Temkin adsorption model

As a conclusion, from these experimental results alone, it is impossible to decide in favour of either adsorption law So, adsorption studies have to resort to other methods than purely kinetic ones in order to unravel the intricacies of an adsorbate-adsorbent system In the case in point, microcalorimetry allows to exclude at least one model,since chemisorption heat is a linear function not of the adsorbed volume, as it should be if the ELOVICH-TEMKIN model were obeyed, but of its logarithm ... 

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... 

Other similar cases exist, such as direct electro-oxidation of alcohols such as methanol and formic acid in low-temperature fuel cells. In these cases, an alternative to the BV formulation that accounts for the limiting adsorption and charge transfer steps is appropriate. Two common models for a surface adsorption limited reaction are the Langmuir and Temkin kinetics. In the simpler Langmuir model, the surface adsorption rate constant is independent of surface coverage. In the Temkin model, the adsorption rate constant is modeled as a function of the surface coverage of adsorbed species. In both models, a two-step reaction mechanism is assumed [6] ... 

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].

Transient deposition of hydrocarbons on zeolites during a cold start operation of the DOC can be modeled by the rate laws based on Langmuir or Temkin mechanism for physical adsorption/desorption (cf., e.g. Goralski et al., 2000 Koltsakis and Stamatelos, 2000 Kruglov and Aris, 1995 Kryl et al., 2005 Twigg, 2006). The rate laws for the adsorption and desorption of hydrocarbons are then... 

The mechanism of hydrogen evolution has been investigated by impedance measurements [371] and hydrogen-tritium kinetic isotope effects [375]. The effect of halides dissolved in solution has been studied [372, 376] these ions increase the overpotential in the sequence Cl- Adsorption isotherms for halides have been derived. They conform to the Temkin adsorption model with partial charge transfer. The lateral interaction between adsorbed particles has been calculated. It is higher for Br- than for I- and increases with overpotential on account of the weakening in the metal-halide bond. Thus, halides are substantial poisons for hydrogen evolution on iron. Poisons also include metal ions such as Cd2+, Zn2+, and Mn2+ [26]. 

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 Temkin isotherm model assumes that the heat of adsorption of all the molecules in the layer decreases linearly with coverage due to adsorbent-adsorbate interactions, and that the adsorption is characterized by a uniform disfribufion of fhe binding energies, up fo some maximum... 

Before examining the NMR, it is useful to consider some adsorption and desorption studies of this standard catalyst. Hydrogen chemisorption data have been modeled by a Langmuir isotherm for pressures between 1 and 80 Torr (Fig. 26a) (80) but also by a Temkin isotherm at pressures between 0.1 and 100 Torr (Fig. 26b) (48). The Langmuir isotherms in Fig. 26a give H/Pt ratios for monolayer adsorption of 1.17 (circles) and 1.06 (triangles). The break point in the Temkin isotherm of Fig. 26b corresponds to H/Pt = 0.82 (48). (The part of the isotherm below 0.1 Torr has not often... 

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].

A comparison of mechanistic models with observed kinetics is strongly dependent on the adsorption isotherm adopted for reactants, products, or intermediates. Because of simplifying assumptions and of the uncertainties about surface species and catalytic sites, more than one isotherm can yield kinetic expressions in accord with the experimental data. The Langmuir isotherm 94a) is still used extensively because of its simplicity. However, the assumption of a homogeneous catalytic surface with localized adsorption is often not valid, as shown above. Hence, the increasing efforts to use the more realistic Temkin isotherm 88). 

The treatment below originated from M.Temkin, who in the late 1930s developed the theory of adsorption and kinetics on real (nonuniform) surfaces and proposed a special model of nonuniformity. Contributions by Zeldovich and Roginskii to this field in the same years were also essential. 

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