Adsorption Frumkin type

Underpotential deposition usually follows Frumkin-type adsorption isotherms due to strong lateral interactions and the interaction parameter, g, varies stepwise with coverage which is a function of the electrode potential. This is due to important structural and electric changes operative in the upd layers as coverage increases. 

Based on a Frumkin type adsorption isotherm (cf. Chapter 2), which after rearrangement into a c(r)-form reads... 

Thus, deviations from the ideal Langmuir isotherm can be caused both by intermolecular interactions, which result in an enthalpy of mixing, and by area differences between molecules, which produce a non-ideal entropy of mixing [18]. For a simple case where the interactions are of the Frumkin type and the partial molar areas of solvent and surfactant are constant the entropic effect of area differences results in typical features of macromolecular adsorption, e.g., a steep initial increase of adsorption ( high affinity adsorption) and a very slow rise once the surface is approximately half filled [18]. 

Let us consider now the case when a solution contains a mixture of two anionic (or cationic) surfactants (for example, homologues RiX and R2X with a eommon eounterion X ) with addition of inorganic electrolyte XY. In such systems the counterion concentration is given by the sum of concentrations of RiX, R2X and XY. For simplicity, the saturation adsorptions of the two homologues will be taken as equal, i.e., o)ix= o)2x=2too. After consideration of the surface-to-bulk distribution of both electroneutral combinations of ions, the surface layer equation of state for the Frumkin-type non-ideality of a mixture of two ionic surfactants can be written in a form similar to Eq. (2.35), where it is assumed that l/tO, = Corresponding... 

In analogy to surfactant molecules able to reorient, we assume here that protein molecules can exist in a number of states with different molar areas and that the non-ideality of enthalpy for protein adsorption layers does not depend on the state of molecules at the surface, that is, the activity coefficients are given by Eqs. (2.72). Assuming an entropy non-ideality (the convention oio = coi) and enthalpic non-ideality contribution of the Frumkin type, and taking into account the contribution of the DEL, Eq. (2.59), one can transform the equation of state for the surface layer (2.26) into... 

Simulations are used to explore the behavior of certain mechanisms see as an example the influence of the attractive or repulsive interaction between molecules (characterized by ab) upon Frumkin-type adsorption on an electrode surface (Fig. 1) [24]. 

Schulz C, Speiser B (1993) Electroanalytical simulations. Part 14. Simulation of frumkin-type adsorption processes by orthogonal collocation under cyclic voltammetric conditions. J Electroanal Chem 354 255-271... 

With this in mind, some important adsorption isotherms were introduced, and we found that each of them describes important characteristics of the adsorption process (Table 6.10). Thus, the Langmuir isotherm considers the basic step in the adsorption process the Frumkin isotherm was one of the first isotherms involving lateral interactions the Temkin is a surface heterogeneity isotherm and the Flory-Huggins-type isotherms include the substitution step of replacing adsorbed water molecules by the adsorbed entities (Fig. 6.98). 

Of course, other types of adsorption isotherms commonly represent the adsorption processes in heterogeneous catalysis, for example, the Freundlich isotherm and, especially in electrode processes, the Temkin and Frumkin isotherms (99). In the latter case... 

The maxima of fo.ads at certain A (Fig. 3.41) more or less coincide with the inflection points of the corresponding I E) isotherms (Fig. 3.36), indicating thatf ct turns maximal for an occupation of half of the adsorption sites of a given pattern. Such behavior is expected if the adsorption and desorption rates are steeply increasing functions of -6 and 9, respectively, near the point of half-coverage. This is true even in a primitive Frumkin or Langmuir-type adsorbate, because in that case... 

The von Szyszkowski isotherm establishes the connection between the change in surface tension y and the surfactant bulk concentration. Stauff (1957) has evaluated the parameters of this semi-empirical adsorption isotherm and has shown that it is in agreement with interfacial thermodynamics. Frumkin s isotherm has often recently been used to describe the adsorption of different types of surfactants, for example by Lunkenheimer (1983), Miller (1986), Wiisteneck et al. (1993), and others. One of the main aims of this book is to show that in the many... 

