The Temkin Isotherm

One might anticipate that the Freundlich isotherm would be more widely applicable for experimental results because it allows for a decrease in the 

Logarithms of each side are taken and the equation is transposed to  

Note that Koc io/RT represents a term. Bo, which is independent of 0, and at intermediate values of 0, the last term varies relatively little with 0 ( 1.4 between 0 = 0.2 and 0.8). For chemisorption aQado RT, thus InP is primarily dependent on aQad 0/RT. Therefore, in regions of 0 not approaching zero or unity, to a good approximation equation 5.66 becomes the Temkin equation, which gives a linear relationship between 0 and InP, i.e.. 

If a nonuniform surface is now considered, it is again neeessary to divide the surface into domains, di, each of which has uniform sites giving a constant heat of adsorption [1]. Within each of these domains, a Langmuir isotherm is 

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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. 

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. 

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. 

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)... 

Taking logarithms in eqn. (176) and neglecting the linear term 0/( 1 — 0) in front of the exponential term in 0, the Temkin isotherm for the electrochemical interface, which is generally valid in the coverage range 0.2 < 0 < 0.8 [5], is obtained... 

When the adsorption energy is the linear function of surface coverage, the Temkin isotherm equation is used ... 

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... 

Some Special Aspects of the Use of the Temkin Isotherm in Electrode Kinetics... 

In this section we shall discuss a few special aspects of the application of the Temkin isotherm to electrode kinetics. 

Tims, we reach the (happy) conclusion that the kinetic equations are independent of the shape of the variation of AGq with 0, making the treatment of electrode kinetics in terms of the Temkin isotherm much more general. In fact, we could have used any unspecified function f(0) in Eq. 291. The result is the same, as long as the function chosen... 

We saw earlier (cf. Section 19) that the potential dependence of adsorption of intermediates formed by charge transfer affects the kinetics of electrode reactions. We have worked out the kinetic parameters for a few mechanisms under so-called Langmuir and Temkin conditions (i.e., when the Langmuir and the Temkin isotherms are applicable, respectively). Here we shall derive the appropriate kinetic equations for the combined adsorption isotherm. 

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