Freundlich adsorption isotherm model

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

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. 

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-... 

Due to the effects of molecular size and shape and pore structure on the kinetics, the model cannot be used for general predictive purposes. In practice, in order to predict PAC adsorption, a series of experiments must first be carried out using the compound of interest, the activated carbon to be applied, and the water in which it is to be used. Equilibrium parameters, determined from the Freundlich adsorption isotherm equation, are used as input into a computer-based HSDM, which uses the method of least squares to minimize the difference between the experimental kinetic data points and the HSDM fit of the data [10]. When the best fit is achieved, the resultant kinetic parameters (liquid film mass transfer coefficient, k(, and the surface diffusion coefficient, DJ can then be used for the prediction of adsorption behavior under different conditions. 

Uptake experiments were carried out on cultures of a planctonic alga, Scenedesmus obliquus, exposed to i Ag at different stages of development . The accumulation of the radionuclide was rapid and intense, and equilibrium was reached in an exposure time of less than 24 hours. The uptake kinetics showed the algal concentration level to be dependent only on the medium concentration and on the cell development at the time of 0 Ag addition. Passive uptake was described by Freundlich adsorption isotherms. During the depuration phase the Ag retention by S. obliquus developed in accordance with an exponential model based on the existence of two biological half-hves i.e. a very short one of a few seconds and a longer one of 115 h. In a similar study the radioactivity of sea water was determined by studying the concentration of metals in squid livers and the distribution of Ag in them. 

Langmuir and Freundlich adsorption models can be used to describe the adsorption behavior of dispersants on an abrasive surface. The Langmuir adsorption isotherm model assumes that the particle surface is homogeneously covered by the monolayer dispersant. It is expressed as follows ... 

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. 

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. 

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. 

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. 

Sheindorf, C., Rebhun, M., and Sheintuch, M. Organic pollutants adsorption from multicomponent systems modeled by Freundlich type isotherm. Water Res., 16(3) 357-362, 1982. 

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. 

The adsorption data is often fitted to an adsorption isotherm equation. Two of the most widely used are the Langmuir and the Freundlich equations. These are useful for summarizing adsorption data and for comparison purposes. They may enable limited predictions of adsorption behaviour under conditions other than those of the actual experiment to be made, but they provide no information about the mechanism of adsorption nor the speciation of the surface complexes. More information is available from the various surface complexation models that have been developed in recent years. These models represent adsorption in terms of interaction of the adsorbate with the surface OH groups of the adsorbent oxide (see Chap. 10) and can describe the location of the adsorbed species in the electrical double layer. 

The above surface complexation models enable adsorption to be related to such parameters as the number of reactive sites available on the oxide surface, the intrinsic, ionization constants for each type of surface site (see Chap. 10), the capacitance and the binding constants for the adsorbed species. They, therefore, produce adsorption isotherms with a sounder physical basis than do empirical equations such as the Freundlich equation. However, owing to differences in the choice of adjustable... 

However, there is no reason to use more complicated isotherm models if two-parameter models, such as Langmuir and Freundlich, can fit the data well. It should be clarified that these models are only mathematical functions and that they hardly represent the adsorption mechanisms. 

Diffusion-type models are two-parameter models, involving kt or Ds and La, while BDST models are one-parameter models, involving only 0, as gmax is an experimentally derived parameter. The determination of La requires the whole experimental equilibrium curve, and in case of sigmoidal or other non-Langmiur or Freundlich-type isotherms, these models are unusable. From this point of view, BDST models are more easily applied in adsorption operations, at least as a first approximation. 

Thus, the passage from an adsorption isotherm of a pure substance to the corresponding adsorption isotherm of a mixture is very easy, supposing that the model of a nonuniform surface is applicable and adsorption coefficients are proportional. If, for instance, adsorption of pure gas A is described by the Freundlich isotherm (135), then for adsorption of A from mixture... 

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). 

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