Solutes 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. 

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 ... 

The rate of adsorption from dilute aqueous solutions by solid adsorbents (zeolites) is a highly significant factor for applications of this process for water quality control. 

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 ... 

R e, C.J., Prausnitz, J.M., Thermotfynamics of multi-solute adsorption from dilute liquid solutions. AIChE Journal 18(4) (1972) pp. 761-768. 

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. 

Radke, C. J., and Prausnitz, J. M. (1972) Thermodynamics of Multi-Solute Adsorption from Dilute Liquid Solutions, Am. Inst. Chem. Eng. J. 18, 761-768. 

Figure 6 n-propanol adsorption (from dilute aqueous n-propanol solutions) of MFI-type zeolites prepared (a) in alkaline medium and (b) in fluoride medium. ... 

IAS model for dilute liquid solution The IAS method was first proposed to accoimt for the adsorption of gas mixtures. It was later extended to multisolute adsorption from dilute liquid solutions [54]. Assuming that both the solution and the adsorbed phase are ideal, the following equation can be derived to calculate multi-solute equilibriirm composition [54]. 

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. 

When the adsorption of aromatic weak electrolytes is governed by nonelec-trostatic interactions, such as tt-tt dispersion or hydrophobic interactions, the area of the adsorbent occupied by the adsorbate depends on the porosity of the former and the molecular size of the latter. Thus, adsorption from diluted aqueous solution and immersion calorimetry measurements [39] showed that phenol and m-chlorophenol are adsorbed as monolayers by both porous and nonporous carbons with basic surface properties, provided that the adsorptive is undissociated at the solution pH. This did not apply where molecular sieve effects reduced the accessibility of the micropore system. 

This chapter shows that a unified explanation can be given of the adsorption from dilute aqueous solutions of different organic solutes, from nonelectrolytes to electrolytes, polyelectrolytes, and bacteria. Thus, the adsorption process is a complex interplay between electrostatic and nonelectrostatic interactions. Electrostatic interactions depend on the solution pH and ionic strength. The former controls the charge on the carbon surface and on the adsorptive... 

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... 

Generally, wastewaters are complex mixtures of solutes, which require theoretical approaches to predict multicomponent adsorption equilibria flxtm pure component adsorption data. The Ideal Adsorbed Solution model (IAS) was first established for a mixed gas adsorption by Myers and Prausnitz [9], and then extended to a multi-solute adsorption from dilute liquid solution by Radke and Prausnitz [10]. The model is based on the fundamental hypothesis that the multicomponent solution has the same spreading pressure s as that of the ideal single solution of the i component, the spreading pressure being the difference between the interfacial tension of the pure solvent and that of the solution containing the solute. This hypothesis is described by the Gibbs equation ... 

There are several methods available that allow the prediction of mixture isotherms based on general single-component information. An application can significantly reduce the necessary number of experiments. The most successful approach is the ideal adsorbed solution (IAS) theory initially developed by Myers and Prausnitz (1965) to describe competitive gas phase adsorption. This theory was subsequently extended by Radke and Prausnitz (1972) to quantify adsorption from dilute (i.e., also ideal) solutions. 

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