Modeling of the separation of two enantiomers using a microbore column

A microbore column packed with Chiralcel OB (cellulose tribenzoate coated silica) was used for the measurement of the single and competitive equilibrium-isotherm data of the 1-indanol enantiomers by frontal analysis. The amount of sample needed for the isotherm data acquisition was about 20 times less than that required with a conventional column. The data obtained were fitted to different single and competitive isotherm models. Both the single and the competitive data sets fitted best to the same Bilangmuir (BL) isotherm model with small differences in the numerical values of the parameters. The best fitted Bilangmuir single and competitive isotherm models were used to predict the overloaded experimental profiles of both pure enantiomers, of the racemic mixture, and of different enantiomeric mixtures. All the calculated profiles were in excellent agreement with the experimental ones. This agreement confirms that in many chiral separations, the competitive isotherms can be derived from data acquired from the mere racemic mixture with a sufficient accuracy for a correct prediction of the band profiles of all kinds of enantiomer mixtures, making possible the computer-assisted optimization of the experimental conditions.     

Numerical determination of the competitive isotherm of enantiomers

A numerical method was developed and used to determine adsorption isotherms in chromatography. The numerical parameters of an isotherm model were derived from the recorded band profiles of the racemic mixture of the 1-phenyl-1-propanol enantiomers, by means of a nonlinear least-squares method. We used the equilibrium-dispersive model of chromatography with several isotherm models. The numerical constants of the isotherm models were tuned so that the calculated and the measured band profiles match as much as possible. We show that this numerical inverse method can be applied even without the knowledge of the individual band profile of the pure enantiomers. The isotherms determined from the--usually unresolved--overloaded band profiles matched extremely well the isotherms determined by frontal analysis. Several isotherm models were used and tested--such as Langmuir, biLangmuir, Tóth, Langmuir-Freundlich. The best-fit isotherm was selected by means of statistical evaluation of the results.     

Adsorption of the enantiomers of 3-chloro-1-phenyl-propanol on silica-bonded chiral quinidine carbamate

The interactions of 3-chloro-1-phenyl-propanol with a quinidine carbamate-bonded chiral stationary phase under NPLC conditions were studied by measuring the adsorption isotherm data of its enantiomers by frontal analysis, modeling these data with a suitable isotherm model, and comparing the experimental overloaded elution band profiles with those calculated with this isotherm and the equilibrium dispersive model of liquid chromatography. The affinity energy distribution was calculated from the adsorption isotherm data. The results show that the surface of the adsorbent is heterogeneous and exhibits a bimodal adsorption energy distribution. This fact is interpreted in terms of the presence of two different types of adsorption sites on the stationary phase, nonselective and enantioselective sites. Albeit the bi-Langmuir isotherm model successfully accounts for the single-component data corresponding to both enantiomers, the competitive bi-Langmuir isotherm model does not allow an accurate prediction of the overloaded band profiles of the racemic mixture. Thermodynamic data are drawn for explanation. Some aspects of the retention mechanism are discussed in the light of the data obtained.     

Study of the competitive isotherm model and the mass transfer kinetics for a BET binary system

The competitive adsorption behavior of the binary mixture of phenetole (ethoxy-benzene) and propyl benzoate in a reversed-phase system was investigated. The adsorption equilibrium data of the single-component systems were acquired by frontal analysis. The same data for binary mixtures were acquired by the perturbation method. For both compounds, the single-component isotherm data fit best to the multilayer BET model. The experimental overloaded band profiles are in excellent agreement with the profiles calculated with either the general rate model or the modified transport-dispersive models. The competitive adsorption data were modeled using the ideal adsorbed solution (IAS) theory. The numerical values of the coefficients were derived by fitting the retention times of the perturbation pulses to those calculated using the IAS theory compiled with the coherence conditions. Finally, the elution profiles of binary mixtures were recorded. They compared very well with those calculated. As a characteristic feature of this case, an unusual retainment effect of the chromatographic band of the more retained component by the less retained one was observed. The combination of the General Rate Model and the adsorption isotherm model allowed an accurate prediction of the band profiles.     

