Gustafsson (1995) in a spodosol. Such isotherm models are of the equilibrium type and include linear and Temkin types of models. 

The transient response experiments were analyzed by a dynamic isothermal PFR model, and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over all runs. It was found that a simple Langmuir approach could not represent the data accurately, and surface heterogeneity had to be invoked. The best fit was obtained using a Temkin-type adsorption isotherm with coverage-dependent desorption energy ... 

Fig. 33 Calculated cell voltage as function of current density based on the model described by Eq. (24-27). Dashed curves correspond to coverage-independent energy of adsorption of CO on Pt, whereas solid curves, which better fit experimental data, correspond to adsorption energy falling with coverage according a Temkin-type isotherm [42].

Adsorption control The kinetics of the adsorption step in the absence of mass transport control was treated by Lorenz [87] and Delahay[89, 90] assuming either a Langmuir- or a Temkin-type formalism. 

Fig. 10. Dynamic adsorption—desorption of NH3 step changes of the NH3 inlet concentration over a model V206-W03/Ti02 catalyst (V2O6 = 1.47% w/w WO3 = 9% wAv) at 280°C. NH3 step addition at t = 0, shut off att = 750 s, and thermal desorption (TPD). Dashed lines ideal inlet NH3 concentration symbols experimental data soUd lines model fit (the Temkin-type coverage dependence = 0.487 m /mol s, = 2.67 Ed-5 l/s,E = d = 22.9 kcal/mol, y = 0.405, SInhs = 270 m /mol (94)).

The most common way to describe ammonia adsorption and desorption in SCR catalysts, in general, is to use the Temkin type isotherm [10, 13, 24, 27, 29]. The Temkin adsorption isotherm considers the adsorbate-adsorbate interactions, and in the models therefore coverage dependent heat of adsorption is used. This also results in that the activation energy for desorption of NH3 is coverage dependent ... 

A good description of the ammonia storage and desorption is critical in order to describe transient features of the SCR system, and usually a Temkin type of kinetics is used that considers the adsorbate-adsorbate interactions. The parameters for these reactions are usually fitted to TPD experiments, but also microcalorimetry studies are presented. The most common approach is to consider one ammonia adsorption site, but more detailed kinetic models use several adsorption sites. Ammonia oxidation is a reaction occurring at high temperatures, which unfortunately decreases the selectivity of the NOx reduction in SCR. It is therefore crucial to include this reaction in kinetic models for this system. 

A simple approach to capture the ammonia adsorption/desorption kinetics is the single-site approach, where NH3 is assumed to adsorb on a global single-surface site. A nonactivated ammonia adsorption process is considered while a Temkin-type coverage dependence of the activation energy is assumed for the desorption process [24]. The reaction rate expression of adsorption is given in Eq. (3.21) ... 

Nonactivated ammonia adsorption is assumed on both sites (/ ads-site-i and ads-site-2) while different rate expressions are used to describe NH3 desorption. Since Site-1 includes different types of Lewis acid sites and also ammonia physisorbed on the catalyst surface, Temkin-type coverage dependent adsorption is adopted in order to take such a site heterogeneity (/ des-site-i) into account. On the contrary, the nature of Br0nsted acid sites is well defined for zeolites, being indeed associated with the so-called bridging hydroxyls, thus it is reasonable to assume that these sites are homogeneous in terms of ammonia adsorption strength. Based on this assumption, simple Arrhenius kinetics are adopted for the NH3 desorption process from Site-2. ... 

V. Bolis, C. Morterra, B. Fubini, R UgUengo, E. Garrone, Temkin-type model for the description of induced heterogeneity—CO adsorption on group-4 transition-metal dioxides. Langmuir 9(6), 1521-1528 (1993). doi 10.1021/la00030a017... 

With this in mind, some important adsorption isotherms were introduced, and we found that each of them describes important characteristics of the adsorption process (Table 6.10). Thus, the Langmuir isotherm considers the basic step in the adsorption process the Frumkin isotherm was one of the first isotherms involving lateral interactions the Temkin is a surface heterogeneity isotherm and the Flory-Huggins-type isotherms include the substitution step of replacing adsorbed water molecules by the adsorbed entities (Fig. 6.98). 

The more desirable approach is to determine f(Q) from an assumed 0(P,T,Q) and the experimental adsorption isotherm. Sips (16) showed that Equation 1 could be treated by a Stieltjes transform, so that in principle an explicit function could be written for f(Q), provided the experimental isotherm function, 0, could be expressed in analytical form. Subsequently, Honig and coworkers (10, 11, 12) investigated this approach further. The difficulty is that only for certain types of assumed functions 0 and 0 is the approach practical. As a consequence the procedure has been first to restrict the choice of 0 to the Langmuir equation, and second to assume certain simple functions for 0 such as the Freundlich and Temkin isotherm equations. The system is thus forced into an arbitrary mold and again it is not certain how much reliance should be placed on the site energy distributions obtained. 

Several other types of adsorption isotherms have been described one applicable to fractional monolayers in which there is linear variation between the amount adsorbed and log C is called Temkin adsorption. 

Of course, other types of adsorption isotherms commonly represent the adsorption processes in heterogeneous catalysis, for example, the Freundlich isotherm and, especially in electrode processes, the Temkin and Frumkin isotherms (99). In the latter case... 

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