Prediction of overloaded concentration profiles under ultra-high-pressure liquid chromatographic conditions.

In this study, overloaded elution profiles under ultra-high-pressure liquid chromatographic (UHPLC) conditions and accounting for the severe pressure and temperature gradients generated, are compared with experimental data. The model system consisted of an C18 column packed with 1.7-µm particles (i.e., a UHPLC column) and the solute was 1,3,5-tri­tert-butylbenzene eluted with a mobile phase composed of 85/15 (v/v) acetonitrile/water. Two thermal modes were considered, and the solute was eluted at the very high inlet pressures necessary to achieve a highly efficient and rapid chromatographic process, as provided by using columns packed with small particles. However, the high inlet pressure and high linear velocity of the mobile phase caused the production of a significant amount of heat, and consequently, the formation of axial and radial temperature gradients. Due to these gradients, the retention and the mobile phase velocity were no longer constant. Thus, simple mathematical models consisting only of the mass balance equations are unsuitable to properly model the elution profiles. Here, the elution concentration profiles were predicted using a combined two-dimensional heat and mass transfer model, also including the calculation of the mobile phase velocity distribution. The isotherm adsorption model was the bi-Langmuir isotherm model with Henry constants that depended on the local temperature and pressure in the column. These adjustments allowed us to precisely account for changes in the shape and retention of the overloaded concentration profiles in the mobile phase. The proposed model provided accurate predictions of the overloaded concentration profiles, demonstrating good agreement with experimental profiles eluted under severe pressure and temperature gradients in the column even in the most extreme cases where the pressure drops reached 846 bar and the temperature gradients equaled 0.15 K mm-1 and 0.95 K mm-1 in the axial and the radial directions, respectively. In such cases 36 % decrease of the retention factor was observed along the column and 2 % increase in radial direction. These changes, combined with the velocity distribution, shifted the overloaded elution profile's shock towards the center of the column, advancing approximately 3 mm from its initial position close to the column wall. Ultimately, this resulted in the broadening of the elution band.

Strategies for predictive modeling of overloaded oligonucleotide elution profiles in ion-pair chromatography.

Due to their potential for gene regulation, oligonucleotides have moved into focus as one of the preferred modalities modulating currently undruggable disease-associated targets. In the course of synthesis and storage of oligonucleotides a significant number of compound-related impurities can be generated. Purification protocols and analytical methods have become crucial for the therapeutic application of any oligonucleotides, be they antisense oligonucleotides (ASOs), small interfering ribonucleic acids (siRNAs) or conjugates. Ion-pair chromatography is currently the standard method for separating and analyzing therapeutic oligonucleotides. Although mathematical modeling can improve the accuracy and efficiency of ion-pair chromatography, its application remains challenging. Simple models may not be suitable to treat advanced single molecules, while complex models are still inefficient for industrial oligonucleotide optimization processes. Therefore, fundamental research to improve the accuracy and simplicity of mathematical models in ion-pair chromatography is still a necessity. In this study, we predict overloaded concentration profiles of oligonucleotides in ion-pair chromatography and compare relatively simple and more advanced predictive models. The experimental system consists of a traditional C18 column using (dibutyl)amine as the ion-pair reagent and acetonitrile as organic modifier. The models were built and tested based on three crude 16-mer oligonucleotides with varying degrees of phosphorothioation, as well as their respective n - 1 and (P = O)1 impurities. In short, the proposed models were suitable to predict the overloaded concentration profiles for different slopes of the organic modifier gradient and column load.

A closer study of overloaded elution bands and their perturbation peaks in ion-pair chromatography.

