# Using artificial neural networks to elucidate retention interactions on stationary phases with amine moieties dedicated to supercritical fluid chromatography

Veronika Pilařová, Kateřina Plachká, Taťána Gazárková, František Švec, Jean-Christophe Garrigues, Lucie Nováková

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Veronika Pilařová, Kateřina Plachká, Taťána Gazárková, František Švec, Jean-Christophe Garrigues, et al.. Using artificial neural networks to elucidate retention interactions on stationary phases with amine moieties dedicated to supercritical fluid chromatography. Separation and Purification Technology, In press, 10.1016/j.seppur.2024.129965. hal-04719213

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# Using Artificial Neural Networks to Elucidate Retention Interactions on Stationary Phases with Amine Moieties Dedicated to Supercritical Fluid Chromatography

Veronika Pilařováª, Kateřina Plachkáª, Taťána Gazárkováª, František Švecª, Jean-Christophe Garriguesᵇ, Lucie Novákováª*

ª Department of Analytical Chemistry, Faculty of Pharmacy in Hradec Králové, Charles University, 500 03 Hradec Králové, Czechia

ᵇ SOFTMAT (IMRCP) Laboratory, SMODD Team, CNRS, Toulouse III Paul Sabatier University, 31400 Toulouse, France

* Corresponding author. Tel.: +420 495067304

E-mail address: nol@email.cz (L. Nováková).

## Highlights

* Artificial neural networks were used to elucidate retention interactions in SFC.

* SFC-dedicated stationary phases with amine moieties were studied.

* 100 analytes described by > 200 molecular descriptors were used to train ANN.

* Differences in retention using 3 organic modifiers were quantitatively determined.

* Retention time shifts over 8 data points collected during 1 year were examined.
ABSTRACT

The retention mechanisms of small molecules on a wide range of stationary phases using different
mobile phase compositions are one of the most discussed topics in current state-of-the-art supercritical
fluid chromatography (SFC). Although various theories have been published on retention behavior,
prediction, and stability over time, an in-depth insight into the mechanisms is still lacking. Our study
focused on the description of the retention mechanisms on columns with amine moieties, i.e., 2-
ethylpyridine, 2-picolylamine, 1-aminoanthracene, and diethylamine, dedicated to SFC, using three
different compositions of organic modifier, i.e., methanol, methanol + 10 mmol/L NH3, and methanol + 2%
H2O, in CO2. An extensive set of analytes was used, and more than 200 molecular descriptors were used
to characterize each analyte. The importance of the effect of each molecular descriptor on the retention
behavior was determined by artificial neural networks. Thus, the descriptors increasing and/or decreasing
retention on individual columns using different mobile phase compositions were defined. The data
collected over one year of column use were statistically evaluated to describe the retention behavior of
small molecules on the tested stationary phases using three organic modifiers and to describe the changes
in retention behavior over time.

As the development of the SFC method can be laborious and time-consuming, this publication offers a
detailed description of the interactions taking place between the analyte and the SFC stationary phase.
Understanding these fundamental processes will enable faster development of SFC methods using quality-
by-design principles.

KEYWORDS

supercritical fluid chromatography, stationary phases, artificial neural networks, retention interactions,
retention stability
GRAPHICAL ABSTRACT

<figure><img src="image_2.png" /></figure>

©BioRender
# 1. INTRODUCTION

The importance of supercritical fluid chromatography (SFC) has been rising in recent years. From the marginal technique, mainly used for the analysis of nonpolar solutes such as beta carotenoids and lipids, SFC became the method of choice in the analysis of chiral and achiral compounds with wide polarity and physicochemical properties, including natural compounds, pharmaceuticals, peptides, and amino acids [1]. However, this technique is still primarily considered a research tool rather than a routine method. Even though the robustness and repeatability of SFC methods have been proven by several studies [2-4], negative aspects related to long-term retention time ($t_R$) stability have also been described for SFC [5, 6]. Additionally, as the concept of Analytical Quality by Design (QbD) has been introduced in the analytical method development, the fundamental understanding of retention behavior in SFC is needed to enable QbD selection of the separation conditions, i.e., appropriate stationary phase and mobile phase composition, which may result in the shortening of the method development [7, 8]. Machine learning with artificial neural networks (ANN) offer an unparallel power and can bring deep insight into the retention mechanism.

The current state-of-the-art SFC uses the mobile phase composed of (i) supercritical carbon dioxide, (ii) an organic modifier affecting the mobile phase physicochemical properties and, thus, elution strength and compound solubility, and (iii) a small amount of additive, i.e., acid, base, salt, and water, that affects the separation of acidic/basic compounds and their peak shapes. Such mobile phases bring several advantages due to their unique physicochemical properties, including low viscosity, high diffusivity, and fast mass transfer, which makes SFC a fast, efficient, and environmentally friendly separation technique. However, the organic modifier, typically methanol, can react with free silanols on the stationary phase surface, forming silyl-ethers. Silyl-ether formation (SEF) reduces the number of free silanols that are no longer involved in the interactions between the stationary phase surface and analytes; thus, the stationary phase's selectivity changes over time [5, 6, 9]. The SEF is a reaction that can be reversed by water, but the effect of SEF on retention time stability in SFC is still not a clearly understood phenomenon. Furthermore, the used additives can be absorbed on the stationary phase surface, resulting in additional retention changes over time, especially when various additives are used on one column [10-12].

A wide spectrum of stationary phases with various chemistries is available for SFC method development, including SFC- and liquid chromatography-dedicated ones [1, 3, 12, 15]. They can be classified according to their selectivity. Nevertheless, their comparison is not easy, as different conditions can be used to achieve optimal separation [13]. The main approach used for column classification is based on the linear solvation energy relationships (LSER) developed and established for SFC by Lesellier and West [13, 15, 16]. Generally,
the LSER equation, $\log k = c + eE + sS + aA + bB + vV$, is based on 5 Abraham's descriptors representing the most important interactions that are related to $n/\pi$ electrons (eE), dipole-dipole interactions (sS), H bond donors/acceptors interactions (aA, bB), and dispersion interactions (vV). Additionally, the descriptors related to the positive and negative charges of molecules ($d^{-}D^{-}$; $d^{+}D^{+}$), shape flexibility ($fF$), and molecular sphericity ($gG$) were introduced to the LSER [17, 18]. The unified classification is displayed as a spider diagram and sorts the individual stationary phases based on their retention behavior and selectivity [13]. However, this model does not show what characteristic of the analyte is responsible for these interactions and if the more detailed parameters, such as localization of the charge and atom connectivity, play a role in the strength of these interactions. To fully understand the retention interactions, we used artificial neural networks (ANN) with deep learning tools to describe the weight by which > 200 molecular descriptors contribute to the observed retention [9]. The use of ANN offers unparalleled power, enabling to find correlations in large data sets based on rigorous rules set for the training cycles. The behavior of ANN is determined by the structure of its interconnected elements and the strength, or weights, of these connections. These weights are automatically adjusted during training until the ANN performs the set task correctly as indicated by operating characteristics in the used software. The key molecular descriptors determined by ANN to have the highest effect on the retention enabled correlation of molecular properties of analytes with interactions expected based on the LSER classifications.