Determination of competitive isotherms of enantiomers by a hybrid inverse method using overloaded band profiles and the periodic state of the simulated moving-bed process

A procedure for determination of adsorption isotherms in simulated moving-bed (SMB) chromatography is presented. The parameters of a prescribed adsorption isotherm model and rate constants are derived using a hybrid inverse method, which incorporates overloaded band profiles of the racemic mixture and breakthrough data from a single frontal experiment. The latter are included to reduce the uncertainty on the estimated saturation capacity, due to the dilution of the chromatograms with respect to the injected concentrations. The adsorption isotherm model is coupled with an axially dispersed flow model with finite mass-transfer rate to describe the experimental band profiles. The numerical constants of the isotherm model are tuned so that the calculated and measured band profiles match as much as possible. The accuracy of the isotherm model is then checked against the cyclic steady state (CSS) of the target SMB process, which is readily and cheaply obtained experimentally on a single-column set-up. This experiment is as expensive and time consuming as just a few breakthrough experiments. If necessary, the isotherm parameters are adjusted by applying the inverse method to the experimental CSS concentration profile. The method is successfully applied to determine the adsorption isotherms of Tr?gers base enantiomers on Chiralpak AD/methanol system. The results indicate that the proposed inverse method offers a reliable and quick approach to determine the competitive adsorption isotherms for a specific SMB separation.     

Separation mechanism of nortriptyline and amytriptyline in RPLC

The single and the competitive equilibrium isotherms of nortriptyline and amytriptyline were acquired by frontal analysis (FA) on the C18- bonded discovery column, using a 28/72 (v/v) mixture of acetonitrile and water buffered with phosphate (20 mM, pH 2.70). The adsorption energy distributions (AED) of each compound were calculated from the raw adsorption data. Both the fitting of the adsorption data using multi-linear regression analysis and the AEDs are consistent with a trimodal isotherm model. The single-component isotherm data fit well to the tri-Langmuir isotherm model. The extension to a competitive two-component tri-Langmuir isotherm model based on the best parameters of the single-component isotherms does not account well for the breakthrough curves nor for the overloaded band profiles measured for mixtures of nortriptyline and amytriptyline. However, it was possible to derive adjusted parameters of a competitive tri-Langmuir model based on the fitting of the adsorption data obtained for these mixtures. A very good agreement was then found between the calculated and the experimental overloaded band profiles of all the mixtures injected.     

Determination of competitive adsorption isotherm parameters of pindolol enantiomers on alpha1-acid glycoprotein chiral stationary phase

In this paper, inverse method (IM) was used to determine the binary competitive adsorption isotherm of pindolol enantiomers by a least-square fitting of the proposed model to the experimentally measured elution curves of racemic pindolol. The isotherm parameters were determined by minimizing the least-square error using an adaptation of genetic algorithm, non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG). An equilibrium dispersive (ED) model combined with bi-Langmuir isotherm was used in predicting the elution profiles. The determined parameters show good agreement with the experimental profiles at various experimental conditions such as sample volume, concentration and flow rates of the racemic mixture. Robustness and validity of the isotherm parameters were also verified by frontal analyses at various step inputs. Results from both the pulse tests and the frontal analysis indicate that adsorption isotherm derived from the inverse method is quite reliable. This method requires relatively less number of experiments to be performed and therefore, lower experimental costs confirming that inverse method is an attractive alternative approach of experimental technique in determining the competitive adsorption isotherm for binary systems.     

Adsorption behavior and prediction of the band profiles of the enantiomers of 3-chloro-1-phenyl-1-propanol. Influence of the mass transfer kinetics

The single-component and competitive adsorption isotherms of the enantiomers of 3-chloro-1-phenyl-1-propanol were measured by frontal analysis. The stationary phase was a cellulose tribenzoate coated on silica, the mobile phase an n-hexane-ethyl acetate (95:5) solution. The adsorption data measured fitted well to the Langmuir isotherm model. The band profiles of single components and of their mixtures were calculated using the equilibrium-dispersive model. These profiles were found to match quite satisfactorily the experimental band profiles. However, the agreement between calculated and experimental band profiles was significantly improved when a more complex model taking into account the mass transfer kinetics was used. The mass transfer rate coefficients, k(f), for both single components were determined by using the transport-dispersive model of chromatography. The coefficients obtained were used to predict the band profiles of mixtures of the two enantiomers to good agreement.     

Determination of the single component and competitive adsorption isotherms of the 1-indanol enantiomers by the inverse method

The inverse method of isotherm determination consists in calculating the numerical values of the coefficients of an isotherm model that give a set of chromatographic profiles in best possible agreement with the set of experimental profiles available. This method was applied to determine the adsorption isotherms of the 1-indanol enantiomers on a cellulose tribenzoate chiral stationary phase. Both single-component and competitive isotherms were determined by using no more than one or two overloaded band profiles. The isotherms determined from the overloaded band profiles agreed extremely well with the isotherms determined by frontal analysis. Several isotherm models were used and tested. The best-fit isotherm was selected by means of statistical evaluation of the results. The results show that the adsorption is best characterized with a model describing heterogeneous adsorption with bimodal adsorption energy distribution.     

