This work introduces the Adsorption Energy Distribution (AED) calculation using competitive adsorption isotherm data, enabling investigation of the simultaneous AED of two components for the first time. The AED provides crucial insights by visualizing competitive adsorption processes, offering an alternative adsorption isotherm model without prior assuming adsorption heterogeneity, and assisting in model selection for more accurate retention mechanistic modeling. The competitive AED enhances our understanding of multicomponent interactions on stationary phases, which is crucial for understanding how analytes compete on the stationary phase surface and for selecting adsorption models for numerical optimization of preparative chromatography. Here, the two-component AED was tested on both synthetic and experimental data, and a very successful outcome was achieved.

In indirect detection, sample components lacking detectable properties are detected by adding a detectable component to the eluent, a so-called probe that interacts with the analytes to be detected. This study focuses on modeling indirect detection in two principally different cases. In case (1), the analyte component has the same charge as the probe component, so the probe acts as a co-ion of the analyte. In case (2), the analyte component has the opposite charge to the probe, so the probe acts as a counter-ion of the analyte. In the co-ion case (1), the analytes are alkyl sulfonates, and a competitive bi-Langmuir isotherm model was used. In the counter-ion case (2), the analytes are amines, and a modified bi-Langmuir isotherm model, incorporating ion-pairing on the stationary phase surface, was derived and applied for simulating the elution profiles. The chromatographic system comprised an XBridge Phenyl column as the stationary phase and an acetonitrile/phosphate buffer mixture with varying concentrations of sodium 2-naphthalenesulfonate as the eluent. In both cases, the detectable probe component was sodium 2-naphthalenesulfonate. The applied isotherm models successfully predicted system peaks with high agreement in both model cases, with calculated relative errors in retention times typically below 4.72 % and often below 1 %. The models were employed to predict the sensitivity of analytical methods, demonstrating excellent agreement between experimental and calculated sensitivities. These findings confirm the validity of the new adsorption isotherm model under these experimental conditions. 

Short interfering RNA (siRNA) represents a rapidly expanding class of marketed oligonucleotide therapeutics. Due to its double-stranded nature, the characterization of siRNA is twofold: (i) at the single-strand (denaturing) level for impurity profiling and (ii) at the intact (nondenaturing) level to confirm duplex formation and quantify excess single strands (including single strand-derived impurities). While denaturing analysis can be carried out using conventional ion-pair reversed-phase liquid chromatography (IP-RPLC), nondenaturing characterization of siRNA is a significantly less straightforward task. Typical IP-RPLC conditions have an intrinsic denaturing effect on siRNA, thereby limiting the development of viable approaches for the intact duplex analysis. In this study, we demonstrate, through the design of experiments of siRNA melting temperatures and chromatography analyses, that the simple addition of salts, such as phosphate-buffered saline and ammonium acetate, to eluents enhances the suitability of IP-RPLC for the nondenaturing analysis of siRNA during both UV- and mass spectrometry-based analysis. This work represents a milestone in overcoming the challenges associated with nondenaturing analysis of siRNAs by IP-RPLC and offers a fresh angle for exploring IP-RPLC of siRNAs.

