Stochastic theory of size exclusion chromatography by the characteristic function approach

A general stochastic theory of size exclusion chromatography (SEC) able to account for size dependence on both pore ingress and egress processes, moving zone dispersion and pore size distribution, was developed. The relationship between stochastic-chromatographic and batch equilibrium conditions are discussed and the fundamental role of the 'ergodic' hypothesis in establishing a link between them is emphasized. SEC models are solved by means of the characteristic function method and chromatographic parameters like plate height, peak skewness and excess are derived. The peak shapes are obtained by numerical inversion of the characteristic function under the most general conditions of the exploited models. Separate size effects on pore ingress and pore egress processes are investigated and their effects on both retention selectivity and efficiency are clearly shown. The peak splitting phenomenon and peak tailing due to incomplete sample sorption near to the exclusion limit is discussed. An SEC model for columns with two types of pores is discussed and several effects on retention selectivity and efficiency coming from pore size differences and their relative abundance are singled out. The relevance of moving zone dispersion on separation is investigated. The present approach proves to be general and able to account for more complex SEC conditions such as continuous pore size distributions and mixed retention mechanism.     

Overloaded gradient elution chromatography on heterogeneous adsorbents in reversed-phase liquid chromatography

Overloaded band profiles of phenol were measured on a C18-Kromasil column in gradient elution conditions. The mobile phase used was a mixture of methanol and water. The volume fraction of methanol was allowed to vary between 0 and 0.5. A general adsorption model, which expresses the amount of phenol adsorbed q* as a function of both its concentration C and the composition phi of the organic modifier (methanol) in the mobile phase, was empirically derived from previous independent adsorption experiments based on frontal analysis (FA) and frontal analysis by the characteristic point (FACP). Accordingly, the general model was an extension of the simplest heterogeneous model, the Bilangmuir model, to non-isocratic conditions. The low-energy sites followed the classical linear solvent strength model (LSSM), but not the high-energy sites whose saturation capacity linearly decreased with phi. The general model was validated by comparing the experimental and simulated band profiles in gradient elution conditions, in linear and non-linear conditions, as well. The band profiles were calculated by means of the equilibrium-dispersive model of chromatography with a finite difference algorithm. A very good agreement was observed using steps gradient (delta phi) from 0 to 50% methanol and gradient times t(g) of 20, 25, 30, 40, 60, 80 and 100 min. The agreement was still excellent for steps gradient from 5 to 45% (t(g) = 25 min), 5 to 35% (t(g) = 50 min), 5 to 25% (t(g) = 50 min) and 5 to 15% (t(g) = 50 min). Significative differences appeared between experience and simulation when the slope of the gradient (delta phi/t(g)) became too strong beyond 3.3% methanol per minute. This threshold value probably mirrored the kinetic of arrangement of the G18-bonded chains when the methanol content increased in the mobile phase. It suggested that the chromatographic system was not in a full thermodynamic equilibrium state when very steep mobile phase gradients were applied.     

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.     

Modeling of overloaded gradient elution of nociceptin/orphanin FQ in reversed-phase liquid chromatography

The Reversed-phase (RP) gradient elution chromatography of nociceptin/orphanin FQ (N/OFQ), a neuropeptide with many biological effects, has been modeled under linear and non-linear conditions. In order to do this, the chromatographic behavior has been studied under both linear and nonliner conditions under isocratic mode at different mobile phase compositions--ranging from 16 to 19% (v/v) acetonitrile (ACN) in aqueous trifluoracetic acid (TFA) 0.1% (v/v)-on a C-8 column. Although the range of mobile phase compositions investigated was quite narrow, the retention factor of this relatively small polypeptide (N/OFQ is a heptadecapeptide) has been found to change by more than 400%. In these conditions, gradient operation resulted thus to be the optimum approach for non-linear elution. As the available amount of N/OFQ was extremely reduced (only a few milligrams), the adsorption isotherms of the peptide, at the different mobile phase compositions examined, have been measured through the so-called inverse method (IM) on a 5 cm long column. The adsorption data at different mobile phase compositions have been fitted to several models of adsorption. The dependence of the isotherm parameters on the mobile phase composition was modeled by using the linear solvent strength (LSS) model and a generalized Langmuir isotherm that includes the mobile phase composition dependence. The overloaded gradient separation of N/OFQ has been modeled by numerically solving the equilibrium-dispersive (ED) model of chromatography under a selected gradient elution mode, on the basis of the previously determined generalized Langmuir isotherm. The agreement between theoretical calculations and experimental overloaded band profiles appeared reasonably accurate.     

