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 analysis of the heterogenous binding sites of molecularly imprinted polymers

The thermodynamic interactions of two polymers, one Fmoc-L-Trp-imprinted (MIP), the other one an unimprinted reference (NIP), with the two Fmoc-tryptophan enantiomers were studied by frontal analysis, which allows accurate measurements of the adsorption isotherms. These isotherms were acquired at temperatures of 40, 50, 60, and 70 degrees C, for sample concentrations ranging between 0.005 and 40 mM. The mobile phase used was acetonitrile with one percent acetic acid as an organic modifier. Within the measured concentration ranges, the tri-Langmuir isotherm model accounts best for the isotherm data of both enantiomers on the MIP, the bi-Langmuir model for the isotherm data of Fmoc-L-Trp on the NIP. These isotherm models were selected using three independent processes: statistical tests on the results from regression of the isotherm data to different isotherm models; calculation of the affinity energy distribution from the raw isotherm data; comparison of the experimental and the calculated band profiles. The isotherm parameters obtained from these best selected isotherm models showed that the enantiomeric selectivity does not change significantly with temperature, while the affinity of the substrates for both the MIP and the NIP decrease considerably with increasing temperatures. These temperature effects on the binding performance of the MIP were clarified by considering the thermodynamic functions (i.e., the standard molar Gibbs free energy, the standard molar entropy of adsorption, and the standard molar enthalpy of adsorption) for each identified type of adsorption sites, derived from the Van't Hoff equation. This showed that the entropy of transfer of Fmoc-L-Trp from the mobile to the MIP stationary phase is the dominant driving force for the selective adsorption of Fmoc-L-Trp onto the enantioselective binding sites. This entropy does not change significantly with increasing temperatures from 40 to 70 degrees C.     

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.     

Impact of an error in the column hold-up time for correct adsorption isotherm determination in chromatography II. Can a wrong column porosity lead to a correct prediction of overloaded elution profiles?

The adsorption isotherm was determined for phenol in methanol/water on a C-8 stationary phase using frontal analysis in staircase mode, assuming different total column porosities, from 1 to 87%. Each set of adsorption isotherm data, with a certain column porosity, was fitted to various adsorption models and the generated parameters were used to calculate overloaded elution band profiles that were compared with experiments. It was found that the bi-Langmuir model had an optimum fit for a porosity that corresponds well with the value found experimentally. The adsorption energy distribution (AED) calculations and error analysis confirmed a bimodal energy distribution. It was also found that band profiles can be accurately predicted with a quite arbitrary chosen porosity, under prerequisite that a wrong but flexible adsorption model is chosen instead of the correct one. The latter result is very useful for quick optimizations of preparative separations where the exact value of the column porosity is not available.     

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.     

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.     

Retention of ionizable compounds in high-performance liquid chromatography. 14. Acid-base pK values in acetonitrile-water mobile phases

Using competitive frontal analysis, the binary adsorption isotherms of the enantiomers of 1-phenyl-l-propanol were measured on a microbore column packed with a chiral stationary phase based on cellulose tribenzoate. These measurements were carried out using only the racemic mixture. The experimental data were fitted to four different isotherm models: Langmuir, BiLangmuir, Langmuir-Freundlich and Tóth. The BiLangmuir and the Langmuir-Freundlich models accounted best for the competitive adsorption data. An excellent agreement between the experimental and the calculated overloaded band profiles for various samples of racemic mixture was obtained when the equilibrium dispersive model of chromatography was used together with the BiLangmuir competitive isotherm. The isotherm parameters measured under competitive conditions were used to calculate the overloaded band profiles of large samples of the pure S- and R-enantiomers, too. A satisfactory agreement between the experimental and calculated band profiles was observed when using in the computation the corresponding single component BiLangmuir isotherm derived from the binary isotherm previously determined. Thus oniy data derived from the racemic mixture are required for computer optimization of the preparative chromatography separation of the enantiomers.     

Effect of the temperature on the isotherm parameters of phenol in reversed-phase liquid chromatography

Adsorption isotherm data of phenol from an aqueous solution of methanol onto a C18-bonded silica (Symmetry-C18) were acquired by frontal analysis (FA) at six different temperatures, in a wide concentration range. The non-linear fitting of these data provided the bi-Langmuir model as best isotherm model, a conclusion further supported by the results of the calculation of the affinity energy distribution (AED). The isotherm parameters were obtained using several methods, the fitting of FA isotherm data, the calculation of the AED, and the inverse method, that uses overloaded elution band profiles. The different values obtained are in close agreement. They allow a quantitative investigation of the separate properties of the low- and the high-energy sites on the adsorbent surface. Increasing the temperature decreases the saturation capacity of the low-energy adsorption sites and the adsorption constant of the high-energy sites. In contrast, increasing the temperature does not cause any significant changes in either the saturation capacity of the high-energy sites or the adsorption constant of the low-energy sites.     