Study of the adsorption behavior of the enantiomers of 1-phenyl-1-propanol on a cellulose-based chiral stationary phase

Using single-step frontal analysis, we measured single-component and competitive adsorption isotherm data for the two enantiomers of 1-phenyl-1-propanol (PP). These experimental data were fitted to several competitive bi-Langmuir models (with 8, 6, 5 and 4 parameters) and to the competitive Langmuir model. The latter model accounted well for the behavior of both PP enantiomers on Chiracel OB (cellulose tribenzoate coated on silica gel). The parameters obtained were used in numerical calculations to predict the band profiles of the two single components and of their mixtures under overloaded conditions. The equilibrium-dispersive model provides satisfactory results, with minor differences between the calculated and the experimental profiles. These differences became negligible when a more complex kinetic model was used, with a concentration-dependent rate coefficient.     

Adsorption behavior of the (+/-)-Tröger's base enantiomers in the phase system of a silica-based packing coated with amylose tri(3,5-dimethyl carbamate) and 2-propanol and molecular modeling interpretation

The binary adsorption isotherms of the enantiomers of Tr?ger's base in the phase system made of Chiral Technologies ChiralPak AD [a silica-based packing coated with amylose tri(3,5-dimethyl carbamate)] as the chiral stationary phase (CSP) and 2-propanol as the mobile phase were measured by the perturbation method. The more retained enantiomer exhibits a S-shaped adsorption isotherm with a clear inflection point, the concentration of the less retained enantiomer having practically no competitive influence on this isotherm: In the entire range of concentrations studied, dq2/dC1 approximately 0. By contrast, the less retained enantiomer has a Langmuir adsorption isotherm when pure. At constant mobile phase concentrations, however, its equilibrium concentration in the adsorbed phase increases with increasing concentration of the more retained enantiomer and dq1/dC2 > 0. This cooperative adsorption behavior, opposed to the classical competitive behavior, is exceedingly rare but was clearly demonstrated in this case. Two adsorption isotherm equations that account for these physical observations were derived. They are based on the formation of an adsorbed multi-layer, as suggested by the isotherm data. The excellent agreement between the experimental overloaded elution profiles of binary mixtures and the profiles calculated with the equilibrium-dispersive model validates this binary isotherm model. The adsorption energies calculated by molecular mechanics (MM) and by molecular dynamics (MD) indicate that the chiral recognition arising from the different interactions between the functional groups of the CSP and the molecules of the Tr?ger's base enantiomers are mainly driven by their Van der Waals interactions. The MD data suggest that the interactions of the (-)-Tr?ger's base with the CSP are more favored by 8+/-(5) kJ/mol than those of (+)-Tr?ger's base. This difference seems to be a contributing factor to the increased retention of the - enantiomer on this chromatographic system. The modeling of the data also indicates that both enantiomers can form high stoichiometry complexes while binding onto the stationary phase, in agreement with the results of the equilibrium isotherm studies.     

Repeatability and reproducibility of high concentration data in reversed-phase liquid chromatography. I. Overloaded band profiles on Kromasil-C18

Single-component adsorption-isotherm data were acquired by frontal analysis (FA) for six low-molecular-mass compounds (phenol, aniline, caffeine, theophylline, ethylbenzene and propranolol) on one Kromasil-C18 column, using water-methanol solutions (between 70:30 and 20:80, v/v) as the mobile phase. Propranolol data were also acquired using an acetate buffer (0.2 M) instead of water. The data were modeled for best agreement between calculated and experimental overloaded band profiles. The adsorption energy distribution was also derived and used for the selection of the best isotherm model. Widely different isotherm models were found to model best the data obtained for these compounds, convex upward (i.e. Langmuirian), convex downward (i.e. anti-Langmuirian), and S-shaped isotherms. Using the same sample size for all columns (loading factor, Lf approximately 10%), overloaded band profiles were recorded on four different columns packed with the same batch of Kromasil-C18 and five other columns packed with different batches of Kromasil-C18. These experimental band profiles were compared to the profile calculated from the isotherm measured by FA on the first column. The repeatability as well as the column-to-column and the batch-to-batch reproducibilities of the band profiles are better than 4%.     

