Freundlich model

Another useful model for isothermal adsorption is the Freundlich model, which is presented by the following equation. 

Most of the isotherms reported for the adsorption of enzymes on solids are of the H or L types and are best fitted either by the Langmuir or the Freundlich model (Table 15.3). 

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,... 

The basis includes an entry Ap for each sorption model considered, except for the K( and Freundlich models, which require no special entry. 

For the K and Freundlich models, as mentioned, there is no basis entry Ap and hence we do not write a residual function of the form Equation 9.42, nor do we carry Jacobian entries for Equations 9.46 or 9.49-9.52. 

To evaluate the Jacobian matrix, we need to compute values for dmq/dnw, dmq/dnii, and dmq/dmp. For the Kt and Freundlich models,... 

No value for dmq/dmp is needed to evaluate the and Freundlich models. For the Langmuir model and the ion exchange model under the Gaines-Thomas and Gapon conventions,... 

Predominantly, Freundlich s fitted adsorption isotherms computed by means of simple linear regression were proposed for the mathematical description of the process studied. Unlike the Langmuir equation, the Freundlich model did not reduce to a linear adsorption expression at very low nor very high solute concentrations, as above resulted. 

The Freundlich model, which was first used to describe gas phase adsorption and solute adsorption, is an empirical adsorption model that has been widely used in environmental chemistry [138]. It can be expressed as... 

Of the various equilibrium and non-equilibrium sorption isotherms or sorption characteristics models, the most popular are the Langmuir and Freundlich models. The correct modeling of an adsorbate undergoing both transport and adsorption through a clay soil-solid system necessitates the selection of an adsorption isotherm or characteristic model which best suits the given system. The use of an improper or inappropriate adsorption model will greatly affect the... 

Equilibrium considerations alone may partly explain the nonlinear sorption isotherm, i.e., when n in the Freundlich model (Eq. 8) is less than unity, intraparticle retardation will increase as the concentration inside the particle declines. However, in some studies it appears that the concentration dependence is steeper than expected based on equilibrium nonlinearity. 

Abstract Removal of the pesticide metobromuron from aqueous solutions by adsorption at the high area activated carbon cloth was investigated. Kinetics of adsorption was followed and adsorption isotherms of the pesticide was also be determined. In kinetic studies a special V-shaped cell with an UV cuvette attached to it was used for adsorption processes. With this cell it was possible to follow the concentration of pesticide molecule by in situ UV spectroscopy as it is adsorbed at the activated carbon cloth. The obtained absorbance vs time data were converted into concentration vs time data and these data were treated according to pseudo-first-order and psendo-second-order kinetic models. Adsorption of that pesticide was fonnd to follow second-order kinetic model with k 87.35 g mol min. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundlich models. The fits of experimental data to these equations were examined and founded that the adsorption isotherm was well represented by Frenndlich model. 

Fig. 22.3 The fit of experimental adsorption data (A) to Langmuir (—) and Freundlich (—) models for metobromuron...

For nonlinear isotherms, the Freundlich model most often is used to describe the relationship between the sorbed (Cs) and the solution phase concentrations (Cw) ... 

Using coal-based sorbents, Sivasamy et al. [62] evaluated their ability to remove fluoride from water. On equilibrium basis, Langmuir and Freundlich models were used to describe the data points, while the kinetic data points were interpreted in terms of reaction and mass transfer processes. Kaolinite, adioctahedral two-layered (silica and alumina) silicate (1 2 type), has also been tested in drinking water defluoridation. Recently, Sugita etal. [58] and earlier Kau etal. [63] and Weerasooriya et al. [10] presented fluoride adsorption results of kaolinite. The fluoride-binding sites in kaolinite consist of aluminol and silinol sites. The authors explained that the fluoride-kaolinite interaction led to the formations of both the inner- and outer-sphere complexes. 

The best results to describe the adsorption isotherm by the selected isotherm equations were achieved by the Toth model. The Freundlich model showed in some cases a lack of flexibility in describing the region were the linear behaviour changed to saturation behaviour (22 MPa) and the Langmuir-model in some cases had difficulties in describing the region were the adsorbate is saturated (16 MPa). 

The suitability of Freundlich model to describe the photoadsorption phenomenon has been further checked by using the Freundlich equation [Equation (20)] in its linear form. Figure 11 reports the values of the fts/W group obtained from runs carried out at equal mass of catalyst vs. the square... 

Figure 11 Linear form of Freundlich model. The left-hand side of Equation (19), n /W, vs. Cl,o° for runs carried out under irradiation with lamp power of 500 W. The solid line represents the Freundlich photoadsorption model [Equation (20)].

Figure 12 Values of kinetic and Freundlich model parameters [see Equation (26)] vs. the absorbed photon flow per unit mass of catalyst. , K a, N , k.

The modeling results indicate that the parameters of the Langmuir and Freundlich models depend on the absorbed photon flow. In order to take into account the dependence on photon flows, it would be necessary to develop a kinetic model based on the proposed reaction mechanism in which the photons appear as reactants. Work on this field is in progress. 

A negative influence of CO2 in Phenanthrene adsorption capacity was observed, probably due to a competitive effect between CO2 and Phenanthrene for the adsorption sites within the carbonaceous material. The Freundlich model was successfully applied to the Phe isotherms at any CO2 concentration suggesting the formation of multilayer during Phe adsorption. 

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