Adsorption from dilute solutions

Adsorption of solutes on active carbons from aqueous and nonaqueous solutions can be carried out simply by placing a known weight of an active carbon in contact with different concentrations of the solute in stoppered or sealed Coming-glass test tubes. The contents are shaken in a mechanical shaker for a certain period of time, which may vary between a few minutes and several hours, depending upon the nature of 

Maximum Surface Coverage of Various Carbons of Different Oxygen Contents by Stearic Acid Adsorbed from Carbon Tetracbloride Solution 

Source Arora, V.M., Ph.D. dissertation, Panjab Univ., Chandigarh, India, 1977. With permission. 

Adsorption of phenol and its derivatives from aqueous solutions on active carbons and carbon blacks has been the subject matter of a large number of investigations. Jaroniec and coworkers,Enrique et al. Worch and Zakke, and Magne and Walker studied the adsorption of several phenols from aqueous solutions and found that the adsorption was partly physical and partly chemical in character. Aytekin, ChapUn, and Kiselev and Krasilinkov observed that the adsorption isotherms of phenol from aqueous solutions were step-wise, suggesting the possibility of rearrangement of phenol molecules in the adsorbed phase and their interaction with active sites on the carbon surface. Morris and Weber, however, found that the adsorption isotherms of phenols on active carbons show two plateaus, even 

Abuzaid and Nakhla, and Vidic et al. found that the adsorption of phenol by activated carbons from aqueous solutions in the presence of molecular oxygen in the test environment resulted in a threefold increase in the adsorption capacity of the carbon. This has been attributed to the oxygen induced polymerization reactions on the surface of the carbon. Juang et al. studied liquid-phase adsorption of eight phenohc compounds on a PAN-based activated carbon Fiber in the concentration range of 40 to 500 mg/L and observed that the chlorinated phenols showed better adsorption than methyl substituted phenols. Moreno-CastiUa et al. studied the adsorption of several phenols from aqueous solutions on activated carbons prepared from original and deminerahzed bituminous coal and found that the adsorption capacity depended upon the surface area and the porosity of the carbon, the solubility of the phenolic compound, and the hydrophobicity of the substituent. The adsorption was attributed to the electron donor-acceptor complexes formed between the basic sites on the surface of the carbon and the aromatic ring of the phenol. 

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As discussed in Chapter III, the progression in adsoiptivities along a homologous series can be understood in terms of a constant increment of work of adsorption with each additional CH2 group. This is seen in self-assembling monolayers discussed in Section XI-IB. The film pressure r may be calculated from the adsorption isotherm by means of Eq. XI-7 as modified for adsorption from dilute solution ... 

Adsorption from Dilute Solutions Isotherm Models.291... 

In the early experiments, when gas-solid adsorption was studied by some 200 years ago, charcoal was the most widely used adsorbent [12]. These investigations, generally limited to adsorption from dilute solutions, gave adsorption isotherms of the form shown in Figure 10.4. These isotherms could be fitted by the equation ... 

In some exceptional cases, however, can be given a definite meaning. This is so in the case of adsorption from dilute solutions [13,21]. Incidentally, these are the conditions usually encountered in preparative chromatography. Let us assume the compound numbered 1 to be the preferentially adsorbed. If its equilibrium concentration (x,) is negligibly small, from Equation 10.36 one obtains... 

ADSORPTION FROM DILUTE SOLUTIONS ISOTHERM MODELS... 

The assumption of linear chromatography fails in most preparative applications. At high concentrations, the molecules of the various components of the feed and the mobile phase compete for the adsorption on an adsorbent surface with finite capacity. The problem of relating the stationary phase concentration of a component to the mobile phase concentration of the entire component in mobile phase is complex. In most cases, however, it suffices to take in consideration only a few other species to calculate the concentration of one of the components in the stationary phase at equilibrium. In order to model nonlinear chromatography, one needs physically realistic model isotherm equations for the adsorption from dilute solutions. 

For adsorption from dilute solutions the activity coefficient approaches unity, in which case the combination of Equations (46) and (48) leads to the result... 

One isotherm that is both easy to understand theoretically and widely applicable to experimental data is due to Langmuir and is known as the Langmuir isotherm. In Chapter 9, we see that the same function often describes the adsorption of gases at low pressures, with pressure substituted for concentration as the independent variable. We discuss the derivation of Langmuir s equation again in Chapter 9 specifically as it applies to gas adsorption. Now, however, adsorption from solution is our concern. In this section we consider only adsorption from dilute solutions. In Section 7.9c.4 adsorption over the full range of binary solution concentrations is also mentioned. 

In summary, adsorption from dilute solutions frequently displays the qualitative form required by the Langmuir equation. If this form is observed, it may be quantitatively described by Equation (75), in which m and b are empirical constants. Sometimes there may be a justification for further interpretation of these parameters in terms of the theoretical model. 

Mills, A. C., and J. W. Biggar, Adsorption of 1,2,3,4,5,6-hexachlorocyclohexane from solution The differential heat of adsorption applied to adsorption from dilute solutions on organic and inorganic surfaces , J. Coll. Int. Sci., 29, 720-731 (1969b). 

A division Into "adsorption from dilute solution" and "adsorption from binary (and multicomponent) mixtures covering the entire mole fraction scale" appears to be useful. For simplicity, we shall designate mixtures covering the entire mole fraction scale as binary mixtures, as opposed to dilute solutions. This distinction is a consequence of issues (1) - (3) above, and reflected in thermodynamic and statistical interpretations. For instance, in dilute solutions locating the Gibbs dividing plane is not a problem, but for a mixture in which one of the components cannot confidently be identified as the solvent, it is. 