There is strong renewed interest in ion-pair chromatography (IPC) because of its great importance for separating new-generation biosimilar pharmaceuticals such as oligonucleotides. Due to the complexity of the IPC process, its mathematical modeling is challenging, especially in preparative mode. In a recent study, Lesko et al. (2021) developed a mathematical model for predicting, with good accuracy, overloaded concentration profiles for sodium benzenesulfonate, describing how the overloaded solute concentration profiles change from Langmuirian to complicated U-shaped, and then back again to Langmuirian profiles, with increasing concentration of the ion-pair reagent in the mobile phase. This study identifies and explains the underlying mechanism generating these complex peak shapes and band-shape transformations; this was only possible by visualizing and modeling the underlying equilibrium perturbations that occur upon injection in preparative IPC. In the 2021 study, the model was derived based on the concentration profiles obtained using a conventional UV detector principle, so the concentration gradients and perturbation zones of the mobile-phase components were not visualized. In this study, the necessary mechanistic information was obtained via complementary experiments combining two detection principles, i.e., refractive index detection and UV detection, with modeling efforts. The models correctly described the invisible equilibrium perturbations and how these formed internal gradients of the mobile-phase components. The models also explained the complex overloaded solute-band deformations reported in the recent study. In addition, a rule of thumb was developed for predicting experimental conditions that could result in deformed solute elution profiles and/or for avoiding these deformations. The latter is crucial for the practical chromatographer, since such U-shaped solute-band profiles are undesirable in preparative separation due to the broader elution zones, resulting in lower productivity than that of normal band shapes.

Experimental and theoretical investigation of high- concentration elution bands in ion-pair chromatography.

The effective separation of many solutes, including pharmaceuticals, can be performed using an ion-pair reagent (IPR) in the mobile phase. However, chromatographic separation and mathematical modelling are a challenge in ionpair chromatography (IPC), especially in preparative mode, due to the complicated chromatographic process. In this study, we present a retention mechanism and a mathematical model that predict overloaded concentration profiles in IPC using a system with X-Bridge C18 as stationary phase and tetrabutylammonium bromide in the 0 - 15 mM concentration range as the IPR. Two different mobile phases were used: (i) 15/85 [v/v] acetonitrile/water, (ii) 25/75 methanol/water. The model compounds were sodium salts of organic compounds with sulfonic acid functions. The analytical and preparative elution profiles were obtained for specified conditions. The analytical data were utilized to calculate the difference in electrical potential between the surface and bulk solution using firm electrostatic theory. In the preparative mode in a certain range of IPR concentrations, complicated U-shaped overloaded profiles were observed. In the other considered cases, Langmuir overloaded elution profiles were recorded. A multilayer adsorption model was derived, which is consistent with the dynamic ion exchange models. The model assumes that lipophilic IPR adsorbs on the stationary phase, creating charged active sites that serve as exchange sites for the solutes. The molecules of the solute can adsorb on the already formed IPR layer. It was also assumed that a subsequent layer of solute can form on the formed layer of complexes due to interactions between the solute molecules. The model takes into account the electrostatic attraction and repulsion of the molecules, depending on the considered situation. The proposed model allowed prediction of the overloaded concentration profiles with very good agreement for the model solute and followed the progression from Langmuirian, through U-shaped, to again Langmuirian profiles.

Predictions of overloaded concentration profiles in supercritical fluid chromatography.

Here, overloaded concentration profiles were predicted in supercritical fluid chromatography using a combined two-dimensional heat and mass transfer model. The heat balance equation provided the temperature and pressure profiles inside the column. From this the density, viscosity, and mobile phase velocity profiles in the column were calculated. The adsorption model is here expressed as a function of the density and temperature of the mobile phase. The model system consisted of a Kromasil Diol column packed with 2.2-µm particles (i.e., a UHPSFC column) and the solute was phenol eluted with neat carbon dioxide at three different outlet pressures and five different mobile phase flow rates. The proposed model successfully predicted the eluted concentration profiles in all experimental runs with good agreement even with high-density drops along the column. It could be concluded that the radial temperature and density gradients did not significantly influence the overloaded concentration elution profiles.

Impact of Methanol Adsorption on the Robustness of Analytical Supercritical Fluid Chromatography in Transfer from SFC to UHPSFC.

