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Ion-pair chromatography is the de facto standard for separating oligonucleotides and related impurities, particularly for analysis but also often for small-scale purification. Currently, there is limited understanding of the quantitative modeling of both analytical and overloaded elution profiles obtained during gradient elution in ion-pair chromatography. Here we will investigate a recently introduced gradient mode, the so-called ion-pairing reagent gradient mode, for both analytical and overloaded separations of oligonucleotides. The first part of the study demonstrates how the electrostatic theory of ion-pair chromatography can be applied for modeling gradient elution of oligonucleotides. When the ion-pair gradient mode is used in a region where the electrostatic surface potential can be linearized, a closed-form expression of retention time can be derived. A unified retention model was then derived, applicable for both ion-pair reagent gradient mode as well as co-solvent gradient mode. The model was verified for two different experimental systems and homo- and heteromeric oligonucleotides of different lengths. Quantitative modeling of overloaded chromatography using the ion-pairing reagent gradient mode was also investigated. Firstly, a unified adsorption isotherm model was developed for both gradient modes. Then, adsorption isotherms parameter of a model oligonucleotide and two major synthetic impurities were estimated using the inverse method. Secondly, the parameters of the adsorption isotherm were then used to investigate how the productivity of oligonucleotide varies with injection volume, gradient slope, and initial retention factor. Here, the productivity increased when using a shallow gradient slope combined with a low initial retention factor. Finally, experiments were conducted to confirming some of the model predictions. Comparison with the conventional co-solvent gradient mode showed that the ion-pairing reagent gradient leads to both higher yield and productivity while consuming less co-solvent.

Tributylamine (TBuA) and triethylamine (TEtA) are the most commonly used ion pair reagents in ion pair chromatography especially for the analysis of oligonucleotides. In order to improve the understanding of the retention and separation mechanism of oligonucleotides in ion pair chromatography, it is important to understand the retention mechanism and the nature of interaction of these ion pair reagents with the stationary phase in the chromatographic column. Adsorption isotherm is helpful in evaluating such interactions, and subsequently predicting the retention mechanism. Alkylamines are very polar molecules which lack suitable chromophore and are commonly present in charged forms. Therefore, their determination and the subsequent acquisition of their adsorption isotherms using traditional liquid chromatography is very difficult. In this study, we first developed an analytical method for the determination of TBuA and TEtA in a typical chromatographic mobile phase (acetonitrile-water) and then used the same method to acquire the adsorption isotherms for tributylammonium acetate (TBuAA) and triethylammonium acetate (TEtAA). This method started with the conversion of the alkylammonium ions to free neutral forms by treating the sample with a strong base, followed by pentane-mediated extraction and finally the analysis of the extracts using gas chromatography-flame ionization detector (GC-FID). This three-step method was validated for parameters like range, linearity, intra-day and inter-day precision and accuracy, limit of detection and limit of quantitation. For the adsorption isotherms, the C18 column was first equilibrated with the solutions having different concentrations of alkylammonium ions and then stripped with eluent devoid of alkylammonium ions. Several stripping eluents were investigated and it was discovered that the eluent requirement could be decreased by the addition of sodium chloride. The effluents from the stripping phase were collected and analyzed using the developed analytical method to acquire the adsorption data. Under the investigated conditions, adsorption of TBuAA and TEtAA showed type III and type I isotherm behavior respectively.

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, Leśko 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.

The traditional approach for analyzing interaction data from biosensors instruments is based on the simplified assumption that also larger biomolecules interactions are homogeneous. It was recently reported that the human receptor angiotensin-converting enzyme 2 (ACE2) plays a key role for capturing SARS-CoV-2 into the human target body, and binding studies were performed using biosensors techniques based on surface plasmon resonance and bio-layer interferometry. The published affinity constants for the interactions, derived using the traditional approach, described a single interaction between ACE2 and the SARS-CoV-2 receptor binding domain (RBD). We reanalyzed these data sets using our advanced four-step approach based on an adaptive interaction distribution algorithm (AIDA) that accounts for the great complexity of larger biomolecules and gives a two-dimensional distribution of association and dissociation rate constants. Our results showed that in both cases the standard assumption about a single interaction was erroneous, and in one of the cases, the value of the affinity constant K-D differed more than 300% between the reported value and our calculation. This information can prove very useful in providing mechanistic information and insights about the mechanism of interactions between ACE2 and SARS-CoV-2 RBD or similar systems.

