Frumkin interaction parameter

The intrinsic parameter, characterizing the type of interactions, is the Frumkin interaction parameter a, which is positive for attractive forces and negative for repulsive forces. In addition, 9 = is the fraction of the electrode covered with deposited material, and f ax is the maximal surface coverage. Combining (2.93) and (2.94) with (2.102), the following integral equation is obtained as a general solution ... 

In contrast to probucol, the slope of the above tine clearly indicates the presence of attractive interactions characterized by a Frumkin interaction parameter of o = 0.251 [105]. 

Table 5.1 Saturation coverages (rs), adsorption coefficients (fi) and Frumkin interaction parameters (g) for single- and two-component mono-layers of 2,7-AQDS and 1,4-AQClOH.

The intrinsic parameter that characterizes this type of interaction is the Frumkin interaction parameter a (in the nomenclature followed by Mirceski et al., 2007), which is positive for attractive forces and negative for repulsive ones. In the presence of lateral interactions, the response is controlled by the kinetic parameter, the charge transfer coefficient, and the interaction product aO. Thus, the kinetic parameter and the interaction product can be unified into a complex kinetic parameter, defined as ... 

Figure 4.1 Frumkin isotherms for various values of the adsorbate interaction parameter g the Langmuir isotherm corresponds to g = 0.

Frumkin isotherms for a few different values of the interaction parameter g. Positive values of g broaden the isotherm because the adsorbed particles repel each other for negative values of g the isotherms are narrow because adsorption is then a cooperative effect. The case g = 0 corresponds to the Langmuir isotherm. 

The Frumkin theory with Eqs. 17-18 presents the first improvement of the Szyszkowski-Langmuir theory and is shown in Pig. 1 by the thick line. The Frumkin theory requires input for the surfactant interaction parameter... 

Gomez etal. [160] have studied specific adsorption of potassium penicillin G (salt K) on Hg electrode from electrocapillary and capacity measurements. The Frumkin isotherm has been found applicable to the quantitative description of the data repulsive interaction parameter equaled —3.5 and standard free Gibbs energy of adsorption at the zero charge was —38.6 kJ mol h depended linearly... 

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. 

FIGURE 7.1. Dependence of surface coverage on phase-boundary potential (a) and corresponding depression of interfacial tension (b) for absorption modelled by Frumkin isotherm at two values of interaction parameters (o = 1.0 (curve 1) and 2.0 (curve 2). Adapted from Figure 1 in Ref. [15]. 

Fig. 8.9 Plot of the fraction FA/rAm against the logarithm of adsorbate activity aa according to the Frumkin isotherm (equation (8.6.20)) with the interaction parameter ad/FAm equal to 0, 2, and 5.

Ordinarily, electrochemical adsorption isotherms would have to be written (e.g., a Frumkin-like isotherm) as given in, for example, Eq. (36), which includes a lateral interaction parameter, g ... 

On the other hand, results are also presented to show the experimental limitations of methods and measuring procedures. As mentioned above, the knowledge of an adsorption isotherm of a surfactant is of fundamental importance for the study of adsorption dynamics. For the surfactants discussed in this chapter, the parameters of the Frumkin isotherm are summarised in the tables of Appendix 5D. In case the interfacial interaction parameter a is zero, the Frumkin isotherm changes into a Langmuir isotherm. 

The equations given above, based on the Frumkin isotherm, assume a random distribution of O and R sites in the film. If the film is structured, such as in an organized mono-layer deposited by the L-B technique, there will be an ordered distribution of the sites. Under these conditions, a statistical mechanical approach is needed to account for the interactions and to find the i-E curve (38). For negative values of the interaction parameter in a structured film, a double wave results, even for a single electrode reaction, while the random distribution produces only a single broadened wave. 

---