In supercritical fluid chromatography (SFC), the retention of a solute depends on the temperature, density, pressure, and cosolvent fraction. Here, we investigate how the adsorption of the cosolvent MeOH changes with pressure and temperature and how this affects the retention of several solutes. The lower the pressure, the stronger the MeOH adsorption to the stationary phase; in addition, at low pressure, perturbing the pressure results in significant changes in the amounts of MeOH adsorbed to the stationary phase. The robustness of the solute retention was lowest when operating the systems at low pressures, high temperatures, and low cosolvent fractions in the eluent. Here, we found a clear relationship between the sensitivity of MeOH adsorption to the stationary phase and the robustness of the separation system. Finally, we show that going from classical SFC to ultrahigh-performance SFC (UHPSFC), that is, separations conducted with much smaller packing diameters, results in retention factors that are more sensitive to fluctuations in the flow rate than with traditional SFC. The calculated density profiles indicate only a slight density drop over the traditional SFC column (3%, visualized as lighter → darker blue in the TOC), whereas the drop for the UHPSFC one was considerably larger (20%, visualized as dark red → light green in the TOC). The corresponding temperature drops were calculated to be 0.8 and 6.5 °C for the SFC and UHPSFC systems, respectively. These increased density and temperature drops are the underlying reasons for the decreased robustness of UHPSFC.

Impact of stationary-phase pore size on chromatographic performance using oligonucleotide separation as a model.

A combined experimental and theoretical study was performed to understand how the pore size of packing materials with pores 60-300 Å in size affects the separation of 5-50-mer oligonucleotides. For this purpose, we developed a model in which the solutes were described as thin rods to estimate the accessible surface area of the solute as a function of the pore size and solute size. First, an analytical investigation was conducted in which we found that the selectivity increased by a factor of 2.5 when separating 5- and 15-mer oligonucleotides using packing with 300 Å rather than 100 Å pores. We complemented the analytical investigation by theoretically demonstrating how the selectivity is dependent on the column's accessible surface area as a function of solute size. In the preparative investigation, we determined adsorption isotherms for oligonucleotides using the inverse method for separations of a 9- and a 10-mer. We found that preparative columns with a 60 Å-pore-size packing material provided a 10% increase in productivity as compared with a 300 Å packing material, although the surface area of the 60 Å packing is as much as five time larger.

Evaluating the advantages of higher heat conductivity in a recently developed type of core-shell diamond stationary phase particle in UHPLC.

In recent studies, the nature and magnitude of the temperature gradients developed in ultra-high pressure liquid chromatography (UHPLC), were found to be dependent on the heat conductivity properties of the column matrices, but also, on the principle used for controlling the temperature over the column. Here, we investigated the potential of using highly heat conductive diamond-based stationary phases (85 times higher than silica), for reducing the temperature gradients. The stationary phases investigated were a (i) Diamond Analytics FLARE column, based on particles comprised of a graphite core surrounded by a very thin diamond shell, and two silica hybrid columns: (ii) a core-shell silica Kromasil Eternity Shell column and (iii) a fully porous silica Kromasil Eternity XT column. Models were developed based on two-dimensional heat transfer theory and mass transfer theory, which were used to model the temperature profiles and the migration of an analyte band accounting for column efficiencies at different flow rates. For the silica-based columns, using water-controlled temperature mode, the temperature gradients along the column axes are suppressed whereas temperature gradients in the radial direction prevails resulting in decreased column efficiencies. Using these columns with air-controlled temperature mode, the radial temperature gradients are reduced whereas temperature gradients along the column prevails resulting in decreased retention times. With the Diamond FLARE column, there was no loss in column efficiency using the water-controlled temperature mode and the van Deemter curves are almost identical using both temperature control modes. Thus, for the Diamond FLARE column, in contrast to the silica-based columns, there are almost no losses of column efficiencies due to reduced radial temperature gradients independent on how the column temperature was controlled.

Investigation of robustness for supercritical fluid chromatography separation of peptides: Isocratic vs gradient mode.

