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.     

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.     

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.     

Fitting adsorption isotherms to the distribution data determined using packed micro-columns for high-performance liquid chromatography

Knowing the adsorption isotherms of the components of a mixture on the chromatographic system used to separate them is necessary for a better understanding of the separation process and for the optimization of the production rate and costs in preparative high-performance liquid chromatography (HPLC). Currently, adsorption isotherms are usually measured by frontal analysis, using conventional analytical columns. Unfortunately, this approach requires relatively large quantities of pure compounds, and hence is expensive, especially in the case of pure enantiomers. In this work, we investigated the possible use of packed micro-bore and capillary HPLC columns for the determination of adsorption isotherms of benzophenone, o-cresol and phenol in reversed-phase systems and of the enantiomers of mandelic acid on a Teicoplanin chiral stationary phase. We found a reasonable agreement between the isotherm coefficients of the model compounds determined on micro-columns and on conventional analytical columns packed with the same material. Both frontal analysis and perturbation techniques could be used for this determination. The consumption of pure compounds needed to determine the isotherms decreases proportionally to the second power of the decrease in the column inner diameter, i.e. 10 times for a micro-bore column (1 mm I.D.) and 100 times for capillary columns (0.32 mm I.D.) with respect to 3.3 mm I.D. conventional columns.     

Examination of the surface heterogeneity of reversed-phase packing materials with solvent adsorption

The adsorption isotherms of acetonitrile, ethanol, 2-propanol, and THF were measured using frontal analysis on six columns packed with octadecyl RP stationary phase. The effect of the bonding density of the end-capped octadecyl bonded phase on the adsorption properties was measured. Adsorption isotherm data were collected from aqueous solutions of the four organic modifiers. The isotherm model for solvent adsorption was selected using two independent parameter estimation methods, the regression analysis and adsorption energy distribution. The fitted isotherm parameters were tested by modeling of overloaded elution bands with the aid of the equilibrium-dispersive model of chromatography. The surface heterogeneity estimations and the effect of the silanol groups on the adsorption of solvents were based on those data.     

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%.     

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.     

Reproducibility of low and high concentration data in reversed-phase liquid chromatography. II. Overloaded band profiles on Chromolith-C18

Single-component adsorption isotherm data were acquired by frontal analysis (FA) for six low molecular weight compounds (phenol, aniline, caffeine, o-toluidine, p-toluidine and propylbenzoate) on one Chromolith-C18 column (#30, Merck, Darmstadt, Germany), using different methanol:water solutions (composition between 60/40 and 15/85 v/v, depending on the solute) as the mobile phase. These data were modeled for best agreement between the experimental data points and the adsorption isotherm model. The adsorption-energy distributions were also derived and used for the selection of the best isotherm model. Widely different models were obtained for these six compounds, four being convex upward (i.e., Langmuirian) and two having at least one inflection point. Overloaded band profiles corresponding to two different sample sizes (a low and a high loading factor) were recorded on six monolithic columns (#30-35) belonging to the same manufactured lot. These experimental band profiles were compared to the profiles calculated from the isotherm measured by FA on the first column, using the equilibrium-dispersive (ED) model of chromatography. For four of the six columns (#30, #32, #33, and #35), the reproducibility was better than 5 and 2.5% for the low and the high concentration profiles, respectively. On the other two columns (#31 and #34), the bands showed significant and systematic retention time shifts for all six compounds (with nearly identical band shapes), the relative adsorption being between 6 and 15% stronger on column #31 or between 2 and 7% lower on column #34. These differences seem to be correlated with the differences in the total porosities of these columns, which differ by 3% from columns #31 to #34, the higher porosity column giving the stronger adsorption.     

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.     

Comparison between adsorption isotherm determination techniques and overloaded band profiles on four batches of monolithic columns

The adsorption isotherms of 4-tert.-butyl phenol were measured on four different monolithic columns, using three different techniques, classical frontal analysis (FA), the perturbation on a plateau method (PP) and the recently introduced numerical procedure known as the inverse numerical method (IN). This last approach requires only the recording of a few overloaded profiles and has the potential advantage of affording a dramatic decrease of the amounts of compounds, solvent, and time needed to determine accurate estimates of the coefficients of the isotherm. The reproducibility of the adsorption data measured on the four columns is discussed with reference to the specific techniques used for obtaining these data and to the most suitable equation used for modeling them. The data obtained for the different columns were highly consistent. The inverse numerical approach was confirmed to provide a powerful, accurate, and economic method for measuring single component adsorption data.     

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.     