In this paper, we focus on SFC-dedicated stationary phases with amine moieties, which are extensively used for the separation of various compounds, including pharmaceuticals, pesticides, vitamins, carotenoids, and others. These stationary phases were used in nearly a quarter of the published SFC experimental works according to our recent review paper [13]. These columns were developed specifically for SFC to improve the separation and peak shape of basic compounds and to reduce the need for mobile phase additives [1, 2, 12, 18].

The 2-ethylpyridine (2-EP) stationary phase (structure shown in Supplementary Material (SM) Figure S1a) was introduced to the market in the 2000s as the first column dedicated to SFC. It is one of the most popular SFC column chemistries, with more than 10% of all SFC applications carried out on this stationary phase [13]. 2-EP is characterized as a polar stationary phase according to the LSER. The nitrogen atom ($pK_b \approx 6.0$) [20, 21] in the aromatic ring plays a crucial role in the retention mechanism. 2-EP exhibits strong hydrogen bonding properties (a and b terms in LSER, SM Figure S1b) because pyridyl can behave as a proton acceptor. The pyridyl is protonated and positively charged when the mobile phase has an acidic pH. On the contrary, this H bonding can be partially deactivated by interactions between nitrogen atoms
and free silanols on the surface of the stationary phase. In addition, free silanols not inactivated by the pyridyl functionalities and its steric hindrance can act as H bond donors, or they can accept a lone pair of electrons and contribute to the retention of basic compounds. Positive values of the *e* and *s* terms in LSER confirm the dipole-dipole and π-π interactions caused by the presence of the aromatic ring and the high electron density. The negative *v* term indicates that no dispersive interactions are observed in the 2-EP [10, 13, 16, 22-24].

2-EP is linked to the silica or bridged-ethylene hybrid (BEH) silica particles without any linker. In order to reduce the interaction of free silanols and to improve the peak shapes of the analytes, Waters introduced the 2^nd^ generation of SFC-dedicated columns with amine moieties on the market. Here, a modified propanediol is used to link the ligands, i.e., 2-picolylamine (2-PIC), 1-aminoanthracene (1-AA), and diethylamine (DEA), to the BEH particles [25].

The 2-PIC stationary phase (SM Figure S1a) has been designed as the stationary phase of the first choice for the analysis of acidic and basic compounds (SM Figure S1c) [25]. 2-PIC is characterized as a polar stationary phase containing two basic groups that behave differently. The pyridine group is considered a weak base with a pK<sub>b</sub> of 8.5 [20, 21], while the secondary amine group is a relatively strong base with a pK<sub>b</sub> determined to be close to 3.1 [20, 21, 26]. Since the pH of the CO<sub>2</sub>/methanol mobile phase is considered acidic and/or neutral based on the used additives [27], only the secondary amine group should be positively charged. Therefore, the positive charge can act as a repulsive shield for the free residual silanols. In addition, the pyridine group can form hydrogen bonds with residual silanols, resulting in their deactivation. Looking at the LSER (SM Figure S1b), the terms *a* and *d*<sup>-</sup> have increased importance compared to 2-EP, corresponding to the increased retentivity of acidic compounds. Apart from H bonding, 2-PIC is characterized by strong π-π interactions (*e* term) [18, 26-28].

The 1-AA stationary phase was designed to be orthogonal to the 2-PIC, and it is recommended as the column of choice for separating neutral species such as steroids, lipophilic vitamins, and related compounds [25]. 1-AA contains a large aromatic anthracene ring substituted by a secondary amine with pK<sub>b</sub> of about 3.9 [20, 21]. The pK<sub>b</sub> of the secondary amine affects the repulsion of basic analytes (*d*<sup>-</sup> term in LSER), which is significantly lower compared to other stationary phases with other basic moieties (SM Figure S1b). Moreover, the amine group in 1-AA is sterically hindered by the aromatic ring, reducing its availability for interactions. On the other hand, basic analytes can easily interact with free silanol groups (*b* term in LSER). The anthracene ring is responsible for hydrophobic and π-π interactions, and the dispersive interactions are stronger than 2-EP and 2-PIC (terms *e*, *v*). Therefore, 1-AA is mainly suitable for the separation of aromatic compounds [18, 26, 28].
The DEA column is also orthogonal to 2-EP but with an emphasis on the separation and better peak shapes of strong basic compounds. This stationary phase provides high repulsion of basic compounds due to the basic diamine ($pK_b$ ≈ 10.6) [20, 21]. However, since free silanols and -OH groups from propanediol linker are not significantly hindered compared to other discussed stationary phases, they may interact with basic compounds. A more pronounced $\alpha$ term in the LSER column characteristic (SM Figure S1b) also confirms strong interactions with acids through the charged amine group. Since the DEA stationary phase cannot provide any $\pi-\pi$ interactions, a different selectivity and retention behavior occurs compared to 1-AA, 2-EP, and 2-PIC [18, 26, 28].

Although these columns with amine moieties should allow the separation of many basic and acidic compounds without additives, it is common to use methanol with the addition of acid, base, salt, and/or water. Thus, the drawbacks associated with retention time stability may occur. These include (i) long equilibration time and saturation of the stationary phase and (ii) adsorption of an additive on the stationary phase surface. As these SFC-dedicated columns are based on the hybrid silica support, (iii) possible SEF must also be considered [5, 6, 10-12].

This paper presents a detailed exploration of the retention behavior of stationary phases with amine moieties, namely 2-EP, 2-PIC, 1-AA, and DEA. These stationary phases have amine moieties with different $pK_b$ values, suggesting that the pH of the mobile phases plays a crucial role in the retention. Thus, more than 100 compounds were analyzed using $CO_2$ with (i) neat MeOH with apparent pH ≈ 5, (ii) MeOH + 2% $H_2O$ with apparent pH ≈ 1, and (iii) MeOH + 10 mmol/L $NH_3$ with apparent pH ≈ 7-8 [27]. The selected organic modifiers belong among the most typically used in SFC. The use of pure MeOH enabled description of retention interactions caused solely by $CO_2/MeOH$ mobile phase and served also as a baseline for the evaluation of SEF. MeOH + 2% $H_2O$ is an example of organic modifier causing acidic apparent pH and its beneficial effect on long-term stability of retention times have been previously described [4, 9]. Organic modifiers with the addition of ammonium salt are commonly used in SFC and MeOH + 10 mmol/L $NH_3$ was selected as the most straightforward example so we can attribute the observed interactions either to MeOH or to $NH_3$.