We investigated and compared the robustness of supercritical fluid chromatography (SFC) separations of the peptide gramicidin, using either isocratic or gradient elution. This was done using design of experiments in a design space of co-solvent fraction, water mass fraction in co-solvent, pressure, and temperature. The density of the eluent (CO2-MeOH-H2O) was experimentally determined using a Coriolis mass flow meter to calculate the volumetric flow rate required by the design. For both retention models, the most important factor was the total co-solvent fraction and water mass fraction in co-solvent. Comparing the elution modes, we found that gradient elution was more than three times more robust than isocratic elution. We also observed a relationship between the sensitivity to changes and the gradient steepness and used this to draw general conclusions beyond the studied experimental system. To test the robustness in a practical context, both the isocratic and gradient separations were transferred to another laboratory. The gradient elution was highly reproducible between laboratories, whereas the isocratic system was not. Using measurements of the actual operational conditions (not the set system conditions), the isocratic deviation was quantitatively explained using the retention model. The findings indicate the benefits of using gradient elution in SFC as well as the importance of measuring the actual operational conditions to be able to explain observed differences between laboratories when conducting method transfer.

Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using Enantiomeric Separations of Omeprazole and Etiracetam as Models: Feasibility of Taguchi Empirical Optimization.

The overreaching purpose of this study is to evaluate new approaches for determining the optimal operational and column conditions in chromatography laboratories, i.e., how best to select a packing material of proper particle size and how to determine the proper length of the column bed after selecting particle size. As model compounds, we chose two chiral drugs for preparative separation: omeprazole and etiracetam. In each case, two maximum allowed pressure drops were assumed: 80 and 200 bar. The processes were numerically optimized (mechanistic modeling) with a general rate model using a global optimization method. The numerical predictions were experimentally verified at both analytical and pilot scales. The lower allowed pressure drop represents the use of standard equipment, while the higher allowed drop represents more modern equipment. For both compounds, maximum productivity was achieved using short columns packed with small-particle size packing materials. Increasing the allowed backpressure in the separation leads to an increased productivity and reduced solvent consumption. As advanced numerical calculations might not be available in the laboratory, we also investigated a statistically based approach, i.e., the Taguchi method (empirical modeling), for finding the optimal decision variables and compared it with advanced mechanistic modeling. The Taguchi method predicted that shorter columns packed with smaller particles would be preferred over longer columns packed with larger particles. We conclude that the simpler optimization tool, i.e., the Taguchi method, can be used to obtain "good enough" preparative separations, though for accurate processes, optimization, and to determine optimal operational conditions, classical numerical optimization is still necessary.

Estimation of Nonlinear Adsorption Isotherms in Gradient Elution RP-LC of Peptides in the Presence of an Adsorbing Additive.

ABSTRACT: In electrostatic repulsive interaction chromatography, using a charged surface hybrid sorbent carrying positive charges can improve the peak shape of peptides in reversed-phase liquid chromatography (RP-LC), especially in overloaded conditions, compared with standard C18 sorbents. However, the positive surface charges can interact with anionic additives commonly used in peptide separations, e.g., trifluoroacetic acid (TFA), complicating adsorption isotherm estimation. We investigated how the competition for available adsorption sites between TFA and two peptides influenced the adsorption isotherm in gradient elution. A model accounting for the competition with TFA was compared with a model neglecting TFA adsorption. We found that the two models predicted elution profiles with the same accuracy. We also found that the adsorption isotherms were extremely similar in shape, leading to the conclusion that neglecting the competition with TFA is a valid approximation enabling faster and more robust adsorption isotherm estimation for the studied type of sorbent.

The importance of ion-pairing in peptide purification by reversed-phase liquid chromatography.

