Frumkin adsorption

TABLE 16 Parameters of Frumkin Adsorption Isotherms Depicted in Fig. 24... 

The basic assumption of the Langmuir adsorption isotherm is that the adsorbed molecules do not interact. This condition is not always fulfilled for adsorption, particularly on electrodes. The Frumkin adsorption isotherm includes interaction between molecules in the adsorption film,... 

Fig. 4.8 The Frumkin adsorption isotherm. The value of the interaction coefficient a is indicated at each curve. The transition in the metastable region is indicated by a dashed...

The electrochemical standard free enthalpy, of dissociation of the surface acid or base sites consists of the chemical standard free enthalpy, AG°, an electrostatic energy, eA, and an interaction energy, m0, for the adsorption coverage in the Frumkin adsorption model is the potential across the compact layer, 0 is the adsorption coverage, and m is the Frumkin parameter [Frumkin, 1925] ... 

The orientation and Frumkin adsorption models have recently been combined to describe adsorption layer for surfactant-protein mixtures in [37] and [38]. 

The Frumkin adsorption isotherm for the surfactant ions gives... 

Fig.l Surface tension versus solution concentration of nonionic surfactant CnEs as measured at r = 298.15 K (data points) [45], and as predicted by the Szyszkowski-Langmuir adsorption model (thin line) described by Eq. 20 and by the Frumkin adsorption model (thick line) described by Eqs. 17-18... 

Fig. 3 Comparison of the surface tension for nonionic surfactant CnEg as measured at T = 298.15 K, data points [45], with improved models considering orientational states of surfactant molecules at the surface. The data shown are obtained by regression analysis minimizing the revised chi-square The calculation with fi = 0 represents the best fit of the improved Szyszkowski-Langmuir model described by Eqs. 21 and 22. The other calculated curve with =- 3.921 shows the best fit of the improved Frumkin adsorption model described by Eqs. 23 and 24...

The standard deviation has been determined as ct = j where v is the number of degrees of freedom in the fit. The parameters for the molecular interaction /3, the maximum adsorption Too, the equilibrium constant for adsorption of surfactant ions Ki, and the equilibrium constant for adsorption of counterions K2, are thus obtained. The non-linear equations for the Frumkin adsorption isotherm have been numerically solved by the bisection method. 

Sander and Henze [50] have performed ac investigations of the adsorption potential of metal complexes at Hg electrode. Later, Sander etal. [51] have studied electrosorption of chromium - diethylenetriaminepentaacetic acid (DTPA) on mercury in 0.1 M acetate buffer at pH 6.2 using a drop-time method. The changes in the interfacial activity of the Cr(III)-DTPA complex with the bulk concentration obeyed the Frumkin adsorption isotherm. 

In contrast to 20H-AQ monolayers, l-amino-2-sulfonic-4-hydroxyanthraquinone (1,2,4-AQASH) adsorbates exhibit significant lateral interactions, thus requiring the use of the Frumkin adsorption isotherm [10]. Figure 4.6 shows that the optimized Frumkin isotherm provides a satisfactory fit to the experimental surface coverages for monolayers assembled from both the reduced and oxidized forms. 

Figure 4.6 Dependence of the surface coverage on the bulk concentration of the quinone (where and A denote the areas under the anodic and cathodic peaks, respectively) and hydroquinone (where denotes both anodic and cathodic data) forms of 1,2,4-AQASH. The supporting electrolyte is 1.0 M HCIO4. The dashed lines represent the best fits to the Frumkin adsorption isotherm where error bars are not shown, the errors determined from at least three independently formed monolayers are comparable to the sizes of the symbols. Reprinted with permission from R.J. Foster, T.E. Keyes, M. Farrell and D. O Hanlon, Langmuir, 16, 9871 (2000). Copyright (2000) American Chemical Society...

A. Surfactant Adsorption. The surface density of surfactant has a relevant role for both the double-layer (via the surface charge density) and the hydration interaction (via the dipole moment density of the ion pairs formed). It will be computed using the Frumkin adsorption isotherm ... 

Fowler-Frumkin isotherm - Frumkin adsorption isotherm... 

The Frumkin epoch in electrochemistry [i-iii] commemorates the interplay of electrochemical kinetics and equilibrium interfacial phenomena. The most famous findings are the - Frumkin adsorption isotherm (1925) Frumkin s slow discharge theory (1933, see also - Frumkin correction), the rotating ring disk electrode (1959), and various aspects of surface thermodynamics related to the notion of the point of zero charge. His contributions to the theory of polarographic maxima, kinetics of multi-step electrode reactions, and corrosion science are also well-known. An important feature of the Frumkin school was the development of numerous original experimental techniques for certain problems. The Frumkin school also pioneered the experimental style of ultra-pure conditions in electrochemical experiments [i]. A list of publications of Frumkin until 1965 is available in [iv], and later publications are listed in [ii]. 

In the special case of Langmuir isotherm we have P = 0, and then =1.) The Bntler eqnation is nsed by many authors as a starting point for development of thermodynamic adsorption models. It shonld be kept in mind that the specific form of the expressions for n, and which are to be snbstituted in Equation 5.16, is not arbitrary, but must correspond to the same thermodynamic model (to the same expression for F,— in our case Equation 5.11). At last, snbstitnting Equation 5.16 into Equation 5.9 we derive the Frumkin adsorption isotherm in Table 5.2, where K is defined by Equation 5.3. 

Figure 1. Apparent adsorption isotherms of Triton-X-100 in 0.55 mol dm-3 NaCl obtained with various accumulation times (I) 30, (2) 60, (3) 180, (4) 300s and theoretical Frumkin adsorption I. olhcrms of Trilon-X-lOO with interaction factors a - 1.0 (curve 5) and 1.25 (curve 6). Batina et al.,...

This is known as the Frumkin adsorption isotherm. Obviously, for / = 0 it reduces to the Langmuir form. If y is negative, va > vd, and the cost of adsorption increases faster than desorption and relative to the case of constant Et, the system is repulsive. For y > 0, on the other hand, the system is cohesive. ... 

Adsorption layers of the same kind as at fluid interfaces are also formed at low-energy solid -water surfaces, as it was established on PE, polystyrene, paraffin, carbon black, and other related materials. The classical Langmuir or Frumkin adsorption isotherm is often applicable to describe this behaviour. Studies on surfactant adsorption at various solid surfaces have been summarised in a great number of reviews [2, 7, 8, 54, 98, 101, 111, 121, 126, 141, 144, 145, 177, 186, 190, 194-198]. The adsorption at the solid/liquid interfaces is governed by a number of factors ... 

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. 

Here the coefficient, B, is called attraction constant, in analogy with the corresponding factor in the Frumkin adsorption isotherm. However, it has got the opposite sign, that is, it reflects the repulsion between the adsorbed species, the amplitude of which is diminished owing to the relaxation of the adsorbed ion ensemble (factor k). The entropy term for the adsorption state is taken without the saturation term , compare Eqs. (71) and (72), since the charging degree for s,p-metals is mostly very low with respect to the complete coverage. 

Traditional models for calculation of adsorption isotherms are based on the assumption that surface-active compounds at the interface can substitute for adsorbed molecules of one solvent but cannot penetrate the second phase. Although these models are useful for metal-water interfaces, recent interest has focused on the surface chemistry of amphiphilic compounds that can penetrate both phases and replace adsorbed molecules of both solvents, for example, water and oil. Amphiphilic molecules consist of two moieties with opposing properties a hydrophilic polar head and a hydrophobic hydrocarbon tail. We present here, a theoretical analysis of the generalized Frumkin adsorption isotherm for amphiphilic compounds. 

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