Isotherms, Freundlich complex

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Empirical Models vs. Mechanistic Models. Experimental data on interactions at the oxide-electrolyte interface can be represented mathematically through two different approaches (i) empirical models and (ii) mechanistic models. An empirical model is defined simply as a mathematical description of the experimental data, without any particular theoretical basis. For example, the general Freundlich isotherm is considered an empirical model by this definition. Mechanistic models refer to models based on thermodynamic concepts such as reactions described by mass action laws and material balance equations. The various surface complexation models discussed in this paper are considered mechanistic models. 

The adsorption data is often fitted to an adsorption isotherm equation. Two of the most widely used are the Langmuir and the Freundlich equations. These are useful for summarizing adsorption data and for comparison purposes. They may enable limited predictions of adsorption behaviour under conditions other than those of the actual experiment to be made, but they provide no information about the mechanism of adsorption nor the speciation of the surface complexes. More information is available from the various surface complexation models that have been developed in recent years. These models represent adsorption in terms of interaction of the adsorbate with the surface OH groups of the adsorbent oxide (see Chap. 10) and can describe the location of the adsorbed species in the electrical double layer. 

The above surface complexation models enable adsorption to be related to such parameters as the number of reactive sites available on the oxide surface, the intrinsic, ionization constants for each type of surface site (see Chap. 10), the capacitance and the binding constants for the adsorbed species. They, therefore, produce adsorption isotherms with a sounder physical basis than do empirical equations such as the Freundlich equation. However, owing to differences in the choice of adjustable... 

In this section, we will discuss PVA-Iodine complexes which are formed at high iodine concentrations of soaking. Figure 22 shows the iodine sorption isotherm of a PVA film, obtained by soaking in iodine-KI solutions at 20 °C. The data in Fig. 22 apparently satisfy a Freundlich relation i.e. InQ increases linearly with InC. At 50 wt % sorption, the distribution coefficient is about 6 which is defined as the ratio of iodine concentration per water in a swollen PVA film to that of the soaking solution. This large distribution coefficient is due to the iodine sorption in the crystalline phase as well as in the amorphous phase. 

From the scientific point of view, however, all approaches in the sense of the Kd concept (Henry, Freundlich or Langmuir isotherm) are unsatisfactory, since the complex processes on surfaces cannot be described by empirical fitting parameters. Boundary conditions like pH value, redox potential, ionic strength, competition reactions for binding sites are not considered. Thus results from laboratory and field experiments are not transferable to real systems. They are only advisable to provide a suitable prognosis model, if no changes concerning boundary conditions are to be expected and if no parameters for deterministic or mechanistic approach can be determined. 

Adsorption isotherms, 178-190 Freundlich, 179 Langmuir, 183 S-type, 178-179 L-type, 178-179 C-type, 178-179 H-type, 178-179 Aerobic decomposition, 323 Alkalinity, 82—91 Definition, 88 Types of alkalinity, 82 Aluminosilicate clays, 102 Aluminum cation, 103, 160 Acidity, 160 Complexation, 160 Polymeric aluminum, 160 Exchangeable, 160,162 Hydrolysis, 69, 75 Solubility, 71 Soluble complexes, 69 Aluminum hydroxide, 78-80 Solubility, 78 pH effect, 79... 

As with iodine, starch forms an inclusion complex with bromine vapor.205 Depending on the starch variety, different colors are developed by the complex. Maize and wheat produce an ochre color, rice produces a light-buff color, potato and sago develop a pale-yellow color, and cassava forms a cream color.69 Iodine cyanide (and bromine)-amylose complexes are brown-black and dark brown, respectively.206 The adsorption of chlorine and iodine proceeds according to the Freundlich isotherm. A discontinuity on the Freundlich isotherm plot is reported, which possibly results from the swelling of starch granules454... 

In Fig. XVII.l the points labeled by O are those for a Freundlich isotherm, fitted by B 0.665 and 6 — 0.86 to the complex l.angmuir isotherm. Over the range of concentrations (A)/X2.i from 0.5 to 8, the two isotherms have a maximum deviation of 8 per cent and an average deviation of about 2 per cent, showing the closeness of the fit which is attainable between them. The fit could have been shifted to lower pressures by choosing different parameters. 