Adsorbed solution model for prediction of normal-phase chromatography process with varying composition of the mobile phase

The adsorbed solution model has been used to predict competitive adsorption equilibria of the solute and the active component of mobile phase in a normal-phase liquid chromatography system. The inputs to the calculations were the single adsorption isotherms accounting for energetic heterogeneity of the adsorbent surface and non-ideality of the mobile phase solution. The competitive adsorption model has been coupled with a model of the column dynamics and used for simulating of chromatography process at different mobile phase composition. The predictions have been verified by comparing the simulated and experimental chromatograms. The model allowed quantitative prediction of chromatography process on the basis of the pure-species adsorption isotherms.     

Effect of the mobile phase composition on the adsorption behavior of tryptophan in reversed-phase liquid chromatography

Single-component adsorption isotherm data of l-tryptophan on a C18-bonded silica column were acquired by frontal analysis (FA), with aqueous mobile phases containing 2.5, 5, and 7.5% of acetonitrile (ACN) or 7, 10, 15, and 20% of methanol (MeOH). Most of these isotherms have two inflection points and three different parts. The low and the high concentration parts exhibit langmuirian behavior. The intermediate part exhibits anti-langmuirian behavior. The inflection points shift toward higher concentrations with increasing mobile phase concentration in ACN or MeOH, which causes the differences in the isotherm profiles. The nature of the organic modifier and its concentration affect only the isotherm profile and the numerical values of its parameters, not the nature of the best model, which is the bi-Moreau model in all cases. The isotherm profiles depend on the experimental conditions because they affect the intensity of the adsorbate-adsorbate interactions. Overloaded band profiles of tryptophan were recorded with the seven mobile phase compositions. They were used to determine the best values of the isotherm coefficients by the inverse method (IM) of chromatography. There is an excellent agreement between the values of these parameters obtained by FA and by IM. Increasing the concentration of either ACN or MeOH in the mobile phase causes a slight decrease in the saturation capacities of the low and the high energy sites, and in the adsorption constant of the low energy sites. The adsorption constant of the high energy sites increases with increasing concentration of either solvent or is little affected. The adsorbate-adsorbate interaction constants of both low and high energy sites increase for both solvents. Saturation capacities of the high energy sites are higher for ACN than for MeOH.     

Effect of water on the retention on diol and amide columns in hydrophilic interaction liquid chromatography

The amount of water adsorbed on polar columns plays important role in hydrophilic interaction liquid chromatography. It may strongly differ for the individual types of polar columns used in this separation mode. We measured adsorption isotherms of water on an amide and three diol‐bonded stationary phases that differ in the chemistry of the bonded ligands and properties of the silica gel support. We studied the effects of the adsorbed water on the retention of aromatic carboxylic acids, flavonoids, benzoic acid derivatives, nucleic bases, and nucleosides in aqueous‐acetonitrile mobile phases over the full composition range. The graphs of the retention factors versus the volume fraction of water in mobile phase show “U‐profile” characteristic of a dual hydrophilic interaction–reversed phase retention mechanism. The minimum on the graph that marks the changing retention mechanism depends on the amount of adsorbed water. The linear solvation energy relationship model suggests that the retention in the hydrophilic interaction liquid chromatography mode is controlled mainly by proton–donor interactions in the stationary phase, depending on the column type. Finally, the accuracy of hydrophilic interaction liquid chromatography gradient prediction improves for columns that show a high water adsorption.     

Characterization of non-linear adsorption properties of dextran-based polyelectrolyte displacers in ion-exchange systems

Experimental studies were carried out on the non-linear adsorption properties of dextran-based polyelectrolytes in anion- and cation-exchange chromatographic systems. By monitoring both the induced salt gradients and sequential breakthrough fronts, parameters were determined for use in a Steric Mass Action (SMA) model of non-linear ion-exchange chromatography. These parameters include: total ion capacity of the columns, characteristic charge, steric factor, equilibrium constant, and maximum adsorptive capacity for each of the polyelectrolytes. In addition the number of functional groups were determined by elemental analysis. The values of the SMA parameters were found to be independent of salt and polyelectrolyte bulk phase compositions. Parameters were also determined for a variety of proteins. Experimental isotherms for the polyelectrolytes and proteins were compared with those simulated by the SMA model. Finally, the implications of polyelectrolyte adsorption properties with respect to their ability to act as efficient displacers in ion-exchange displacement systems are discussed.     

木糖和木糖醇的色谱模型

利用集总模型，以柱床的物料衡算方程式、吸附等温线模型、传质推动力及初始和边界条件组成木糖、木糖醇的色谱模型，用计算机模拟得到柱中液相浓度分布仿真结果。     

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.     

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.     

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.