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.     

Thermodynamic characterization of separations on alkaline-stable silica-based C18 columns: why basic solutes may have better capacity and peak performance at higher pH

A systematic study was made to explain the large improvements in separation performance and capacity of basic compounds at alkaline conditions. The adsorption of three probe components was investigated on four alkaline-stable silica-based C18 columns at three different pH-levels: 3, 7 and 11. The probes were 3-phenyl-1-propanol (neutral), 2-phenylbutyric acid (acidic) and metoprolol (basic). Adsorption isotherms were acquired over a broad concentration range, in order to detect both high and low energy sites. Before the choice of the proper adsorption isotherm model, the adsorption energy distribution (AED) was calculated yielding the number of different kinds of interaction sites between the solute and the stationary phase. The neutral probe was entirely unaffected by pH and its AED was unimodal (one site) indicating homogenous adsorption. For the acidic probe the interactions were unimodal at pH 3 where the probe is uncharged and at least bimodal (two sites) at pH 7 and 11 where the probe is charged. For the basic probe, the interactions were heterogeneous at both pH 3 and 11. The equilibrium constants of the high and low energy sites were different by a factor of 55-100 at pH 3 and only 6-7 at pH 11. The difference in saturation capacities between the two sites was much smaller at pH 11 where 20% of the total capacity is from the high energy site, as compared to pH 3 where the high energy site was only 2-5% of the total capacity. This explains why peaks of amines (basic solutes) tail at low pH while their peaks are symmetrical at alkaline pH. The Langmuir model fit the unimodal data and the bi-Langmuir model fit the bimodal AED data. The calculated band profiles based on these parameters agreed excellently with the experimental data. The electrostatic-modified Langmuir, on the other hand, did not describe this adsorption process well.     

Empirical development of a binary adsorption isotherm based on the single-component isotherms in the framework of a two-site model

The adsorption behavior of mixtures of the enantiomers of 2,2,2-(trifluoro)-1-(9-anthryl)-ethanol (TFAE) on a quinidine carbamate bonded stationary phase was studied as an example of competitive binary adsorption on a Pirkle-type chiral adsorbent. A model of the adsorption isotherms is proposed and discussed. Binary adsorption isotherms derived by combination of the single-component isotherms of the two enantiomers in the framework of the classical bi-Langmuir model allow the correct prediction of the retention times of the elution bands of the components of binary mixtures but fail properly to predict the separation of the two enantiomers. Use of a quadratic model was needed to improve the agreement between calculated and experimental chromatograms of binary mixtures. The existence of a third type of adsorption sites besides the high-energy enantioselective and the low-energy nonselective sites was assumed. These sites have a low interaction energy, exhibit some affinity toward (S)-TFAE, but none toward (R)-TFAE.     

Adsorption-desorption isotherm hysteresis of phenol on a C18-bonded surface

Single component adsorption and desorption isotherms of phenol were measured on a high-efficiency Kromasil-C18 column (N = 15000 theoretical plates) with pure water as the mobile phase. Adsorption isotherm data were acquired by frontal analysis (FA) for seven plateau concentrations distributed over the whole accessible range of phenol concentration in pure water (5, 10, 15, 20, 25, 40, and 60 g/l). Desorption isotherm data were derived from the corresponding rear boundaries, using frontal analysis by characteristic points (FACP). A strong adsorption hysteresis was observed. The adsorption of phenol is apparently modeled by a S-shaped isotherm of the first kind while the desorption isotherm is described by a convex upward isotherm. The adsorption breakthrough curves could not be modeled correctly using the adsorption isotherm because of a strong dependence of the accessible free column volume on the phenol concentration in the mobile phase. It seems that retention in water depends on the extent to which the surface is wetted by the mobile phase, extent which is a function of the phenol concentration, and of the local pressure rate, which varies along the column, and on the initial state of the column. By contrast, the desorption profiles agree well with those calculated with the desorption isotherms using the ideal model, due to the high column efficiency. The isotherm model accounting best for the desorption isotherm data and the desorption profiles is the bi-Langmuir model. Its coefficients were calculated using appropriate weights in the fitting procedure. The evolution of the bi-Langmuir isotherm parameters with the initial equilibrium plateau concentration of phenol is discussed. The FACP results reported here are fully consistent with the adsorption data of phenol previously reported and measured by FA with various aqueous solutions of methanol as the mobile phase. They provide a general, empirical adsorption model of phenol that is valid between 0 and 65% of methanol in water.     