Figure 4 Comparison of sorption models. Several commonly used sorption models are compared with respect to the independent constants they require. These constants are vahd only under specific conditions, which must be specified in order to properly use them. In other words, the constants are conditional with respect to the experimental variables described in the third column of the figure. is the radionuclide distribution constant K and n are the Freundlich isotherm parameters and are surface complexation constants for protonation and deprotonation of surface sites K-, are surface complexation constants for sorption of cations and anions in the constant...

Between the simplicity of the model and the complexity of the TLM, there are several other sorption models. These include various forms of isotherm equations (e.g., Langmuir and Freundlich isotherms) and models that include kinetic effects. The generalized two-layer model (Dzombak and Morel, 1990) (also referred to as the DLM) recently has been used to model radionuclide sorption by several research groups (Langmuir, 1997a Jenne, 1998 Davis, 2001). Constants used in this model are dependent upon the concentration of background electrolytes and... 

Modifications to the Langmuir and Freundlich isotherm equations have been made to extend their flexibihty for accomodating the effects on As adsorption of pH variability (Anderson et al., 1976) and ionic competition (Kingston et al., 1971 Roy et al., 1986a). However, even these modified equations are limited in their abihty to simulate As adsorption in complex natural environments. 

Natural surfaces generally are too complex to be characterized as having uniform solute interaction energies, however. It is therefore not unexpected that sorption equilibrium data for natural soils and sediments are rarely described adequately by the Langmuir model. Such data are commonly described more satisfactorily by the empirical Freundlich isotherm model, which has the form... 

Some examples of simple and complex Freundlich and Langmuir isotherm plots are shown in Fig. 10.12 from Domenico and Schwartz (1990). 

Several models have been developed to describe reactions between aqueous ions and solid surfaces. These models tend to fall into two categories (1) empirical partitioning models, such as distribution coefficients and isotherms (e.g., Langmuir and Freundlich isotherms), and (2) surface-complexation models (e.g., constant-capacitance, diffuse-layer, or triple-layer model) that are analogous to solution complexation with corrections for the electrostatic effects at the solid-solution interface (Davis and Kent, 1990). These models have been described in numerous articles (Westall and Hohl, 1980 Morel, Yeasted, and Westall, 1981 James and Parks, 1982 Barrow, 1983 Westall, 1986 Davis and Kent, 1990 Dzombak and Morel, 1990). Travis and Etnier (1981) provided a comprehensive review of the partitioning and kinetic models typically used to define sorption of ions by soils. The reader is referred to the cited articles for details of the models. 

A more complex and correct function was proposed by Herbert Max Finlay Freundlich (1880-1941). It is called Freundlich sorption isotherm ... 

Henry and Freundlich isotherms did not provide for C. value growth limit. Irving Langmuir (1881-1957) in 1916 introduced such limit C and proposed a more complex but more accurate equation. He viewed the adsorption balance as a result of the competition between the rates of adsorption and desorption. If maximum adsorbent capacity relative component i is j> it may be assumed that the adsorption rate is proportion-... 

Most of the research on metal sorption at the mineral/water interface has dealt with equilibrium aspects. Numerous studies have used macroscopic approaches such as adsorption isotherms, empirical and semi-empirical equations (e.g., Freundlich, Langmuir), and surface complexation models (e.g., constant capacitance, triple layer) to describe adsorption, usually based on a 24 hour reaction time. 

In addition, to these binding parameters the corresponding affinity distribution can likewise be generated from the corresponding affinity distribution equation (Eq. (15)). This expression is more complex than the affinity distribution equation for the Freundlich isotherm (Eq. (8)) [26]. However, it is still a simple algebraic expression that calculates the number of binding site (Ni) having an association... 

Liquid adsorption isotherms have many different shapes and may be quite complex. It is difficult to generalize over the whole range of possible concentrations. In dilute solutions, the common application in the chlor-alkali industry, the Freundlich isotherm fiequendy applies ... 

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