Support vector regression models are created and used to predict the retention times of oligonucleotides separated using gradient ion-pair chromatography with high accuracy. The experimental dataset consisted of fully phosphorothioated oligonucleotides. Two models were trained and validated using two pseudo orthogonal gradient modes and three gradient slopes. The results show that the spread in retention time differs between the two gradient modes, which indicated varying degree of sequence dependent separation. Peak widths from the experimental dataset were calculated and correlated with the guanine cytosine content and retention time of the sequence for each gradient slope. This data was used to predict the resolution of the n - 1 impurity among 250 0 0 0 random 12-and 16-mer sequences; showing one of the investigated gradient modes has a much higher probability of exceeding a resolution of 1.5, particularly for the 16-mer sequences. Sequences having a high guanine-cytosine content and a terminal C are more likely to not reach critical resolution. The trained SVR models can both be used to identify characteristics of different separation methods and to assist in the choice of method conditions, i.e. to optimize resolution for arbitrary sequences. The methodology presented in this study can be expected to be applicable to predict retention times of other oligonucleotide synthesis and degradation impurities if provided enough training data.

Oligonucleotide drugs represent an emerging area in the pharmaceutical industry. Solid-phase synthesis generates many structurally closely related impurities, making efficient separation systems for purification and analysis a key challenge during pharmaceutical drug development. To increase the fundamental understanding of the important preparative separation step, mass-overloaded injections of a fully phosphorothioated 16mer, i.e., deoxythymidine oligonucleotide, were performed on a C18 and a phenyl column. The narrowest elution profiles were obtained using the phenyl column, and the 16mer could be collected with high purity and yield on both columns. The most likely contribution to the successful purification was the quantifiable displacement of the early-eluting shortmers on both columns. In addition, the phenyl column displayed better separation of later-eluting impurities, such as the 17mer impurity. The mass-overloaded injections resulted in classical Langmuirian elution profiles on all columns, provided the concentration of the ion-pairing reagent in the eluent was sufficiently high. Two additional column chemistries, C4 and C8, were also investigated in terms of their selectivity and elution profile characteristics for the separation of 5–20mers fully phosphorothioated deoxythymidine oligonucleotides. When using triethylamine as ion-pairing reagent to separate phosphorothioated oligonucleotides, we observed peak broadening caused by the partial separation of diastereomers, predominantly seen on the C4 and C18 columns. When using the ion-pair reagent tributylamine, to suppress diastereomer separation, the greatest selectivity was found using the phenyl column followed by C18. The present results will be useful when designing and optimizing efficient preparative separations of synthetic oligonucleotides. Electronic supplementary material The online version of this article (10.1007/s00216-019-02236-9) contains supplementary material, which is available to authorized users.

Thermal imaging was used to visualise axial temperature gradients in chromatography columns running solvents of water, methanol and acetonitrile at various compositions. The non-monotonic relationship between solvent composition and viscosity enabled the testing of solvent conditions with equivalent viscosities, but with different percentages of water. It was observed that at equivalent power the increase in water composition leads to an increase in the magnitude of the axial temperature gradients (ΔTA). Observing the change in temperature at defined points (ΔTP) with increasing power indicates that the relationship between ΔTP and power is not linear but deviates at higher power. The degree of this deviation depends on what point along the column axis is observed as well what solvent composition is used. Being able to monitor the entire length of the column using thermography also allowed for the observation of different rates of heat transfer through to the bulky stainless steel end fittings from solvent to solvent. Revealing that water is able to transfer heat to the stainless steel surface in such a way that the temperature profile of transition point between columns to end fitting is more gradual compared to when methanol or acetonitrile is used. This evidence plus video data collected indicates that at constant flow rate an equilibrium between heat generated and heat dissipated through the stainless steel is formed, which differs from solvent to solvent. Moreover any disruption to this equilibrium, i.e. a change in flow rate will momentarily change the shape of the temperature profile.

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.

A B S T R A C T Here it was investigated how oligonucleotide retention and selectivity factors are affected by electrostatic and non-electrostatic interactions in ion pair chromatography. A framework was derived describing how selectivity depends on the electrostatic potential generated by the ion-pair reagent concentration, co-solvent volume fraction, charge difference between the analytes, and temperature. Isocratic experiments verified that, in separation problems concerning oligonucleotides of different charges, selectivity increases with increasing surface potential and analyte charge difference and with decreasing co-solvent volume fraction and temperature. For analytes of the same charge, for example, diastereomers of phosphorothioated oligonucleotides, selectivity can be increased by decreasing the co-solvent volume fraction or the temperature and has only a minor dependency on the ion-pairing reagent concentration. An important observation is that oligonucleotide retention is driven predominantly by electrostatic interaction generated by the adsorption of the ion-pairing reagent. We therefore compared classical gradient elution in which the co-solvent volume fraction increases over time versus gradient elution with a constant co-solvent volume fraction but with decreasing ion-pair reagent concentration over time. Both modes decrease the electrostatic potential. Oligonucleotide selectivity was found to increase with decreasing ion pairing reagent concentration. The two elution modes were finally applied to two different model anti sense oligonucleotide separation problems, and it was shown that the ion-pair reagent gradient increases the selectivity of non-charge & ndash;based separation problems while maintaining charge-difference & ndash;based selectivity. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

