Temkin-type adsorption isotherm

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 ... 

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. 

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. 

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... 

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].

Very often the fall in heat of adsorption is more nearly linear than logarithmic, and it is this type of behavior that led to the derivation of the Temkin adsorption isotherm. The isotherm is, in fact, derived from the Langmuir adsorption isotherm by inserting the condition that the heat of adsorption decreases linearly with surface coverage. Such an effect can arise from repulsive forces on a uniform surface or from surface heterogeneity of the surface. 

The adsorption on a solid surface, the types of adsorption, the energetics of adsorption, the theories of adsorption, and the adsorption isotherm equations (e.g., the Langmuir equation, BET equation, Dubinin equation, Temkin equation, and the Freundlich equation) are the subject matter of Chapter 2. The validity of each adsorption isotherm equation to the adsorption data has been examined. The theory of capillary condensation, the adsorption-desorption hysteresis, and the Dubinin theory of volume fllhng of micropores (TVFM) for microporous activated carbons are also discussed in this chapter. 

A typical Temkin analysis of friction-derived adsorption isotherm is illustrated in fig. 13.23. As can be seen in fig. 13.23, In (G ) vs. 0 is linear in the range 0.2 9 < 0.8, as was predicted by the model. Table 13.3 compares AG j data obtained from the Temkin model with those obtained using the Langmuir model. The data in table 13.3 are obtained from the analysis of adsorption isotherms derived from steel-steel and copper-copper boundary-friction measurements [19-23,37]. Three types of adsorbates are compared in table 13.3 triglycerides, esters of long-chain fatty alcohols and fatty acids, and methyl esters of fatty acids. As expected, the... 

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 ... 

The second type of isotherms are S-shape curves, which happen frequently in experimental measurements, corresponding to the adsorption on mesoporous (pore size >20 nm) solid materials. The first bend in the isotherm should correspond to the monolayer saturation, but no horizontally stable level appears which means that adsorption can be multilayer rather than monolayer. The section of the curve at high pressures goes up very fast due to the occurrence of capillary condensation in small pores. Other types of isotherms also predict the occurrence of multilayer adsorption. So, the assumption of monolayer absorption proposed by Langmuir has to be modified, and thereafter BET, Temkin s and Preudlich s adsorptive theory were developed. 

The dependencies of these three types of isotherms on the heat of adsorption is illustrated in Figure 5.5. Some adsorbate/adsorbent systems approximate Langmuir behavior up to certain levels of coverage [12,13], whereas many more exhibit Temkin behavior, as shown in Table 5.2. 

Not all systems obey the Langmuir isotherm, because certain basic hypotheses of the model may not be valid. It is sometimes observed that the enthalpy of adsorption varies with 0j. To take this into account, the Temkin isotherm assumes that the enthalpy of adsorption decreases as a function of the coverage. For a gas this results in a relationship of the type ... 

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