The analyzed compounds were described using 226 molecular descriptors. Artificial neural networks (ANN) were used to identify the weights by which each molecular descriptor affected the retention under the tested chromatographic conditions. These results were then used to (i) provide a fundamental description of retention behavior, (ii) describe changes in retention behavior during 1 year of column use and explain them with a proposed interpretation of changes on the stationary phase surface, and (iii) determine the effect of the regeneration procedure on retention behavior.
## 2. MATERIALS AND METHODS

### 2.1 Chemicals and reagents

Methanol (MeOH), acetonitrile (ACN), and water in LC/MS grade quality were provided by VWR International (Prague, Czechia). Ammonia 4 mol/L solution in methanol for LC/MS was purchased from Sigma-Aldrich (Steinheim, Germany) and pressurized liquid CO2 4.5 grade (99.9995%) from Messer (Prague, Czechia). All 107 reference standards listed in SM Table S1 were obtained from Sigma-Aldrich (Prague, Czechia) except for several standards kindly donated by Zentiva, k.s. (Prague, Czechia).

### 2.2 Analytical conditions

The analytical conditions and protocols used in this study are described in detail in the first article of this series, focusing on polar stationary phases with -OH moieties [9] and summarized in Figure 1. Briefly, the standard stock solutions of all reference standards were prepared by dissolving each compound in MeOH and then divided into working solution mixtures based on retention time ($t_R$) with a final concentration of 50 µg/mL. ACN was used for dilution. Experiments were carried out on an Acquity UPC2 supercritical fluid chromatography system (Waters, Milford, MA, USA) with a binary pump, an autosampler, a column thermostat, a back pressure regulator (BPR), a PDA detector, and a single quadrupole detector (QDa, Waters) with a commercial SFC-MS dedicated pre-BPR splitter device with an additional isocratic pump for make-up solvent delivery (Waters). The mobile phase consisted of CO2 and organic modifier, the column temperature was 40°C, the BPR was 130 MPa (1885 psi), the autosampler was kept at 10°C, and the injection was 2 µL. Three different organic modifiers were tested: MeOH, MeOH + 10 mmol/L NH3, and MeOH + 2% H2O. The BPR pressure was adjusted prior to each sequence to ensure that the system pressure remained within ± 0.07 MPa (10 psi) of the pressure at the 1st injection. Peak detection and integration were carried out using the PDA detector in the range of 210 to 400 nm. The single quadrupole detector with electrospray ionization in positive and negative modes was used to confirm the identity of each analyte with MeOH + 10 mmol/L NH3 as make-up solvent at 0.3 mL/min.
<figure><img src="image_3.png" /><figcaption>Figure 1: Workflow of the study with used analytical conditions. The figure was created in BioRender.</figcaption></figure>

The 2-ethylpyridine bridge ethylene hybrid with direct modification of hybrid silica particles (Viridis BEH 2-EP, Waters, 2-EP), hybrid silica with propanediol modified by diethylamine (Torus DEA, Waters, DEA), hybrid silica with propanediol linking 2-picolylamine (Torus 2-PIC, Waters, 2-PIC), and hybrid silica with propanediol linking 1-aminoanthracene (Torus 1-AA, Waters, 1-AA) columns were tested in this study, all with the dimensions of 100 x 3.0 mm packed with 1.7 µm particles.

Similar to the study focusing on polar stationary phases with -OH moieties [9], this study was carried out in accordance with established recommendations including the use of separate columns for each of the organic modifiers to avoid switching additives within one column, the use of long equilibration with higher proportions (20 – 30%) of organic modifier to ensure repeatable coverage of the stationary phase surface, the flushing of the column after its use with large volumes of organic solvent and neat CO₂, and storing the columns in neat CO₂ to prevent SEF (Figure 1).

## 2.3 Data processing and evaluation

Raw data were assessed using Empower 3 software, and retention times were collected for all compounds. The percentage change in tR over time was calculated for each analyte, column, and organic
modifier using Excel. Retention factors (k') were calculated to allow direct comparison of retention behavior.

Semi-empirical AM1 quantum mechanical calculations (MOPAC application of Chem 3D Pro version 14.0 software, CambridgeSoft) were used to optimize the 3D structures of all analytes. An RMS gradient of 0.100 was used to minimize energy for all compounds. 226 2D and 3D molecular descriptors were calculated using CDK Descriptor Calculator (v.1.4.8) based on these optimized structures (SM Table S2). All molecular descriptors and k' values were normalized by dividing by their respective maximum values.

ANN were created using the neural network simulator in Matlab R2023a with the deeplearning toolbox V.23.2 (The MathWorks, Inc., Massachusetts, USA), including a sigmoid activation function and a backpropagation learning algorithm with 500 learning cycles. The input layer was connected to the 226 molecular descriptors and the output layer was connected to the retention factor of each analyte under examined conditions. The weights assigned to each input neuron were extracted and the key parameters were examined. The higher the weight assigned by the ANN, the more the descriptor had an effect on retention [29]. Ten molecular descriptors with the highest positive and negative weights were used to elucidate the retention mechanisms on each column. The differences based on the used organic modifier were noted. The standard deviations (SD) of these parameters at different time points were calculated and correlated with the observed changes in $t_R$. In addition, the molecular descriptors that exhibited the most significant changes in weight over time were identified and utilized to characterize changes in the stationary phase surface.

### 3. RESULTS AND DISCUSSION

The largest changes in $t_R$ over time were observed on DEA columns (Figure 2). A comparison of %-changes in $t_R$ was made using the 1st injection as 100%. In fact, less than 15% of the compounds had $t_R$ within ± 0.5% of the 1st injection in month 9 (M9) regardless of used organic modifier. The best stability of $t_R$ was observed on 2-EP and 2-PIC columns, especially when using MeOH+H₂O. Although the same linker, i.e., propanediol, is used in 2-PIC and 1-AA columns, a higher fluctuation of $t_R$ was observed on the latter.

ANN were used to determine which properties of the analytes played a crucial role in retention and, thus, in $t_R$ shifts over time. 500 training cycles were used resulting in a statistically significant weight assigned to each molecular descriptor under the particular SFC conditions used and at each data point. These weights were used to explain the retention behavior on each stationary phase and to explain the changes on the stationary phase surface over time.
<figure><img src="image_4.png" /><figcaption>Figure 2: Retention time shifts over time (M-month) using (A) MeOH, (B) MeOH+NH3, and (C) MeOH+H2O as organic modifiers, expressed as %-difference: < 0.5% (dark blue), 0.5-1.0% (light blue), 1.0-2.0% (yellow), 2.0-5.0% (light red), and > 5.0% (dark red).</figcaption></figure>

## 3.1 Retention mechanisms on stationary phases with amine moieties

78 of the 107 analytes originally tested (SM Table S1) eluted on all four stationary phases using the three organic modifiers, i.e., MeOH, MeOH + NH3, and MeOH + H2O. However, when the stationary phases were evaluated separately, 86, 93, 97, and 95 analytes eluted on 2-EP, 2-PIC, 1-AA, and DEA, respectively. Initially, only a simple comparison of the molecular descriptor weights affecting retention by the highest extent was carried out to directly compare the 4 tested columns. Positive weights correspond to stronger retention and negative weights correspond to lower retention. The common set of 78 analytes was used for this comparison with experimental data obtained using MeOH as an organic modifier (Figure 3A).
<figure><img src="image_5.png" /><figcaption>Figure 3: Principal component analysis of weights assigned by ANN to molecular descriptors based on (A) narrow and (B) extended set of compounds analyzed on 2-ethylpyridine (●), 2-picolylamine (■), 1-aminoanthracene (x), and diethylamine (□) stationary phases using MeOH (blue), MeOH + 2% H₂O (green), and MeOH + 10 mmol/L NH₃ (yellow). Multiple marks correspond to different data points.</figcaption></figure>

