Adsorption isotherms frontal analysis

Note that knowledge of the initial slopes of the adsorption isotherms gives some constraint to be fullfilled between parameters X, N, and K. In order to fit the adsorption isotherms, frontal analysis has performed with the pure components at 1, 25, 50, 75 and 100 g on the analytical column at 1 ml min k... 

Other gas-chromatographic techniques besides frontal analysis were also utilized at finite concentration to determine the adsorption isotherms frontal analysis through characteristic points [145], elution through characteristic points [146—148] and, elutipn on a plateau [149, 150]. 

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 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 ... 

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]. 

According to the equilibrium dispersive model and adsorption isotherm models the equilibrium data and isotherm model parameters can be calculated and compared with experimental data. It was found that frontal analysis is an effective technique for the study of multicomponent adsorption equilibria [92], As has been previously mentioned, pure pigments and dyes are generally not necessary, therefore, frontal analysis and preparative RP-HPLC techniques have not been frequently applied in their analysis. 

O. Lisec, P. Hugo and A. Seidel-Morgenstein, Frontal analysis method to determine competitive adsorption isotherms. J. Chromatogr.A 908 (2001) 19-34. 

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]. 

Computer-aided frontal analysis chromatography can be used to determine surface areas and adsorption isotherms (4). Both permanent gases and adsorbates that are liquids above room temperature could be used in this system. 

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. 

One of the most important applications of frontal chromatography is the determination of equilibrium adsorption isotherms. It was introduced for this purpose by Shay and Szekely and by James and Phillips [4,5], The simplicity as well as the accuracy and precision of this method are reasons why the method is so popular today and why it is often preferred over other chromatographic methods e.g., elution by characteristic points (ECP) or frontal analysis by characteristic points (FACP) [6,7]. Frontal chromatography as a tool... 

Nonlinearity of the Langmuir adsorption isotherms is observed even in noncompetitive chromatographic processes. Individual adsorption isotherms can be found experimentally using frontal analysis at overload conditions however, the adsorption isotherms in the separation of mixtures are different because of the interference of other compounds in the mixture. In PHPLC method development, it is necessary to optimize separation conditions and column loading experimentally. 

The dynamic methods are based on direct chromatography and are popular because they are faster and easier to automate. Four direct chromatographic methods that are available for determination of adsorption isotherms are frontal analysis (FA) [13, 109] frontal analysis by characteristic points (FACP) [109], elution by characteristic points (ECP) [109] and the perturbation peak (PP) method [118-121], The FACP and ECP methods have... 

The accurate determination of the adsorption isotherm parameters of the two enantiomers on a CSP is of fundamental importance to do computer-assisted optimization to scale up the process. Such determinations are usually done with an analytical column and the most traditional method to determine the parameters and saturation capacity is by frontal analysis (see section 3.4.2). The aim of paper III was to investigate the adsorption behavior and the chiral capacity of the newly developed Kromasil CHI-TBB column using a typical model compound. Many of the previous studies from the group have been made on low-capacity protein columns which has revealed interesting information about the separation mechanism [103, 110, 111], For this reason a column really aimed for preparative chiral separations was chosen for investigation [134], As solute the enantiomers of 2-phenylbutyric acid was chosen. 

The isotherm data acquired from frontal analysis over a broad concentration range fitted well to the bi-Langmuir model, see Figure 18, demonstrating that the adsorption on Kromasil CHI-TBB is heterogeneous with two types of sites. The saturation capacity of site II obtained from the bi-Langmuir isotherm parameters were qs>n = 130 mM for (R)-(-)-2-phenylbutyric acid and qs,n= 123 mM for (S)-(+)-2-phenylbutyric. 

Figure 18. Isotherms for (R) and (S)-2-phenylbutyric acid, experimentally acquired by frontal analysis and compared with their fits with bi-Langmuir adsorption isotherm parameters. The lines are calculated data using the best single bi-Langmuir isotherm parameters.

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 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]. 

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]. 

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 4.22 Experimental concentration profiles in the column effluent for adsorption isotherm determination by binary frontal analysis. (Left) Bottom trace solid line, experimental UV profile dotted line reconstructed profile of 3-phenylpropanol (P) dashed line reconstructed profile of 2-phenylethanol (E). Arrows 1-5 indicate the time when the eluent sample was taken for on-line analysis. Top trace On-line analysis of the sampled eluent. Reproduced with permission from J. Zhu, A. Katti and G. Guiochon, J. Chromatogr. 552 (1991) 71 (Fig. 1). (Right) Examples of one-step binary frontal analyses for the determination of the competitive isotherms of N-benzoyl-D,L-alanine. Injection of large volumes (5 mL) of solutions of increasing concentrations of racemic mixture. Reproduced with permission from S.C. Jacobson, A. Felinger and G. Guiochon, Biotechnol. Progr., 8 (1992) 533 (Fig. 1), 1992 American Chemical Society.

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).

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