Systematic errors in the measurement of adsorption isotherms by frontal analysis Impact of the choice of column hold-up volume, range and density of the data points

Besides the accuracy and the precision of the measurements of the data points, several important parameters affect the accuracy of the adsorption isotherms that are derived from the data acquired by frontal analysis (FA). The influence of these parameters is discussed. First, the effects of the width of the concentration range within which the adsorption data are measured and of the distribution of the data points in this range are investigated. Systematic elimination of parts of the data points before the calculation of the nonlinear regression of the data to the model illustrates the importance of the numbers of data points (1) within the linear range and (2) at high concentrations. The influence of the inaccuracy of the estimate of the column hold-up volume on each adsorption data point, on the selection of the isotherm model, and on the best estimates of the adsorption isotherm parameters is also stressed. Depending on the method used to measure it, the hold-up time can vary by more than 10%. The high concentration part of the adsorption isotherm is particularly sensitive to errors made on t(0,exp) and as a result, when the isotherm follows bi-Langmuir isotherm behavior, the equilibrium constant of the low-energy sites may change by a factor 2. This study shows that the agreement between calculated and experimental overloaded band profiles is a necessary condition to validate the choice of an adsorption model and the calculation of its numerical parameters but that this condition is not sufficient.     

Investigation of the adsorption behaviour of a chiral model compound on a tartardiamide-based network-polymeric chiral stationary phase

The adsorption behaviour of the enantiomers of 2-phenylbutyric acid on the chiral stationary phase (CSP) Kromasil CHI-TBB was studied using hexane/MTBE (90/10) as eluent. Adsorption isotherms were acquired at 40 different enantiomer concentrations in the interval between 7.6 microM and 305 mM, an approximately 40,000-fold dynamic range. The adsorption data fitted well to the bi-Langmuir model, indicating a heterogeneous surface with two different types of adsorption sites having different equilibrium constants and capacities; namely one chiral site and one non-chiral site. A comparison with earlier adsorption studies on modern CSPs revealed that the capacity value of the "true" chiral site of Kromasil CHI-TBB is the largest reported so far. The elution profiles simulated with these parameters show excellent agreement with the corresponding experimental profiles. Guidelines for comparisons of loading capacities of CSPs are presented.     

Characterization of an unusual adsorption behavior of racemic methyl-mandelate on a tris-(3,5-dimethylphenyl) carbamoyl cellulose chiral stationary phase

An interesting adsorption behavior of racemic methyl mandelate on a tris-(3,5-dimethylphenyl)carbamoyl cellulose chiral stationary phase was theoretically and experimentally investigated. The overloaded band of the more retained enantiomer had a peculiar shape indicating a type V adsorption isotherm whereas the overloaded band of the less retained enantiomer had a normal shape indicating a type I adsorption behavior. For a closer characterization of this separation, adsorption isotherms were determined and analyzed using an approach were Scatchard plots and adsorption energy distribution (AED) calculations are combined for a deeper analysis. It was found that the less retained enantiomer was best described by a Tóth adsorption isotherm while the second one was best described with a bi-Moreau adsorption isotherm. The latter model comprises non-ideal adsorbate-adsorbate interactions, providing an explanation to the non-ideal adsorption of the more retained enantiomer. Furthermore, the possibility of using the Moreau model as a local model for adsorption in AED calculations was evaluated using synthetically generated raw adsorption slope data. It was found that the AED accurately could predict the number of adsorption sites for the generated data. The adsorption behavior of both enantiomers was also studied at several different temperatures and found to be exothermic; i.e. the adsorbate-adsorbate interaction strength decreases with increasing temperature. Stochastic analysis of the adsorption process revealed that the average amount of adsorption/desorption events increases and the sojourn time decreases with increasing temperature.     

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.     

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.     

Features of the adsorption of naproxen enantiomers on weak chiral anion-exchangers in nonlinear chromatography

The retention mechanism of the enantiomers of naproxen on a Pirkle-type chiral stationary phase (CSP) was studied. This CSP is made of a porous silica grafted with quinidine carbamate. It can interact with the weak organic electrolyte naproxen either by adsorbing it or by ion-exchange. Using frontal chromatography, we explored the adsorption equilibrium under such experimental conditions that naproxen dissociates or cannot dissociate. Under conditions preventing ionic dissociation, the adsorption isotherms were measured, the adsorption energy distributions determined, and the chromatographic profiles calculated. Three different types of the adsorption sites were found for both enantiomers. The density and the binding energy of these sites depend on the nature of the organic modifier. Different solute species, anions, neutral molecules, solvent-ion associates, and solute dimers can coexist in solution, giving rise to different forms of adsorption. This study showed the unexpected occurrence of secondary steps in the breakthrough profiles of S-naproxen in the adsorption mode at high concentrations. Being enantioselective, this phenomenon was assumed to result from the association of solute molecules involving a chiral selector moiety. A multisite Langmuir adsorption model was used to calculate band profiles. Although this model accounts excellently for the experimental adsorption isotherms, it does not explain all the features of the breakthrough profiles. A comparison between the calculated and experimental profiles allowed useful conclusions concerning the effects of the adsorbate-adsorbate and adsorbate-solvent interactions on the adsorption mechanism.