The retention of three peptides was studied under analytical and overloaded conditions at different concentrations of trifluoroacetic acid (TFA) and water added to the co-solvent methanol (MeOH). Four columns with different stationary phase properties, i.e., silica, diol, 2-ethylpyridine and cyanopropyl (CN) columns, were evaluated in this investigation. The overall aim was to get a deeper understanding on how column chemistry as well as water and TFA in the co-solvent affect the analytical and overloaded elution profiles using multivariate design of experiments and adsorption measurements of co-solvent components. Multivariate experimental design modeling indicated that water had on average around five times higher effect on the retention than the addition of TFA. The results also showed that the retention increases with the addition of TFA and water to the co-solvent on all columns except the CN column, on which the retention decreased. When examining the effect of adding water to the co-solvent, evidence of a hydrophilic interaction liquid chromatography (HILIC)-like retention mechanism was found on the three other columns with more polar stationary phases. However, on the CN column water acted as an additive, decreasing the retention due to competition with the peptide for available adsorption surface. Adsorption isotherm measurements of the polar solvent MeOH showed that MeOH adsorbs much weaker on the CN column than on the other columns. Addition of TFA and water to the co-solvent substantially sharpened the elution profiles under both overloaded and analytical conditions. Adding a small amount of TFA (from 0 % to 0.05 %) to the co-solvent substantially improved the peak shape of the elution profiles, while further addition (from 0.05 % to 0.15 %) had only a minor effect on the elution profile shape. The reduced retention on the CN column could not be explained by TFA adsorption, which was very weak on all studied columns (retention factor, 0.05–0.15). One could therefore speculate that the ion-pairing complex formed between the peptide and TFA in the mobile phase, reduce the retention due to its reduced polarity. On the other columns displaying HILIC-like properties, the TFA probably just decreased the pH of the mobile phase, thereby promoting the partitioning of the peptide into the water-rich layer. Finally, peak deformation due to diluent–eluent mismatch was observed under overloaded conditions. This was most severe in the cases where MeOH adsorption to the stationary phase was strong and the peptides were only mildly retained. Adding 1,4-dioxan to the diluent resolved this issue. 

Creating resilient machine learning (ML) systems has become necessary to ensure production-ready ML systems that acquire user confidence seamlessly. The quality of the input data and the model highly influence the successful end-to-end testing in data-sensitive systems. However, the testing approaches of input data are not as systematic and are few compared to model testing. To address this gap, this paper presents the Fault Injection for Undesirable Learning in input Data (FIUL-Data) testing framework that tests the resilience of ML models to multiple intentionally-triggered data faults. Data mutators explore vulnerabilities of ML systems against the effects of different fault injections. The proposed framework is designed based on three main ideas: The mutators are not random; one data mutator is applied at an instance of time, and the selected ML models are optimized beforehand. This paper evaluates the FIUL-Data framework using data from analytical chemistry, comprising retention time measurements of anti-sense oligonucleotide. Empirical evaluation is carried out in a two-step process in which the responses of selected ML models to data mutation are analyzed individually and then compared with each other. The results show that the FIUL-Data framework allows the evaluation of the resilience of ML models. In most experiments cases, ML models show higher resilience at larger training datasets, where gradient boost performed better than support vector regression in smaller training sets. Overall, the mean squared error metric is useful in evaluating the resilience of models due to its higher sensitivity to data mutation. 

This study investigated the influence of pH on the retention of solutes using a mixed-mode column with carboxyl (-COOH) groups acting as weak cation exchanger bonded to the terminal of C18 ligands (C18-WCX column) and a traditional reversed-phase C18 column. First, a model based on electrostatic theory was derived and successfully used to predict the retention of charged solutes (charged, and ionizable) as a function of mobile phase pH on a C18-WCX column. While the Horváth model predicts the pH-dependent retention of ionizable solutes in reversed-phase liquid chromatography (RPLC) solely based on solute ionization, the developed model incorporates the concept of surface potential generated on the surface of the stationary phase and its variation with pH. To comprehensively understand the adsorption process, adsorption isotherms for these solutes were individually acquired on the C18-WCX and reversed-phase C18 columns. The adsorption isotherms followed the Langmuir model for the uncharged solute and the electrostatically modified Langmuir model for charged solutes. The elution profiles for the single components were calculated from these isotherms using the equilibrium dispersion column model and were found to be in close agreement with the experimental elution profiles. To enable modelling of two-component cases involving charged solute(s), a competitive adsorption isotherm model based on electrostatic theory was derived. This model was later successfully used to calculate the elution profiles of two components for scenarios involving (a) a C18 Column: two charged solutes, (b) a C18 Column: one charged and one uncharged solute, and (c) a C18-WCX Column: two charged solutes. The strong alignment between the experimental and calculated elution profiles in all three scenarios validated the developed competitive adsorption model. 

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-tri‑tert-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. 