Band splitting in overloaded isocratic elution chromatography II. New competitive adsorption isotherms

The equations of two new binary competitive isotherms models are derived. The first of these models assumes that the isotherms of the two pure, single compounds have distinct monolayer capacities. Its derivation is based on kinetic arguments. The ideal adsorbed solution (IAS) framework was applied to derive the second model that is a thermodynamically consistent competitive isotherm. This second model predicts the competitive adsorption isotherm behavior of a mixture of two compounds that have single-component adsorption behavior following a BET and/or a Langmuir isotherms. Both models apply well to the binary adsorption of ethylbenzoate and 4-tert.-butylphenol on a Kromasil-C18 column (with methanol-water, 62:38, v/v, as the mobile phase). The best single-solute adsorption isotherms of these two compounds are the liquid-solid extended multilayer BET and the Langmuir isotherms, respectively. The kinetic and thermodynamic new competitive models were compared, regarding the accuracy of their prediction of the elution band profiles of mixtures of these two compounds. A better agreement between experimental and calculated profiles was observed with the kinetic model. The IAS model failed because the behavior of the ethylbenzoate/4-tert.-butylphenol adsorbed phase mixture is probably non-ideal. The most striking result is the qualitative prediction by these models of the peak splitting of 4-tert.-butylphenol during its elution in presence of ethylbenzoate.     

Application of the general rate model and the generalized Maxwell-Stefan equation to the study of the mass transfer kinetics of a pair of enantiomers

The general rate model of chromatography can be coupled with the generalized Maxwell-Stefan equation that describes the surface diffusion flux. The resulting model is useful to describe the behavior of two enantiomers during their separation on chiral phases, cases in which the mass transfer kinetics is known to be sluggish. A case in point is the modeling of the elution profiles of the racemic mixture of the two enantiomers of 1-phenyl-1-propanol on cellulose tribenzoate coated on silica, a popular chiral stationary phase. The competitive equilibrium isotherm behavior of the two enantiomers on the chiral stationary phase was described using the competitive Tóth isotherm model. An excellent agreement between the experimental and the calculated profiles was observed in the whole range of experimental conditions investigated, at low and high column loadings.     

Numerical determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose-based chiral stationary phase

The use of inverse method for the determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose tris(3,5-diethylphenyl carbamate) stationary phase is proposed in this work. Non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG) was applied to acquire the isotherm parameters by minimizing the sum of square deviations of the model predictions from the measured elution profiles. Three different competitive isotherm models, i.e., Langmuir, biLangmuir and Tóth, combined with transport-dispersive chromatographic model were used in predicting the elution profiles. Orthogonal collocation on finite element (OCFE) method was applied to obtain the calculated elution profiles. Results indicate that biLangmuir isotherm and Tóth isotherm give remarkably similar equilibrium isotherms within the investigated liquid concentration range. Band profiles calculated from both isotherm models are in good agreement with the experimental data. The validity of the determined parameters was verified by comparing the model predictions with experimental elution profiles at various experimental conditions.     

Adsorption isotherms of the fullerenes C60 and C70 on a tetraphenylporphyrin-bonded silica

The single-component adsorption isotherms of the C60 (from 0 to 15 g/L) and C70 (from 0 to 8 g/L) buckminsterfullerenes on a tetraphenylporphyrin-bonded silica were acquired by frontal analysis, using a solution of toluene-1-methylnaphthalene (40:60, v/v) as the mobile phase. The best isotherm model derived from the fitting of these adsorption data was the bi-Langmuir model, a choice supported by the bimodal affinity energy distribution (AED) obtained for C60. The isotherm parameters derived from the inverse method (IM) of isotherm determination (by fitting calculated profiles to experimental overloaded band profiles of C60 and C70) are in very good agreement with those derived from the FA data. According to the isotherm parameters found by these three methods (FA, AED, IM), the tetraphenylporphyrin-bonded silica can adsorb 54 and 42 mmol/L of C60 and C70 fullerenes, respectively, a result that is consistent with the relative molecular size of these two compounds. The 20% lower surface accessibility for C70 is compensated by a three times higher equilibrium constant on the low-energy sites, giving a selectivity alpha(C70/C60) = 3.6. Large volumes (0.2, 0.8 and 1.7 mL) of mixtures of C60 (3.2 g/L) and C70 (1.3 g/L) were injected and their elution profiles compared to those calculated from the competitive bi-Langmuir model derived from the single-component isotherm data. A good agreement is obtained between calculated and experimental profiles, which supports the two-site adsorption mechanism derived from the single-component adsorption data. The measurements of the influence of the pressure on the retention of C60 and C70 demonstrate that the partial molar volumes of the two buckminsterfullerenes are 12 mL/mol larger in the stationary than in the mobile phase.     

