Frumkin, isotherm

Frumkin was the pioneer of Russian electrochemistry [14], Frumkin assumed that there is some interaction between the adsorbates. The free enthalpy of adsorption is then AG = AGo + ys. If the adsorbates attract one another, then y 0. If they repel, then y 0. In the case that y = 0, we recover the Langmuir result. The Frumkin isotherm [15] is written as 

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An adsorption equation known as the Frumkin isotherm has the form... 

The Frumkin isotherm can be regarded as a general isotherm from which both the Temkin and Langmuir isotherms can be obtained as special cases. Szklarska-Smialowski and Wieczorek found that the adsorption of various aliphatic compounds (acids, alcohols and amines) on steel in H2SO4 conformed with the Frumkin isotherm. 

FIG. 24 ct-c Isotherms at 22°C for purified alkanesulfonates. The curve is fitted by the Frumkin isotherm. , Sodium n-decanesulfonate x, sodium /i-dodecanesulfonate. 

The parameters of the Frumkin isotherms shown in Fig. 24 are listed in Table 16. 

Frumkin Isotherm In 1928, Frumkin derived an eqnation for interaction between the adsorbed particles. Mntnal attraction leads to an increase in the heat of adsorption, whereas repnlsion leads to a decrease. Qnantitatively, these elfects depend on the degree of snrface coverage and can be written as = Qq whereis... 

FIG. 3 Adsorption isotherm of ONS at the polarized water-DCE interface (square) experimental, (dotted) Langmuir isotherm, and (solid) Frumkin isotherm. (From Ref. 55, cop5right American Chemical Society.)... 

The same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were fitted to a Frumkin isotherm, i.e., the ions were supposed to be specifically adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. 

Kakiuchi et al. [75] used the capacitance measurements to study the adsorption of dilauroylphosphatidylcholine at the ideally polarized water-nitrobenzene interface, as an alternative approach to the surface tension measurements for the same system [51]. In the potential range, where the aqueous phase had a negative potential with respect to the nitrobenzene phase, the interfacial capacity was found to decrease with the increasing phospholipid concentration in the organic solvent phase (Fig. 11). The saturated mono-layer in the liquid-expanded state was formed at the phospholipid concentration exceeding 20 /amol dm, with an area of 0.73 nm occupied by a single molecule. The adsorption was described by the Frumkin isotherm. 

Figure3.4 (a) Experimental l-E curve obtained at 0 C and curves computed from the assumption of a Langmuir isotherm, a = experimental curve b = partial curve for the strongly bound hydrogen, c = partial curve Tor the weakly bound hydrogen, d = computed net curve, (b) Experimental l - E curve obtained at 70 C and curves computed from the assumption of a Frumkin isotherm, a = experimental curve b = partial curve for the strongly bound hydrogen, c = partial curve for the weakly bound hydrogen, d = computed net curve. After Breiter(1964).

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. 

Since C < Co, this work is positive, and the coverage decreases away from the pzc. Equations (4.13) and (4.17) can be combined with the Frumkin isotherm, resulting in ... 

The Langmuirian analysis depicted so far assumes that interactions between the bound molecules are negligible. This condition is not fulfilled in many systems, especially when the coverage comes close to saturation. In such circumstances, a Frumkin isotherm that describes equilibrium and the corresponding kinetic law may profitably replace the Langmuirian, description ... 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

Frumkin isotherms, reaction order, 38 53 Fuel, 24 222, 223 potential poisons in, 27 315, 316 unleaded, 27 312 Fuel cells... 

In the case of a Frumkin isotherm, the equilibrium constant y " is given by... 

In many works in which the adsorption process is described using the Frumkin isotherm, the solvent activity is considered as constant for every value of ag in view of the fact that the ratio of the molar fractions Xg/Xg is small. Hence,... 

On the other hand, the data for some organic compounds are often fitted into the Frumkin isotherm equation in a modified form... 

The relation between a universal Gibbs energy of adsorption AG°(= -RT np) and the energies calculated from different isotherms can be expressed as follows a. Frumkin isotherm... 

The study of thiourea adsorption on an Hg electrode from ethanolic solutions shows that different supporting electrolytes can make a comparison of the adsorption parameters more difficult. The data obtained for various electrolytes (KF, KPFe, LiCl, NH4NO3, and KCNS) suggest that coadsorption, size, and polarizability of ions strongly influence the interfacial behavior of TU, at high concentration of the ions in particular. The effect of the electrolyte on AG° and parameter A in the Frumkin isotherm is illustrated in Table 6. 

The description of a mixed adsorption layer of ionic and nonionic surfactants requires the appropriate adsorption isotherms. For example, the Frumkin isotherm gives... 

The adsorption of ionic surfactants creates an adsorption layer of surfactant ions, a Stern layer of counterions and a diffusive layer distributed by the electric field of the charged surface. Every layer has its own contribution to surface tension. For example, the adsorption of dodecyl sulfate (DS") ions from the sodium dodecyl sulfate solution is described by the modified Frumkin isotherm as... 

The adsorption of reactant in the Cd(II)-I system [44], and the influence of electrolyte concentration (1-6 M NaCl04) on the parameters of the Frumkin isotherm system were investigated [45]. The obtained data indicated that the maximum surface concentration of Cdl2 (/kaax = 1 x... 

Frumkin isotherm of Pb adsorption has been used to explain the shape of voltammetric peaks on polycrystalline electrodes and on the polycrystalline gold surface [279]. 

Sottomayor etal. [273] have investigated adsorption of n-hexanol on Au(lll) electrode from 0.2 M NaCl04 aqueous solution, applying chronocoulometry to measure dynamic capacitance and capacitive charge. They have found that in this case, adsorption may be described by the Frumkin isotherm and have determined the corresponding parameters. The obtained results were discussed and... 

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... 

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