Langmuir and Freundlich isotherms

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 distribution coefficient assumes that adsorption is linear (i.e., the amount of adsorption is directly proportional to the concentration of the compound in solution) and is actually a special case of the Langmuir and Freundlich isotherms, which are nonlinear.31 32... 

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). 

Table 21.2 The parameters of Langmuir and Freundlich isotherm equations for the adsorption of eateehol and resoreinol...

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. 

In the cases of Langmuir and Freundlich isotherms, it has been assumed that the total disappearance rate of substrate per imit surface area, Vj, follows a pseudo-first-order kinetics with respect to the substrate concentration which is expressed by its fractional coverage. The same assumption is made for R-P isotherm however, as the R-P isotherm relates an adsorbed amount (and not a fractional coverage) with the equilibrium concentration... 

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-... 

In this paper, we present the unusual adsorption properties of ETS-10 towards heavy metal ions Pb and Cu. Adsorption equilibrium and kinetic data are reported. Fitting of the experimental equilibrium results to both Langmuir and Freundlich isotherms and the kinetic data to both pseudo-first- and pseudo-second-order kinetic models is described. 

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... 

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. 

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. 

The secondary effluent from a biological treatment plant is treated with the activated carbon adsorption process and allowed to arrive at eqnilibrinm. The equilibrium data in terms of phenol are given below. Determine the constants for the Langmuir and Freundlich isotherms. 

Mathematical analysis of adsorption is beyond the scope of this entry, but it is important to point out that the equilibria used are often based on adsorption isotherms. The three isotherms shown in Fig. 3 occur in practice, although linear isotherms are very rare. The nonlinearity of the Langmuir and Freundlich isotherms makes scale-up and analysis tedious. The Freundlich isotherm is based on empirical data analysis and occurs more commonly in practice than the Langmuir isotherm, which has a theoretical basis. 

Figure 10.12 Examples of Langmuir and Freundlich isotherms. From R A. Domenico and F. W. Schwartz, Physical and chemical hydrogeology. Copyright 1990 by John Wiley Sons. Reprinted by permission of John Wiley Sons, Inc.

Write the equations that describe the Langmuir and Freundlich isotherms and be able to determine the constants from batch-type adsorption test results. 

The Langmuir and Freundlich isotherms are the most common isotherms it is likely that the constants in these isotherms for many sorbate-sorbent pairs have already been measured (see Tables 3.1 and 3.2, respectively). 

An adsorption isotherm relates the amount of the substance adsorbed at thermodynamic equilibrium to the amount present in the liquid or gas stream (concentration or partial pressure) at a constant temperahue. Langmuir and Freundlich isotherms are the most common adsorption isotherms. 

Figure 9.6b shows a q-p plot of the experimental data and the corresponding predictions of the Langmuir and Freundlich isotherms. It is evident from the plot that in this case, the Langmuir isotherm fits the data significantly better than the Freundlich isotherm. 

Figure 9.6b Langmuir and Freundlich isotherms fitted to data of Example 9.4.

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. 

The applicability of the isotherm equations was compared on the basis of correlation coefficient, R. Table 17.7 gathers together results deduced from Langmuir and Freundlich isotherms for a series of modified cellulose fibres. 

Langmuir and Freundlich isotherms performed better than the BET therm. 

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