The adsorption mechanism for three peptides was studied under overloaded conditions through adsorption isotherm measurements in the presence of an ion-pairing reagent, trifluoroacetic acid (TFA), on an end-capped C18-bonded stationary phase. The overall aim of the study was to obtain a better understanding of how the acetonitrile and the TFA fractions in the eluent affected the overloaded elution profiles and the selectivity between peptides using mechanistic modelling and multivariate design of experiments. When studying the effect of TFA, direct evidence for ion pair formation between a peptide and TFA in acetonitrile-water solutions was provided by fluorine-proton nuclear Overhauser NMR enhancement experiments and the adsorption of TFA on the stationary phase was measured by frontal analysis. The adsorption isotherms for each peptide were then determined by the inverse method at eight TFA concentrations ranging from 2.6mM to 37.3mM (0.02-0.29vol-%) in isocratic elution. The equilibrium between the peptide ion and the peptide-TFA complex was modelled by coupling the mass-balance to reaction kinetics and determining separate adsorption isotherms for the two species. We found that a Langmuir isotherm described the elution profile of peptide-TFA complex well while the peptide ion was described by a bi-Langmuir adsorption isotherm since it exhibited strong secondary interactions. The elution profiles had an unfavorable shape at low TFA concentrations consisting of a spike in their front and a long tailing rear due to the secondary interactions for the peptide ion having very low saturation capacity. The acetonitrile dependence on the adsorption isotherms was studied by determination of adsorption isotherms directly from elution profiles obtained in gradient elution which enabled a broad acetonitrile interval to be studied. Here, it was found that the column saturation capacity was quickly reached at very low acetonitrile fractions and that there were significant variations in adsorption with the molecular weight. Finally, practical implications for method development are discussed based on an experimental design where gradient slope and TFA concentrations are used as factors.

A practical approach for predicting retention time shifts due to pressure and temperature gradients in ultra-high-pressure liquid chromatography.

Large pressure gradients are generated in ultra-high-pressure liquid chromatography (UHPLC) using sub-2µm particles causing significant temperature gradients over the column due to viscous heating. These pressure and temperature gradients affect retention and ultimately result in important selectivity shifts. In this study, we developed an approach for predicting the retention time shifts due to these gradients. The approach is presented as a step-by-step procedure and it is based on empirical linear relationships describing how retention varies as a function of temperature and pressure and how the average column temperature increases with the flow rate. It requires only four experiments on standard equipment, is based on straightforward calculations, and is therefore easy to use in method development. The approach was rigorously validated against experimental data obtained with a quality control method for the active pharmaceutical ingredient omeprazole. The accuracy of retention time predictions was very good with relative errors always less than 1% and in many cases around 0.5% (n=32). Selectivity shifts observed between omeprazole and the related impurities when changing the flow rate could also be accurately predicted resulting in good estimates of the resolution between critical peak pairs. The approximations which the presented approach are based on were all justified. The retention factor as a function of pressure and temperature was studied in an experimental design while the temperature distribution in the column was obtained by solving the fundamental heat and mass balance equations for the different experimental conditions. We strongly believe that this approach is sufficiently accurate and experimentally feasible for this separation to be a valuable tool when developing a UHPLC method. After further validation with other separation systems, it could become a useful approach in UHPLC method development, especially in the pharmaceutical industry where demands are high for robustness and regulatory oversight.

Combining Chemometric Models with Adsorption Isotherm Measurements to Study Omeprazole in RP-LC.

The adsorption of the proton-pump inhibitor omeprazole was investigated using RP-LC with chemometric models combined with adsorption isotherm modelling to study the effect of pH and type of organic modifier (i.e., acetonitrile or methanol). The chemometric approach revealed that omeprazole was tailing with methanol and fronting with acetonitrile along with increased fronting at higher pH. The increased fronting with higher pH for acetonitrile was explored using a pH-dependent adsorption isotherm model that was determined using the inverse method and it agreed well with the experimental data. The model indicated that the peaks exhibit more fronting at high pH due to a larger fraction of charged omeprazole molecules. This model could accurately predict the shape of elution profiles at arbitrary pH levels in the studied interval. Using a two-layer adsorption isotherm model, the difference between acetonitrile and methanol was studied at the lowest pH at which almost all omeprazole molecules are neutral. Omeprazole had adsorbate-adsorbate interactions that were similar in strength for the acetonitrile and methanol mobile phases, while the solute-adsorbent interactions were almost twice as strong with methanol. The difference in the relative strengths of these two interactions likely explains the different peak asymmetries (i.e., tailing/fronting) in methanol and acetonitrile. In conclusion, thermodynamic modelling can complement chemometric modeling in HPLC method development and increase the understanding of the separation.

