Competitive Adsorption Isotherm Parameters

The FACP and ECP methods cannot be used to determine adsorption isotherm parameters from multicomponent mixtures. By contrast FA can be used to determine multi-component adsorption data but it is a complex and time-consuming process [124, 125], 

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Because of the limited surface capacity of the stationary phase, the column often operates under overloaded conditions. This is why a further increased sample load results in a smaller amount of the fraction adsorbed. Thus, nonlinear conditions prevail. A further complication in the preparative case is that the different types of components compete with each other for the same binding site, an effect that ultimately results in strong band interactions and band contaminations. The functions describing this complex behavior are called competitive adsorption isotherm parameters. Because of... 

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],... 

Preparative chromatography is widely used for the purification of different compounds, but this procedure needs to be optimized to achieve the minimum production costs. This can be done by computer-assisted modeling. However, this approach requires a priori determination of accurate competitive adsorption isotherm parameters. The methods to determine this competitive information are poorly developed and hence often a time limiting step or even the reason why the computer-assisted optimization is still seldom used. In this thesis in papers IV-VI, a new injection method was developed that makes it possible to determine these competitive adsorption isotherm parameters more easily and faster than before. The use of this new... 

I hope that my thesis can be used as a contribution in the future for analysis and validation in biotechnology, and also for the rapid determination of competitive adsorption isotherm parameters so that computer-assisted simulations may be used more extensively, in scaling-up and optimization of large scale chromatography. 

In this section a short overview is given of preparative chromatography and the determination of adsorption isotherm parameters - single and competitive - to be used for computer-assisted optimization of separations. 

There are, so far, only two reports on the determination of isotherm data from mixtures containing more than two components. In both cases, the FA method was used for ternary mixtures [135, 136], There are no reports on the experimental determination of adsorption isotherms for quaternary mixtures using any chromatographic method. The competitive quaternary adsorption isotherm parameters could be very valuable for the separations of the four isomers of a compound with two chiral centers, or for the preparative separation of two compounds in the presence of one or two impurities. 

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]. 

Figure 4.10 Experimental competitive adsorption isotherm data of ds- and fraws-andro-sterone. Same phase system as in Figure 4.9. Comparison of the Langmuir competitive model (bottom) and the two-term expansion of the LeVan-Vermeulen isotherm (top). In both cases, the best-fit parameters are used to calculate the Unes. Experimental data A ds-androsterone o trafjs-androsterone. Theory czs-androsterone (dotted lines) trans-androsterone (solid Hnes). a and d 2 1 mixture b and e 1 1 mixture and c and f 1 2 mixture. Reproduced with permission from S. Golshan-Shirazi, J.-X. Huang and G. Guiochon, Anal. Chem., 63 (1991) 1147 (Figs. 1 and 2), ( )1991 American Chemical Society.

It is general, in the literature, ion-exchange (and adsorption) processes are evaluated by a linearized isotherm. The number of active sites and the K isotherm parameter characteristic of the sorption affinities are determined from the slope and the intercept of the plot. When the isotherm is not linear, a heterogeneous surface is supposed. The isotherms are divided into linear portions, and different Q and K values are determined for the linear portions. However, for competitive processes, including competitive adsorption and ion exchange is not correct because the so-called intercept is a complex quantity containing the concentration of the competing substance. 

It should be noted that the Tafel slopes just given were calculated for the combined isotherm under Langmuir conditions, namely at very low coverage. The same type of calculation can be repeated to obtain the kinetic parameters for different mechanisms both at low and at intermediate values of the coverage. The effect on the Tafel slope of competition with water is rather small for small molecules. Thus, for n = 1 the Tafel slope changes only by about 2 mV for the two mechanisms just discussed. This is within experimental error in most cases, perhaps explaining why the need to use the combined adsorption isotherm is not... 

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.

The FA method gives isotherm data. To be useful in preparative chromatography, these data must be fitted to an isotherm model. There are presently no numerical procedures available to smooth the data from multidimensional plots, similar to the 2-D splines or French curves and obtain purely empirical isotherms. Therefore, the major difficulty is the selection of adequate models. The Langmuir isotherm is too simplistic in most cases, and the LeVan-Vermeulen isotherm is complicated and difficult to use as a fitting fimction. Several methods have been described to extract the "best" set of Langmuir parameters which could accormt for a set of competitive adsorption data [108]. These methods have been compared. The most suitable method seems to depend on the aim of the determination and on the deviation of the system from true Langmuir behavior [108]. 

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.

To deduce riso, the elementary rate constant of isomerization, kjso, has been assumed to be rate hmiting. The competition of protonic sites adsorption for alkane or alkene has been exphcitly included in the kinetic scheme of reactions. Using available data on the adsorption isotherms of alkane and theoretical protonation energies, the elementary rate constant parameters of A/iso can be deduced from experiment by measuring the rate of isomerization... 

Hoeft [44] also studied the cooperative and competitive adsorption of ionic surfactant mixtures onto hydrophobic surfaces. When shorter alkyl chain surfactants (sodium octyl sulfonate and sodium decyl sulfonate) are adsorbed, the decyl will displace the octyl surfactant. For mixtures of sodium dodecyi sulfonate and sodium octyl sulfonate, however, there appears to be an association between the surfactant molecules leading to enhanced adsorption of the sodium dodecyi sulfonate with no depletion of the octyl sulfonate adsorption. This is shown in Fig, 2, where the lines indicate the expected adsorption determined using a two-component Langmuir adsorption isotherm with the adsorption parameters determined analyzing the data from adsorption of each species individually. Also shown in Fig. 2 is the concentration of surface-active materials in the aqueous phase at equilibrium. In each of these experiments the total molar concentration and amount of surfactant solution added to the latex was a constant, as was the amount of latex. Thus a lower value for the bulk concentration corresponds to greater adsorption. 

More national and international standardization procedures for mercury porosimetry and the derivation of pore size distributions from adsorption isotherms are in preparation. Regarding the weakness of the two-parameter BET model for surface area determination in addition the three-parameter BET equation or improved approximations [26] should be considered. Competitive evaluation methods, like the method of Dubinin, Horwath-Kawazoe, Kaganer and Radushkevich are being discussed. 

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