Adsorption Freundlich-Langmuir type

Adsorption Isotherms of Langmuir Type and Freundlich Type... 

In obtaining the Langmuir isotherm equations, several aspects of the adsorption system were presupposed in the derivations. The most important of these, and the one that has been subject to the greatest doubt, is that a uniform surface is assumed, In other words, any active site has the same attraction for an impinging molecule as does any other site. Isotherms different from the Langmuir types, such as the Freundlich isotherm, may be derived based on various assumptions concerning the adsorption system, including different types of nonuniform surfaces. 

The Mo adsorption process can be studied by using adsorption isotherms. Langmuir and Freundlich equations are the two major types of isotherms used to describe the Mo adsorption process. The Langmuir equation is based on the kinetic theory of gaseous adsorption onto solids, but is often used to model the adsorption of ions from solution (Ellis and Knezek, 1972). A common form of the Langmuir equation is... 

Adsorption at the solid-liquid interface is generally similar to the adsorption at the solid phase-gaseous phase interface. Theoretical modelling of the adsorption process is more difficult because, in addition to adsorbing dissolved substances, solvent is present (e.g. water), the molecules of which can also adsorb, and interactions of adsorbed molecules with molecules of the solvent may occur. Molecular adsorptions, when molecules of a substance are adsorbed, and ion adsorptions, in which ions of a substance are adsorbed, can similarly take place. Solid phase-liquid phase interfaces are usually described by empirical equations and theoretically derived equations of the Freundlich and Langmuir type. 

However, Eq. (10) for the local adsorption isotherm of the Langmuir type and the physically realistic distributions x,(e,) is still difficult to solve. It is worth mentioning that valuable results have been obtained for the Jovanovich-type local isotherm [171]. The assumption that the adsorption energies are not correlated at all has been used also to derive the Langmuir-Freundlich-type isotherm for the overall adsorption [174] ... 

In general, the pattern of protein adsorption equilibrium isotherms at solid-liquid interfaces assumes either a Langmuir-type or Freundlich-type shape. The Langmuir-type model is described by... 

The number of sites available for direct (primary) adsorption is limited. The adsorption isotherm therefore has mostly a curved, convex shape (Freundlich or Langmuir-type isotherm). A curved isotherm leads to an asymmetrically shaped zone in case of a convex isotherm there are tails and in case of a concave one there are beards . The positions of the zones are highly concentration-dependent. If the concentration range during chromatography includes only the initial approximately linear part of the isotherm, the bands may be rather symmetrical and their position concentration-independent, as shown by TLC. 

Figures 6.16-6.18 display the simulation results when the adsorption of dyes by fibres follows the Nemst adsorption isotherm. Figures 6.19 and 6.20 present the concentration of dye adsorbed by fibres Cf) throughout the package at 1, 5, 10, 20, 30 and 40 time units, for Freundlich and Langmuir type adsorption isotherms, respectively.

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). 

Freundlich Adsorbents that follow the Freundlich isotherm equation are assumed to have a heterogeneous surface consisting of sites with different adsorption potentials, and each type of site is assumed to adsorb molecules, as in the Langmuir equation (Perry and Green, 1999) ... 

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 more desirable approach is to determine f(Q) from an assumed 0(P,T,Q) and the experimental adsorption isotherm. Sips (16) showed that Equation 1 could be treated by a Stieltjes transform, so that in principle an explicit function could be written for f(Q), provided the experimental isotherm function, 0, could be expressed in analytical form. Subsequently, Honig and coworkers (10, 11, 12) investigated this approach further. The difficulty is that only for certain types of assumed functions 0 and 0 is the approach practical. As a consequence the procedure has been first to restrict the choice of 0 to the Langmuir equation, and second to assume certain simple functions for 0 such as the Freundlich and Temkin isotherm equations. The system is thus forced into an arbitrary mold and again it is not certain how much reliance should be placed on the site energy distributions obtained. 

Equilibrium between solution and adsorbed or sorbed phases is a condition commonly used to evaluate adsorption or sorption processes in soils or soil-clay minerals. As previously stated, equilibrium is defined as the point at which the rate of the forward reaction equals the rate of the reverse reaction. Two major techniques commonly used to model soil adsorption or sorption equilibrium processes are (1) the Freundlich approach and (2) the Langmuir approach. Both involve adsorption or sorption isotherms. A sorption isotherm describes the relationship between the dissolved concentration of a given chemical species (adsorbate) in units of micrograms per liter (pg L 1), milligrams per liter (mg L-1), microequivalents per liter (pequiv L-1), or millimoles per liter (mmol L-1), and the sorbed quantity of the same species by the solid phase (adsorbent) in units of adsorbate per unit mass of adsorbent (solid) (e.g., pg kg-1, mg kg-1, peq kg-1, or mmol kg 1) at equilibrium under constant pressure and temperature. Sorption isotherms have been classified into four types, depending on their general shape (Fig. 4.13) ... 

Adsorption isotherms, 178-190 Freundlich, 179 Langmuir, 183 S-type, 178-179 L-type, 178-179 C-type, 178-179 H-type, 178-179 Aerobic decomposition, 323 Alkalinity, 82—91 Definition, 88 Types of alkalinity, 82 Aluminosilicate clays, 102 Aluminum cation, 103, 160 Acidity, 160 Complexation, 160 Polymeric aluminum, 160 Exchangeable, 160,162 Hydrolysis, 69, 75 Solubility, 71 Soluble complexes, 69 Aluminum hydroxide, 78-80 Solubility, 78 pH effect, 79... 

The extent of adsorption can have a profound effect on the rate of the surface reaction. Equilibrium isotherms of many kinds have been reported for adsorption from solution and have been classified by Giles et al. [24-27], The shapes of these adsorption curves often furnish qualitative information on the nature of the solute-surface interactions. Several of the types of isotherm observed in dilute solution are represented reasonably well by three simple and popular isotherm equations, those of Henry, Langmuir, and Freundlich. Their shapes are illustrated in Fig. 1. Each of these isotherms relates the surface concentrations cads (mol m"2) to the bulk equilibrium concentration c of the solute species in question. When few surface sites are occupied, Henry s law adsorption... 

Obstacles to practical application of the Langmuir and Freundlich isotherm theories include the following (1) These isotherms do not effectively address adsorption versus degradation and competitive adsorption (2) the conclusions are not all inclusive i.e., adsorption constants and coefficients do not hold true in all cases within similar oil types let alone across different oil types (3) the process has so many variables that the additive variance is commonly too great to prove any subtle difference between clays other than a vastly different level of activity (this problem is especially true when using log vs. log plots with incremental changes on the order of 0.1%) and (4) the adsorption constants and coefficients have limited use for the refiner. 

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

Write the equations that describe the Langmuir and Freundlich isotherms and be able to determine the constants from batch-type adsorption test results. 

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