Freundlich isotherm characteristics

If it is assumed that the disorder is predominantly biographical in origin, i.e., Z = 0, the conventional Langmuir isotherm is obtained. If, on the other hand, the disorder is assumed to have a thermal origin, i.e., X = 0, then the characteristic Freundlich isotherm = kp1/n is obtained. 

The commonest gel for adsorption purposes is silica gel but measurement have also been carried out on ferric oxide, aluminium oxide, stannous oxide and titanium oxide. The characteristics of adsorption on silica gel differ somewhat from those for charcoal, particularly with respective Freundlich isotherm which holds fairly accurately. Moreover, deviation from Henry s Law even, seems to be much less than for charcoal. Water is somewhat exceptional. Silica and alumina gels are used as adsorbents for removing moisture and for controlling humidities of rooms. 

The oxygen and nitrogen exhibited similar characteristics they were both correlated well by the Freundlich isotherm. Their similar molecular structure might account for this, with differences in their polarizability being the major reason for their relative adsorbability. 

Design data are available for the specific oiganics on the EPA s priority pollutant hst. For mixed wastewaters, a laboratory study is necessary to determine adsorption characteristics. Wastewater is contacted with a range of concentrations of powdered carbon and adsorption occurs, as graphed in the form of a Freundlich Isotherm, shown in Figure 19. 

The capacity and intensity with which either GAC or PAC adsorbs a given solute has been modeled in several ways. The most commonly applied method is referred to as a Freundlich isotherm. The capacity of the activated carbon is defined as a function of the intrinsic characteristics of the carbon itself, the nature of the solute, and the final equilibrium concentration of the solute. The eapacity is defined as ... 

Sorption. The interaction of a pesticide with the soil solids or organic matter, termed sorption, retards the pesticide movement through the unsaturated zone. This interaction is being increasingly associated with the soil organic matter (18), with the extent of the interaction dependent upon the type of organic materials and the molecular characteristics of the pesticide (19). Linear and Freundlich isotherms have been used to describe sorption, where... 

The two constants K and n (n a 1) are characteristic of a given adsorption system. The Freundlich isotherm is derivable from certain rather artificial assumptions [e.g.. Ref. (10)], but it is essentially an empirical fitting function. Equation (3-7) commonly provides a good match for experimental adsorption data over a limited range in sample concentration. Systems which exhibit an extended linear isotherm region (and these are today of greatest interest in adsorption chromatography) are less well described by the Freundlich isotherm. 

The results are commonly expressed in the form of a sorption isotherm or a plot of the concentration of chemical sorbed (jj,g/g) versus the concentration remaining in solution (jj,g/L). Sorption isotherms generally exhibit one of three characteristic shapes depending on the sorption mechanism. These isotherms are referred to as the Langmuir isotherm, the Freundlich isotherm, and the linear isotherm (a special case of the Freundlich isotherm). The reader is referred to ref 1 for more details on sorption isotherms. 

Normally, homogeneous or heterogeneous adsorptions of ions are considered by using Langmuir or Freundlich isotherms, respectively, in order to determine characteristic membrane materials parameters. 

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... 

The transfer rate in the mixed side-pore model is proportional to the difference in concentration between the flowing-water and immobile-water phases. The transfer-rate constant kgA is a characteristic-rate parameter for diffusion in the immobile-water phase. Without the Freundlich sorption mechanism, this third model is the same as the dead-end pore model developed by Coats and Smith (19). The Freundlich sorption isotherm was included by van Genuchten and Wierenga (18) in their study, but they solved for the linear case only. Grove and Stollenwerk (20) described a similar model but included Langmuir sorption and a continuous immobile-water film phase. 

The abilily of activated carbon to remove a broad spectrum of orj nic compounds from wastewater is well documented. The Freundlich single-solute isotherm constants, as tabulated in [32], are reproduced in Table 2. These data illustrate clearly the wide range of organic compounds of different structures, sizes, functionality, etc. that can be adsorbed by an activated carbon. It can also be observed that these compounds exhibit different adsorption characteristics. Indeed, the adsorption behavior is affected by various factors related to molecular structure [33], like the adsorbate solubility, the kind of substituent groups of aromatic compounds, the size of tire molecule, its polarity and its hydrophobicity. 

Table I gives Freundlich parameters for selected additional systems where the isotherm was established with many data taken over a wide concentration range. Most of these isotherms are nonlinear. Inspection of Figure 2a and Table I reveal the following. /) Nonlinearity applies to both polar and apolar compounds, ii) Nonlinearity applies to soils both high and low in NOM. Hi) Nonlinearity is a characteristic of sorption to humic materials because it occurs even in soils with very little mineral content. Many of our studies have been carried out on Pahokee peat soil, a high-organic ( -7% ash), well-humified reference material. This material consists of jagged amber-like translucent particles containing opaque inclusions, and is absent of undecomposed plant fibers. Furthermore, nonlinearity persists in cases where the mineral component of the peat has been stripped by HF/HCl treatment (cf., entry 1 vs entry 15, Table I), iv) Nonlinearity is not an artifact of insufficient equilibration time, since isotherms typically become increasingly nonlinear with time.

It is possible to get rid of the most stringent ( and most unlikely) of these hypotheses by assuming that the surface is not uniform, i e thatEQ g,E, and AH vary during the adsorption The non uniformity is callli intrinsic when these variations are due solely to the nature of the adsorbent Induced non-uniformity arises when it is the presence of an adsorbed particle on one site which leads to a variation in the energy characteristics of a neighbouring site It is possible to show ( Ref 1, p 136 and ff ) that in the former case, a FREUNDLICH adsorption isotherm is obtained ... 

For the reader s convenience, some of the most frequently used adsorption isotherms and surface equations of state (that of Henry, Langmuir, Freundlich, Volmer, Frumkin, and van der Waals) [35,49-51] are summarized in Table 1 the respective expressions for dT/ dc and the Gibbs elasticity, stemming from the various isotherms are also given F, Bf, and m are characteristic parameters of the Freundlich adsorption isotherm. 

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