A strategy to match any retention shifts due to increased or decreased pressure drop during supercritical fluid chromatography (SFC) method transfer is presented. The strategy relies on adjusting the co-solvent molarity without the need to adjust the back-pressure regulator. Exact matching can be obtained with minimal changes in separation selectivity. To accomplish this, we introduce the isomolar plot approach, which shows the variation in molar co-solvent concentration depending on the mass fraction of co-solvent, pressure, and temperature, here exemplified by CO2–methanol. This plot allowed us to unify the effects of the co-solvent mass fraction and density on retention in SFC. The approach, which was verified on 12 known empirical retention models for each enantiomer of six basic pharmaceuticals, allowed us to numerically calculate the apparent retention factor for any column pressure drop. The strategy can be implemented either using a mechanistic approach if retention models are known or empirically by iteratively adjusting the co-solvent mass fraction. As a rule of thumb for the empirical approach, we found that the relative mass fraction adjustment needed is proportional to the relative change in the retention factor caused by a change in the pressure drop. Different proportionality constants were required to match retention in the case of increasing or decreasing pressure drops.

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.

The fundamental aspects to be considered during method transfer in supercritical fluid chromatography (SFC) are reviewed. The review is limited to mobile phases, stationary phases, and operating conditions generally encountered in current practice. First, the fundamentals of retention in SFC will be explored in relation to fluid composition, co-solvent adsorption to the stationary phase, pressure, and temperature. Second, considerations regarding predictable method transfer will be discussed in relation to instrumentation, columns, retention shifts, and method robustness. This review is not intended to be comprehensive but rather to highlight important issues for understanding and performing reliable method transfer and to give practical guidelines relating to the fundamentals covered.

A combined experimental and theoretical study was performed to understand how the pore size of packing materials with pores 60-300 angstrom 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 angstrom rather than 100 angstrom 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 angstrom-pore-size packing material provided a 10% increase in productivity as compared with a 300 A packing material, although the surface area of the 60 angstrom packing is as much as five time larger.

The impact of eluent components added to improve separation performance in supercritical fluid chromatography was systematically, and fundamentally, investigated. The model system comprised basic pharmaceuticals as solutes and eluents containing three amines (i.e., triethylamine, diethylamine, and isopropylamine) as additives with MeOH as the co-solvent. First, an analytical-scale study was performed, systematically investigating the impact of the additives/co-solvent on solute peak shapes and retentions, using a design of experiments approach; here, the total additive concentration in the eluent ranged between 0.021 and 0.105 % (v/v) and the total MeOH fraction in the eluent between 16 and 26 % (v/v). The co-solvent fraction was found to be the most efficient tool for adjusting retentions, whereas the additive fraction was the prime tool for improving column efficiency and peak analytical performance. Next, the impacts of the amine additives on the shapes of the so-called overloaded solute elution profiles were investigated. Two principal types of preparative peak deformations appeared and were investigated in depth, analyzed using computer simulation with mechanistic modeling. The first type of deformation was due to the solute eluting too close to the additive perturbation peak, resulting in severe peak deformation caused by co-elution. The second type of deformation was also due to additive–solute interactions, but here the amine additives acted as kosmotropic agents, promoting the multilayer adsorption to the stationary phase of solutes with bulkier aryl groups. This article was published as manuscript in Emelie Glennes PhD dissertation.

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 degrees C for the SFC and UHPSFC systems, respectively. These increased density and temperature drops are the underlying reasons for the decreased robustness of UHPSFC. Artikeln ingick som manuskript i Glennes doktorsavhandling (2019), då med titeln: Impact of Methanol Adsorption on Robustness in Supercritical Fluid Chromatography

A protocol was developed for the visualisation of axial temperature gradients on a Kinetex column (1.3 μm C18 100 A 50 × 2.1 mm) operated at near maximum pressure of the system (Pmax) using an infrared camera. Real time viscous frictional heating effects across the entire column length was observed, and showed that with increasing flow rate there was an increase in the maximum temperature of the column, and the difference between the inlet and outlet temperatures. Temperature profile data over the entire length of the column revealed the dynamics of heat exchange processes along different parts of the column, and raises the question on potential heating effects on eluents. The axial temperature gradients of eluents such as pure methanol, isopropyl alcohol and acetonitrile near Pmax were compared; finding that acetonitrile which had the highest flow velocity at Pmax gave the highest overall temperature increase for these eluents.

