Adsorption from multicomponent solutions

The simplest case of adsorption from multicomponent solutions is the adsorption from ternary solutions. The isotherms of components adsorption in such systems are expressed... 

Thus liquid chromatography makes it possible to determine the equilibrium constant at small coverage (the retention volume or Henry constant) and to characterize the compounds adsorption from multicomponent solutions. From the dependence of retention volumes on temperature the changes of enthalpy and entropy of adsorption can be calculated. 

Adsorption from multicomponent solutions is a basis of a number of industrial processes, such as separation, purification, recovery of chemical compounds, and so forth. Numerous practical applications of adsorption from multicomponent solutions require the formulation of theoretical foundations for interpretation of the experimental data. However, the difficulties mentioned... 

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. 

The most studies of adsorption from solution have been concerned with the adsorption from two-component mixture, for example [1,2], Practical use of adsorption however deals with the adsorption from multicomponent systems. In liquid chromatography in a many cases for the separation of mixture of solutes the multicomponent eluents are used. The most difficulties in the investigation of adsorption from multicomponent systems arise at the determination of some component concentration at once in equilibrium solution over the adsorbent. Moreover for the determination of adsorption isotherm in this case large experimental data are needed. 

The chromatographic method of analysis makes it possible to investigate the adsorption from multicomponent systems. For study of adsorption from solutions of volatile compounds gas chromatography can be used and for the investigation of solid compound or non-volatile substances liquid chromatography is used. In this cases chromatography is applied as method of determination of components concentration in equilibrium solution over the adsorbent [3-5]. 

Multisolute Adsorption from Dilute Aqueous Solutions.—Earlier work on adsorption from multicomponent systems has been reviewed in references 2 (p. 103) and 3 (p. 75). The work of Radke and Prausnitz, Fritz and Schliinder, and of Myers and Minka has been developed in a paper on the thermodynamics of multisolute adsorption from dilute aqueous solutions by Jossens, Prausnitz, Fritz, Schliinder, and Myers. The experimental work... 

Using the thermodynamics of regular solutions and adsorption from multicomponent liquid mixtures, Oscik (15) derived an equation for the value of solute chromatographed in an n-component mobile phase. 

For this study, mass transfer and surface diffusions coefficients were estimated for each species from single solute batch reactor data by utilizing the multicomponent rate equations for each solute. A numerical procedure was employed to solve the single solute rate equations, and this was coupled with a parameter estimation procedure to estimate the mass transfer and surface diffusion coefficients (20). The program uses the principal axis method of Brent (21) for finding the minimum of a function, and searches for parameter values of mass transfer and surface diffusion coefficients that will minimize the sum of the square of the difference between experimental and computed values of adsorption rates. The mass transfer and surface coefficients estimated for each solute are shown in Table 2. These estimated coefficients were tested with other single solute rate experiments with different initial concentrations and different amounts of adsorbent and were found to predict... 

Athes et al. (2004) compared the data from three static headspace methodologies (VPC, PRV and LC-SH) for determining gas/liquid partition coefficients of two aroma compounds in hydroalcoholic, multicomponent solutions at infinit dilution. They found that PRV was a simpler method compared to VPC and LC-SH and that VPC and PRV were more accurate than LC-SH since errors due to gas leaks and adsorption in gastight syringes are avoided. They suggested that these issues could be responsible for significant bias (50% lower values) obtained when using the LC-SH method. Nevertheless, all three methods were able to find an effect of ethanol (up to 20%) on the release of aroma compounds from their model system (Fig. 8F.1). 

Unfortunately, the study of phase equilibria in solution, e.g., liquid-solid adsorption, is not a highly popular area of research. Gas-solid adsorption and vapor-solution equilibria have been studied in far more detail, although most of the information available concerns the fate of single components in a diphasic system. Liquid-solid adsorption has benefited mainly from the extension of the concepts developed for gas phase properties to the case of dilute solutions. Multicomponent systems and the competition for interaction with the stationary phase are research areas that have barely been scratched. The problems are difficult. The development of preparative chromatography and its applications are changing this situation. 

Many empirical and theoretically derived equations of adsorption isotherms of gases in mono- and multicomponent systems have been published [1,2] and a few of these equations are frequently used in studies of adsorption from solution. 

Sheindorf et al. (1981,1982) developed a multicomponent Freundlich-type equation to describe the adsorption of binary solute mixtures containing arsenate and phosphate or arsenate and molybdate. The derivation of the Sheindorf-Rebhun-Sheintuch (SRS) equation was based on the assumption that there is an exponential distribution of adsorption energies available for each solute. The SRS equation can be written for the solute i from a binary solute mixture as... 

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 ... 

Most real protein-containing fluids of interest, such as blood, are multicomponent systems so that the influence of one protein on another may become important. With respect to adsorption, the main consideration is whether adsorbed amounts are in proportion to solution concentration or whether surfaces "select one protein in preference to another. Presumably if proteins act independently of each other one should be able to predict adsorbed amounts in mixtures from relative affinities derived from single protein studies. Although there have been no systematic attempts to make such predictions it seems likely that they would fail. In general it has been found that preferential or selective adsorption occurs so that certain proteins may be enriched in the surface relative to the solution and vice versa. There have as yet been no attempts to determine the properties of protein-surface systems that govern the relative surface affinity of different proteins. More will be said on this topic when adsorption from plasma is discussed. 

We have considered the case of multicomponent adsorption under isothermal conditions in the last section. Such an isothermal condition occurs when the particle is very small or when the environment is well stirred or when the heat of adsorption is low. If these criteria are not met, the particle temperature will vary. Heat is released during adsorption while it is absorbed by the particle when desorption occurs, leading to particle temperature rise in adsorption and temperature drop in desorption. The particle temperature variation depends on the rate of heat released and the dissipation rate of energy to the surrounding. In the displacement situation, that is one or more adsorbates are displacing the others, the particle temperature variation depends also on the relative heats of adsorption of displacing adsorbates and displaced adsorbates. Details of this can only be seen from the solution of coupled mass and heat balance equations. 

Adsorption equilibria for polymers out of concentrated solutions as function of concentration frequently exhibit very pronounced maxima (Fig. 12). These unusual curves can be accounted for if one assumes that the adsorbed species are in aggregation equilibrium in the solution, depending upon the amount of surface area per unit volume of solution. Hence one expects that the adsorption equilibrium out of concentrated polymer solution may not only be approached with "infinite slowness but is also a function of the system characteristics, and the definition of reproducible conditions contains many more variables than one is used to from the more common work with dilute solution. This complexity is particularly awkward when one deals with the important case of competitive adsorption of polymers out of concentrated multicomponent solutions, a common phenomenon in many industrial processes, such as paint adhesion, corrosion prevention, lubrication, especially wear prevention, etc. 

The ideal adsorption solution theory described in Section IVA is the simplest approach to multicomponent adsorption from the point of view of the general thermodynamic theory of the surface phase. The lAST is comparable with potential adsorption theory by predictability. Both theories need the correlation of experimental data for pure components in order to estimate adsorption of mixtures. However, in general, the predictions of the two theories are different, as illustrated in Section IVD. Let us analyze assumptions on which the two theories may become similar. 

Reflect now on what is being achieved in elution iduro-matography. By having the bulk flow of the mobile phase (solvent) perpendicular to the direction of force (for adsorption from the mobile phase to the stationary particle phase for desorption from the stationary particle phase to the mobile phase), a multicomponent mixture of solutes is separated, as long as Rs values are reasonable. If the feed mixtures were simply equilibrated with the adsorbent particle phase without any mobile-phase flow perpendicular to the force direction, no such separation would have been achieved. 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

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