Columns packed with 2-EP and 2-PIC stationary phases clustered closely together in the principal component analysis (PCA) suggesting similar retention interactions (Figure 3A). Decreased retention was observed for compounds with high values of (i) BCUTp-1l describing polarizability, (ii) HybRatio calculated as the ratio of sp³ carbons to sp³+sp² carbons, (iii) number of -NH₂ groups in the molecule (khs.sNH2), (iv) number of H bond acceptors (nHBAcc), (v) ratio of polar surface area/molecular size (tpsaEfficiency), and (vi) relative negative charge of the molecule (RNCG) (Figure 4A). Contrary, increased retention was associated with (i) high values of the Moreau-Broto autocorrelation descriptors using partial charges (ATSc5), (ii) high number of methine groups in the molecule (singly bond carbon bonded to three other carbons, C3SP3), (iii) higher cyclicity of the molecule expressed as the ratio of heavy atoms in the framework to the total number of heavy atoms in the molecule (FMF), (iv) high relative polar surface area (RPSA), and high numbers of (v) -NH groups, (vi) H bond donors, and (vii) basic groups in the molecule (Figure 4B). These molecular descriptors are consistent with the results of LSER evaluation showing preferential interactions via H bonding where the stationary phase is proton acceptor.

Quite similar behavior was also observed for 1-AA with several exceptions (Figure 4). The decreasing effects of -NH₂ groups and tpsaEfficiency were not as pronounced as in case of 2-EP and 2-PIC. Contrary, the number of basic groups in the molecule increased the retention to a greater extent. This result is
consistent with the original purpose of 2-EP and 2-PIC, which were designed to repel basic compounds, allowing their elution in narrow symmetrical peaks. Thus, higher retention of basic compounds on orthogonal 1-AA was expected although 1-AA was originally designed specifically for the analysis of neutral compounds.

<figure><img src="image_6.png" /><figcaption>Figure 4. Comparison of molecular descriptors with the highest (A) decreasing and (B) increasing effect on the retention on 2-EP (blue), 2-PIC (purple), 1-AA (yellow), and DEA (green) stationary phases using MeOH as organic modifier.</figcaption></figure>

A completely different retention mechanism was observed on DEA (Figure 4). HybRatio, ATSc5, and RPSA had opposite effects on the retention on DEA vs. 2-EP/2-PIC/1-AA. Moreover, high polarizability and high negative charge reduced the retention on DEA more strongly. Compounds with high cyclicity (FMF), number of -NH groups and H bond donors were more strongly retained on DEA (Figure 4B), confirming the suitability of DEA for the analysis of strong bases.

Subsequently, the detailed analysis for each column was carried out separately to account for all eluting compounds and possible interactions (Figure 3B). The affinity of the stationary phase for specific analytes has to be accounted for in the evaluation to mitigate the bias of the results [9]. When all compounds eluting on each stationary phase were included in the training of the ANN, the differences in retention mechanism became more pronounced with four distinct clusters (Figure 3B) where even 2-EP and 2-PIC clustered separately. Thus, in the next step, the retention mechanism was evaluated separately for each column and differences caused by additive in organic modifier were noted. A strong correlation between pK<sub>b</sub> of the functional group on the surface of the stationary phase and the apparent pH of the mobile phase
was expected. The ANN determined the weights by which each molecular descriptor affects the retention
now using the full set of analytes eluting on each stationary phase (SM Figures S2-S5).

**3.2 Retention mechanisms of 2-ethylpyridine stationary phase**

Eight additional compounds eluted on the 2-EP column compared to the set common for all stationary phases tested. These compounds included analytes with neutral, basic, and acidic properties with pK<sub>b</sub> ranging from 4.0 to 14.7. BCUTp-1l was still the main molecular descriptor that decreased the retention (Figure 5A). BCUT is a weighted version of the Burden matrix that evaluates both the connectivity and the atomic properties of a molecule. The BCUTp parameters describe the highest (-1h) and lowest (-1l) polarizability in the molecule, respectively. If the BCUTp-1l is more pronounced, the compound cannot induce dipole moment and interact via dipole-dipole interactions with the stationary phase resulting in decreased retention. The important effect of polarizability of the molecule on the retention, i.e., the importance of dipole-dipole interactions, is further confirmed by ATSp5, which corresponds to the autocorrelation descriptor weighted by polarizability. Similarly, BCUTc parameters describing the highest (-1h) and lowest (-1l) partial charges in the molecule and ATSm5 as the autocorrelation descriptor weighted by scaled atomic mass also reduced the retention.

Although π-π interactions are expected on 2-EP, the presence of a ring (nRings) in the molecule usually
had a decreasing effect on the retention except for 5-atom ring with positive effect and 3-atom ring with
negligible effect. The negative effect was particularly pronounced in the case of 4-atom rings (SM Figure
S6A). Here, we need to take into account that these molecular descriptors count all 3-, 4-, and 5-membered
rings without considering their aromaticity. However, even the descriptor nAromRings counting only
aromatic rings had slightly decreased retention (SM Figure S2). Moreover, π donor-acceptor interactions
are observed between low energy empty orbital, i.e., acceptor, and a high energy filled orbital, i.e., donor.
This corresponds with other molecular parameters that play an important role in the retention, namely
molecular connectivity expressed as VC-4, VC-5, VC-6, and Kier3. These topological indexes, based on the
molecular connectivity approach, include three types of indexes: the molecular connectivity Chi indexes
that characterize the structural attributes of molecule, the kappa indexes of molecular shape, and the
topological equivalence state T values characterizing atoms and groups in the molecular framework [30].
The VC molecular descriptors encode the valence connectivity, i.e., the electronic identity of the atom in
terms of valence electrons and the number of core electrons. This takes into account the possibility of
dispersive interactions. Kier3 then describes the shape index of the molecule considering the number of
atoms in the hydrogen-suppressed graph, the number of bonds in the hydrogen-suppressed graph, and
the number of paths of a given length [30].
<figure><img src="image_7.png" /><figcaption>Figure 5. Molecular descriptors affecting the retention on (A) 2-EP and (B) 2-PIC stationary phases by the highest weights as determined by ANN using MeOH+H₂O (green), MeOH (blue), and MeOH+NH₃ (yellow) as organic modifiers.</figcaption></figure>