For a modelling of adsorption processes the well-known integro-differential equation (4.1) derived by Ward and Tordai [3] is used. It is the most general relationship between the dynamic adsorption r(t) and the subsurface concentration e(0,t) for fresh non-deformed surfaces and is valid for kinetic-controlled, pure diffusion-controlled and mixed adsorption mechanisms. For a diffusion-controlled adsorption mechanism Eq. (4.1) predicts different F dependencies on t for different types of isotherms. For example, the Frumkin adsorption isotherm predicts a slower initial rate of surface tension decrease than the Langmuir isotherm does. In section 4.2.2. it was shown that reorientation processes in the adsorption layer can mimic adsorption processes faster than expected from diffusion. In this paragraph we will give experimental evidence, that changes in the molar area of adsorbed molecules can cause sueh effectively faster adsorption processes. 

As mentioned above, a complete set of equation involves and equation of the type of Eq. (7.35), otherwise a numerical solution of the Ward-Tordai equation is not available. The software package includes all adsorption models described in Chapter 3, i.e. the classical Langmuir and Frumkin model as well as the reorientation and 2D-aggregation models. 

Figure 21 shows model predictions based on Eq. (53) when X ranges from 0 to 5. It is seen that in general the heterogeneity effect does not seriously disturb the adsorption properties for values of X smaller than 2 - 3. It is also interesting to observe that the model predicts Frumkin s type adsorption isotherms even at high X values (Figure 21B). This may explain the validity ofthe Frumkin isotherm in a number of studies using solid polycrystalline electrodes of high hydrogen overpotential. ...

Among adsorption isotherms of various types, those that can take into account the intermolecular interaction between adsorbed molecules are required to describe reaction (5). The Frumkin isotherm [91], which is based on the mean-field approximation, is the most frequently used in electrochemistry where electrochemical reactions involve adsorption and desorption processes. The Frumkin isotherm predicts the FWHM for the desorption peak to be 60 mV near the critical point, much broader than experimentally observed values of about 20 mV. To describe the phase transition of adsorbed molecules, Retter examined several isotherms and found that those based on the I sing model can reproduce the sharper phase transitions experimentally observed in the adsorption of heterocyclic compounds on mercury [92]. 

Adsorption isotherm To a first approximation it can be assumed that the coverage of the electrode 0 is proportional to the adsorbed amount r, 0 = T/T = TS, where is the maximum adsorbed amount per 1 cm and S the area covered by 1 mole of adsorbed substance [3], [1]. The dependence of the surface coverage on the volume concentration c at constant temperature is called the adsorption isotherm. There may be different types of adsorption isotherms according to the properties of the systems studied and the theoretical approach (see [1-5]). Only the proper model for the given experimental conditions should be used [73-82]. For adsorption of organic molecules the Frumkin adsorption isotherm is generaly used [1], [3] ... 

It should be noted the result mentioned earlier holds only for the van der Waals (or Volmer) isotherm. Instead, if the Frumkin (or Langmuir) isotherm is used, the value of a obtained from the surface tension fits is about 33% greater than that obtained from molecular size [44], A possible explanation of this difference could be the fact that the Frumkin (and Langmuir) isotherm is statistically derived for localized adsorption and is more appropriate to describe adsorption at solid interfaces. In contrast, the van der Waals (and Volmer) isotherm is derived for nonlocalized adsorption, and they provide a more adequate theoretical desaiption of the surfactant adsorption at liqnid-flnid interfaces. This conclnsion refers also to the calculation of the surface (Gibbs) elasticity by means of the two types of isotherms [44]. 

The results in Table 6 were obtained on carbon electrodes for which the efficiency of H2O2 production is smaller than 100%. Experiments which allow to decide whether the main path of the O2 reduction is the sequence of reactions 13 and 15 or reaction 4 have not yet been carried out on carbon electrodes. As demonstrated by Frumkin and coworkers [74—77], the adsorption of oxygen on carbon occurs in two different forms. The formation of the first type requires the dissociation of the O2 molecules into O atoms. The second type is formed without dissociation. It was suggested [36] that the ratio /13//4 of the rates of reactions 13 and 4 depends upon the ratio between the rate constant of the electrochemical production of H2O2 and the rate constant for the formation of the first type of adsorbed oxygen. Thus the mechanism of the O2 reduction on carbon will vary with the type of carbon and the pretreatment of the surface. 

---