Isotherm measurement competitive isotherms

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 ... 

It may seem from the above discussion that it is impossible to use even batch isotherm measurements to design HPLC (or SPE) separations. This is not so, however, at least when the HPLC separation occurs under near-equilibrium conditions. Nonlinear chromatographic peaks can be simulated [38] once the corresponding isotherms have been measured. In this case one does not need a physical interpretation of the isotherm equation s constants they can be regarded merely as interpolation factors. Separately measured isotherms of the two compounds are satisfactory in many cases because - as mentioned above - competition often has only minor influence on the separated peaks position and shape. 

Single-component isotherm parameters cannot always predict elution profiles with satisfied accuracy [122, 123], Therefore, to be able to predict accurate overloaded multi-component elution profiles where competition occurs competitive adsorption isotherm parameters are often necessary. Measurement of isotherms from a mixture is also often necessary because the pure enantiomers are not always accessible in large quantities. However, there exist only a small number of reports on the determination of multi-component adsorption isotherm parameters. FA can be used to determine binary isotherm data but it is time-consuming. The PP method is an alternative method to determine isotherm parameters from binary mixtures. It has been reported that the PP method works well up to weakly non-linear conditions [118, 119],... 

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]. 

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... 

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. 

Experimental results demonstrate the importance of the adsorbate-adsorbate interactions in the control of the adsorption equilibrium constant [92]. Good agreement is achieved when estimating some of the parameters from the results of independent measurements. However, these estimates are quite approximate and the physical meaning of the model has not been demonstrated. The suitability of the model for competitive isotherm studies has not been established either. It would require that the competitive isotherm could be derived simply from the... 

There is a dearth of competitive adsorption data, in a large part because they are difficult to measme, but also because little interest has been devoted to them, as, until recently, there were few problems of importance whose solution depended on their understanding. Besides the static methods, which are extremely long and tedious and require a large amoimt of material, the main methods of measurement of competitive isotherms use column chromatography. Frontal analysis can be extended to competitive binary isotherms [14,73,93-99], as well as pulse techniques [100-104]. The hodograph transform is a powerful method that permits an approach similar to FACP for competitive binary isotherms [105,106]. 

Figure 4.24 Reproductibility of the measurement of the competitive isotherms of cis- and frans-androsterone using a 2 1 mixture before and after a long series of experiments. 50 X 4.6 mm column packed with Partisil 10 treated with a phosphate buffer mobile phase ACN/CHCI3 (15 85) at 1 mL/min. Reproduced with permission from J.-X. Huang and G. Guiochon, ]. Colloid and Interf Sci., 128 (1989) 577 (Fig. 8).

The major drawbacks of the frontal analysis method are the important number of measurements to be made, the considerable amount of time that it takes to determine a set of competitive isotherms and the large amount of sample required. The competitive isotherms are sets of n surfaces in an n -b 1 space where n is the number of components. For a binary mixture, we have two surfaces, /i(Ci, C2) and /2(Ci, C2). These surfaces depend minimally on four parameters, often on more, depending on the isotherm model selected. 

The Hybrid Method of Mass Balance (HMMB) This method is a modification of the MMB method in which, instead of measuring a series of values of C which is cumbersome, these concentrations are estimated through Eqs. 4.85 and 4.86 by using the isotherm parameters, , and determined by the MCV method. This hybrid approach employs MCV only to estimate the mezzanine concentrations, so it is more acciurate than MCV when the actual isotherm deviates from the Langmuir competitive isotherm. 

As an example, we show in Figure 4.25 the competitive isotherms of the mixture of p-cresol (Figure 4.25a) and phenol (Figure 4.25b) on octadecyl silica [14], and those of N-benzoyl-D- and L-alanine on BSA immobilized on silica [29]. The isotherms in Figure 4.25 were measured by binary frontal analysis (Section 4.2.1). 

