Temkin model

Temkin was the first to derive the ideal solution model for an ionic solution consisting of more than one sub-lattice [13]. An ionic solution, molten or solid, is considered as completely ionized and to consist of charged atoms anions and cations. These anions and cations are distributed on separate sub-lattices. There are strong Coulombic interactions between the ions, and in the solid state the positively charged cations are surrounded by negatively charged anions and vice versa. In the Temkin model, the local chemical order present in the solid state is assumed to be present also in the molten state, and an ionic liquid is considered using a quasi-lattice approach. If the different anions and the different cations have similar physical properties, it is assumed that the cations mix randomly at the cation sub-lattice and the anions randomly at the anion sub-lattice. 

With Amix//m = 0 the ideal Temkin model for ionic solutions [13] is obtained. If deviations from ideality are observed, a regular solution expression for this mixture that contains two species on each of the two sub-lattices can be derived using the general procedures already discussed. The internal energy is again calculated... 

This principle serves as the basis for a number of models of fused salt systems. Perhaps the best known of these is the Temkin model, which uses the properties of an ordered lattice to predict thermodynamic quantities for the liquid state [79]. However, certain other models that have been less successful in making quantitative predictions for fused salts may be of interest for their conceptual value in understanding room temperature ionic liquids. The interested reader can find a discussion of the early application of these models in a review by Bloom and Bockris [71], though we caution that with the exception of hole theory (discussed in Section II.C) these models are not currently in widespread use. The development of a general theoretical model accurately describing the full range of phenomena associated with molten salts remains a challenge for the field. 

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... 

Comparison of AGads (kcal/mol) of Vegetable Oils Obtained from the Analysis of Metal-Metal Friction Data Using the Langmuir and Temkin Models... 

FIG. 6. Partial molar entropies of the alkali chloride in binary liquid mixtures with magnesiimi chloride. Broken lines represent values calculated from the Temkin model. (From 0stvold ). 

The Temkin model holds in binary silicate melts, M0-Si02. 

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] ... 

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