Isotherm Langmuir-Freundlich

From these data can you distinguish which of the three isotherms-Langmuir, Freundlich, or Temkin—is best obeyed ... 

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. 

This three-parameter equation behaves linearly in the Henry s law region and reduces to the Langmuir isotherm for m = 1. Other well-known isotherms include the Langmuir-Freundlich isotherm or Sips isotherm [Sips,/. Chem. Phys., 16, 490 (1948) Koble and Corrigan, Ind. Eng. Chem., 44,383 (1952)] or loading ratio correlation with prescribed temperature dependence [Yon and Turnock, AlChE Symp. Sen, 67(117), 75 (1971)]... 

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. 

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. 

Umpleby II RJ, Baxter SC, Chen Y, Shah RN, Shimizu KD. Characterization of molecularly imprinted polymers with the Langmuir-Freundlich isotherm. Anal Chem 2001 73 4584-4591. 

Classical Adsorption Isotherms of Langmuir, Freundlich and Tfimkin. 107... 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

Several different mathematical relationships (referred to as isotherms) have been developed to describe the relationship of fractional surface coverage with respect to the adsorbing species. Work by Langmuir, Freundlich, Tempkin, and others have attempted to describe the above mentioned pressure differential to fractional surface coverage. The most widely used and accepted isotherm is the BET equation, named after its orignators, Brunauer, Emmett, and Teller, and is as follows 29... 

At this point, it is feasible to correlate the liquid-phase adsorption equilibrium single component data, with the help of isotherm equations developed for gas-phase adsorption, since, in principle, it is feasible to extend these isotherms to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [92], These equations are the Langmuir, Freundlich, Sips, Toth, and Dubinin-Radushkevich equations [91-93], Nevertheless, the Langmuir and Freudlich equations are the most extensively applied to correlate liquid-phase adsorption data. [2,87],... 

There have been numerous attempts to assign mathematical isothermal adsorption relations to various experimental data. Among the most frequently used isotherm equations are Langmuir, Freundlich, and BET. 

In the past, much attention was given to the study of dye and iodine adsorption by active carbons (Bmnauer, 1945 Orr and Dalla Valle, 1959). Many studies have been made with dye molecules of well-known size, shape and chemical properties, but the results have not been easy to interpret (Giles et al., 1970 McKay, 1982, 1984). In a systematic study of iodine adsorption (from aqueous solution) on a carbon black and four activated carbons (Femandez-Colinas etal., 1989b), it was found that the iodine isotherms could be analysed by the as-method. In this way it was possible to assess values of the available volume in pores of effective width of 0.5-1.5 nm. The adsorption of iodine was also featured in a recent study by Ziolkowska and Garbacz (1997), who applied the Langmuir, Freundlich and other isotherm equations. 

The adsorption capacity of activated carbon may be determined by the use of an adsorption isotherm. The adsorption isotherm is an equation relating the amount of solute adsorbed onto the solid and the equilibrium concentration of the solute in solution at a given temperature. The following are isotherms that have been developed Freundlich Langmuir and Brunauer, Emmet, and Teller (BET). The most commonly used isotherm for the application of activated carbon in water and wastewater treatment are the Ereundlich and Langmuir isotherms. The Freundlich isotherm is an empirical equation the Langmuir isotherm has a rational basis as will be shown below. The respective isotherms are ... 

In a kinetically controlled separation system using CMS or zeolite 4A as adsorbents, it is necessary to use more accurate rate model. Therefore, concentration dependent diffusivity model based on Darken equation combined with Langmuir-Freundlich isotherm was applied and each result was compared with the experimental data. 

Adsorption isotherm of Langmuir-Freundlich for multi-component is defined by... 

Adsorption of single components in zeolites can often be described by a simple Langmuir isotherm, Eq. (18), or the Langmuir-Freundlich isotherm, Eq. (26) [50-52] ... 

Table 1. The constants for adsorption isotherm in Freundlich and Langmuir equations.

When two coexisting phases are subjected to the condition that one or several of the ionic components cannot pass from one phase to the other, a particular type of equilibrium is set up, called a Dorman equilibrium. This type of ionic equilibrium is unique for ionic absorbents containing a fixed ion, and the isotherm describing such equilibria differs from the established Langmuir Freundlich and Bru-nauer, Emmett, and Teller types which are found for neutral species. 

For the special values of heterogeneity parameters m = m s (0,1) the isotherm (7) reduces to the known Langmuir-Freundlich (LF) equation. 

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... 

Figure 4.16 Experimental isotherm data (symbols) of R and S-l-indanol obtained by competitive frontal analysis on a narrow bore column packed with Chiracel OB. The data were fitted to the Toth (dash-dot), the bi-Langmuir (dash), the Langmuir-Freundlich (dot), and the Langmuir (solid) models. The inset shows low concentration data. Reproduced with permission from D. Zhou, K. Kaczmarski, A. Cavazzini, X. Liu, G. Guiochon, J. Chromatogr. A, 1020 (2003) 199 (Fig 4).

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