Single Component Adsorption Isotherm Parameters

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 

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Determination of Single Component Adsorption Isotherm Parameters - Characterization of a New CSP (Paper III)... 

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],... 

The three-parameter Toth equation is considered particularly successful in representing adsorption data over extensive ranges (from zero to full mono-layer coverage). For using LAST it is thus necessary to have a very good fit of single-component adsorption isotherms for all the gases involved. This in turn requires experimental data at each temperature/gas considered. 

To study the influence of the pore network connectivity on multicomponent adsorption equilibria, we used ethyl propionate, ethyl butyrate, and ethyl isovalerate as the adsorbates and Filtrasorb-400 and Norit ROW 0.8 activated carbon as the adsorbents. For predicting binary isotherms we used known parameters for single component adsorption of these compounds as previously determined. The effect of the pore network connectivity was taken into account in... 

Figure 2. Single-component adsorption equilibria of the normal alkane series Q-C4 on SSC carbon. Symbols denote experimental data and lines represent predictions from the D-A isotherm model with parameters given by Eq. (8) and fi = 0.47, ft = 0.65, ft = 0.76, ft = 0.93. The average error over 364 data points is 6.8%. The temperatures (K) are (C ) 284,298,323 (C2) 287,299,314,324 (C3) 284,298,323 (C4) 273,288,298,324.

The agreement that was observed between the experimental results and the prediction of a competitive Langmuir model based on the use of single-component Langmuir isotherms in the case of the adsorption of enantiomeric derivatives of amino acids on immobilized serum albumin [26] is imusual. It demonstrates the validity of the competitive Langmuir model based on the use of the parameters of the single-component Langmuir model. However, as explained before, the experimental conditions are exceptionally favorable since the column saturation capacities for the two enantiomers are equal. Nevertheless, Zhou et ah have shown that it is possible, in certain favorable cases, to derive the equilibrium isotherms of the pure enantiomers and to calculate isotherm equilibrium data for any mixture of... 

Figure 12.29 Comparison of theoretical and experimental displacement separations of resorcinol and catechol by phenol. Calculations using the equilibrium-dispersive model, the LeVan- Vermeulen isotherm model, and single-component adsorption data. Experimental results on a 4.6x250 CIS Nucleosil 5 fim column, F = 0.4 carrier, water, Fj, = 0.2 mL/min, T = 20°C 1 1 mixture, = 0.5 mL displacer, 80 g/L phenol in water = 30%, Lf = 16.5%. (a) Calculation with LeVan-Vermeulen isotherm, (b) Calculation with quadratic isotherm, three floating parameters, (c) Calculation with competitive Langmuir isotherm, single-component isotherm parameters, (d) Calculation with Langmuir isotherm, best adjusted parameters. Reproduced with permission from. C. Bellot and J.S. Condoret, J. Chromatogr., 657 (1994) (Figs. 3c, 4c, 6c, 8c) 305.

Fig.4 and Fig.5 show adsorption isotherms for single component systems, obtained from fixed bed experiments and molecular simulation, respectively. Adosorption equilibria were simulated well. Except EtOH system, quantitative order of amount adsorbed was good agreement with experimental data. As for BEN and TOL systems, the amount of adsorbed for simulations were lower than experimental data. So it is necessary to examined van der Waals parameter for benzene ring. Fig.6 and Fig.7 show adsorption equilibria For binary component systems, obtained from fixed>bed experiments and molecular simulation, respectively. These are examples, which show azeotropic adsorption. Especially, IPA-TCE, BEN-EtOH systems show two azeotropic points. Result of simulation shows only one azeotropic point. More investigative is necessary. 

The equilibrium parameters used in this study have been taken from independent single-component experiments using volumetric method at several temperatures. Adsorption isotherms on each adsorbent are shown in Figures 2 and 3. 

The adsorption isotherm has the most influence on the chromatogram. Consequently, single- and multi-component isotherms have to be determined with high accuracy to achieve good agreement between simulation and experiment, using all model parameters measured so far (Fig. 6.9). 

