Frontal Analysis isotherm measurements

Isotherm Measure by frontal analysis, perturbation Measure by peak-maximum method Measure with ECP... 

Experiments Sorption equihbria are measured using apparatuses and methods classified as volumetric, gravimetric, flow-through (frontal analysis), and chromatographic. Apparatuses are discussed by Yang (gen. refs.). Heats of adsorption can be determined from isotherms measured at different temperatures or measured independently by calorimetric methods. 

For determining the adsorption isotherm, the equilibrium concentrations of bound and free template must be reliably measured within a large concentration interval. Since the binding sites are part of a solid, this experiment is relatively simple and can be carried out in a batch equilibrium rebinding experiment or by frontal analysis. 

The precise measurement of competitive adsorption isotherms not only of theoretical importance but may help the optimization of chromatographic processes in both analytical and preparative separation modes. The methods applied for the experimental determination of such isotherms have been recently reviewed [90], Frontal analysis using various flow rates can be successfully applied for the determination of competitive adsorption isotherms [91]. 

Using this methodology via measurement of adsorption isotherms, Guiochon and coworkers investigated site-selectively the thermodynamics of TFAE [51] and 3CPP [54] on a tBuCQD-CSP under NP conditions using the pulse method [51], the inverse method with the equilibrium-dispersive model [51, 54], and frontal analysis [54]. 

Calculation of the isotherm can be done by the method of Cremer and Huber [7] for pulse measurements or by the approach of James and Phillips [8] for frontal analysis. 

There is a fundamental relationship described in chromatographic theory between the retention volume of a elution peak and the mid-point of a breakthrough curve achieved by operating the column under frontal analysis conditions (41 ). In the Henry s Law region of the adsorption isotherm, the net retention volume and its measurement can be used to describe the variation of sorbate breakthrough volume as illustrated in Figure 8. Utilizing the experimental apparatus described in the last section, retention volumes were measured as a function of pressure at 40°C (T =... 

Direct determination of the column saturation capacity requires measurement of the adsorption isotherm. Use of methods such as frontal analysis, elution by characteristic point are classical techniques. Frontal analysis and elution by characteri.stic point require mg or gram quantities of pure product component. It is also possible to estimate the column saturation capacity from single-component overloaded elution profiles using the retention time method or using an iterative numerical method from a binary mixture [66J. 

The method is advantageously combined with the frontal analysis method, which also requires a concentration plateau and thus shares the disadvantage of high sample consumption if operated in open mode. As indicated in Fig. 6.24, the measurement procedure starts at maximum concentration. This concentration plateau is reduced step-by-step by diluting the solution. To reduce the amount of samples needed for the isotherm determination the experiments can be done in a closed loop arrangement (Fig. 6.17). It is also possible to automate this procedure. 

The primary use of isotherm data measurements carried out on single-component elution profiles or breakthrough curves is the determination of the single-component adsorption isotherms. This could also be done directly, by conventional static methods. However, these methods are slow and less accurate than chromatographic methods, which, for these reasons, have become very popular. Five direct chromatographic methods are available for this purpose frontal analysis (FA) [132,133], frontal analysis by characteristic point (FACP) [134], elution by characteristic point (ECP) [134,135], pulse methods e.g., elution on a plateau or step and pulse method) [136], and the retention time method (RTM) [137]. 

Figure 3.40 Illustration of the method of isotherm measurements by computation of elution profiles. R-l-indanol on cellulose tribenzoate chiral stationary phase. Mobile phase, n-hexane and 2-propanol (92.5 7.5, v/v). (Left) Calculated (using the bi-Langmuir isotherm) and experimental chromatograms recorded for 46.25 (main figure) and 9.251 mg (insert) of R-l-indanol. The isotherm was determined from the band profile obtained for 46.25 mg. (Right) Bi-Langmuir isotherms obtained by the inverse method (lines) and by frontal analysis (symbols) for the R- and S-l-indanol enantiomers. Cmax indicates the maximum elution concentration. Reproduced with permission from A. Felinger, D. Zhou, G. Guiochon, /. Chromatogr. A, 35 (2003) 1005 (Figs. 2 and 3).

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]. 

Lisec et al. [23] measured by frontal analysis the ternary isotherm data for phenol, 2-phenylethanol and 3-phenyl-l-propanol on Kromasd-Cig, with a water/methanol (1/1) solution. The data were fitted to the model equations of the competitive Langmuir and competitive bi-Langmuir models and to the LAS and RAS models derived from the Langmuir model. No substantial improvements were observed with the more complex models. Satisfactory agreement was observed between experimental band profiles and the profiles calculated from the ternary Langmuir isotherm. 

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]. 

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. 

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]. 

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. 

In a binary system, a nonlinear regression to these last five equations can be performed using the values of Vj determined by measuring the retention volumes of breakthrough curves in frontal analysis experiments. This method affords the determination of the parameters of the binary Langmuir isotherms fl/ and fej of the two components of the mixture. Jacobson and Frenz [108] have used this approach to develop two new methods. 

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).

In all these figures, we used the competitive Langmuir isotherm model to calculate the band profiles. However, the coefficients of the isotherms used for Figures 11.21 are the coefficients of the single-component isotherms determined by frontal analysis, while the coefficients of the isotherms used to calculate the profiles in Figure 11.22 are measured by the simple wave method (Chapter 4, Section 4.2.4). These latter coefficients are certainly empirical coefficients, and their use would not permit an accurate prediction of single-component bands. However, they permit the calculation of band profiles that are in much better agreement... 

Figure 12.16 Adsorption isotherms and displacement chromatogram for 3,4-dihydroxyphenyl, 2-hydroxyphenyl, and 4-hydroxyphenyl acetic acids. (Left) Adsorption isotherms measured by frontal analysis on a 250 x4.6 mm column packed with 10 tm Partisil ODS-2 from 0.1 M phosphate buffer, pH 2.12 at 25°C. The soUd Unes are a least-squares fit of the data points to the Langmuir isotherm. (Right) Displacement chromatogram, carrier 0.1 M phosphate buffer, pH 2.12 displacer n-butanol at 0.97 M. Flow rate 0.05 mL/min at 25°C. Feed 1.5 mL of 30, 35, and 45 mg of 3,4 dihydroxy-, 4-, and 2-hydroxyphenylacetic acids, respectively. Fraction size, 0.15 mL. Fraction 40 marks 12 mL of eluent volume. Reproduced with permission from Cs. Horvath, A. Nahum and J.H. Frenz, J. Chroniatogr. 218 (1981) 365 (Figs. 6 and 7).

Quinones et al. measured by frontal analysis the single-component, binary and ternary isotherms of benzyl alcohol (BA), 2-phenyl ethanol (PE) and 2-methyl benzyl alcohol (MBA) on Symmetry-Cis, using a binary mobile phase (MeOH HaO... 

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