Competitive adsorption isotherm, model calculation

FIGURE 1.10 Model calculations of ion exchange and competitive adsorption isotherm. 

The IAS theory was later extended to account for the adsorption of gas mixtures on heterogenous surfaces [52,53]. It was also extended to calculate the competitive adsorption isotherms of components from hquid solutions [54]. At large solute loadings, the simplifying assumptions of the LAS theory must be relaxed in order to account for solute-solute interactions in the adsorbed phase. The IAS model is then replaced by the real adsorbed solution (RAS) model, in which the deviations of the adsorption equilibrium from ideal behavior are lumped into an activity coefficient [54,55]. Note that this deviation from ideal beha dor can also be due to the heterogeneity of the adsorbent surface rather than to adsorbate-adsorbate interactions, in which case the heterogeneous IAS model [55] should be used. 

Figure 4.10 Experimental competitive adsorption isotherm data of ds- and fraws-andro-sterone. Same phase system as in Figure 4.9. Comparison of the Langmuir competitive model (bottom) and the two-term expansion of the LeVan-Vermeulen isotherm (top). In both cases, the best-fit parameters are used to calculate the Unes. Experimental data A ds-androsterone o trafjs-androsterone. Theory czs-androsterone (dotted lines) trans-androsterone (solid Hnes). a and d 2 1 mixture b and e 1 1 mixture and c and f 1 2 mixture. Reproduced with permission from S. Golshan-Shirazi, J.-X. Huang and G. Guiochon, Anal. Chem., 63 (1991) 1147 (Figs. 1 and 2), ( )1991 American Chemical Society.

More recently, Jiang and Sandler carried out similar studies for the adsorption of CO2, N2, and their mixture [33] on the same schwarzite model adsorbent. As an illustration of their results. Fig. 14.2 shows the calculated (competitive) adsorption isotherms, as well as the selectivities of CO2 over N2 as a function of pressure for a CO2-N2 (0.21 0.79) mixture (the composition of this mixture corresponds to the flue gas emitted from the complete combustion of carbon with air). As the isotherms show, the use of the ab initio potential results in a larger difference between the amounts of adsorbed CO2 and N2... 

Adsorption of albumin, y-globulin, and fibrinogen from single solutions onto several hydrophobic polymers was studied using internal reflection IR spectroscopy. The adsorption isotherms have a Langmuir-type form. The calculated rate and amount of protein adsorbed was dependent on the polymer substrate and the flow rate of the solution. Competitive adsorption experiments were also investigated to determine the specific adsorption of each I-labelled protein from a mixture of proteins. Platelet adhesion to these proteinated surfaces is discussed in relation to a model previously proposed. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

Similar results were obtained with the enantiomers of methyl mandelate separated on 4-methylcellulose tribenzoate immobilized on silica [30]. Figure 4.4a shows the experimental adsorption data for the two pure enantiomers (symbols), the best bi-Langmuir isotherms (solid lines) and the best LeVan-Vermeulen isotherms [33]. The data (symbols) were obtained by ECP. Figures 4.4b-d compare the competitive isotherm data measured with three mixtures of different composition and the isotherms calculated from the single component isotherms (Figure 4.4a) using the competitive bi-Langmuir model (Eq. 4.10). Results obtained... 

Unfortunately, the available experimental results suggest that the column saturation capacity is often not the same for the components of a binary mixture, so Eq. 4.5 does not account accurately for the competitive adsorption behavior of these components [48]. A simple approach was proposed to turn the difficulty (next subsection). Although it is applicable in some cases, more sophisticated models seem necessary. Numerous isotherm models have been suggested to solve this problem. Those resulting from the ideal adsorbed solution (IAS) theory developed by Myers and Prausnitz [49] are among the most accurate and versatile of them. Later, this theory was refined to accormt for the dependence of the activity coefficients of solutes in solution on their concentrations, leading to the real adsorption solution (RAS) theory. In most cases, however, the equations resulting from IAS and the RAS theories must be solved iteratively, which makes it inconvenient to incorporate those equations into the numerical calculations of column dynamics and in the prediction of elution band profiles. 