Choice of Model for Estimation of Adsorption Isotherm Parameters in Gradient Elution Preparative Liquid Chromatography.

The inverse method is a numerical method for fast estimation of adsorption isotherm parameters directly from a few overloaded elution profiles and it was recently extended to adsorption isotherm acquisition in gradient elution conditions. However, the inverse method in gradient elution is cumbersome due to the complex adsorption isotherm models found in gradient elution. In this case, physicochemically correct adsorption models have very long calculation times. The aim of this study is to investigate the possibility of using a less complex adsorption isotherm model, with fewer adjustable parameters, but with preserved/acceptable predictive abilities. We found that equal or better agreement between experimental and predicted elution profiles could be achieved with less complex models. By being able to select a model with fewer adjustable parameters, the calculation times can be reduced by at least a factor of 10.

Method transfer from high-pressure liquid chromatography to ultra-high-pressure liquid chromatography. II. Temperature and pressure effects.

The importance of the generated temperature and pressure gradients in ultra-high-pressure liquid chromatography (UHPLC) are investigated and compared to high-pressure liquid chromatography (HPLC). The drug Omeprazole, together with three other model compounds (with different chemical characteristics, namely uncharged, positively and negatively charged) were used. Calculations of the complete temperature profile in the column at UHPLC conditions showed, in our experiments, a temperature difference between the inlet and outlet of 16 °C and a difference of 2 °C between the column center and the wall. Through van't Hoff plots, this information was used to single out the decrease in retention factor (k) solely due to the temperature gradient. The uncharged solute was least affected by temperature with a decrease in k of about 5% while for charged solutes the effect was more pronounced, with k decreases up to 14%. A pressure increase of 500 bar gave roughly 5% increase in k for the uncharged solute, while omeprazole and the other two charged solutes gave about 25, 20 and 15% increases in k, respectively. The stochastic model of chromatography was applied to estimate the dependence of the average number of adsorption/desorption events (n) and the average time spent by a molecule in the stationary phase (τs) on temperature and pressure on peak shape for the tailing, basic solute. Increasing the temperature yielded an increase in n and decrease in τs which resulted in less skew at high temperatures. With increasing pressure, the stochastic modeling gave interesting results for the basic solute showing that the skew of the peak increased with pressure. The conclusion is that pressure effects are more pronounced for both retention and peak shape than the temperature effects for the polar or charged compounds in our study.

Method transfer from high-pressure liquid chromatography to ultra-high-pressure liquid chromatography. I. A thermodynamic perspective.

This is the first investigation in a series that aims to enhance the scientific knowledge needed for reliable analytical method transfer between HPLC and UHPLC using the quality by design (QbD) framework. Here, we investigated the differences and similarities from a thermodynamic point of view between RP-LC separations conducted with 3.5µm (HPLC) and 1.7µm (UHPLC) C18 particles. Three different model solutes and one pharmaceutical compound were used: the uncharged cycloheptanone, the cationic benzyltriethylammonium chloride, the anionic sodium 2-naphatlene sulfonate and the pharmaceutical compound omeprazole, which was anionic at the studied pH. Adsorption data were determined for the four solutes at varying fractions of organic modifier and in gradient elution in both the HPLC and UHPLC system, respectively. From the adsorption data, the adsorption energy distribution of each compound was calculated and the adsorption isotherm model was estimated. We found that the adsorption energy distribution was similar, with only minor differences in degree of homogeneity, for HPLC and UHPLC stationary phases. The adsorption isotherm model did not change between HPLC and UHPLC, but the parameter values changed considerably especially for the ionic compounds. The dependence of the organic modifier followed the same trend in HPLC as in UHPLC. These results indicates that the adsorption mechanism of a solute is the same on HPLC and UHPLC stationary phases which simplifies design of a single analytical method applicable to both HPLC and UHPLC conditions within the QbD framework.