Strangely shaped overloaded bands were recently reported using a standard supercritical fluid chromatographic system comprising a diol column as the stationary phase and carbon dioxide with methanol as the mobile phase. Some of these overloaded elution profiles appeared strongly deformed and even had "anti-Langmuirian" shapes although their solute compounds had "Langmuirian" adsorption. To obtain a more complete understanding of the generality of these effects, the investigation was expanded to cover also other common co-solvents, such as ethanol, 2-propanol, and acetonitrile, as well as various stationary phase materials, such as silica, and 2-ethylpyridine. From this expanded study it could be confirmed that the effects of deformed overloaded solute band shapes, due to co-solvent adsorption, is general phenomena in supercritical fluid chromatographic. It could also be concluded that these effects as well as previously observed "solvent effects" or "plug effects" are entirely due to competition between the solute and solvent molecules for the adsorption sites on the stationary phase surface. Finally, guidelines were given for how to evaluate the risk of deformations occurring for a given solvent-column combination, based simply on testing retention times of solutes and co-solvent.

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.

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.

The phenomenon known as viscous fingering has been shown to be very detrimental to separation performance in preparative and size exclusion chromatography, and also in multidimensional HPLC. However, there are few reports of viscous fingering in analytical scale high performance liquid chromatography (HPLC), despite samples very often being introduced to the analytical-size HPLC columns in a solvent have a substantially different viscosity than the mobile phase. With this study we aim at first hand to investigate if viscous fingering or any similar and related effects to these in preparative levels also take place in analytical scale HPLC and if so, what impact this have on the separation performance. We could show that not only viscous finger does occur in analytical scale columns but also that peak distortions are apparent already at viscosity ratios between eluent and sample solution approaching unity. The latter indicates that a pre-viscous phenomenon is occurring that could be more important than the viscous fingering itself at the analytical format. As the viscosity contrast increases, the leading edge of the sample band distorts and the band volume increases, both leading to a decrease in performance.

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.

A strategy for determining a suitable solvent gradient in silico in preparative peptide separations is presented. The strategy utilizes a machine-learning-based method, called ELUDE, for peptide retention time predictions based on the amino acid sequences of the peptides. A suitable gradient is calculated according to linear solvent strength theory by predicting the retention times of the peptides being purified at three different gradient slopes. The advantage of this strategy is that fewer experiments are needed to develop a purification method, making it useful for labs conducting many separations but with limited resources for method development. The preparative separation of met-enkephalin and leu-enkephalin was used as model solutes on two stationary phases: XBridge C18 and CSH C18. The ELUDE algorithm contains a support vector regression and is pre-trained, meaning that only 10-50 peptides are needed to calibrate a model for a certain stationary phase and gradient. The calibration is done once and the model can then be used for new peptides similar in size to those in the calibration set. We found that the accuracy of the retention time predictions is good enough to usefully estimate a suitable gradient and that it was possible to compare the selectivity on different stationary phases in silico. The absolute relative errors in retention time for the predicted gradients were 4.2% and 3.7% for met-enkephalin and leu-enkephalin, respectively, on the XBridge C18 column and 2.0% and 2.8% on the CSH C18 column. The predicted retention times were also used as initial values for adsorption isotherm parameter determination, facilitating the numerical calculation of overloaded elution profiles. Changing the trifluoroacetic acid (TFA) concentration from 0.05% to 0.15% in the eluent did not seriously affect the error in the retention time predictions for the XBridge C18 column, an increase of 1.0 min (in retention factor, 1.3). For the CSH C18 column the error was, on average, 2.6 times larger. This indicates that the model needs to be recalibrated when changing the TFA concentration for the CSH column. Studying possible scale-up complications from UHPLC to HPLC such as pressure, viscous heating (i.e., temperature gradients), and stationary-phase properties (e.g., packing heterogeneity and surface chemistry) revealed that all these factors were minor to negligible. The pressure effect had the largest effect on the retention, but increased retention by only 3%. In the presented case, method development can therefore proceed using UHPLC and then be robustly transferred to HPLC.

This study presents a systematic investigation of factors influencing the chromatographic separation of diastereomers of phosphorothioated pentameric oligonucleotides as model solutes. Separation was carried out under ion-pairing conditions using an XBridge C18 column. For oligonucleotides with a single sulfur substitution, the diastereomer selectivity was found to increase with decreasing carbon chain length of the tertiary alkylamine used as an ion-pair reagent. Using an ion-pair reagent with high selectivity for diastereomers, triethylammonium, it was found the selectivity increased with decreased ion-pair concentration and shallower gradient slope. Selectivity was also demonstrated to be dependent on the position of the modified linkage. Substitutions at the center of the pentamer resulted in higher diastereomer selectivity compared to substitutions at either end. For mono-substituted oligonucleotides, the retention order and stereo configuration were consistently found to be correlated, with Rp followed by Sp, regardless of which linkage was modified. The type of nucleobase greatly affects the observed selectivity. A pentamer of cytosine has about twice the diastereomer selectivity of that of thymine. When investigating the retention of various oligonucleotides eluted using tributylammonium as the ion-pairing reagent, no diastereomer selectivity could be observed. However, retention was found to be dependent on both the degree and position of sulfur substitution as well as on the nucleobase. When analyzing fractions collected in the front and tail of overloaded injections, a significant difference was found in the ratio between Rp and Sp diastereomers, indicating that the peak broadening observed when using tributylammonium could be explained by partial diastereomer separation. Electronic supplementary material The online version of this article (10.1007/s00216-019-01813-2) contains supplementary material, which is available to authorized users.

