Freundlich theory

Freundlich-Type Relations A binary Freundlich isotherm, obtained from the ideal adsorbed solution theory in loading-explicit closed form [Crittenden et al., Environ. Sti. TechnoL, 19,1037 (1985)], is... 

In this chapter, we consider several simple models of ion sorption and exchange that can be applied within the context of a geochemical model. These models include distribution coefficients, Freundlich and Langmuir isotherms, and ion exchange theory. In the following chapter (Chapter 10), we consider surface com-plexation theory, which is more complicated but in some ways more robust than the models presented here. 

The Freundlich equation proved to be applicable to the adsorption of liquids with only limited ranges of concentration. It was replaced by the Langmuir equation (see later on) and others which had a theoretical basis in the kinetic theory of gases. It is clear that neither the Freundlich nor the Langmuir equation can describe isotherms of the shape shown in Figure 10.5. 

In addition to the interphase potential difference V there exists another potential difference of fundamental importance in the theory of the electrical properties of colloids namely the electro-kinetic potential, of Freundlich. As we shall note in subsequent sections the electrokinetic potential is a calculated value based upon certain assumptions for the potential difference between the aqueous bulk phase and some apparently immobile part of the boundary layer at the interface. Thus represents a part of V but there is no method yet available for determining how far we must penetrate into the boundary layer before the potential has risen to the value of the electrokinetic potential whether in fact f represents part of, all or more than the diffuse boundary layer. It is clear from the above diagram that bears no relation to V, the former may be in fact either of the same or opposite sign, a conclusion experimentally verified by Freundlich and Rona. 

Significantly later, foreign scientists reached a similar conclusion regarding the Freundlich isotherm. In the USSR, a theory of adsorption on an inhomogeneous surface was developed independently by M. I. Temkin of the Karpov Physico-Chemical Institute in connection with electrochemical research by Academician A. N. Frumkin. M. I. Temkin s work on a logarithmic isotherm was cited in [74] and published in [75]. The theory of adsorption and catalysis on an inhomogeneous surface was especially extensively developed by S. Z. Roginskii. 

Freundlich s precirculated paper suggested, as in his remarks at the 1929 Berlin colloquium, [31] that current experimental results did not permit a clear decision between the rival theories, [32] and Polanyi s paper argued the usefulness of both Langmuir s and his approaches. [33]... 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

The reader interested in the development of the theory of the structure of mono-molecular surface films will find excellent accounts in the following, to all of which the author is indebted. Rideal, Surface Chemistry, 2nd. ed., chap, iii (1930) Mar-celin, Solutions SuperficieUes (1931) Freundlich, Kapillarchemie, 3rd. ed., pp. 438 ff. (1930) Heymann, Kolloid-Z., 57, 81 (1931) other reviews by the author may be found in Chemical Reviews, 3, 163 (1926) Science Progress, 21, 621 (1927) KoUoid ., 57, 125 (1931) 61, 168 (1932). 

Up till about 1921, it was often supposed that the potential could be identified with the single potential difference at the phase boundary. Freundlich and his collaborators1 showed that this is quite impossible, since the variation with concentration, and the influence of adsorbed substances, are entirely different in the two cases sometimes indeed the two potentials may have different signs. The phase boundary potential, if defined as the Volta potential, is the difference between the energy levels of the charged component, to which the phase boundary is permeable, inside the two phases when these are both at the same electrostatic potential. We have seen that it is difficult, or impossible, to define the phase boundary potential in any other way (see 2 and 3). It includes the work of extraction of the charged component from each phase, and this includes the part of the double layer which according to Stern s theory is fixed. The potential is merely the potential fall in the mobile, diffuse part of the double layer, and is wholly within one phase. 

Equation 6.9 is the same as the Freundlich empirical equation 6.1. This agreement was taken as a proof for the theory of monomolecular adsorption advanced by Langmuir. 

Theory The Freundlich isotherm developed in 1924 by Freundich (16) is widely used to study oil processing adsorption. It is applied as an empirical expression to describe the reversible adsorption of a single solute from aqueous solution at equilibrium at a fixed temperature, and it is expressed as... 

Obstacles to practical application of the Langmuir and Freundlich isotherm theories include the following (1) These isotherms do not effectively address adsorption versus degradation and competitive adsorption (2) the conclusions are not all inclusive i.e., adsorption constants and coefficients do not hold true in all cases within similar oil types let alone across different oil types (3) the process has so many variables that the additive variance is commonly too great to prove any subtle difference between clays other than a vastly different level of activity (this problem is especially true when using log vs. log plots with incremental changes on the order of 0.1%) and (4) the adsorption constants and coefficients have limited use for the refiner. 

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