Heterogeneity of adsorption mechanisms in chiral normal-phase liquid chromatography. 2-Propanol and ethyl acetate adsorption equilibria

The adsorption equilibria of two commonly employed strong mobile phase modifiers, ethyl acetate and 2-propanol, on a polysaccharide-based chiral stationary phase have been studied by modeling nonlinear perturbation peaks measured after equilibration of the column with hexane (the weak component of the binary mixture). The investigation of adsorption processes from dilute solutions for species that are strongly retained on the stationary phase could be performed by this approach. On the opposite, limits of traditional linear perturbation technique for isotherm determination, in presence of strong interactions, have been evidenced. Alcohol adsorption has been modeled by a single Langmuir isotherm, while the ester has required a BiLangmuir model. These findings have found to be in a semi-quantitative agreement with available spectroscopic data about 2-propanol and ethyl acetate adsorption on thin silica sol-gel films in contact with a weak solvent. Experimental features observed for racemic separation on polysaccharide-based chiral stationary phases, such as the dependence of the separation factor on the amount and type of the employed additive, have been explained in light of these measurements.     

Modeling of the adsorption behavior and the chromatographic band profiles of enantiomers : Behavior of methyl mandelate on immobilized cellulose

The adsorption isotherms of (−)- and (+)-methyl mandelate from a hexane-isopropanol (90:10) solution were measured on a chromatographic column packed with 4-methylcellulose tribenzoate coated on silica. These isotherms are accounted for by a bi-Langmuir isotherm model, the two Langmuir terms having widely different initial slopes and saturation capacities, but each term having the same saturation capacity for the two enantiomers. The competitive isotherms were also measured. They are in excellent agreement with the prediction of a competitive bi-Langmuir model based on the single-component isotherms. The individual band profiles are in agreement with the profiles calculated from these isotherms. Thus, a simplified competitive isotherm can be used to model a separation on a chiral stationary phase the recognition mechanism of which is not well identified and the adsorption behavior of which is certainly not ideal.     

Thermodynamic functions and intra-particle mass transfer kinetics of structural analogues of a template on molecularly imprinted polymers in liquid chromatography

The parameters of the thermodynamics and mass transfer kinetics of the structural analogues (L-enantiomers) of the template were measured on an Fmoc-L-tryptophan (Fmoc-L-Trp) imprinted polymer, at different temperatures. The equilibrium isotherm data and the overloaded band profiles of these compounds were measured at temperatures of 298, 313, 323, and 333 K. The isotherm data were modeled. The thermodynamic functions of the different adsorption sites were derived from the isotherm parameters, using van't Hoff plots. The mass transfer parameters were derived by comparing the experimental peak profiles and profiles calculated using the lumped pore diffusion (POR) model for chromatography. These data show that (1) the strength between the substrate molecules and the MIP increases with increasing number of functional groups on the substrates; (2) enthalpy is the driving force for the affinity of the substrates for the MIP; (3) surface diffusion is the dominant mass transfer mechanism of the substrates through the porous MIP. For those substrate molecules that have the same stereochemistry as the template, the energetic surface heterogeneity needs to be incorporated into the surface diffusion coefficients. Heterogeneous surface diffusivities decrease with increasing affinity of the substrates for the MIP.     

New thermodynamically consistent competitive adsorption isotherm in RPLC

A new equation of competitive isotherms was derived in the framework of the ideal adsorbed solution (IAS) that predicts multisolute adsorption isotherms from single-solute isotherms. The IAS theory makes this new isotherm thermodynamically consistent, whatever the saturation capacities of these single-component isotherms. On a Kromasil-C(18) column, with methanol-water (80/20 v/v) as the mobile phase, the best single-solute adsorption isotherm of both toluene and ethylbenzene is the liquid-solid extended multilayer BET isotherm. Despite a significant difference between the monolayer capacities of toluene (370 g/l) and ethylbenzene (170 g/l), the experimental adsorption data fit very well to single-component isotherms exhibiting the same capacities (200 g/l). The new competitive model was used for the modeling of the elution band profiles of mixtures of the two compounds. Excellent agreement between experimental and calculated profiles was observed, suggesting that the behavior of the toluene-ethylbenzene adsorbed phase on the stationary phase is close to ideal. For example, the concentrations measured for the intermediate plateau obtained in frontal analysis differ by less than 2% from those predicted by the IAS model.