The double bonds in the molecule also decreased the retention on 2-EP column. This was confirmed by a molecular descriptor C1SP2, which counts carbons with double bonds to another carbon (methylene groups with double bond), including aromatic cycles. In fact, the type of carbon hybridization, i.e., the electron density, affects the retention. This is also shown by the HybRatio descriptor calculated as a ratio
between sp³ carbons and the sum of sp³ and sp² carbons. In general, a sp³ hybridized carbon is a tetravalent carbon forming single covalent bonds as opposed to sp² carbon forming double bond. Thus, the value of HybRatio decreases as the number of sp² carbons, i.e., double bonded carbons, in the molecule increases. Unlike the C1SP2 descriptor, HybRatio counts not only double bonds to other carbon, but also to oxygen and nitrogen atoms. Therefore, higher number of -C=C- decreases the retention, but a higher number of =O and/or =N decreases the value of HybRatio and mitigates its negative effect on retention. Retention on 2-EP also decreased with increasing number of atoms in the largest chain (nAtomLC) and with increasing molecular distance edge between tertiary carbons (MDEC-33). The 3D structure of the molecule plays an important role as also shown by MDEC-24, MDEC-23, MDEC-34, and MDEO-22 describing the molecular distance edges between carbons and/or oxygens. The high value of the distance edge between secondary oxygens increases the retention by the highest extent. Thus, compounds containing ether and/or ester oxygens were more strongly retained on 2-EP. As expected, the number of carbons bonded to four carbons (C3SP3), meaning branched molecules, increased the retention, i.e., had an opposite effect to the C1SP2 counting -C=C-. The descriptors increasing retention included also the Wlambda parameter related to molecular size along a principal axis and the FMF descriptor related to cyclicity of the molecule. FMF represents the ratio of heavy atoms in the framework to the total number of heavy atoms in the molecule. Thus, acyclic molecules have a value of 0 and higher values of FMF are assigned to compounds with a cyclic part.

Moreover, the retention increased with the total polar surface area (TPSA) of the molecule. This is confirmed by other molecular descriptors shown in Figure 5. Indeed, the retention is increased with higher number of H bond donors, -OH groups, -NH, and >N- groups in the molecule. This means that groups with free hydrogen and/or free electron pairs are available for more interactions with the pyridine group of the stationary phase. However, the increasing effect of -NH and >N- groups was surprising as interactions of two amine moieties, i.e., the analyte and 2-EP, are not common. This behavior could be explained by interactions with free silanols and/or by the formation of pseudo-stationary phase on the surface of the stationary phase as previously suggested by several authors [11, 31, 32].

Surprisingly, no significant changes in retention were observed based on the used organic modifier with or without additive as the weights of most molecular descriptors remained similar. However, it should be noted that these results were based on t<sub>R</sub> only and did not take into account other peak characteristics such as peak width and shape. The similarity of t<sub>R</sub> suggests that the ionization state of the 2-EP moiety on the surface of the stationary phase does not play a role in the interaction with analytes. The 2-EP should be ionized at apparent pH 1 when using MeOH+H<sub>2</sub>O as opposed to its unionized state at apparent pH 8
when using MeOH+NH₃. The molecular descriptors with the largest weight differences between MeOH+H₂O and MeOH+NH₃ are listed in SM Figure S6B. However, these differences are quite small as confirmed also by the PCA analysis (Figure 3B) and the comparison of tR observed using each of the organic modifiers tested. Figure 6 shows the correlation of tR observed with MeOH to tR observed with MeOH+H₂O and MeOH+NH₃ having R² > 0.98 in both cases. Thus, the main advantage of the organic modifier with additive on 2-EP is the possibility to elute some specific analytes and/or to affect the peak width. Compared to pure MeOH, the use of MeOH+H₂O allowed the elution of three additional very polar compounds. On the other hand, the use of MeOH+NH₃ enabled the elution of 12 additional compounds. These compounds were either strongly acidic, such as 2,3-dihydroxy benzoic acid, and/or strongly basic, such as beta-blockers acebutolol, atenolol, and metoprolol (SM Table S3).

<figure><img src="image_8.png" /><figcaption>Figure 6. Comparison of tR observed using MeOH+H₂O (colored) and MeOH+NH₃ (gray) with tR obtained using MeOH.</figcaption></figure>

When the ANN were used to determine the molecular descriptor weights using the whole set of analytes eluting from 2-EP with MeOH+NH₃, some changes in the molecular descriptor weights were observed. However, the main parameters affecting the retention remained the same. The presence of rings, sp³/sp² carbons ratio, and valence clusters still decreased the retention. In addition, the decreasing effect of =O in
the molecule became more pronounced. The 3D structure expressed as molecular edge distance remained the most influential parameter increasing retention. Similarly, the number of H bond donors, Wlambda, and number of C3SP3 carbons still increased the retention. The effect of polar surface area was expressed here by RPSA in contrast to the original TPSA.

### 3.3 Retention mechanism of 2-picolylamine stationary phase

Since the 2-PIC is chemically close to 2-EP, similar retention behavior was expected. Many important molecular descriptors were the same, including number of aromatic rings in the molecule, HybRatio, MDEC-33, and ATSp5 decreasing retention. Again, the 3D structure expressed as molecular distance edge between carbons, nitrogens, and oxygens had a crucial effect on the retention as shown by the weights of MDEO-12, MDEO-22, MDEN-12, MDEN-22, MDEC-23, and MDEC-44 (Figure 5B). Molecular connectivity, expressed as simple cluster Chi chain descriptor (SC-5) and valence path Chi chain descriptor (VP-6), also decreased the retention on 2-PIC as did high values of topological shape (topoShape) and density (Weta3.unity). The opposite behavior of FMF and topoShape further confirms the crucial effect of cyclicity on the retention on 2-PIC. Whereas the value 0 is assigned to acyclic compound for FMF and value 1 to cyclic compound, topoShape values are assigned contrary. This means that cyclic molecules will have a topoShape value of 0 and cyclic compounds will have a value of 1. Thus, the opposite weights of these two descriptors are related to the same behavior, i.e., stronger retention of cyclic compounds.

VC-3 as valence cluster Chi chain descriptor increased retention similar to the molecular charge (ATSc2) and high polarizability (BCUTp-1h). This was consistent with expected dipole-dipole and π-π interactions. Increasing lipophilicity of the molecule resulted in decreasing retention (Figure 5B) as shown by the descriptor ALogP, which is one of the most widely used methods estimating log P [33]. The aromatically bonded sulfur (khs.aaS) had decreasing effect.

