Isotherms competitive

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 ... 

W. Piatkowski, D. Antos, F. Gritti and G. Guiochon, Study of the competitive isotherm model and mass transfer kinetics for a BET binary system. J. Chromatogr.A 1003 (2003) 73-89. 

Competitive Langmuir Adsorption Isotherm When two or more substances can be adsorbed on a surface, the so-called competitive isotherms are applied. The Langmuir isotherm was improved for the adsorption of two gases by Markham and Benton (1931). Of course, the four assumptions of Langmuir isotherms are valid here, too. The surface-adsorbed quantity of component 1 is... 

Following elution of the isotachic train and the displacer solution from the column, the column must be regenerated and reequilibrated with the carrier before any subsequent displacement separation. This reequilibration step can be lengthy and is frequently considered a major Umitation to efficient displacement operation. Displacement chromatography requires the competitive isotherms of the solutes and the displacer to be convex upward and to not intersect each other. (See the entry Distribution Coefficient for related information.)... 

The use of these profiles for the determination of competitive isotherms in the binary case has been developed by Jacobsen et al. [8]. 

Keywords High performance liquid chromatography (HPLC), Analytical biotechnology, Sample preparation, Diode-array-detection (DAD), Mass spectrometry (MS), Validation, Preparative chromatography, Competitive isotherm parameters, Perturbation peak (PP) method... 

Also for the bi-Langmuir isotherm, that describes a surface which is covered with two different kinds of sites, we can account for the competitive behavior of a mixed sample by using the bi-Langmuir competitive isotherm [109, 112] ... 

The Martire isotherm model can also give rise to a competitive isotherm model which is discussed in Chapter 4. 

Competitive Isotherms Models for Other Modes of Chromatography..186... 

In this chapter, we discuss first a number of models that have been used to accoimt for competitive isotherm data. Although the multi-component extension of many of these models is straightforward, most of them have been used almost exclusively with binary mixtures. In the second part of this chapter, we describe the methods of determination of competitive isotherms. Finally, we discuss the methods of data acquisition for multi-component adsorption and we present a few examples. 

Obviously, the amoimt, qi, of the component i that is adsorbed at equilibrium is proportional to the surface area covered by its molecule so the competitive isotherm is written... 

Competitive isotherms such as the Langmuir isotherm (Eq. 4.5) are represented by surfaces in a suitable space. The single-component isotherm is represented by a curve in the q, C) plane (see Chapter 3). Binary competitive isotherms are represented by two surfaces, one in the three-dimensional space qi, Ci, C2), the other one in the space q2, C, C2). Figure 4.1 shows an example of these plots [11]. These surfaces intersect, as is easy to show. Consider a vertical cylinder centered on the vertical axis of coordinates (Ci = 0, C2 = 0). This cylinder intersects the plane (Ci, C2) along a circle of radius C. It intersects the surface q C, C2) along a curve that decreases from qi (C, 0) to 0 when we move from the axis Ci to the axis C2 on the cylinder. In the same time, the intersection of the isotherm surface qiiCi, C2) is a curve increasing from 0 (on axis Cx) to q2(C, 0). These two curves intersect in one point of coordinates (Ci, C2). In this point we have... 

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],... 

Few multicomponent competitive isotherms have been measured so far although the progress in the development of methods and the pressure arising from the development of preparative chromatography and the need better to understand competitive isotherms combine to render such investigations attractive. The experimental data of two ternary isotherms were measured by frontal analysis [17, 23] while those of a quaternary isotherm were determined by the perturbation method [24]. 

As with the competitive Langmuir isotherm, the coefficients of this competitive isotherm are those obtained for the single-component isotherms of the two components. 

Figure 4.3 Experimental competitive isotherm data (symbols) and best bi-Langmuir competitive isotherm (solid lines) for bradykinin and kallidin. Reproduced with permission from D. Zhou, K. Kacztmrski, G. Guiockon, ]. Chromatogr. A, 1015 (2003) 73 (Fig. 1).

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]. 

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... 

Figure 4.4 Competitive isotherms of the 0 and enantiomers of methyl mandelate on 4-methylcellulose tribenzoate, with hexane/2-propanol (90 10) as the mobile phase, (a) Single-component isotherms at 30°C solid lines, competitive Langmuir model dotted lines, LeVan-Vermeulen isotherm, (b) Experimental (symbols) and calculated (lines) competitive isotherms ratio C(+)/C(-) = 1.05. (c) Same as (b), but ratio C(+)/C(-) = 2.43. (d) Same as (b), but ratio C(+)/C(-) = 0.32. Reproduced from F. Charton and G. Guiochon, ]. Chro-matogr., 630 (1993) 21 (Figs. 2 and 3).

Jandera et al. [35] measured by frontal analysis the competitive isotherms of the enantiomers of mandeHc acid, phenyl-glycine and tryptophan on the glyco-peptide Teicoplanin, in water/methanol or ethanol solutions. The less retained L enantiomers of the two amino acids follow Langmuir isotherm behavior while the D isomers foUow bi-Langmuir behavior. The enantiomeric separation factors increase with increasing alcohol concentration while the solubilities of these com-poimds decrease. Similar results were reported by Loukih et al. [36] for the separation of the enantiomers of tryptophan on a teicoplanin- based CSR The authors insisted on the importance of the nature of the ions in a supporting salt. Optimization of the experimental conditions for maximum production rate must take this effect into account. 

Figure 4.6 illustrates the use of the IAS model to account for the competitive isotherm data of a ternary mixture of benzyl alcohol (BA), 2-phenylethanol (PE) and 2-methyl benzyl alcohol (MBA) in reversed phase liquid chromatography. The RAS model accounts for the nonideal behaviors in the mobile and the stationary phases through the variation of the activity coefficients with the concentrations. Figures 4.6d and 4.6e illustrate the variations of the activity coefficients in the stationary and the mobile phases, respectively. The solutes exhibit positive deviations from ideal behavior in the adsorbed phase and negative deviations from ideal behavior in the mobile phase. 

Figure 4.6 Competitive isotherms of a ternary mixture of benzyl alcohol (BA), phenyl-2-ethanol (PE) and methyl-benzyl alcohol (MBA) on Cig-sUica with MeOH/H20 as the mobile phase, at different relative concentrations. Adsorbed amormts of (a) benzyl alcohol, (b) 2-phenylethanol, (c) 2-methyl benzyl alcohol, (d) activity coefficient in the mobile phase versus concentration. In Figures (a), (b), (c), the open circles are for equal parts of BA, PE and MBA, the diamonds for three parts of BA, 1 part PE and 1 part MBA), the triangles for one part of BA, one part of PE and three parts of MBA and the stars for the singlecomponent isotherms. The solid line is the Flory-Huggins model and the dashed lines are the IAS model isotherms. In Figures (d) and (e), the circles are for BA, the squares for PE, the triangles for MBA and the diamonds for the solvent. Reproduced from I. Quinones, J. Ford, G. Guiochon, Chem. Eng. Set, 55 (2000) 909 (Figs. 12,13 and 14).

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