In supercritical fluid chromatography (SFC) the mobile phase comprises of carbon dioxide (CO2) as main solvent and smaller amounts of an organic polar solvent (often an alcohol) as co-solvent. The co-solvent is considered to function by changing the overall polarity of the eluent, i.e. by acting as a “modifier”. However, recent studies indicate that the co-solvent methanol can also adsorb to some common SFC stationary phases. Hence, the co-solvent should also be able to function as an “adsorbing additive”, i.e. an eluent component that competes with the injected solutes about the stationary phase surface. In this study it was found by fitting different mechanistic models to systematic experimental data, that the co-solvent methanol can have both functions: at low co-solvent fractions, methanol acts as an additive whereas at larger fractions it acts as a modifier. Moreover, it was found that when the co-solvent adsorbs more strongly to the stationary phase than the solute, “bizarre” deformations of the preparative band shapes can occur. This is illustrated by a solute that converts from a normal “Langmuirian” band shape to an “anti-Langmuirian” shape when changing from neat carbon dioxide (CO2) to an eluent containing co-solvent. This peak shape transition is dependent on both (i) the relative retention of the solute and co-solvent to the stationary phase in eluent containing neat CO2 and on (ii) the relative retention of the additive perturbation peak and the solute peak in eluent containing also co-solvent.

A fundamental investigation of the pressure effect on individual adsorption sites was undertaken based on adsorption energy distribution and adsorption isotherm measurements. For this purpose, we measured adsorption equilibrium data at pressures ranging from 100 to 1000bar at constant flow and over a wide concentration range for three low-molecular-weight solutes, antipyrine, sodium 2-naphthalenesulfonate, and benzyltriethylammonium chloride, on an Eternity C18 stationary phase. The adsorption energy distribution was bimodal for all solutes, remaining clearly so at all pressures. The bi-Langmuir model best described the adsorption in these systems and two types of adsorption sites were identified, one with a low and another with a high energy of interaction. Evidence exists that the low-energy interactions occur at the interface between the mobile and stationary phases and that the high-energy interactions occur nearer the silica surface, deeper in the C18 layer. The contribution of each type of adsorption site to the retention factor was calculated and the change in solute molar volume from the mobile to stationary phase during the adsorption process was estimated for each type of site. The change in solute molar volume was 2-4 times larger at the high-energy site, likely because of the greater loss of solute solvation layer when penetrating deeper into the C18 layer. The association equilibrium constant increased with increasing pressure while the saturation capacity of the low-energy site remained almost unchanged. The observed increase in saturation capacity for the high-energy site did not affect the column loading capacity, which was almost identical at 50- and 950-bar pressure drops over the column.

In this review we discuss how viscosity contrasts between the injection plug and the mobile phase may lead to loss in separation performance, especially in UHPLC columns or SFC environments. Firstly, the wall effect is discussed, and how it can amplify viscosity contrast effects. We then illustrate how viscosity contrasts lead to the phenomenon known as viscous fingering, and we detail the destructive effects of this phenomenon. We expand on the viscous fingering component, however, demonstrating that viscosity contrast effects begin to deteriorate performance long before the conditions are such that viscous fingering occurs. Subtle changes in band-shape are apparent even with very low viscosity contrasts. Lastly we illustrate how viscosity contrast effects lead to severe peak distortions in SFC. Analysts who seek high efficiency separations must make every effort to eliminate, or at least minimise the viscosity contrast between the injection plug and the mobile phase.

An approach for reliable transfer from analytical to preparative scale supercritical fluid chromatography was evaluated. Here, we accounted for the conditions inside the columns as well as to the fact that most analytical instruments are volume-controlled while most preparative scale units are mass-controlled. The latter is a particular problem when performing pilot scale experiments and optimizations prior to scaling up to production scale. This was solved by measuring the mass flow, the pressure and the temperature on the analytical unit using external sensors. Thereafter, it was revealed with a design of experiments approach that the methanol fraction and the pressure are the two most important parameters to control for preserved retention throughout the scale-up; for preserved selectivity the temperature was most important in this particular system. Using this approach, the resulting chromatograms from the preparative unit agreed well with those from the analytical unit while keeping the same column length and particles size. A brief investigation on how the solute elution volume varies with the volumetric flow rate revealed a complex dependency on pressure, density and apparent methanol content. Since the methanol content is a parameter of great importance to control during the scale up, we must be careful when changing operational and column design conditions which generates deviations in pressure, density and methanol content between different columns.