Molecular parameters that had a strong effect on retention included the positive surface and the positive charge of the molecule, namely the relative positive charge (RPCG), FPSA-3, and RHSA. RPCG, calculated as the most positive charge/total positive charge, decreased retention. This means that molecules with high positive charge on one part of the molecule but with low total positive charge will have a higher value of RPCG and thus lower $t_R$ on 2-PIC. Similarly, FPSA-3 as a ratio of charge weighted partial positive surface area to total molecular surface area, also decreased the retention. When the total molecular surface area is low, the value of FPSA-3 increases and its decreasing effect on retention is more pronounced. TpsaEfficiency calculated as the ratio of polar surface area/molecular size, indicates that a molecule with a low molecular size, but a high polar surface area has lower $t_R$. RHSA is the sum of solvent accessible surface areas of atoms with an absolute value of partial charges less than 0.2/total molecular surface area.
It has an opposite effect on retention to RPSA, which is the sum of solvent accessible surface areas of
atoms with absolute value of partial charges ≥ 0.2/total molecular surface area. Thus, an analyte with
higher representation of partial charges on the solvent-accessible area of the molecule is retained more
strongly on 2-PIC because it can interact via dipole-dipole. DPSA-1 calculates the difference between the
positive and negative parts of the molecule, i.e., the sum of the surface area on the positive parts of
molecule minus sum of surface area on negative parts of the molecule, and has an increasing effect on
retention. Overall, analytes with acidic properties have lower DPSA-1 values than alkaline analytes. This
means that molecules with predominantly positive parts of the molecules, such as alkaline molecules, are
retained more strongly. This is quite surprising since an ionized form of 2-PIC is expected in the SFC mobile
phase resulting in positive charge on the stationary phase surface. We suppose that the slightly acidic
mobile phase may be attracted to the positively charged stationary phase to form a negatively charged
layer, i.e., pseudo-stationary phase [32], which can then interact with the positively charged analyte. This
pseudo-stationary phase then probably covers also the aromatic ring in the functional groups of 2-EP and
2-PIC limiting their possible interactions which would correspond to the negative weights assigned to
molecular descriptors related to the presence of aromatic rings in the analyte.

The use of additive in the organic modifier had a more pronounced effect on the molecular descriptor
weights in case of 2-PIC as opposed to 2-EP. The weights of most molecular descriptors increased in the
order MeOH+H₂O < MeOH < MeOH+NH₃. This suggests that the described interactions are more important
when the 2-PIC is in non-ionized form at apparent pH 8 corresponding to MeOH+NH₃. Nevertheless, the
same parameters of the molecule are responsible for the interactions with the stationary phase resulting
in similar tR regardless of used organic modifier (Figure 5B). Again, the correlation between tR observed
using MeOH and MeOH with additive is shown in Figure 6. Almost identical tR was observed using
MeOH+H₂O as confirmed by R² > 0.99. tR from MeOH+NH₃ correlated with tR from MeOH with R² > 0.97.
However, several outliers were detected where the organic modifier played a more critical role.

In contrast to 2-EP, changing the organic modifier did not result in the elution of additional analytes. The
same analytes were eluted with all three organic modifiers tested, except for farnesol, which did not elute
with pure MeOH and rivastigmine which did not elute using MeOH+H₂O. Comparison of tR on 2-EP vs 2-
PIC using MeOH showed comparable elution profiles. Overall, lower retention was observed on 2-EP for
most of the compounds (SM Figure S7). Chromatograms for representative compounds analyzed on both
2-EP and 2-PIC are shown in Figure 7. Even though close tR were observed for most compounds, for
example α-tocopherol, agomelatine, aldosterone, and darifenacin in Figure 7, slightly lower retention
could be observed on 2-PIC for basic daclatasvir contrary to stronger retention of acidic ibuprofen,
atorvastatin impurity C, and shikimic acid. Retention and elution of two compounds, salbutamol and luteolin, was only possible on 2-PIC. Apigenin, atomoxetine, and cetirizine eluted on 2-EP only with MeOH with both additives, but their elution was possible on 2-PIC even using pure MeOH. Atenolol, cytosine, dasatinib, sitagliptin, and metoprolol eluted from 2-PIC with all organic modifiers tested in contrast to 2-EP where the use of MeOH+NH₃ was necessary. Based on the observed chromatograms, it appears that these compounds did not elute from 2-EP due to too strong retention and the addition of NH₃ was necessary to facilitate the elution. This suggests that the residuals silanols are sterically hindered by the linker used in 2-PIC columns and/or the column can be more covered by the 2-PIC moiety reducing the number of free silanols. Contrary, the combination of 2-EP and MeOH+NH₃ allowed the analysis of dihydroxybenzoic acids which was not possible with 2-PIC.

<figure><img src="image_9.png" /><figcaption>Figure 7. Comparison of chromatograms of selected compounds analyzed on 2-ethylpyridine (full line) and 2-picolylamine (dashed line) columns using the same SFC conditions and methanol as organic modifier.</figcaption></figure>

### 3.4 Retention mechanism of 1-aminoanthracene stationary phase

The additive in the organic modifier had more significant effect on the retention on 1-AA column (Figure 8A). Some of the important molecular descriptors affecting the retention were the same as in case of 2-EP and 2-PIC columns, including polarizability (BCUTp-1l), Chi cluster indices (SC-4, VC-4, VC-5, VC-6), Chi chain indices (VCH-6, SCH-5, SCH-6), Chi path indices (VP-6, SP-7), Moreau-Broto autocorrelation descriptors using partial charges (ATSc4, ATSc5), and distance edges between oxygens (MDEO-12, MDEO-22), nitrogens (MDEN-12), and carbons (MDEC-12, MDEC-14, MDEC-22, MDEC-24). The higher distance edge between all secondary oxygens (MDEO-22) the higher retention was observed on 1-AA especially when using MeOH+NH₃ contrary to negative effect of the molecular distance edge between primary and
secondary oxygens (MDEO-12). A high number of methyl groups, i.e., a carbon singly bonded to another carbon (C1SP1), decreased the retention, in contrast to high number of quaternary carbons in the molecule, i.e., a carbon singly bonded to four other carbons (C4SP1). Therefore, higher retention should be expected for branched molecules. The branching in the molecule also results in lower surface area. This corresponds to the FPSA-2, FNSA-2, and RPSA parameters. High total polar surface area (TPSA) and relative polar surface area (RPSA) calculated as TPSA/total molecular surface area increased the retention on 1-AA. FPSA-2 and FNSA-2 are calculated as partial positive or negative surface area times total positive or negative charge on the molecule/total molecular surface area. This means that negative values are assigned to FNSA-2 contrary to positive values of FPSA-2. According to ANN, both positive and negative partial charges in the molecule have an increasing effect on the retention. However, the ANN considers all molecular descriptor values mathematically meaning that compounds with mathematically higher values of FNSA-2 have practically lower negative partial charge. Therefore, compounds with high positive partial charge are retained more strongly while compounds with high negative partial charge are repelled from the stationary phase resulting in lower retention. Furthermore, the strength of the partial charge effect is opposite when using different additives in organic modifiers. Molecules with higher FPSA-2, i.e., positive partial charge, are more retained using MeOH+H₂O with apparent pH around 1. In this case, the 1-AA functional groups are fully ionized. Thus, we expect that the mobile phase forms a negatively charged layer on the surface of the positively charged stationary phase, which can easily interact with positively charged analytes. Interaction with silanols is also possible but they should not be ionized at pH 1 and should be sterically hindered. Therefore, the hypothesis of pseudo-stationary phase formation is more probable. The effect of the number of basic groups in the molecule is affected by organic modifier type in a similar way to FPSA-2. A high number of these basic groups, i.e., groups that easily accept a proton, results in higher retention corresponding to the behavior described by FPSA-2. The highest number of protons will be present in the mobile phase at the lowest pH, i.e., using MeOH+H₂O as a modifier, thus the highest retention of basic compounds is expected. Here, the basic groups of the analyte should be preferentially in the ionized state with positive charge resulting in a stronger interaction with presumed negative layer of the mobile phase on the surface of the stationary phase.

