Sorption isotherm Freundlich

Recent reports on biosorbents based on diverse types of macrophytes are found widely in the literature. Free-floating aquatic plants from the genera Salvinia, Azolla, Eichhornia, Lemna, and Pistia have been described the most. S. natans biomass was able to uptake As(V) at low initial concentrations from 0.25 to 2 mg/L (74.8% and 54%, respectively). The experimental data fitted well to both Langmuir and Freundlich isotherms. The effect of pH and biomass quantities on sorption rate has also been investigated along with some metabolic parameters.105... 

The Langmuir and Freundlich equations have often been employed to model the sorption of metal ions by bacteria. Mullen et al. (1989) used the Freundlich isotherm to describe the sorption of Cd and Cu by B. cereus, B. subtilis, E. coli and P. aeruginosa over the concentration range of 0.001-lmM. The respective values of the Freundlich constant (Kf) indicated that E. coli was most efficient at sorbing Cd2+ and Cu2+. 

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). 

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

The Freundlich isotherm (or Freundlich model) is an empirical description of species sorption similar to the K, approach, but differing in how the ratio of sorbed to dissolved mass is computed. In the model, dissolved mass, the denominator in the ratio, is raised to an exponent less than one. The ratio, represented by the Freundlich coefficient Kf, is taken to be constant, as is the exponent, denoted f, where 0< f <1. As before, the masses of dissolved and sorbed species are entered, respectively, in units such as moles per gram of dry sediment and moles per cm3 fluid. Since the denominator is raised to an arbitrary exponent rif, the units for Kf are not commonly reported, and care must be taken to note the units in which the ratio was determined. 

Geochemical models, as with the approach, are commonly formulated with a variant of the Freundlich isotherm based on a chemical reaction, like Reaction 9.1. In this approach, known as the reaction Freundlich model or the activity Freundlich model, the extent of sorption by the reaction can be expressed,... 

Fig. 5.4.4. Sorption isotherms of AE homologues on sediment (EPA-12), showing the fits obtained with the Freundlich isotherm (from Brownawell et al. [6]).

Nevertheless, surfactant sorption isotherms on natural surfaces (sediments and biota) are generally non-linear, even at very low concentrations. Their behaviour may be explained by a Freundlich isotherm, which is adequate for anionic [3,8,14,20,30], cationic [7] and non-ionic surfactants [2,4,15,17] sorbed onto solids with heterogeneous surfaces. Recently, the virial-electrostatic isotherm has been proposed to explain anionic surfactant sorption this is of special interest since it can be interpreted on a mechanistic basis [20]. The virial equation is similar to a linear isotherm with an exponential factor, i.e. with a correction for the deviation caused by the heterogeneity of the surface or the energy of sorption. 

Fig. 4.18 shows the result of Cd2+ adsorption on illite in presence of Ca2+ (Comans, 1987). The data are fitted by Freundlich isotherms after an equilibration time of 54 days. It was shown in the experiments leading to these isotherms that adsorption approaches equilibrium faster than desorption. Comans has also used 109Cd to assess the isotope exchange he showed that at equilibrium (7-8 weeks equilibration time) the isotopic exchangeabilities are approximately 100 % i.e., all adsorbed Cd2+ is apparently in kinetic equilibrium with the solution. The available data do not allow a definite conclusion on the specific sorption mechanism. 

A very common mathematical approach for fitting experimentally determined sorption data using a minimum of adjustable parameters employs an empirical relationship known as the Freundlich isotherm ... 

Figure 9.13 (a) Freundlich isotherm (closed diamonds) observed for pyrene sorption to an aquifer sediment by Xia and Ball (1999.) Lower line represents expectations if K,i = /oc Kias with /oc = 0.015 (measured) and Kioc = 104,7 (Gaw-lik et al., 1997), while upper line shows predictions assuming K,d =... 

Sorption is measured by recording sorption isotherms, which themselves are a way to express the amount of surfactant sorbed as function of the concentration of the compound in the solution. The Freundlich isotherm (Equation II) is a general sorption isotherm which describes sorption behavior and often is used in studies of surfactant sorption. KF is the Freundlich sorption coefficient which expresses the affinity of a surfactant for a given solid... 

Assuming that the sorption-desorption of TCE follows a linear Freundlich isotherm (Bruell et al., 1992), the retardation factor can be expressed as... 

If solute-solute interactions occur (e.g., because of the presence of a limited number of sorption sites), then sorption can be modeled by fitting the experimentally derived isotherm to theoretical equations, the Freundlich isotherm... 

