Dongmei Zhou

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.

Influence of pressure on the chromatographic behavior of insulin variants under nonlinear conditions

The effect of pressure on the chromatographic behavior of two insulin variants in RPLC was investigated on a YMC-ODS C18 column, under nonlinear conditions. The adsorption isotherm data of porcine insulin and Lispro were measured at average column pressures ranging from 52 to 242 bar. These data fit well to the Toth and the bi-Langmuir isotherm models. The saturation capacity increases rapidly with increasing pressure while the affinity (or equilibrium) constant and the parameter characterizing the surface heterogeneity decrease. It is noteworthy that the distribution coefficient of the insulin variants increases with increasing pressure whereas their equilibrium constant b decreases for porcine insulin and increases for Lispro. The association constant b(ds), which characterizes the adsorption and desorption equilibrium of insulin in the system, increases with increasing pressure. The excellent agreement between the experimental overloaded profiles recorded under different pressures and those calculated using the POR model suggests that the chromatographic behavior of insulin is controlled more by equilibrium thermodynamics than by the mass transfer kinetics. The latter seems to be nearly independent of the average column pressure. Thus, increasing the average column pressure is an efficient, albeit costly, way to increase the loading capacity of the column, hence the production rate in preparative chromatography.

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.

Application of the general rate model with the Maxwell-Stefan equations for the prediction of the band profiles of the 1-indanol enantiomers

The adsorption isotherm data of R- and S-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. These experimental data were fitted to the single-component and the modified competitive Bilangmuir isotherms. The overloaded elution profiles of bands of the pure enantiomers and of the racemic mixture were calculated for different sample sizes, using the best competitive isotherm model and the General Rate Model of chromatography coupled with the generalized Maxwell–Stefan equation that describes the surface diffusion flux. The calculated and the experimental profiles were found to be in excellent agreement in all cases. The parameters of the model of the mass transfer kinetics were derived from the band profiles obtained for the pure enantiomers. The same values of these parameters give an excellent prediction of the profiles of multicomponent bands. The new model described here allows a satisfactory interpretation of the competitive mass transfer kinetics.

Prediction of the band profiles of the mixtures of the 1-indanol enantiomers from data acquired with the single racemic mixture

Abstract The adsorption isotherm data of R- and S-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. These data were then fitted to the Langmuir, the Bilangmuir, the Toth, and the Langmuir–Freundlich isotherm models. The single component data fitted well to both the Bilangmuir and the Toth models. Combined with the lumped pore diffusion model (POR) of chromatography, these isotherms were used to calculate overloaded elution profiles of the pure enantiomers. The calculated and the experimental profiles agree excellently in all cases if the former are derived from the Bilangmuir model. The competitive experimental data also gave excellent agreement with the Bilangmuir model. The simultaneous fit of all the data, for the single components and the racemic mixture, gave again superior agreement with the bilangmuir model. The overloaded elution profiles of samples of the racemic mixture calculated with the Bilangmuir isotherm model combined with the POR model of chromatography gave results in very good agreement with the experimental band profiles of large samples of the racemic mixture. This confirms that in numerous cases the whole set of competitive isotherms of two enantiomers can be derived from the experimental data obtained only with the racemic mixture.

Prediction of Band Profiles of Mixtures of Bradykinin and Kallidin from Data Acquired by Competitive Frontal Analysis

The competitive adsorption isotherms of two closely related peptides, bradykinin and kallidin, were measured by frontal analysis on a Zorbax SB‐C18 microbore column. An aqueous soluton at 20% acetonitrile (0.1% TFA) was used as the mobile phase. The competitive isotherm data were fitted to four different models: Langmuir, Bilangmuir, Langmuir‐Freundlich, and Toth. These data fitted best to a Bilangmuir isotherm model. The influence of the pressure on the retention factors of the two peptides was found to be small and was not investigated in detail. The band profiles of large samples of the single components and of their mixtures were recorded. The overloaded profiles calculated using either the equilibrium‐dispersive or POR model are in excellent agreement with the experimental profiles in all cases. Our results confirm that the competitive isotherm data derived from mixtures may suffice for a reasonably accurate prediction of the band profiles of all mixtures of the two components, provided their composition is close to 1/1.

Modeling of preparative reversed-phase HPLC of insulin

The adsorption isotherms of three recombinant proteins, human insulin, porcine insulin, and Lispro, were measured by frontal analysis on a YMC‐ODS C18 column with an aqueous solution at 31% acetonitrile (0.1% TFA) as the mobile phase. The retention behavior of insulin, its related molecular structure, its conformation, and its aggregation in this phase system are discussed. The experimental isotherm data were fitted to the Langmuir, the Langmuir‐Freundlich, and the Toth models. The results allow for a quantitative comparison of the saturation capacities, the equilibrium constants, and the exponents that represent the heterogeneity of the stationary phase obtained for the different insulin variants studied. The Toth model provided the best fit of the experimental data. The overloaded band profiles were calculated using the lumped pore diffusion and the equilibrium‐dispersive model of chromatography. An excellent agreement between calculated and experimental profiles was demonstrated.

Equivalent Models of Indanol Isomers Adsorption on Cellulose Tribenzoate

The adsorption isotherm data of ( R)‐ and ( S)‐1‐indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. The experimental data for each enantiomers were fitted to the single‐component bilangmuir isotherm model. The competitive experimental data were fitted to the ideal adsorption solution model (IAS), the real adsorption solution model (RAS), and the bilangmuir thermodynamically consistent model (BTC). The mass transfer kinetic parameters were estimated from systematic comparisons between the experimental single‐component band profiles and profiles calculated using the general rate model (GR) of chromatography coupled with the generalized Maxwell‐Stefan equation (GMS). The validation of the isotherm model and of the mass transfer kinetic model was made by comparing the experimental band profiles obtained for solutions of the two enantiomers and those calculated with the competitive GR‐GMS model. The excellent agreement observed proves that a combination of the BTC isotherm model and the GMS kinetic model, using the best values of the BTC and GMS parameters estimated from single component experiments, allows an excellent prediction of the binary isotherm and the binary mass transfer kinetics.

Comparison of the binary equilibrium isotherms of the 1-indanol enantiomers on three high-performance liquid chromatography columns of different sizes

The competitive isotherm data for the enantiomers of 1-indanol were measured on three columns, a microbore column (15 cm x 0.1 cm), a conventional analytical column (15 cm x 0.46 cm), and a semi-preparative column (20 cm x 1.0 cm), packed with Chiralcel OB. The sets of isotherm data measured on each one of these three columns could be fitted well by a bi-Langmuir isotherm model. The experimental elution band profiles of mixtures of the 1-indanol isomers were recorded on the three columns. The isotherm model, combined with the equilibrium dispersive model of chromatography, gave calculated profiles that are in excellent agreement with the experimental profiles in all cases investigated. It was found that the value of the inner diameter of the column is an important parameter in the calculation of the isotherm parameters from the measured isotherm data. In order to use isotherm data obtained on one column to account for the phase equilibrium on another one, the inner diameters of these columns must be measured accurately. The diameters of the three columns were all slightly off their nominal value. Without correction, an important systematic error was made on the isotherm data obtained with the microbore column while only negligible errors were made on the data obtained with the other two columns. After due correction for this effect, the relative difference between the isotherm data for the microbore and the semi-preparative column is still, on the average, about 10%, a difference that might be explained by the limited precision of the measurement of the microbore column diameter. The relative difference between the isotherm data for the analytical and the semi-preparative columns was about 1%, a reasonable value, since the two columns came from different batches of the same packing material.