We recall sec. 1.2.22, and in particular fig. 1.2.13 where the consequences of basing the Gibbs plane on a major or a minor component are illustrated. Statistically, adsorption from dilute solution is easy when the solvent may be interpreted primitively, i.e. as a structureless continuum. Then, much of chapter 1 may be applied after minor modification. For binary mixtures this becomes more problematic. In practice, adsorption from (dilute) solution is more frequently met than that from binarj mixtures. 

Summarizing, interpretation of adsorption from binary mixtures poses more problems than adsorption from dilute solutions, but it also exhibits the basic issues more clearly. Therefore, we shall treat these problems first (secs. 2.3, 2.4 and 2.6) and thereafter, starting with sec. 2.7. address dilute solutions. 

The excess is the quantity that is usually measured for adsorption from dilute solutions. Now the reference system has the same volume, in which c is constant up to the phase boundary. V is the total volume minus the volume of the adsorbent which we assumed constant. Working with volumes can have advantages when the fluid density remains constant. For such a constant fluid density (i.e. the molar volumes and depending on x, persisting... 

So far ellipsometry has been used for adsorption from dilute solution, especially for surfactants, polymers and proteins. Examples will be given where appropriate. For further experimental details, we refer to the literature. ... 

For type a curves the Intercept n° may be interpreted as n°, that is the real value of n° In a complete layer from which all 1 Is expelled (n = 0). This is the plateau value attained by the individual Isotherm of 2, Indicated by the dashed curve In fig. 2.23. When an assumption Is made about the molecular cross-section from n° the specific surface area can be obtained. In principle, this method Is not different from finding from, say the plateau In a Langmuir Isotherm, the only difference being that horizontal Langmuir plateaus (for adsorption from dilute solution) are replaced by linear upper parts, approaching zero at 1 (for excess adsorption from binary mixtures). 

To Judge by the number of papers published annually on adsorption from dilute solution, this subject is more important than adsorption from binary solutions. However, the basic issues can be better illustrated from the latter so we have emphasized them in the previous sections. Now we shall review some important features of adsorption from dilute solutions. The examples to be given are merely meant to illustrate certain points and do not claim to be a selection based on a "quality test" among the. say. 10 isotherms published in the literature. 

Reconsidering the seven characteristics, discussed in sec. 2.1, the following may be said for adsorption from dilute solutions... 

Adsorption from dilute solution is also an exchange process and. hence. 

It is particularly point 3) that makes adsorption from dilute solution so much easier to deal with. Besides the easier analytical accessibility, it may be added that ... 

The next step is to derive a relation between, J and K. It is a matter of taste, or convenience, which of these variables to take as the independent variable. For adsorption from dilute solutions it is customary to take the concentration (i.e. g ) as independent. On the other hand, for many theoretical analyses it is easier to assume a certain spatial geometry and then And out the g of the solvent with which the curved interface is at equilibrium. Let us foUow the second route, i.e. we want to establish dg / 3J rmd dg / 8K. These differential quotients can be obtained from [4.7.11 by changing variables and cross-differentiation. For instance. 

Adsorption from dilute solutions - some novel aspects... 

The study of a particular adsorption process requires the knowledge of equilibrium data and adsorption kinetics [4]. Equilibrium data are obtained firom adsorption isotherms and are used to evaluate the capacity of activated carbons to adsorb a particular molecule. They constitute the first experimental information that is generally used as a tool to discriminate among different activated carbons and thereby choose the most appropriate one for a particular application. Statistically, adsorption from dilute solutions is simple because the solvent can be interpreted as primitive, that is to say as a structureless continuum [3]. Therefore, all equations derived firom monolayer gas adsorption remain vafid. Some of these equations, such as the Langmuir and Dubinin—Astakhov, are widely used to determine the adsorption capacity of activated carbons. Batch equilibrium tests are often complemented by kinetics studies, to determine the external mass transfer resistance and the effective diffusion coefficient, and by dynamic column studies. These column studies are used to determine system size requirements, contact time, and carbon usage rates. These parameters can be obtained from the breakthrough curves. In this chapter, I shall deal mainly with equilibrium data in the adsorption of organic solutes. 

Adsorption isotherms of poorly purified solutes on heterogeneous or impure adsorbents often pass through a maximum in adsorption. Although such phenomena are possible in adsorption from concentrated solutions or from the gas phase, it is difficult to justify on theoretical grounds the existence of these phenomena in adsorption from dilute solutions of surfactants. They often disappear upon purification of the adsorbent and the solute and are believed to be due to the presence of impurities (Kitchener, 1965). 

For neutral polymers adsorbing at a bare surface, this is all there is. Hence initial rates of adsorption from dilute solutions satisfy the simple equation... 

Freundlich and Langmuir isotherm equations have been employed to explain the earlier results of adsorption from dilute solutions on carbon. However, as mentioned earlier, the Freundlich isotherm lacks a theoretical basis, and the Langmuir isotherm assumes a constant energy of adsorption over the surface, which is certainly not true in the case of active carbons. Consequently, modified theoretical approaches were advanced to fit the experimental data over a wide range of concentrations. Radke and Prausnitz proposed the equation... 

Potential Theory of Adsorption from Dilute Solutions... 

Marczewski, A. W., and M. Jaroniec. 1983. A new isotherm equation for single-solute adsorption from dilute solutions on energetically heterogeneous solids. Monatshefte fiir Chemie-Chemical Monthly 114, no. 6-7 711-715. doi 10.1007/BF01134184. 

Adsorption from Dilute Solution (Particularly Phenols)... 

General.—Adsorption from dilute solutions can, in the limit of sufficiently low concentrations, be described by a linear (Henry s law) isotherm, which may, however, be expressed in various forms. Among the possible definitions are the... 

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