Competitive adsorption isotherm, model

Figure 4.2 illustrates the best competitive adsorption isotherm model for benzyl alcohol and 2-phenylethanol [16]. The whole set of competitive adsorption data obtained using Frontal Analysis was fitted to obtain the Langmuir parameters column saturation capacity qs =146 g/1), equilibrium constant for benzyl alcohol bsA = 0.0143) and the equilibrium constant for 2-phenylethanol (bpE = 0.0254 1/g). The quality of the fit obtained with this simple model is in part explained by the small variation of the activity coefficients of the two solutes in the mobile phase when the solute concentrations increased from 0 to 50 g/1. The Langmuir competitive adsorption isotherm simplifies also in the case where activity coefficients are of constant value in both phases over the whole concentration range [17]. 

Ilic, M., Flockerzi, D., and Seidel-Morgenstern, A. (2010) A thermodynamically consistent explicit competitive adsorption isotherm model based on second-order single component behaviour. /. Chromatogr. A, 1217, 2132-2137. 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

Fig. 9-16. Competitive adsorption isotherms experimental (points) and model (lines) results.

The steps when designing a SMB which would allow one to process a given amount of feed per unit time have been described in detail [46, 57]. The procedure described was based on modeling of nonlinear chromatography. The procedure is rigorous, versatile and mainly requires the determination of competitive adsorption isotherms. If the adequate tools and methods are used, the procedure is not tedious and requires less work than is sometimes claimed. The procedure is briefly described below. 

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

Preparative chromatography is widely used for the purification of different compounds, but this procedure needs to be optimized to achieve the minimum production costs. This can be done by computer-assisted modeling. However, this approach requires a priori determination of accurate competitive adsorption isotherm parameters. The methods to determine this competitive information are poorly developed and hence often a time limiting step or even the reason why the computer-assisted optimization is still seldom used. In this thesis in papers IV-VI, a new injection method was developed that makes it possible to determine these competitive adsorption isotherm parameters more easily and faster than before. The use of this new... 

Fang, F., Szleifer, I. Competitive adsorption in model charged protein mixtures Equilibrium isotherms and kinetic behavior. J. Chem. Phys. 2003,119,1053-65. 

As a consequence, the competitive Langmuir isotherm model offers no possibility to account for a reversal in the elution order of two components with increasing concentration. On the contrary, experimental results show that such an inversion is possible, and that it is not even unusual when the column saturation capacities of the two single-component isotherms are different. For example, experimental adsorption data and chromatograms of mixtures of tmns- and a s-androsterone show an inversion of the elution order when the sample size increases (see later. Figure 4.8 and the related discussion below) [9-11]. 

On the other hand, the quantitative prediction of competitive isotherm behavior for the components of binary mixtmes is not possible using the competitive Langmuir isotherm model when the difference between the column satmation capacities for the two components exceeds 5 to 10%. For example, the adsorption isotherms of pure cis- and trans-androsterone on sihca are well accoimted for by the Langmuir model [9]. However, the two column saturation capacities differ by 30%, due to the nearly flat structure of the trans isomer compared to the folded structure of the cis isomer. As a consequence, the competitive Langmuir model accounts poorly for the competitive adsorption data [9,10]. Much improved results are obtained with the more complex LeVan-Vermeulen isotherm (Section 4.1.5). Another approach could use the random adsorption site model, with different exclusion siuface areas for the competing molecules [12],... 

This isotherm model has been used successfully to accoimt for the adsorption behavior of numerous compounds, particularly (but not only) pairs of enantiomers on different chiral stationary phases. For example, Zhou et ah [28] foimd that the competitive isotherms of two homologous peptides, kallidin and bradyki-nine are well described by the bi-Langmuir model (see Figure 4.3). However, most examples of applications of the bi-Langmuir isotherm are found with enantiomers. lire N-benzoyl derivatives of several amino acids were separated on bovine serum albumin immobilized on silica [26]. Figure 4.25c compares the competitive isotherms measured by frontal analysis with the racemic (1 1) mixture of N-benzoyl-D and L-alanine, and with the single-component isotherms of these compounds determined by ECP [29]. Charton et al. foimd that the competitive adsorption isotherms of the enantiomers of ketoprofen on cellulose tris-(4-methyl benzoate) are well accounted for by a bi-Langmuir isotherm [30]. Fornstedt et al. obtained the same results for several jS-blockers (amino-alcohols) on immobilized Cel-7A, a protein [31,32]. 

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.

Because of unsatisfactory results obtained with the competitive Langmuir isotherm model, several empirical equations have been suggested, based on hybrids of common models. One of the most popular of these isotherm models addresses the problem of strong adsorption observed at low concentrations and its rapid subsidence at increasingly large concentrations. This equation combines conven-... 

Although the general phenomena and the qualitative results described in this section remain valid for any isotherm model, provided they are convex upward and do not intersect, the quantitative results of the shock layer theory presented in Chaptersl4 and 16 are valid only when the adsorption behavior of the mixture components is properly described by the competitive Langmuir isotherm model. The theory shows conclusively that, when the separation factor decreases, the shock layer thickness, hence the width of the mixed zone in the isotachic train, increases in proportion to oc + l)/ a — 1) (Eqs. 16.27a and 16.27b). At the same time, the column length required to reach isotachic conditions increases also indefinitely, as predicted by the ideal model. 

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