The adsorption and desorption behavior of volatile nitrogen-containing compounds in vapor phase by solid-phase microextraction Arrow (SPME-Arrow) and in-tube extraction (ITEX) sampling systems, were investigated experimentally using gas chromatography-mass spectrometry. Three different SPME-Arrow coating materials, DVB/PDMS, MCM-41, and MCM-41-TP and two ITEX adsorbents, TENAX-GR and MCM-41-TP were compared to clarify the selectivity of the sorbents towards nitrogen-containing compounds. In addition, saturated vapor pressures for these compounds were estimated, both experimentally and theoretically. In this study, the adsorption of nitrogen-containing compounds on various adsorbents fol-lowed the Elovich model well, while a pseudo-first-order kinetics model best described the desorption kinetics. Pore volume and pore sizes of the coating sorbents were essential parameters for the deter-mination of the adsorption performance for the SPME-Arrow sampling system. MCM-41-TP coating with the smallest pore size gave the slowest adsorption rate compared to that of DVB/PDMS and MCM-41 in the SPME-Arrow sampling system. Both adsorbent and adsorbate properties, such as hydrophobicity and basicity, affected the adsorption and desorption kinetics in SPME-Arrow system. The adsorption and desorption rates of studied C6H15N isomers in the MCM-41 and MCM-41-TP sorbent materials of SPME-Arrow system were higher for dipropylamine and triethylamine (branched amines) than for hexylamine (linear chain amines). DVB/PDMS-SPME-Arrow gave fast adsorption rates for the aromatic-ringed pyridine and o-toluidine. All studied nitrogen-containing compounds demonstrated high desorption rates with DVB/PDMS-SPME-Arrow. Chemisorption and physisorption were the sorption mechanisms in MCM-41-and MCM-41-TP-SPME-Arrow, but additional experiments are needed to confirm this. An active sampling technique ITEX gave comparable adsorption and desorption rates on the selective MCM-41-TP and univer-sal TENAX-GR sorbent materials for all the compounds studied. Vapor pressures of nitrogen-containing compounds were experimentally estimated by using retention index approach and these values were compared with the theoretical ones, calculated using the COnductor-like Screening MOdel for Real Sol-vent (COSMO-RS) model. Both values agreed well with those found in the literature proving that these methods can be successfully used in predicting VOC's vapor pressures, e.g. for the formation of secondary organic aerosols.

Toxicity of β-blockers is one of the most common causes of poison-induced cardiogenic shock throughout the world. Therefore, methodologies for in vivo removal of the drugs from the body have been under investigation. Intralipid emulsion (ILE) is a common commercial lipid emulsion used for parenteral nutrition, but it has also been administered to patients suffering from drug toxicities. In this work, a set of β-blockers of different hydrophobicity’s (log KD values ranging from 0.16 to 3.8) were investigated. The relative strength of the interactions between these compounds and the ILE was quantitatively assessed by means of binding constants and adsorption constants of the formed β-blocker-ILE complexes. The binding constants were determined by capillary electrokinetic chromatography and the adsorption constants were calculated based on different adsorption isotherms. Expectedly, the binding constants were strongly related to the log KD values of the β-blockers. The binding and adsorption constants also show that less hydrophobic β-blockers interact with ILE, suggesting that this emulsion could be useful for capturing such compounds in cases of their overdoses. Thus, the use of ILE for treatment of toxicities caused by a larger range of β-blockers is worth further investigation. 

Preparative chromatography is the best generic method currently available for purifying small drugs and valuable chemical components at the 10-kg level. Progress in computer technology, the development of new non-chiral/chiral stationary phases, and numerous improvements in reliability and economic performance have considerably increased the interest in modeling in academia and industry. This chapter introduces the modeling of preparative liquid chromatography in order to improve the purification process for valuable chemical components such as drugs and chiral components. We review the most important column and adsorption models and the methods for determining the essential thermodynamic adsorption data for both column characterization and process improvement. We also cover important operational modes (e.g., separation in gradient mode), cases involving additives or ion-pair reagents, and operational conditions sometimes neglected in the modeling process, for example, involving the impact of injection profiles.