FNSA-2 describing negative partial charge has the opposite effect and affects the retention when using MeOH+NH₃. The negatively charged analytes can probably easily interact with the highly abundant NH₄⁺ ions from the mobile phase, reducing their negative charge and allowing stronger interactions with the stationary phase.
An opposite behavior was observed for H bond donors and acceptors. The presence of H bond acceptor groups significantly decreased the retention, especially when using MeOH+H₂O, suggesting that the stationary phase interacting with the analytes also acts as H bond acceptor in this case. This effect is significantly attenuated when MeOH+NH₃ is used, indicating a change in the surface of the stationary phase. This can serve as further confirmation of our hypothesis. In contrast, the presence of H bond donors groups increase retention when MeOH+NH₃ is used suggesting that the -NH₂ groups of 1-AA can act as H bond acceptors in this case.

High values of HybRatio increased the retention when using MeOH+H₂O. This means that the lower number of carbons with three covalent bonds as opposed to four covalent bonds increased the retention using MeOH+H₂O. However, similar to 2-EP and 2-PIC, HybRatio decreased the retention using MeOH and MeOH+NH₃. The presence of aromatically bonded N increased retention on 1-AA using MeOH+H₂O, but its effect was mitigated using other organic modifiers.

The differences in retention behavior caused by the additive in organic modifier were also reflected in the correlation between the respective t<sub>R</sub>. The t<sub>R</sub> observed using MeOH and MeOH+H₂O correlated quite strongly with R² > 0.95. On the other hand, differences in t<sub>R</sub> were observed for MeOH+NH₃ when compared to MeOH as confirmed by R² of 0.83 (Figure 6). However, changing the composition of the organic modifier did not change the profile of analyzable compounds except for naringin, which eluted only with MeOH+H₂O and dasatinib and luteolin eluting only using MeOH+NH₃.
<figure><img src="image_10.png" /><figcaption>Figure 8. Molecular descriptors affecting the retention on (A) 1-AA and (B) DEA stationary phases by the highest weights as determined by ANN. Organic modifiers: MeOH+H₂O (green), MeOH (blue), and MeOH+NH₃ (yellow).</figcaption></figure>

## 3.5 Retention mechanism of diethylamine stationary phase
Similar retention mechanism was observed on DEA using MeOH and MeOH+NH₃ in contrast to MeOH+H₂O clustering separately (Figure 3B). This can be related to the change in apparent pH of the mobile phase and thus the ionization state of the DEA.

Reduced $t_R$ was observed with higher number of ring blocks (nRingBlocks) in the analyte and with increasing number of atoms in the longest aliphatic chain (nAtomLAC). The retention on DEA decreased also with increasing lipophilicity expressed as both XLogP and ALogP (Figure 8B).

Increased $t_R$ were observed for compounds with high values of MDEO-22 determined as the distance edge between all secondary oxygens and for cyclic molecules expressed as FMF which is similar to 2-EP, 2-PIC, and 1-AA. The positive effect of FMF, i.e., the cyclicity of the molecule, was confirmed by the positive effect of nAtomLC, which calculates the number of atoms in the longest non-aliphatic chain. It also shows the crucial role of heteroatoms in the retention. Indeed, the retention on DEA increased not only with increasing molecular distance edge between secondary oxygens (MDEO-22) but also between primary-tertiary and secondary-tertiary nitrogens (MDEN-13, MDEN-23). High polarizability of the compounds (BCUTp-1h) increased their retention contrary to compounds with high values of BCUTc-1l. On the other hand, low polarizability of the molecule (BCUTp-1l) had a similar decreasing effect independently of used organic modifier.

The compounds with more branching were more strongly retained on DEA than linear molecules, as demonstrated by the MDEC-44, i.e., molecular distance edge between quaternary carbons, and MDEC-13 calculating the molecular distance edge between primary-tertiary carbons. In contrast, the presence of doubly bonded methylene groups (=CH₂, C1SP2) suggesting linear parts of the molecules decreased the retention. Overall, the stronger retention of cyclic compounds with branching and short aliphatic chains suggests that formation of cycle by weak interactions between diethylamine functional group and hydroxyl from the propanediol linker is possible. Surprisingly, high values of MDEC-34 also decreased retention. However, MDEC descriptors do not distinguish between single and double bonds and count all covalent bonds even to heteroatoms. The ratio of single and double bonded carbons can be expressed as HybRatio which decreased retention, especially with MeOH.

Chi chain indices had ambiguous effect based on the particular definition of each molecular descriptor (VC-5, SC-5, SC-6, SC-5). The density of the molecule expressed as Weta3.unity increased retention as well as Wlambda2.unity related to the molecular size. ECCEN is the eccentric connectivity index. This topological characteristic is based on the distance-cum-adjacency taking into account also the eccentricity and valency of each vertex of the molecule [34]. Compounds with high values of ECCEN show lower retention on DEA compared to compounds with lower ECCEN. The critical role of the 2D structure of the
compound was further confirmed by WPATH. WPATH as the Wiener index, is a distance-based topological index calculated using molecular graph as the sum of distances between all vertex pairs [34, 35].

In accordance with LSER classification, strong retention of compounds with acidic groups (nAcid) was observed indicating interactions with amine groups of the stationary phase. Consistently, a high number of basic groups (nBase) in the molecule resulted in repulsion of this compound from the stationary phase and lower retention. This effect was particularly pronounced when MeOH was used, whereas it was slightly attenuated when MeOH with additive was used. This repulsion between positively charged stationary phase and compounds with basic groups with partial positive charge on the surface was further confirmed by negative weights of relative positive charge (RPCG). RPCG shows that the localization of the partial positive charge on the molecular surface is also important. Compounds with a strong positive charge localized at one part of the molecule will be more strongly repelled than the molecules with more groups on the surface with lower charge.

The presence of H bond acceptors (nHBAcc) in the molecule also had a decreasing effect on retention, which was further confirmed by a slight positive weight for H bond donor groups. This suggests that the surface of the stationary phase also acts as H bond acceptor to repel the analyte. The presence of electronegative fluorine group (khs.sF) decreased retention confirming the decreasing effect of H bond acceptors.

Contrary to 2-EP, 2-PIC, and 1-AA, the formation of pseudo-stationary phase was not observed on DEA. As the silanols on the DEA surface are not sterically hindered by the aromatic ring as in case of 2-EP, 2-PIC, and 1-AA, we can hypothesize that these silanols and/or hydroxyls from the propanediol linker can interact with amine moieties of the DEA functional groups. In this case, these amine moieties are no longer available for the adsorption of the mobile phase and thus formation of the pseudo-stationary phase.

Comparison of $t_R$ showed that most compounds eluted in similar $t_R$ using all 3 tested organic modifiers (Figure 6), confirming similar retention mechanisms. The coefficient of determination between $k'$ obtained with MeOH and $k'$ obtained with MeOH with additive was > 0.99 in both cases. Several compounds were eluted only using specific organic modifier. These compounds included 2-hydroxycinnamic acid, 3-hydroxycinnamic acid, and catechin for MeOH+NH₃ and 2-methoxyestradiol for both additives.