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 (CO

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 Funding textAcknowledgements This work was supported by the Swedish Knowledge Foundation as part of the KKS SYNERGY project 2016 “BIO-QC: Quality Control and Purification for New Biological Drugs” (grant number 20170059) and by the Swedish Research Council (VR) as part of the project “Fundamental Studies on Molecular Interactions aimed at Preparative Separations and Biospecific Measurements” (Grant number 2015-04627). We also thank the National Science Centre, Poland for support via Grant number 2015/18/M/ST8/00349. We are grateful to AstraZeneca and UCB Pharma for kindly giving us omeprazole and etiracetam, respectively, and to Kromasil/Akzo Nobel Pulp and Performance Chemicals AB for giving us the AmyCoat columns.

When using biosensors, analyte biomolecules of several different concentrations are percolated over a chip with immobilized ligand molecules that form complexes with analytes. However, in many cases of biological interest, e.g., in antibody interactions, complex formation steady-state is not reached. The data measured are so-called sensorgram, one for each analyte concentration, with total complex concentration vs time. Here we present a new four-step strategy for more reliable processing of this complex kinetic binding data and compare it with the standard global fitting procedure. In our strategy, we first calculate a dissociation graph to reveal if there are any heterogeneous interactions. Thereafter, a new numerical algorithm, AIDA, is used to get the number of different complex formation reactions for each analyte concentration level. This information is then used to estimate the corresponding complex formation rate constants by fitting to the measured sensorgram one by one. Finally, all estimated rate constants are plotted and clustered, where each cluster represents a complex formation. Synthetic and experimental data obtained from three different QCM biosensor experimental systems having fast (close to steady-state), moderate, and slow kinetics (far from steady-state) were evaluated using the four-step strategy and standard global fitting. The new strategy allowed us to more reliably estimate the number of different complex formations, especially for cases of complex and slow dissociation kinetics. Moreover, the new strategy proved to be more robust as it enables one to handle system drift, i.e., data from biosensor chips that deteriorate over time.

It has been shown that not only the packing homogeneity, but also factors external to the column bed, such as, frits and distributors can have important effects on the column performance. This current communication is the first in a series focusing on the impact of exogenous factors on the column bed heterogeneity. This study is based on several observations by us and others that chromatographic runs often, for technical reasons, include more or less portions of air in the injections. It is therefore extremely important to find out the impact of air on the column performance, the reliability of the results derived from analyses where air was injected, and the effect on the column homogeneity. We used a photographic approach for visualising the air transport phenomena, and found that the air transport through the column is comprised of many different types of transport phenomena, such as laminal flow, viscous fingering like flows, channels and bulbs, and pulsations. More particularly, the air clouds within the column definitely interact in the adsorption, i.e. mobile phase adsorbed to the column surface is displaced. In addition, irrespective of the type of air transport phenomena, the air does not penetrate the column homogeneously. This process is strongly flow dependent. In this work we study air transport both in an analytical scale and a semi-prep column.

The retention behaviour of a homologous series of polyaromatic hydrocarbons was evaluated on two phenyl-type stationary phases in reversed phase supercritical fluid chromatography (SFC). These phas ...

In SFC the sample cannot be dissolved in the mobile phase, so it is often dissolved in pure modifier, or another liquid, sometimes resulting in serious distortions of the eluted peak profiles already at moderately high injection volumes. It is suspected the reasons for these effects are solvent strength mismatch and/or viscosity mismatch. This study presents a systematic and fundamental investigation of the origin of these peak deformations due to the injection solvent effects in SFC, using both systematic experiments and numerical modeling. The first set of experiments proved that the injection volume and the elution strength of the sample solution had a major impact of the shapes of the eluted peaks. Secondly, the sample band elution profile was numerically modeled on a theoretical basis assuming both un-retained and retained co-solvent injection plugs, respectively. These calculations quantitatively confirmed our first set of experiments but also pointed out that there is also an additional significant effect. Third, viscous fingering experiments were performed using viscosity contrast conditions imitating those encountered in SFC. These experiments clearly proved that viscous fingering effects play a significant role. A new method for determination of adsorption isotherms of solvents was also developed, called the “Retention Time Peak Method” (RTPM). The RTPM was used for fast estimation of the adsorption isotherms of the modifier and required using only two experiments.

A selectivity study was undertaken using two types of phenyl-type (Synergi polar RP and Cosmosil 5PBB) stationary phases in supercritical fluid chromatography. The mobile phases used in the SFC environment employed CO2 with methanol as the modifier. These columns were tested using linear polynuclear aromatic hydrocarbons as the test solutes. The retention behaviour of these PAHs in SFC was compared to their behaviour in HPLC and there were very distinct differences. On the Synergi-polar stationary phase the PAH selectivity was highly dependent on the methanol modifier concentration, but in comparison on the Cosmosil column, the selectivity between the members of this PAH test group showed almost no change as a function of the methanol concentration, even though the retentivity on the Cosmosil stationary phase was far greater than the Synergi stationary. In fact, the mobile phase played a very passive role in the separations observed on the Cosmosil stationary phase.

