Freundlich model parameters

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. 

Figure 4 Comparison of sorption models. Several commonly used sorption models are compared with respect to the independent constants they require. These constants are vahd only under specific conditions, which must be specified in order to properly use them. In other words, the constants are conditional with respect to the experimental variables described in the third column of the figure. is the radionuclide distribution constant K and n are the Freundlich isotherm parameters and are surface complexation constants for protonation and deprotonation of surface sites K-, are surface complexation constants for sorption of cations and anions in the constant...

In this review we concentrate on the studies that attempt to elucidate the importance of carbon surface properties in controlling the equilibrium uptakes of aromatic and aliphatic adsorbates. Rather than comparing model parameters, such as Langmuir or Freundlich constants, we examine the uptakes at comparable equilibrium concentrations and attempt to rationalize the differences observed under different conditions and on different adsorbents. 

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. 

The gas adsorption results are consistent with the dual-mode model upon assumption that some of the nanopores available to CO2 within the organic matrix are potential adsorption sites for organic compoimds. Consistent with this assumption, Xing and Pignatello (77) found an inverse correlation between C02-determined porosity and the Freundlich V parameter, and a direct correlation between porosity and the magnitude of the competitive effect for chlorinated benzenes in NOM particle suspensions. Obviously, the correlation needs to be tested with other systems. 

Sudha et al. (2008) and Dinesh Karthik et al. (2009) reported on the removal of heavy metal cadmium and chrominm from industrial wastewater using chitosan-coated coconut charcoal and chitosan impregnated polyurethane foam, respectively. Adsorption and determination of metal ions such as zinc (11) and vanadium (II) onto chitosan from seawater have been studied (Muzzarelli et al. 1970, Muzzarelli and Sipos 1971, Muzzarelli and Rocchetti 1974). Adsorption of strontium (II), cobalt (11), zinc (11), and iron (III) on chitosan from sodium chloride solution have been reported (Nishimura et al. 1995). Adsorption behavior of Cu (II) (Minamisawa et al. 1996, Wu et al. 2000) and cobalt (11) (Minamisawa et al. 1999) were investigated. The amount of cadmium removed by chitin increases with increase of these parameters at a specific time. The application to experimental results of the Langmuir and Freundlich models shows that the Langmuir model gives a better correlation coefficient. 

Figure 4 Comparison of sorption models. Several commonly used sorption models are compared with respect to the independent constants they require. These constants are valid only under spedlic conditions, which must he specified in order to properly use them. In other words, the constants are conditional with respect to the experimental variables described in the third column of the figure. is the radionuclide distrihution constant K and n are the Freundlich isotherm parameters and f3 are surface complexation constants for protonation and deprotonation of surface sites K, K-, 13, are surface complexation constants for sorption of cations and anions in the constant capacitance model and TLM, respectively C, Ci, and are capacitances for the electrical double layers rr, ov, and oj, are surface charges at different surface planes (Me) and (S) are concentrations of the sorbing ions and the surface sites, (M), (L) are concentrations of other cations and ligands in solution, respectively I is the ionic strength of the background electrolyte and 5a are the site density and specific surface of the substrate, respectively. The requirements of the DLM are similar to those of the constant capacitance model.

Change the chemical equilibrium parameters (K and Cmax) to see how they effect the distribution and transport of the solute (see Lyman et al. (1982) for a comprehensive set of data). Experiment by using a different model for the adsorption of the solute, e.g., Freundlich linear adsorption. 

Figure 4.9. Stem-Volmer intensity quenching of (a) Ru(bpy)32+, (b) Ru(phen)32 and (c) Ru(Ph2phen)32+ on hydrophilic Cab-O-Sil silica disks. The solid lines are the best fits using a two-parameter Freundlich adsorption model. (Reprinted from Ref. 33 with permission. Copyright 1991, American Chemical Society.)...

Figure4.9 shows the best Freundlich quenching model plots. While more complex models could fit the data, this simple two-parameter model fits all the data within experimental error. Since the decays are highly nonexponential, the parameters represent lumped parameters that are some average over the available sites, lifetimes, and A sv s. A detailed discussion of the different models tried is given elsewhere.

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. 

From the scientific point of view, however, all approaches in the sense of the Kd concept (Henry, Freundlich or Langmuir isotherm) are unsatisfactory, since the complex processes on surfaces cannot be described by empirical fitting parameters. Boundary conditions like pH value, redox potential, ionic strength, competition reactions for binding sites are not considered. Thus results from laboratory and field experiments are not transferable to real systems. They are only advisable to provide a suitable prognosis model, if no changes concerning boundary conditions are to be expected and if no parameters for deterministic or mechanistic approach can be determined. 

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 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... 

A new mathematical model was developed to predict TPA behaviors of hydrocarbons in an adsorber system of honeycomb shape. It was incorporated with additional adsorption model of extended Langmuir-Freundlich equation (ELF). LDFA approximation and external mass transfer coefficient proposed by Ullah, et. al. were used. In addition, rate expression of power law model was employed. The parameters used in the power model were obtained directly from the conversion data of hydrocarbons in adsorber systems. To get numerical solutions for the proposed model, orthogonal collocation method and DVODE package were employed. 

As recently as 1998, Zhou et al. [445] analyzed the widely varying uptakes of substituted benzenes and phenols (nitrobenzene > benzaldehyde > nitro-4-phenol > 4-cresol > phenol > aniline) using models such as those of Langmuir, Freundlich, and preferably—when the solute concentration range was large— Redlich-Peterson and Jossens-Myers, in which the parameters are not related to the properties of the adsorbent instead, they are related to the solubility and the Hammett constant of the solutes (.see Section IV.B.2). 

A common method of extracting f K) from Eq. 3.82 is to assume a form of the distribution function by differentiation of a smooth fimction describing the data. The function obtained by this method is called the affinity spectrum (AS) and the method, the AS method [71]. The most general approach uses a cubic spline to approximate the data. However, a simpler procedure uses a Langmuir-Freundlich (LF) isotherm model and the AS distribution is derived from the best parameters of a fit of the experimental isotherm data to the LF model [71]. This approach yields a unimodal distribution of binding affinity with a central peak, if the range... 

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. 

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