Like single-component isotherms, competitive isotherms depend on the composition of the mobile phase and the temperature [10]. Figure 4.11 [10] illustrates for a 1 1 mixture of ds- and trans-androsterone the effects of the mobile phase composition and temperature, respectively, on the adsorption isotherm. The general trend is for adsorption to decrease with increasing concentration of the strong solvent and with increasing temperature. These experimental parameters must be... 

If we apply one of these equations to single-component isotherm data, we see that Eqs. 4.54 and 4.55 can be applied to the competitive adsorption data for a binary mixtiue only if Eq. 3.31 applies to the single-component data for each component. Then the six parameters can be derived from the single-component isotherms and only the coefficient b has to be measured with the mixture. Using more complicated models, Lin et al. [70] and Moreau et al. [71] have derived similar isotherms. Attempts at reducing the number of independent parameters as well as at determining these parameters from sets of experimental data have had limited success so far. 0onsiderable attention is required to clarify this issue. 

Figure 4.14 Comparison between the experimental adsorption data of 2-phenylethanol (a, c) and 3-phenylpropanol (b, d) and the best competitive Fowler isotherms derived from the best single-component parameters. For mixtures, the mobile phase concentration is expressed via the relative composition of PE and PR All concentrations in mg/ml. Symbols data for single component, o data for 3 1 mixtures (3/1 PE and PP), x data for 1 1 mixtures (1/1 PE and PP), + and data for 1 3 mixtures (1/3 PE and PP),. The RSS are the residual sum of squares calculated for each set of experiments performed with a constant relation of the mobile phase concentrations of the phenylalcohols. ODS silica from Vydac and water-methanol mixture (50 50) at room temperature. I. Quinones, G. Guiochon, Langmuir, 12 (1996) 5433 (Figs 1 and 2) and J. Zhu, A. Katti and G. Guiochon,. Chromatogr. 552 (1991) (Figs 7 and 8)71.

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. 

The adsorption isotherms have the most pronounced influence on the courses of the chromatograms. Consequently, single-component and multicomponent isotherms should be determined with high accuracy in order to achieve a good agreement between simulations and experiments, including all model parameters measured so far (Figure 6.9). 

Characteristic parameters of nearly all types of adsorption isotherm models are the Henry coefficients as well as the saturation capacities valid for large concentrations. In general, it is advisable to check the validity of the identified single-component isotherm equation before further considering the determination of additional multicomponent interaction parameters. In general, the decision on a certain isotherm equation should be made on the basis of the ability to predict experimentally observed overloaded concentration profiles. In any case, consistency with the Henry coefficients determined from initial pulse experiments with very low sample amounts must be assured. 

When binary activity coefficients can only be obtained from experimental equilibrium data, there is no way to predict multicomponent adsorption equiUbria which are only based on single component isotherms however, such a procedure would be desirable. The SPDM (spreading pressure dependent model) contains only predictive parameters with the exception of the binary parameter (Markmarm 1999 Mersmann et al. 2002). Setting p j = 0, this method allows to calculate multicomponent adsorption equilibria without experimental data obtained for binary mixtures. 

Adsorption kinetics of a single particle (activated carbon type) is dealt with in Chapter 9, where we show a number of adsorption / desorption problems for a single particle. Mathematical models are presented, and their parameters are carefully identified and explained. We first start with simple examples such as adsorption of one component in a single particle under isothermal conditions. This simple example will bring out many important features that an adsorption engineer will need to know, such as the dependence of adsorption kinetics behaviour on many important parameters such as particle size, bulk concentration, temperature, pressure, pore size and adsorption affinity. We then discuss the complexity in the dealing with multicomponent systems whereby governing equations are usually coupled nonlinear differential equations. The only tool to solve these equations is... 

The extension of the simple statistical model to adsorption of a binary mixture is given by Eq. (3.102) and further extension to multicomponent systems follows naturally. " The parameters of the model (the Henry con-stant and effective molecular volume for each component) are derived from the single-component isotherms so that an a priori prediction of the mixture... 

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