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. Graphical abstract

Preparative chromatography is the best generic method today for the purification of small drugs and valuable chemical components at

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.

The Perturbation Peak (PP) method and Frontal analysis (FA) are considered as the most accurate methods for adsorption isotherms determination in liquid chromatography. In this study we investigate and explain why this is not the case in Supercritical Fluid Chromatography (SFC), where the PP method does not work at all, using a modern analytical system. The main reason was found to be that the solute to be studied must be dissolved in the MeOH reservoir before it is mixed with CO2. Since the solute occupies a certain partial volume in the reservoir, the larger the solute content the larger this fractional volume will be, and the final MeOH fraction in the mobile phase will then be smaller compared to the bulk mobile phase without solute in the modifier. If the retention of small injections on the concentration plateaus, i.e., "analytical-size" perturbation peaks, is sensitive to small variations of MeOH in the eluent, this will seriously decrease the accuracy of the PP method. This effect was verified and compensated for and we also demonstrated that the same problem will occur in frontal analysis, another concentration plateau method.

In this study we investigated how the maximum productivity for commonly used, realistic separation system with a competitive Langmuir adsorption isotherm is affected by changes in column length, packing particle size, mobile phase viscosity, maximum allowed column pressure, column efficiency, sample concentration/solubility, selectivity, monolayer saturation capacity and retention factor of the first eluting compound. The study was performed by generating 1000 random separation systems whose optimal injection volume was determined, i.e., the injection volume that gives the largest achievable productivity. The relative changes in largest achievable productivity when one of the parameters above changes was then studied for each system and the productivity changes for all systems were presented as distributions. We found that it is almost always beneficial to use shorter columns with high pressure drops over the column and that the selectivity should be greater than 2. However, the sample concentration and column efficiency have very limited effect on the maximum productivity. The effect of packing particle size depends on the flow rate limiting factor. If the pumps maximum flow rate is the limiting factor use smaller packing, but if the pressure of the system is the limiting factor use larger packing up to about 40μm.

Adsorption energy distribution (AED) calculations were successfully applied to partial-filling affinity capillary electrophoresis (PF-ACE) to facilitate more detailed studies of biomolecular interactions. PF-ACE with AED calculations was employed to study the interactions between two isoforms of apolipoprotein E (apoE) and dermatan sulfate (DS), and a quartz crystal microbalance (QCM) was used in combination with AED calculations to examine the interactions of the 15-amino-acid peptide fragment of apoE with DS. The heterogeneity of the interactions was elucidated. Microscale thermophoresis was used to validate the results. The interactions studied are of interest because, in vivo, apolipoprotein E localizes on DS-containing regions in the extracellular matrix of human vascular subendothelium. Two-site binding was demonstrated for the isoform apoE3 and DS, but only one-site binding for apoE2-DS. Comparable affinity constants were obtained for the apoE2-DS, apoE3-D3, and 15-amino-acid peptide of apoE-DS using the three techniques. The results show that combining AED calculations with modern biosensing techniques can open up another dimension in studies on the heterogeneity and affinity constants of biological molecules.

In this study, a numerical tool is introduced—based on thermodynamic and kinetic separation theory—for validating the regeneration of monolithic rod columns after cutting their inlet sections. A long-used RP-18e monolithic column was deemed to be unfit for further coffee analysis because of poor separation performance. The columns brownish inlet section was physically removed with a lathe, leaving a clean white inlet section. The original and regenerated columns were extensively analyzed and compared using numerical tools for processing adsorption data. The perturbation peak method was used to measure the adsorption isotherm of phenol on the original and regenerated monolith and the adsorption energy distributions were calculated for identifying any change in the degree of heterogeneity. Although peak shapes improved considerably after regeneration, no significant differences were found in the detailed characterization of the processed adsorption data between the original column and the regenerated one. This indicates that the removal of a section of the monolithic bed can be undertaken without damaging the column and columns in which their inlet head sections are contaminated may still function with normal adsorption behavior. In addition, the combined thermodynamic and kinetic methodology could accurately be used to evaluate any regeneration method of columns.

The need to determine the actual operational conditions, instead of merely using the set operational conditions, was investigated for in packed supercritical fluid chromatography (SFC) by design of experiments (DoE) using a most important type of compounds, pharmaceutical basics, as models. The actual values of temperature, pressure, and methanol levels were recorded and calculated from external sensors, while the responses in the DoE were the retention factors and selectivity. A Kromasil CelluCoat column was used as the stationary phase, carbon dioxide containing varying methanol contents as the mobile phase, and the six racemates of alprenolol, atenolol, metoprolol, propranolol, clenbuterol, and mianserin were selected as model solutes. For the retention modeling, the most important term was the methanol fraction followed by the temperature and pressure. Significant differences (p0.05) between most of the coefficients in the retention models were observed when comparing models from set and actual conditions. The selectivity was much less affected by operational changes, and therefore was not severely affected by difference between set and actual conditions. The temperature differences were usually small, maximum ±1.4°C, whereas the pressure differences were larger, typically approximately +10.5bar. The set and actual fractions of methanol also differed, usually by ±0.4 percentage points. A cautious conclusion is that the primary reason for the discrepancy between the models is a mismatch between the set and actual methanol fractions. This mismatch is more serious in retention models at low methanol fractions. The study demonstrates that the actual conditions should almost always be preferred.

