Equilibrium adsorption isotherm Temkin

Of the equilibrium adsorption isotherms observed on real surfaces, three hold particular positions. They are the Temkin isotherm, the Freundlich isotherm, and the Dubinin-Ra-dushkevich isotherm, and are reviewed in Refs. [22, 23]. The analysis carried out in Ref. [24] of several previously reported, often quoted, adsorption systems has shown that the Freundlich and the Dubinin-Radushkevich isotherms are the high-pressure and low-pressure limits, respectively, of a unique isotherm referred to as FDR. In turn, the FDR isotherm is a special case of a more general isotherm proposed by Jajoniec [25] on the basis of a previous idea of Heer [26],... 

As we have mentioned, the Elovich equation for adsorption kinetics is associated mainly with the systems in which the equilibrium adsorption isotherm is described by Temkin s equation [3],... 

Following Temkin and Pyzhev, the empirical equation (1) when combined with the assumption of equilibrium according to (6) leads to a logarithmic adsorption isotherm for nitrogen... 

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. 

At equilibrium, the sulphur coverage of the nickel surface, 0, can be calculated by a Temkin-like adsorption isotherm dependent on the temperature and the H2S/H2-ratio 1,9) with the parameters found by Alstrup et al (P) equation 5. 

Whatever is the mechanism of OHad and Oad formation, the principal point of this adsorption theory is that Pt surface atoms are stable in their positions in the lattice and the integrity of the Pt lattice is retained after an adsorption-desorption cycle in the voltammetry studies. The formation of adsorbed layer is described quantitatively by adsorption isotherms at equilibrium, e.g., Temkin or Frumkin adsorption isotherms and corresponding kinetic equations such as the Elovich equation. Intrinsic to the adsorption theory is the concept of the maximum surface concentration corresponding to monolayer coverage by the ad-particles on all available adsorption sites. " ... 

Temkin s equilibrium isotherm corresponds to a logarithmic form of a nonlinear adsorption isotherm given by... 

References 23 and 24 address sulfur poisoning in significant detail. Reference 23 illustrates the relative activity of a catalyst as a function of mean sulfur coverage. Also, that reference lists a Temkin-like adsorption isotherm for equilibrium sulfur coverage, as a function of temperature, hydrogen, and hydrogen sulfide mole Ifaction. As stated, it takes years to establish sulfur equilibrium in a reformer. 

On another hand, the Temkin and Freundlich isotherms are just two among the several isotherms (like Dubinin-Radushkevich, Toth, and their blends) often met in equilibrium adsorption. This observation immediately generates the problem of explaining why the kinetic equivalents of the latter isotherms are not observed or (alternatively) identifying their kinetic equivalents in the reported experimental data. 

In order to overcome this difficulty Temkin and Pyzhev proposed to abandon the Langmuir adsorption concept, which basically assumes the surface of the catalyst to be energetically uniform. Instead they chose to use for the adsorption equilibrium the isotherm proposed by Frumkin and Slygin [19],... 

Nal concentration, up to 1 X 10 They also obtained steady-state data using a potential step method. The applied potential was initially set at -0.9 V, where no iodide absorption occurs. The electrode was stepped to various positive potentials and A/(ad) was recorded until equilibrium values were obtained. Similar measurements were done in an electrolyte without Nal, and A/(no-ad) was recorded as a reference. The net change in frequency was determined as IAA/I = A/(ad) -A/(no-ad). Figure 27.22 shows I AA/I vs. E plots for various Nal concentrations. Analysis of the data showed that iodide adsorption occurred in accordance with the Temkin isotherm. 

The condition for equilibrium is that the rates of adsorption and desorption are equal. Isotherms may be obtained by equating these rates. Three theoretical isotherms, those of Langmuir (1918), Freun-dlich (1926) and Temkin (Brunauer et al. 1942) are important. Only the Langmuir isotherm is presented here because it is the one most widely used in work related to gas-solid catalytic systems. 

Thus, in the limit of a strong surface heterogeneity leading to the Temkin equilibrium isotherm, the assumption of a strongly "activated" adsorption leads us to the rate expression... 

That the Temkin isotherm could be ascribed to adsorption on equilibrium surfaces was first guessed by lonescu, but his derivation was based on rather weak arguments. The above consideration, on the contrary, is already satisfactory and can be made more precise by inserting distribution function (28) in equation (4) and by computing this integral numerically. The results in a log-log plot are shown in Figure 5, and confirm the Henry behaviour at low pressures and the saturation at high pressures. 

A simplified model of equilibrium surface suggests that the DR behaviour is observed in low-pressure adsorption on patchwise, weakly heterogeneous surfaces which were grown in equilibrium conditions and hence were quenched at the adsorption temperature. At higher pressures, these surfaces should exhibit the Freundlich behaviour, while in the case of strong heterogeneity adsorption should be described by the Temkin isotherm. The three classic empirical isotherms, Freundlich, Dubinin-Radushkevich, Temkin, seem therefore to be related to adsorption on equilibrium surfaces, and the explanation of these experimental behaviours can be seen as a new chapter of the theory of adsorption the theory of physical adsorption on equilibrium surfaces. 

The steady-state coverage with carbonaceous species may be determined rather by the balance of the rates of different electrochemical reactions than by an adsorption equilibrium. The treatment [13] of the dependence of the coverage with C HpOq upon potential and methanol bulk concentration b M is an example based on Eq. 4. This treatment by Biegler and Koch predicts variations of coverage and current with bCv, which are similar to those obtained [11] by Bagotzky and Vasiliev under the assumption that the adsorption equilibrium is established and follows a Temkin isotherm. It is questionable for this reason whether the recent determination [22] of the heat of chemisorption of C HpOq, formed under anodic polarization from methanol on platinum in sulfuric acid solution, is meaningful. 

We have estabhshed earlier [21-23] that Gly and a-Ala anions are adsorbed on the surface of polycrystalline Pt-electrode in a wide enough double layer potential range. Their adsorption is not accompanied by dissoeiation with the detaehment of H [24], and the equilibrium coverage of the smfaee ean equally be deseribed by the Temkin and the Frumkin isotherms. The results of preliminary kinetie investigations have confirmed the anodic destruction of Gly and a-Ala on platinum, though at much more positive potentials. So the question arises, whether the oxidation of Gly (and, probably, of a-Ala ) proeeeds from the adsorbed state, as is suggested in [19], and what is the role of a possible adsorption of the products of the anodic reaction, whose nature requires additional specification. 

Remark.- The homographic law with the root of the pressure comes from equilibrium of the Langmuir isotherm for adsorption. The choice of another isotherm wonld lead to another law of pressure, for example, the Temkin isotherm would give a logarithm law of pressure for a mode with an external interface reaction as the rate determining step. 

---