Langmuir-Freundlich model

Figure 4.17 Competitive experimental isotherm data for 2-phenylethanol and 3-phenylpropanol fitted to the competitive Fowler-Guggenheim/Langmuir-Freundlich model. Reproduced from I. Quinones, G. Guiochon, J. Chromatogr. A, 796 (1998) 15 (Figs. 3 and 4).

Radke-PrausnitThis model (31) is also known as the Langmuir-Freundlich model ... 

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. 

Fig. 7 - Comparison between Langmuir (— ), Freundlich (—) model fittings and the experimental equilibrium data (points) of Fig. 3...

Cd, Cu, A Zn Langmuir-Freundlich Model FIGURE 15.8 Sorption of copper, cadmium, and zinc ions onto bone char. 

Lichen biomass from Parmelina and Cladonia genera have resulted good biosorbents of Pb(II), Cr(III), and Ni(II) ions. The Langmuir, Freundlich, and Dubinin-Radushkevich (D-R) models... 

Sorption and desorption are usually modeled as one fully reversible process, although hystersis is sometimes observed. Four types of equations are commonly used to describe sorption/desorption processes Langmuir, Freundlich, overall and ion or cation exchange. The Langmuir isotherm model was developed for single layer adsorption and is based on the assumption that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no transmigration of adsorbate on the surface phase. 

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). 

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. 

Sips [38] modified the Langmuir adsorption model by introducing a power law expression of the Freundlich equation ... 

The Sips [38] model (Eq. 10) can easily be extended to binary or multicomponent systems [34, 74]. The resulting expression for the multicomponent Langmuir-Freundlich adsorption model is ... 

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...

It will be noted that the universal isotherm equation as written here has formal similarity to pressure explicit forms of Langmuir, Langmuir-Freundlich and LRC models. One key advantage of the universal form is that the heat of adsorption and the adsorption equilibrium are bound to be self-consistent. 

It can often be inverted to allow either pressure explicit forms or loading explicit forms. The LRC model published by UOP is a form very similar to the Langmuir-Freundlich form. 

When measured adsorption data are plotted against the concentration value of the adsorbate at equilibrium, the resulting graph is called an adsorption isotherm. The mathematical description of isotherms invariably involves adsorption models described by Langmuir, Freundlich, or Brauner, Emmet and Teller (known as the BET-model). Discussion of these models is given in Part 111, as conditions relevant to chemical-subsurface interactions are examined. 

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 fitting of the Langmuir, Freundlich, and R-P models to the data has been firstly applied to the photoreactivity results obtained from runs carried out at equal mass of cafalysf and lamp power. For the Langmuir model, the following procedure has been followed. In order to have an estimate of parameters values, the data at high initial concentration of benzyl alcohol have been fitted to Equation (A6) (see Appendix Al) and those at low initial concentration to Equation (A13). The parameters obtained by these fitting procedures have been used to determine Ng by means of Equation... 

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. 

---