Figure 4.12 Competitive isotherms of the (-)- and (+)- enantiomers of Troger base on microcrystalline cellulose triacetate, with ethanol as mobile phase, (a) Single-component adsorption isotherm of (+)-TB (squares) and (-)-TB (triangles) at 40° C. Experimental data and best fit to a Langmuir, (+)-TB, and a quadratic, (-)-TB, isotherm model, (b) Competitive isotherms of (-)-TB in enantiomeric mixtures for increasing concentrations (0, 0.5,1,1.5,2, 2.5, 3 g/L) of (+)-TB, calculated with IAS theory, (c) Competitive isotherms of (+)-TB in enantiomeric mixtures for increasing concentrations (0, 0.5, 1, 1.5, 2, 2.5, 3 g/L) of (-)-TB calculated with IAS theory. Reproduced from A. Seidel-Morgenstem and G. Guiockon, Chem. Eng. Sci., 48 (1993) 2787 (Figs. 4, 6, and7).

Migliorini et al. [65] used both the IAS and the RAS theory to accoimt for the experimental binary competitive isotherm data of the Troger s base enantiomers on microcrystalline triacetate cellulose (CTA), using ethanol as the solvent. For the calculations of the RAS theory, they used the Wilson model for the solution, including the empirical spreading pressure dependence [66]. They concluded that the IAS model imderestimates the extent of the competition between the two enantiomers in this system while the RAS model accormts accurately for the complex competitive adsorption behavior exhibited by these enantiomers. 

Figure 12.29 Comparison of theoretical and experimental displacement separations of resorcinol and catechol by phenol. Calculations using the equilibrium-dispersive model, the LeVan- Vermeulen isotherm model, and single-component adsorption data. Experimental results on a 4.6x250 CIS Nucleosil 5 fim column, F = 0.4 carrier, water, Fj, = 0.2 mL/min, T = 20°C 1 1 mixture, = 0.5 mL displacer, 80 g/L phenol in water = 30%, Lf = 16.5%. (a) Calculation with LeVan-Vermeulen isotherm, (b) Calculation with quadratic isotherm, three floating parameters, (c) Calculation with competitive Langmuir isotherm, single-component isotherm parameters, (d) Calculation with Langmuir isotherm, best adjusted parameters. Reproduced with permission from. C. Bellot and J.S. Condoret, J. Chromatogr., 657 (1994) (Figs. 3c, 4c, 6c, 8c) 305.

In this study, a binary adsorption of 2-methylphenol/2,4-dimethylphenol was performed on F400 and BC-21. Figure 6.8a and b presents the binary adsorption isotherms of phenoI/2-methylphenol for F400 and BC-21, respectively. Meanwhile, the Myers parameters obtained from the single solute anoxic isotherm was applied into the lAST model to predict the competitive adsorption behavior. The evaluation of the predictability of lAST was also done by calculating the sum of squares of relative errors (SSREs). All the detailed concentration combination and SSRE values of both runs for both adsorbents are shown in Table 6.4. 

More national and international standardisation procedures for mercury porosimetry and the derivation of pore size distributions from adsorption isotherms are in preparation. Regarding the ueakness of the two-parameter BET model for surface area determination in addition the three-parameter BET equation or improved approximations (ref. 10) should be introduced. The more lengthy calculations can be easily managed using a computer. Competitive evaluation methods, like the method of Dubinin,... 

Figure 3.31 Distribution of the equilibrium constants of adsorption calculated by means of the biToth model for 1-indanol on cellulose tribenzoate. The arrows indicate the equilibrium constants derived from the competitive bi-Langmuir isotherm. Reproduced with permission from A. Felinger, D. Zhou, G. Guiochon,. Chromatogr. A, 1005 (2003) 35.

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