This equation has been successfully applied to many sorption and desorption reactions of dissolved metals and organic compounds. In the case of irreversible sorption (hysteresis), sorption and desorption isotherms are not identical. However, both sorption and desorption Freundlich isotherm equations can be substituted into the transport equation(2) ... 

Sorption and Desorption Isotherms. To model radionuclide transport in groundwater through geologic media, it is necessary to mathematically describe sorption and desorption in terms of isotherms. The Freundlich isotherm was found to accurately describe sorption and desorption of all radionuclides studied in the interbed-groundwater systems, except when precipitation of the radionuclide occurred. 

Rate-limited sorption can also be modeled assuming a kinetic rate expression coupled with a nonlinear equilibrium expression. If we assume a Freundlich isotherm and a first-order rate expression, we can use the following equation to model sorption kinetics [21] ... 

Many studies indicated that in the presence of DOM, the metal sorption capacity decreased markedly for most soils, and the effect on the calcareous soil was greater than on the acidic sandy loam. Figure 10.4 shows the metal sorption equilibrium isotherms onto soils with or without the addition of 400 mg C/l of DOM. The equilibrium isotherms could be better depicted according to the linear Freundlich equation with the high value for the correlation coefficient of determination (r2) ... 

Adsorption and desorption processes of F in soils and soil components has been studied extensively. Bar-Yosef et al. (1988) studied F sorption by montmorillonite and kaolinite and reported that F affinity was greatest in K-kaolinite and least with Ca-montmorillonite. These authors also concluded that the Langmuir model satisfactorily fit F sorption by these adsorbents. Fluoride sorption in soils has been described by both Langmuir and Freundlich isotherms (Omuetti and Jones, 1977 Chhabra et al., 1980 Morshina, 1980 Gupta et al., 1982). Peek and Volk (1985) reported that the Langmuir isotherm is applicable only for limited concentrations of F in soils. 

For polymer/penetrant combinations where strong interactions between specific functional groups occur and binding to specific sites predominates, a localized sorption model is more appropriate. Figure 5.15(b) represents such a model, which is equivalent to the Langmuir and Freundlich isotherm models presented in the context of adsorption in the previous section. This behavior has been ob-... 

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... 

However, the sorption of a number of pesticide compounds to some soils has been found to be more accurately described by the nonlinear Freundlich isotherm (e.g., Hamaker and Thompson, 1972 Widmer and Spalding, 1996), i.e.. 

Figure 13.2. Evidence for reversibility for sorption on illite. Adsorption-desorption equilibrium for Cd(II) on illite after 54 days of equilibration. The solution contains HCO, 2 X 10 M Ca, and has a pH = 7.8. Freundlich isotherms are based on separate adsorption ( ) and desorption (o). Adsorption approaches equilibrium faster than desorption. The data do not allow a conclusion on the specific absorption mechanism. (Data are from Comans, 1987.)...

FIGURE 1-10 Freundlich isotherms having exponents less than, equal to, and greater than one. An exponent of one corresponds to a linear isotherm, in which case the relationship between the aqueous concentration of a chemical and the chemical s concentration on a solid phase at equilibrium with the water can be described by a single partition coefficient. If the exponent is less than one, the ratio of sorbed concentration to aqueous concentration decreases as the chemical concentration in the system increases. Such a decrease would happen, for example, if the solid contained a finite number of sites that became filled (saturated) at higher aqueous chemical concentrations. An exponent greater than one might occur if the sorbed chemical modified the solid phase to favor further sorption. 

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... 

Figure 2. Logarithmic transforms of surface-area-normalized data and the corresponding Freundlich isotherm for sorption of TCB by a shale isolate.

Figure 7. Comparisons of carbon normalized data and Freundlich isotherms for sorption of TCB by different soils with sorption predicted by a linear partitioning...

The simplest mathematical models to describe sorption from solution are the so-called isotherm equations. The simplest of these is the Freundlich isotherm equation, which may be written ... 

To decide if the experimental sorption behavior of a substance obeys the Freundlich isotherm or K, model, the approach generally used is to first linearize the isotherm by taking the logarithm of expression (10.2), which yields... 

The Freundlich isotherm is assumed obeyed if the experimental sorption data plotted in the form of Eq. (10.3), yields a straight line. The intercept of the line then equals log K and the slope is n. The Freundlich isotherm and approaches assume an infinite supply of unreacted sorption sites. Values of - 0 for a nonreactive sorbate, and may exceed 100 for a reactive one. 

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