Effect of pressure on retention factors in HPLC using a non-porous stationary phase

Summary Pressure and temperature have significant influence on retention in HPLC. This study investigates the effect of pressure and temperature on the retention behavior of aromatic hydrocarbons (toluene, ethyl benzene, butyl benzene, pentyl benzene) and polar, acidic and basic samples (phenol, acetophenone, N,N-dimethyl aniline, benzophenone) on a reversed phase column. The effect has been studied on non-porous, tetradecyl (C₁₄) coated silica particles. We found that the adsorption-induced decrease of the partial molar volume of the solutes investigated was between ΔV _m =5–15 cm³ mol⁻¹. The increment of the decrease of the partial molar volume due to the addition of one CH₂ group, for the homologous series of the aromatic hydrocarbons is approximately ΔV _CH2 =2.3 cm³mol⁻¹. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001.     

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.     

Analysis of the band profiles of the enantiomers of phenylglycine in liquid chromatography on bonded teicoplanin columns using the stochastic theory of chromatography.

The retention behaviour of the enantiomers of underivatized phenylglycine was studied on a Chirobiotic T column packed with amphoteric glycopeptide teicoplanin covalently bonded to the surface of silica gel. The retention and the selectivity of separation of the enantiomers increase with rising concentration of ethanol or of methanol in aqueous-organic mobile phases. The band profiles of the less retained L-phenylglycine are symmetrical, but the band profiles of the more strongly retained D-phenylglycine are tailing in all mobile phases tested. The band broadening does not diminish even at very low concentrations of phenylglycine, so that it cannot be attributed to possible column overload. The analysis of the band profile using the stochastic theory of chromatography suggests that the broadening can be attributed to at least two additional chiral centres of adsorption in the stationary phase contributing to the retention of the more strongly retained enantiomer in addition to the adsorption of the less retained one. This behaviour can be explained by the complex structure of the teicoplanin chiral stationary phase.     

Excess isotherms as a new way for characterization of the columns for reversed-phase liquid chromatography

In this work, we present the excess isotherm of acetonitrile for stationary phases with different coverage density. Data obtained with the minor disturbance method were compared with (29)Si cross-polarization/magic-angle spinning NMR spectra to find dependence between acetonitrile adsorption on C18 chemically bonded stationary phases and coverage density of stationary phase. The preferential adsorption of acetonitrile on the bonded phase and the adsorption of water on the silica surface can be well correlated with the coverage density.     

Retention controlling and peak shape simulation in anion chromatography using multiple equilibrium model and stochastic theory

The stochastic theory of chromatography and an equilibrium based approach were used for the prediction of peak shape and retention data of anions. This attempt incorporating the potential advantages of two different chromatographic phenomena for analytical purposes. It is an integrated method to estimate kinetic and thermodynamic properties for the same chromatographic run of ions. The stochastic parameters of eluted anions, such as the residence time of the molecule on the surface of the stationary phase, and the average number of adsorption steps were determined on the basis of a retention database of organic and inorganic anions (formate, chloride, bromide, nitrate, sulphate, oxalate, phosphate) obtained by using carbonate/bicarbonate eluent system at different pHs (9-11) and concentrations (7-13 mM). In the investigated IC system the residence times are much higher and the average number of sorption steps is somewhat smaller than in RP-HPLC. The simultaneous application of the stochastic and the multispecies eluent/analyte model was utilized to peak shape simulation and the retention controlling of various anions under elution conditions of practical importance. The similarities between the measured and the calculated chromatograms indicates the predictive and simulation power of the combined application of the stochastic theory and the multiple species eluent/analyte retention model.     

Adsorption behavior of a teicoplanin aglycone bonded stationary phase under harsh overload conditions

Silica-bonded teicoplanin aglycone allows enantioseparation of amino acids by reversed-phase liquid chromatography with a low organic solvent content. However, a reversible change in the adsorption behavior leading to a retention time shift (RTS) was observed when a preparative scale column was treated with harsh preparative chromatography-like conditions between finite-injection HPLC runs conducted under exactly the same conditions. This behavior was observed for all five investigated aliphatic and aromatic amino acids. In all cases, the retention times were prolonged after the overload conditions and the RTS was more pronounced for the later eluting d-enantiomer. We defined a standardized method for measuring the RTS and performed a systematic investigation on the influence of experimental conditions (type and concentration of pH modifier and organic modifier, temperature, pH) on the RTS. In this way a solvent composition--90/10 50 mM NH4Ac pH 5.8/MeOH--was identified that yielded no observable shift in retention time after overload conditions for both enantiomers. In order to treat the observed phenomenon on a mechanistic level, we applied band profile analysis based on the stochastic theory of chromatography and identified two different enantioselective sites. When the band profile analysis was performed on elution profiles obtained from runs with prolonged retention time after harsh overload conditions, the retention time shift could be attributed to both differentiable types of adsorption sites. One site was found to make both, enantioselective and non-selective contributions.