Freundlich-type adsorption isotherm

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. 

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. 

An adsorbate A is adsorbed in a fixed-bed adsorber that is of 25 cm height and packed with active charcoal particles of 0.6 mm diameter. The concentration of A in a feed solution is 1.1 mol m , and the feed is supplied to the adsorber at an interstitial velocity of 1.6 m h L The adsorption equilibrium of A is given by the following Freundlich-type isotherm. 

Zeolite could selectively adsorb A -nitrosamines in the solution of methylene chloride or water, and the equilibrium data were fitted to Freundlich-type isotherms. Textural and acid-basic properties of zeolite determined their adsorption capacity. The extraordinary adsorption properties of NaA zeolite for iV-nitrosamines is inferred that the adsorbates inert the channel with the group -N=N-0. Larger amount of A-nitrosamines was adsorbed on ZSM-5 zeolite in water instead in methylene chloride, due to the hydrophobicity of the zeolite. Application of zeolite to remove A-nitrosamines from beer seems successful. Up to 100% of the worst carcinogenic compounds could thus be removed with 1.4 g/L of zeolite which was proven to be better adsorbent than silica or alumina. On Na 3 zeolite and MCM-41 mesoporous material A-nitrosodimethylamine decomposed above 573 K and the liberated NOx could be detected even at 773 K during the TPSR process, indicating the strong adsorption of A-nitrosamines on molecular sieves that makes zeolite become the functional materials for environmental protection. 

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] ... 

The linear equilibrium isotherm adsorption relationship (Eq. 11) requires a constant rate of adsorption, and is most often not physically valid because the ability of clay solid particles to absorb pollutants decreases as the adsorbed amount of pollutant increases, contrary to expectations from the liner model. If the rate of adsorption decreases rapidly as the concentration in the pore fluid increases, the simple Freundlich type model (Eqs. 8 and 9) must be extended to properly portray the adsorption relationship. Few models can faithfully portray the adsorption relationship for multicomponent COM-pollutant systems where some of the components are adsorbed and others are desorbed. It is therefore necessary to perform initial tests with the natural system to choose the adsorption model specific to the problem at hand. From leaching-column experimental data, using field materials (soil solids and COMs solutions), and model calibration, the following general function can be successfully applied [155] ... 

Murillo et al. (2004) studied the adsorption of phenanthrene (polycyclic aromatic hydrocarbon -PAH) from helium as carrier gas on a coke fixed-bed adsorber, at 150 °C. The isotherm of the phenanthrene-coke system at 150 °C was found to be of Freundlich type with Fr = 0.161 and KF = 1.9 (mol/kg)(m3/mol)0161. The isotherm has been derived for phenanthrene concentrations between 1.71 X 10 4 and 1.35 X 10-2 mol/m3. Finally, the average solid-phase diffusion coefficient, calculated from several experimental runs, was found to be 6.77 X 10-8 cm2/s. 

Adsorption Isotherms of Langmuir Type and Freundlich Type... 

In practice, the following Freundlich-type empirical isotherm can be used for many liquid-solid adsorption systems ... 

Estimate the equilibrium concentration of the solution. An adsorption isotherm of the Freundlich type is given as... 

Experimental studies of the partitioning of sodium into aragonite, calcite, and dolomite have been carried out by White (1977, 1978), who concluded that the mode of substitution was as Na2CC>3 rather than as Na bicarbonate or hydroxide. The behavior of Na+ does not follow that normally described by a simple partition coefficient, but rather coprecipitation is better described by a Freundlich-type adsorption isotherm equation, implying that adsorption is important. 

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) ... 

Secondly, the adsorption equilibrium on a sparsely covered surface is approximately proportional to the square root or to the cube root of the equilibrium pressure, tending, however, to follow a lesser power of the equilibrium pressure at higher coverage. This nearly corresponds to the Freundlich type of adsorption isotherm. From this Kwan suggests... 

Some theoretical proton adsorption isotherms based on Eq. (87) and different types of surface groups are reported in [32,102]. Benjamin and Leckie [86] and Kinniburg et al. [14, 15] used Freundlich type equations to describe metal ion binding to ferrihydride. A discussion of this work has been given by Van Riemsdijk et al. [52, 53]. 

Adachi et al. (2006) Beer bran Organic compounds 90 min 76-95% Freundlich type of adsorption isotherms, adsorption capacity higher than that of activated carbon... 

Abstract Infrared spectroscopic methodsfor the measurement of adsorption and adsorption kinetics of some aromatics (benzene, ethylbenzene, p-xylene), pyridine, and paraffins in solid microporous materials such as zeolites (MOR, ZSM-5, silicalite-1) are described as well as the evaluation of the spectroscopically obtained data. The adsorption isotherms are of the Langmuir-Freundlich type. Isosteric heats of adsorption, transport diffusivities, and activation energies of diffusion as deduced from the spectroscopic measurements are compared with literature data as far as available, and they are found to be in reasonable agreement with results provided by independent techniques. Special attention is paid to sorption and sorption kinetics of binary mixtures, especially the problems of co- and counter-diffusion. ... 

Hinzu studied the adsorption of nonionic surfectants on a C18 bonded phase (Resolve C18, Table 4.1) [16]. H-type isotherms similar to the ones obtained with ionic surfactants (Figures 4.2 and 4.4) were establish for two polyoxyethylene dodecyl ether surfactants (Brij 22 and Brij 35). The surfactant adsorption increased beyond the surfactant cmc. The adsorbed Brij 22 amount increased from 1.4 pmol/m at 20 cmc (0.0002 M, cmc=10 M) to 2 pmol/m at 1700 cmc (0.16 M or 100 g/L), a 40% increase. The increase of the Brij 35 adsorbed amount was almost continuous. It was about 0.3 pmol/m at 2 cmc (0.0002 M, cmc=10 M) and 0.9 pmol/m at 850 cmc (0.08 M or 100 g/L), a 200% increase. The log Cg versus log C , Freundlich plot of the Brij 22 ackorption data showed a bilinear curve similar to the plots found in Figures 4.3 and 4.5. The log Cg versus log C Freundlich plot of the Brij 35 adsorption data was a straight line without a break at the cmc concentration. Brij 35 is a polar and highly water soluble surfactant, it may have a low affinity for the apolar bonded Resolve C18 stationary ph e [16]. 

The form of polymer sorption isotherms has received mnch attention and many adsorption equations have been proposed and employed. In the present case, conformance was found with an equation of the Freundlich type ... 

As a typical example of an adsorption isotherm in aqueous phase, adsorption of propionic acid on activated carbon is shown in Hg. 3.16. At higher concentrations isotherms can be correlated by the Freundlich type equation, but at low coverage (q<0.l mmol/g), the slope of isotherms becomes steeper and seems to reach Henry s type relation. From isotherms at different temperatures, isosteric heat of adsorption was obtained as a function of the amount adsorbed as shown in Figs. 3.17 and 3.18. At higher coverage, measured isosteric heat of adsorption seems to decrease with increasing amount adsorbed. 

The extended Langmuir (Markham-Benton) isotherm has limited applicability especially for liquid phase adsorption, since even singlecomponent isotherms in liquid phase are rarely explained by the Langmuir equation. There have been several trials to extend the Freundlich type equation to mixture isotherms. Fritz and Schliinder (1974) gave the following equation. 

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