Bi-Langmuir adsorption isotherm

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

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.

Bi-Langmuir adsorption isotherms of enantiomeric pairs and CSPs were determined to gain information on chiral mechanisms. In the few cases fully studied, it was found that the two isomers interacted with type I nonselective sites as well as with type II enantioselective sites [18]. The bi-Langmuir equation is expressed as ... 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

Bi-layer adsorption is not uncommon and the development of the bi-layer adsorption isotherm equation is a simple extension of that used for the mono-layer equation. The Langmuir equation for bi-layer adsorption is as follows ... 

Electrochemical impedance spectroscopy was used to determine the effect of isomers of 2,5-bis( -pyridyl)-l,3,4-thiadiazole 36 (n 2 or 3) on the corrosion of mild steel in perchloric acid solution <2002MI197>. The inhibition efficiency was structure dependent and the 3-pyridyl gave better inhibition than the 2-pyridyl. X-ray photoelectron spectroscopy helped establish the 3-pyridyl thiadiazoles mode of action toward corrosion. Adsorption of the 3-pyridyl on the mild steel surface in 1M HCIO4 follows the Langmuir adsorption isotherm model and the surface analysis showed corrosion inhibition by the 3-pyridyl derivative is due to the formation of chemisorbed film on the steel surface. 

The chromatographic resolution of bi-naphthol enantiomers was considered for simulation purposes [18]. The chiral stationary phase is 3,5-dinitrobenzoyl phenyl-glycine bonded to silica gel and a mixture of 72 28 (v/v) heptane/isopropanol was used as eluent. The adsorption equilibrium isotherms, measured at 25 °C, are of bi-Langmuir type and were proposed by the Separex group ... 

Adsorption Isotherm Measurements and Site-Selective Thermodynamics. For heterogeneous surfaces like CSPs, the adsorption isotherms are usually composite isotherms and often a Bi-Langmuir model (Equation 1.15) describes reasonably well the adsorption behavior [54]. 

Adsorption isotherms of the bi-Langmuir-type were measured (see Tab. 2). An initial set of parameters was obtained by the perturbation method [6], Subsequently, a peak fitting approach based on the equilibrium-dispersive model was used for refinement (for details, see [4]). Fig. 4 shows a good agreement between models and experiments. 

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 3.2 Linear, Langmuir, and bi-Langmuir isotherms. The Linear, Langmuir, and bi-Langmuir isotherms are used as models to fit the experimental adsorption data for N-Benzoyl-D-phenylalanine. Parameters Linear isotherm a = 13.1 Langmuir isotherm a = 13.1, b = 241 bi-Langmuir isotherm ai = 9.6, bi = 1920, fl2 = 7.1, 2 = 33-8- Data from S. Jacobson, S. Golshan-Shirazi and G. Guiochm, AIChE /., 37 (1991) 836. Reproduced by permission of the American Institute of Chemical Engineers. 1991 AIChE. All rights reserved.

Actual surfaces are heterogeneous and the adsorption data on real adsorbents are usually not well accounted for by one of the two models discussed in the section above. The distribution of the adsorption energy (AED) on a homogeneous surface is a Dirac distribution. On an actual surface, the adsorption energy distribution has a finite width. It can be unimodal or multi-modal. The isotherm models discussed in this section correspond to such surfaces. Each of them can be related to a different AED. In all cases, however, there are no adsorbate-adsorbate interactions. In this group, the most useful models are the bi-Langmuir and multi-Langmuir isotherms, the Toth isotherm, and the Freundlich isotherm. 

Similar adsorption data have also been reported for the adsorption isotherms of many compounds in various systems. For example, the adsorption data of several jS-blockers, particularly those of propranolol acquired in a 1 to 7000 relative concentration range, on an immobilized cellulase. Cel 7A, fit very well to the bi-Langmuir model, as illustrated in Figure 3.13 [47,55]). The enantioselective site was identified as a pair of amino acid residues in the tunnel formed by the main chain of the protein. The parameters of the isotherm depend on the pH as illustrated in Figure 3.14. A bi-Langmuir model was also found to accoimt well for the separation of pairs of enantiomers on polymers molecularly imprinted with one of the enantiomers [56]. Note, however, that there are also many systems in which the adsorption isotherms of enantiomers are not accounted for by a bi-Langmuir model showing that enantioselectivity is often achieved by a complex... 

Finally, it should be emphasized that the successful use of a bi-Langmuir isotherm model (as of any other combination of models that multiplies the number of model parameters) to account for a set of experimental adsorption data requires that these data are acquired in a wide concentration range [55]. This is even more... 

This model was used by Gritti and Guiochon to account for the behavior of propranolol on several Cig-bonded silica adsorbents, from methanol/water solutions. Similar results were obtained for Kromasil-Cig [101,102], XTerra-Cjs [84], Symmetry-Ci8 [103]. When the mobile phase contains a high concentration of a monovalent salt, the adsorption follows bi-Langmuir isotherm behavior [101]. In the absence of salt, at low concentrations of a monovalent salt or with di- (e.g., phthalate, succinate, naphthalene sulfonate) or tri-valent salts (e.g., citrate), the isotherm data are best modeled by a bi-Moreau isotherm [91,104]. 

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