Fast estimation of adsorption isotherm parameters in gradient elution preparative liquid chromatography II: the competitive case.

Experimental competitive adsorption isotherms were successfully determined directly from overloaded elution profiles in gradient elution mode using an extended inverse method. This approach differs from the existing methods in one important aspect - no isocratic experiments are necessary which makes it possible to study adsorption of substances whose retention factors vary strongly with the mobile-phase composition. The approach was verified with simulated binary data and with experimental data from gradient separations of a cyclohexanone/cycloheptanone mixture. For the synthetic data, the original adsorption isotherm parameters were found using a two-step estimation procedure. In the first step analytical peaks were used to estimate the "analytical" part of the Langmuir equation and in the second step the association equilibrium parameters were estimated from two simulated overloaded elution profiles. For the experimental data, a three-step approach was used. The two first steps were used to reduce the calculation time so that parameter estimation could be performed on an ordinary computer. In the first step, analytical peaks were used to estimate the "analytical" part of the bi-Langmuir equation. In the second step, initial guesses for all other parameters were determined separately for each solute using the faster Rouchon algorithm. In the final and third step, the more accurate orthogonal collocation on finite elements algorithm, was used to fine-tune the isotherm parameters. The model could accurately predict the shape of overloaded elution profiles. The shape of the adsorption isotherms agreed well with those determined with the standard isocratic method, although the numerical values were not the same. The extended inverse method is well suited for process optimization where few experiments and accurate predictions are important.

Modelling of retention in analytical supercritical fluid chromatography for CO2-Methanol mobile phase.

Mathematical modelling of the chromatography process requires knowledge of the isotherm model. Therefore a necessary step in calculations is estimation of the isotherm model parameters. In this study the inverse method has been successfully used to estimate the linear isotherm model parameters in supercritical fluid chromatography (SFC). Estimation was based on measured retention times of experimental band profiles. The solute was n-octadecylbenzene. The mobile phase was carbon dioxide-methanol, 95/5% (v/v), and the column was 250mm×4.6mm i.d. packed with 5-micron Luna C18(2) particles. The experiments were done for outlet pressures from 100bar to 150bar at different flow rates and different sets of experimental conditions: (1) column operated under convective air (CA); (2) column operated in still air conditions. Moreover in the latter thermal mode were considered two cases. In the first case the temperature of the oven air was different from the inlet temperature of the mobile phase. In the second case the temperature of the oven air was the same as inlet temperature of the mobile phase. The column efficiency was also analysed.

Fast estimation of adsorption isotherm parameters in gradient elution preparative liquid chromatography. I: the single component case.

The inverse method is a numeric method for fast estimation of adsorption isotherm parameters directly from overloaded elution profiles. However, it has previously only been used for isocratic experiments. Here we will extend the inverse method so it can be used for gradient elution too. This extended inverse method will make it possible to study the adsorption of substances whose retention factor vary strongly with the mobile-phase composition, like peptides and proteins, where the classic methods will fail. Our extended inverse method was verified using both simulations and real experiments. For simulated overloaded elution profiles we were able to determine almost exact Langmuir adsorption isotherm parameters with the new approach. From real experimental data, bi-Langmuir adsorption parameters were estimated using both the perturbation peak method and the extended inverse method. The shape of the acquired adsorption isotherms did match over the considered concentration range; however, the adsorption isotherm parameters found with the two methods were not the same. This is probably due to the fact that adsorption isotherm estimated with the inverse method is only a good approximation up to the highest eluted concentration in the used chromatograms. But this is not a serious drawback from a process point of view where the main objective is to make accurate predictions of elution profiles. The bi-Langmuir adsorption isotherm obtained with both methods could accurately predict the shape of overloaded elution profiles.