Figure 4.26 Comparison of the competitive adsorption isotherm measured by FA and calculated by two different methods. p-Cresol (Left) and phenol (Right), Top Data from the mass balance method (MMB, binary frontal analysis) at molar ratios of 3 1 (Q)/ Id ( ) and 1 3 (A). Solid hnes calculated by the method of composition velocity (MMC). Bottom Comparison of the competitive isotherms obtained by MMB (Q) and HBBM (square s)nnbol) (n) for p-ciesol and phenol in three concentration regimes. Reproduced with permission from J. Jacobson and J. Frenz, ]. Chromatogr., 499 (1990) 5 (Figs. 2 and 5).

As shown by Helfferich and Peterson [110], if a small pulse of one of the mixture components, isotopically labeled, is injected in a multicomponent solution, the labeled component moves at a velocity that is proportional to the slope of the corresponding chord of the isotherm. In the same time, as many system peaks as there are components in the mixtiure arise and move at velocities related to the slopes of the corresponding isotherms (see Figure 4.27a,c,e). This assumes that equilibrium has previously been reached throughout the column. In the tracer pulse technique, only the labeled component is detected. Successive injections of a sample of each labeled component (or the simultaneous injection of all of them if their separate identification is possible) permit the direct determination of the competitive isotherms of all the components. From a theoretical point of view, the presence of large concentrations of the other components does not complicate the measurement nor its evaluation, since the retention time of each isotopic pulse is a linear fimction of the slope of the corresponding chord Aq / AC, see Eq. 2.15). 

The method has been used for the determination of competitive isotherms in cases in which the deviation from the Langmuir model is moderate [115]. An HPLC chromatograph configured so as to permit injecting into the column a wide rectangular pulse, e.g., by pumping into it either the pure mobile phase or, for a known time, a solution of the compound of interest, was used to make the measurements described [115]. Excellent agreement was observed with other experimental data and with the experimental band profiles recorded in overloaded elution for binary samples of various compositions [48]. 

Many reports in the literature deal with the determination of the competitive isotherms of particular systems. Many of them have already been referred to in this chapter. In this last section, we discuss the specific issues encountered in the measurement of these isotherms. This problem is particularly important from both practical and fundamental view points because these pairs of compounds have imusual properties arising from the identity of all their properties that are not chiral. 

Experimental band profiles have been measured and compared to profiles calculated with the equilibrium-dispersive model using various possible calculation procedures. Most often, the degree of agreement between calculated and experimental profiles depends on the accuracy with which the competitive isotherm data have been measured and modeled. 

Furthermore, this separation problem, which is theoretically simple, is also highly relevant to the pharmaceutical industry. An example is the separation of mixtures of N-benzoyl-D- and L-alanine on immobilized BSA (see Figures 11.20). We have explained in Chapters 3 and 4 (i) that a competitive bi-Langmuir isotherm can be employed to account for the competitive behavior of these components (Figure 4.25c) and (ii) that, because the chiral selective retention mechanism involves adsorption of the enantiomers in the hydrophobic cavity of BSA, the column saturation capacity of the chiral selective mechanism is the same for the two enantiomers. This competitive bi-Langmuir isotherm model is simply derived from the parameters obtained from single-component isotherm measurements. 

All these results demonstrate that the calculation of band profiles that are in very good agreement with experimental results is possible provided an accurate model of the competitive equilibrium isotherms is available. The main practical difficulty in the modeling of separations is in the accurate measurement and modeling of these competitive isotherms. Once such a model has been validated, it is possible to calculate the performance of a chromatographic unit and to optimize its performance [27]. 

Although for the sake of clarity the previous discussion was limited to the case of a binary mixture, these results are easily generalized to the study of an n-component mixture. Because of the coupling between the mobile phase components, the velocity eigenvalues are related to the slopes of the tangents to the n-dimensional isotherm surface, in the n composition path directions. These slopes can be calculated when the isotherm surface is known. Conversely, systematic measurement of the retention times of very small vacancy pulses for various compositions of the mobile phase may permit the determination of competitive equilibrium isotherms, but only if a proper isotherm model is available. Least-squares fitting of the set of slope data to the isotherm equations allows the calculation of the isotherm parameters. If an isotherm model, i.e., a set of competitive isotherm equations, is not available, the experimental data cannot be used to derive an empirical isotherm (see Chapter 4). 

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