Temkin-isotherm

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 

Substituting in Equation (11), the Temkin relationship (Equation (A19)) produces 

Taking the derivative of Equation (A20) with respect to time, it yields dCi 

Substituting Equation (A22) in the left-hand side term of Equation (A21), one obtains 

Equation (A24) contains five unknown parameters, Kj, Ng, k, /, and Cl.o/ whose determination may be carried out by a best fitting procedure. As done in the cases previously described, integration of Equation (A24) must be performed with the condition that at f = 0 the substrate concentration in the liquid phase is that in equilibrium with the initial photoadsorbed amoimt, Cl.o this initial concentration is unknown, but it may be determined by the regression analysis carried out with the experimental data obtained after the start of irradiation. 

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This isotherm is consistent with the modified electrochemical Langmuir isotherm, the Nemst equation and the potential-work function equivalence. For intermediate 0j and Pj values the isotherm of Eq. (6.58) is well approximated both by the Fowler-Guggenheim and by the Temkin isotherms. 

Temkin Isotherm Numerous deparmres of the experimental data from the Langmuir isotherm can be explained in terms of insufficient arguments for the third... 

On inhomogeneous surfaces where adsorption obeys the Temkin isotherm, an exponential factor will appear in the kinetic equation ... 

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. 

At Pt electrodes, adsorption of oxygen species is supposed to be controlled by the Temkin isotherm in the low overpotential region [Damjanovic and Bockris, 1966], whereas in the higher overpotential region, the absence of an oxide layer leads to... 

The dependence of the relative coverage of the platinum electrode with methanol on its concentration in solution indicates that the adsorption of methanol obeys the Temkin isotherm (4.3.46). 

The idea that the surface will adsorb A with essentially the same enthalpy for all values of 0 is clearly very simplified and attempts have been made to establish more realistic isotherms. Perhaps the best known of these is the Temkin isotherm which is based on the notion that the magnitude of the enthalpy of adsorption would decrease as the coverage increases. If the free energy of adsorption at 0 = 0 is AG , then the simplest assumption is that... 

Finally, combining (1.9) with the Temkin isotherm leads to the most general isotherm commonly used to describe the coverage of neutral or ionic species at the electrode surface ... 

As the plots show, the Temkin isotherm provides the best fit, although the Freundlich also is close. 

Hydrogen evolution reaction, mechanism, 1135, 1151, 1163, 1164, 1189 catalytic pathway, 1163,1194, 1255 electrocatalysis, 1280 Frumkin-Temkin isotherm, 1194 Langmuir isotherm, 1194 Hydrogen coadsorption... 

Tafel equation, 1054,1066,1106,1115,1133, 1249,1404,1440, 1456,1507,1528 applications, 1508 and distribution of electronic states, importance, 1466 importance, 1508 in quantum calculations, 1495 in semiconductors, 1085 tunneling, 1495 Tafel, Julius, 1106 Tafel lines, oxygen reduction, 1207 Tamm states, 1082 Tarasevich, 1495 Taylor, electrodeposition, 1303 Temkin isotherm, 927, 938, 1195... 

Whenever the adsorption process can be represented by a Temkin isotherm (see Section 6.8.10), a linear decrease of Awith 0 exists because this is the basis of the Temkin isotherm. 

This is the complete Temkin isotherm. In the second part of this equation, the term pj represents the value of p when 5 = 1, and Po> the value of p when s = 0. If the appropriate conditions exist such that pjC 1 p0c, i.e., all the patches with large p are full and the others are empty independently of the concentration, then,... 

In Section 6.8.10 we saw that the Temkin isotherm is based on the Langmuir isotherm. One advantage of the Temkin isotherm is that it considers the heterogeneity of the surface. However, like the Langmuir isotherm, it does not take into account lateral interactions between the adsorbates. 

Table 6.10 gives a list of several isotherms, including the ones already discussed, and some of their main characteristics. The isotherms we have presented here are focused on particular aspects of the adsorption phenomenon. For example, the Langmuir isotherm focuses on the basic process of transferring a molecule from the bulk to the electrode the Temkin isotherm focuses on interpreting the adsorption process in terms of the heterogeneity of the adsorbing surface etc. 

How does the Temkin isotherm (Eq. 6.206) reduce at (a) very low concentrations and (b) very high concentrations (Gamboa-Aldeco)... 

When Should One Use the Frumkin-Temkin Isotherms in Kinetics Rather than the Simple Langmuir Approach ... 

If the relative values of the rate constants among the consecutive or parallel steps in reactions such as that of hydrogen evolution have the most decisive influence here, Frumkin-Temkin should be used. If they lead to a situation in which the intermediate radical coverage tends toward zero or one, the matter is decided. As remarked above, for 0 — 0 or 0 — 1, the Frumkin and Temkin isotherms coincide in effect with that of Langmuir. 

In the following discussion, an example is given that serves to show that introducing a Frumkin-Temkin isotherm does affect the kinetic relation between the current density, i, and the corresponding overpotential. The example chosen will use the hydrogen evolution reaction once more because it is relatively simple but at the same time involves consecutive steps and alternative pathways thus it has characteristics of many practical electrode reactions likely to be met in practice.68... 

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