Adsorption 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). 

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... 

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...

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. 

In literature the existing experimental data base of supercritical adsorption equilibria is limited and most of the data have been modelled with one of three common adsorption isotherm models - the Langmuir, the Freundlich and the Toth. The models define adsorption isotherms with a similar shape and they have 2 or 3 adjustable parameters which allow an accurate correlation. 

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). 

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. 

The Freundlich isotherm is shown in Figure 3.19 for several values of n between 1 and 5. For n = 1, a linear isotherm is obtained. The inset illustrates the initial tangent of the isotherm. In Figure 3.20, experimental data are fitted to the Freundlich model for three different dyes [70]. The isotherms are well accounted for by the FreundUch model, with values of n of the order of 4. The extremely strong adsorption at low concentrations is clearly visible. 

Adsorption isotherms are typically used to describe the equilibrium relationship between the bulk aqueous phase activity (concentration) of the adsorbate and the amount adsorbed on the interface at a given temperature. The more common models used are empirical models such as the linear model and the Freundlich model. First principles models such as the Langmuir model are also used. 

Given in Table 10.7 are the surface reactions and corresponding activity adsorption isotherm model equations used in MINTEQA2 as presented by Allison et al. (1991). In these expressions SOH and SOH M represent unoccupied surface sites and surface sites occupied by species M. Because the and Freundlich isotherm models assume an infinite number of available sorption sites, the con-... 

Empirical adsorption equilibrium models like Langmuir and Freundlich can generally be used to describe type I pure water vapour adsorption isotherms on aluminas [6] ... 

The parameters in the adsorption isotherms were estimated from the experimental equilibrium data using MATLAB Curve Fitting Toolbox. The comparison of experimental and estimated data by Langmuir, Freundlich, Redlich-Peterson and combined Langmuir-Freundlich models for the investigated systems are presented in Figures 1 to 3 for six investigated systems. 

Given the data below, determine if the adsorption of 2,4,5-T conforms to the Langmuir or the Freundlich models and determine the appropriate adsorption parameters (K, n, b). You may need to restrict your attention to a limited concentration range. 

Fit experimental data to the Langmuir and Freundlich adsorption isotherm models. 

Another adsorption equilibrium model, attributed to Freundlich, is the empirical relation... 

Langmuir and Freundlich models assume an adsorption mechanism of surface coverage-type. A useful model for correlating experimental data with adsorption phenomena based on a pore filling-type mechanism, is the Dubinin-Astakhov equation ... 

Langmuir model is an excellent fit for the adsorption of SO2 and NH3 on Pentalofos tuff and a fairly good representation in the case of CO2. In the latter case, the Freundlich model appears, however, to be more suitable. On the contrary, as expected, in the fitting of the water vapour adsorption isotherm, best results are obtained using the Dubinin-Astakhov equation. 

The Langmuir and Freundlich models were adopted to fit the experimental adsorption isotherms. The former model was developed for weU-defined localized adsorption sites having the same adsorption energy independent of surface coverage, and with no interaction between adsorbed molecules. In this model ... 

Figure 2.23 Adsorption and desorption isotherm of cadmium at loading 40%, 70% and 100% with palygorskite, sepiolite and calcite. Solid and dashed lines are the same isotherms calculated from Freundlich model (Shirvani et al, 2006). a. palygorskite, b. sepiolite, c. calcite.

Natural occurring sawdust, polysaccharides and carbon-related materials have been fabricated with PANI and widely apphed in wastewater purification. PANI/sawdust composites had been applied to adsorb diclofenac sodium, [46] Cd(II), [47] Cu(II), [48] and Cr(VI) [49]. The average adsorption capacity for Cu(II) can reach 58.23 mg/g, [48] while Cd(II) was removed by pseudo-second-order kinetics and a Freundlich model [47]. Acidic condition (pH < 2) was required for Cr(VI) removal and the mechanism was proposed via an anion exchange process [49]. 

The dependence of the surface coverage with the heat of adsorption was accounted on two other models. The Freundlich model presents the coverage surface as ... 

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