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.

In this study we demonstrate the importance of proper data processing in adsorption isotherm estimations. This was done by investigating and reprocessing data from five cases on two closely related platforms: liquid chromatography (LC) and biosensors. The previously acquired adsorption data were reevaluated and reprocessed using a three-step numerical procedure: (i) preprocessing of adsorption data, (ii) adsorption data analysis and (iii) final rival model fit. For each case, we will discuss what we really measure and what additional information can be obtained by numerical processing of the data. These cases clearly demonstrate that numerical processing of LC and biosensor data can be used to gain deeper understanding of molecular interactions with adsorption media. This is important because adsorption data, especially from biosensors, is often processed using old and simplified methods.

Band deformations might take place for acids and bases in preparative applications and adsorption studies where it is necessary to use overloaded injections. In this study, we focus on how deformations can be prevented without using highly concentrated buffers that may precipitate in the eluent. We have systematically investigated how the elution zones depend on which protolytic form the analyte has when it is dissolved. Basic and acidic model compounds are investigated using eluents with different pH values and the resulting elution profiles are compared when the analytes are dissolved in their protonated and deprotonated form, i.e., in uncharged form or as different kinds of salts. Depending on the analyte's protolytic form, a sample zone is created at the column inlet whose pH deviates, more or less, from the bulk eluent's. If the local adsorption strength in this sample zone is greater than the bulk eluent's, the elution profiles are compressed. Under opposite conditions, the eluted bands are more or less deformed and may even be split; completely different deformations can even take place for different kinds of salt combinations. Explanations of these, and other, effects, together with detailed guidelines for proper sample preparation to avoid peak deformations, are given.

In this study we will demonstrate the potential of modern integrated commercial analytical SFC-systems for rapid and reliable acquisition of thermodynamic data. This will be done by transferring the following adsorption isotherm determination methods from liquid chromatography (LC) to supercritical fluid chromatography (SFC): Elution by Characteristic Points (ECP), the Retention Time Method (RTM), the Inverse Method (IM) and the Perturbation Peak (PP) method. In order to transfer these methods to SFC in a reliable, reproducible way we will demonstrate that careful system verification using external sensors of mass flow, temperature and pressure are needed first. The adsorption isotherm data generated by the different methods were analyzed and compared and the adsorption isotherms ability to predict new experimental elution profiles was verified by comparing experiments with simulations. It was found that adsorption isotherm data determined based on elution profiles, i.e., ECP, IM and RTM, were able to accurately predict overloaded experimental elution profiles while the more tedious and time-consuming PP method, based on small injections on concentration plateaus, failed in doing so.

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.

This study investigates if deeper understanding is achieved when combining nonlinear and linear chromatographic column characterization methods. As test systems, two hybrid columns (Phenomenex Gemini-NX C18 and Kromasil Eternity C18) and one classic one (Kromasil-C18) were selected. The nonlinear methods were based on firm adsorption theory and involved determination of adsorption isotherms followed by calculations with a new numerical tool, adsorption energy distribution, on probe components at different pH values. The linear methods involved the hydrophobic subtraction model and selected probe components retention factors as a function of pH. The combined analysis indicated that both complementary and confirmative information can be achieved regarding the actual model systems.

This study is an in-depth investigation on how numerical optimization strategies that also account for the additive type and concentration, in preparative batch chromatography, should be performed. As a model system, the separation of Z-(R,S)-2-aminobutyric acid enantiomers on a quinidine carbamate-based chiral stationary phase in polar organic mode was used, with different additive strengths of acetic acid or hexanoic acid in methanol. The inverse method was used to determine the competitive adsorption isotherm parameters for the enantiomers and the additives. Three different optimization strategies were examined: (1) injection volume optimization, (2) optimization of injection volume and additive concentration, and (3) full optimization including injection volume, additive concentration, sample concentration and flow rate. It was concluded that (i) it is important to incorporate the additive concentration in the optimization procedure to achieve the highest production rates, (ii) the full optimization strategy had the overall best results, and (iii) the selection of additive is very important (here acetic acid additive was superior to the hexanoic acid additive). By including the additive in the adsorption model and in the numerical optimization it is not only possible to achieve higher production rates but also to properly select the additive that is most advantageous for the specific separation problem.