### 3.6 Retention time shifts over time

Changes in $t_R$ over time were observed even by simple overlay of the obtained chromatograms, especially on the DEA column. Subsequently, the weights determined by ANN for each molecular descriptor at each data point were compared to enable elucidation of changes in the stationary phase
surface and/or retention mechanism. Standard deviations (SD) were calculated between the molecular descriptor weights at each data point. The SDs were then divided into 5 groups based on their value to allow comparison of retention time stability based on stationary phase/organic modifier. This comparison is shown in Figure 9A, and the molecular descriptors with the largest changes in weights over time are listed in SM Figure S8 and S9.

The most stable retention behavior on the 2-EP column was observed using MeOH+H₂O with most SD < 0.3 (Figure 9A). Only the effect of polarizability, expressed as BCUTp-1l, and molecular framework, expressed as FMF, changed more significantly with time corresponding to dipole-dipole and π-π interactions (SM Figure S8). However, these changes were still within SD < 0.5. On the other hand, the effect of several molecular descriptors significantly changed when pure MeOH was used. The general trend suggests an increasing effect of these molecular descriptors, including BCUTp-1l, Kier3, FNSA-1, TPSA, and ATSc5. The greatest variation of molecular descriptor weights was observed when MeOH+NH₃ was used. In contrast to MeOH, a decreasing/increasing effect was observed following the U pattern suggesting that the effect of MeOH is dominant up to M6 followed by the effect of the additive. Indeed, the profile of the changes up to M6 followed the trend observed with MeOH. Subsequently, a decrease in the effect of the described molecular descriptors was observed. Overall, the same molecular descriptors were affected by time using all 3 organic modifiers, i.e., BCUTp-1l, FNSA-1, and Kier3 (SM Figure S8).

Even higher stability was observed on 2-PIC (Figure 9A), especially when using MeOH and MeOH+H₂O. On the other hand, the use of MeOH+NH₃ resulted in changes in weights of three molecular descriptors in particular, namely FMF, MDEO-12, and MDEO-22 (SM Figure S8). The higher fluctuation using MeOH+NH₃ can be explained by the effect of the additive interacting with free silanols as opposed to the SEF.

Surprisingly, a significantly higher variation of molecular descriptor weights was observed on the 1-AA column although the same linker is used as in 2-PIC. The highest stability comparable to the t<sub>R</sub> stability on 2-PIC was observed with MeOH+NH<sub>3</sub>. On the other hand, the use of MeOH and MeOH+H<sub>2</sub>O resulted in 17 and 18 molecular descriptors, respectively, with SD of weights > 0.5. For MeOH, an abrupt change in most weights was observed between M9 and M12. For MeOH+H<sub>2</sub>O, the changes were more gradual. However, for all organic modifiers tested, only about 20% of the compounds showed a t<sub>R</sub> shift within ± 0.5% of the t<sub>R</sub> at the first injection after 12 months of column use. The molecular descriptors most affected were those describing the 3D structure of the analytes suggesting positional changes of the 1-AA moiety (SM Figure S9).

The highest instability of t<sub>R</sub> over time was observed on the DEA column, especially with MeOH and MeOH+NH<sub>3</sub>. Indeed, the addition of water had a significant beneficial effect on the retention stability.
Nevertheless, only 20% of the compounds had t<sub>R</sub> within ± 0.5% of the first injection after 12 months of column use (Figure 2). A fluctuation in the molecular descriptor weights was observed when MeOH+H<sub>2</sub>O was used. On the other hand, a significant abrupt change in molecular descriptor weights occurred between M9 and M12 with MeOH and M6 and M9 with MeOH+NH<sub>3</sub>. This suggests a sudden change in the stationary phase. However, Figure 2 shows that the % of compounds with stable t<sub>R</sub> gradually decreased over time using all three organic modifiers. All stationary phases tested in this study except for 2-EP use propanediol linker which should reduce the number of free silanols and shield them from SEF and other undesirable interactions. The only notable difference between 2-EP, 2-PIC, and DEA stationary phases is the presence of aromatic ring that could also shield these silanols. Our results indeed suggest that DEA was more susceptible to SEF. Molecular descriptor ALogP related to the lipophilicity of the analyte belong among molecular descriptors with the highest change in weights over time. Lipophilic analytes were less retained on DEA in months 0–6 but this effect was mitigated in the subsequent measurements (SM Figure S9). This suggests that the surface of the stationary phase changed resulting in higher number of places for lipophilic interactions, i.e., silyl-ethers could be present instead of original silanols. Stronger retention of branched and cyclic molecules was observed on DEA as discussed above suggesting the formation of a cycle by weak interactions of hydroxyl group from propanediol linker and DEA functional group. However, this increasing effect of cyclicity (FMF) and decreasing effect of long aliphatic chains (nAtomLAC) were significantly reduced after 6 months of column use (SM Figure S9). Thus, further changes on the stationary phase surface are probable.
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

Figure 9. (A) Percentage of molecular descriptors with standard deviations between weights determined by ANN at each data point: < 0.1 (dark blue), 0.1-0.3 (light blue), 0.3-0.5 (yellow), 0.5-1.0 (light red), > 1.0 (dark red). (B) Percentage of compounds with %-error between t<sub>R</sub> at the 1st injection and after regeneration procedure: < 0.5 (dark blue), 0.5-1.0 (light blue), 1.0-2.0 (yellow), 2.0-5.0 (light red), > 5.0 (dark red).

3.7 Effect of the regeneration procedure
The t<sub>R</sub> shifts observed especially on 1-AA and DEA columns were quite severe preventing the possibility of long-term studies being carried out using these stationary phases. Therefore, the possibility of regeneration was tested. To determine the effectiveness of the used regeneration procedure, the %-error between the t<sub>R</sub> after regeneration and the t<sub>R</sub> at the first injection was calculated to describe the possibility of achieving the original retention. Two % differences between k' and peak width were then compared: (i) at the first injection and at M12 vs. (ii) at the first injection and after regeneration. If the latter %-difference is lower than the former, it means that the regeneration procedure resulted in a t<sub>R</sub> closer to the first injection than the t<sub>R</sub> observed after M12.

Overall, around 50% of the compounds had the t<sub>R</sub> after the regeneration within ± 0.5% of the original t<sub>R</sub> at the first injection, with most of these were even within ± 0.1%. At the same time, > 10% of the compounds had %-error > 1%. The lowest ratio was observed for these unstable compounds on the 2-PIC column while the lowest ratio of %-errors < 0.1% was also observed here. However, the t<sub>R</sub> shifts occurring after the 12 months of column use also need to be considered. The retention stability significantly differed between stationary phases and organic modifiers. Therefore, the second comparison of k' had to be carried out to show whether the regeneration procedure reduced the t<sub>R</sub> shifts compared to the shifts observed at M12 (Figure 10).

The regeneration procedure improved the t<sub>R</sub> only for about 20% of the analytes on 2-EP, while other compounds remained unaffected. Slightly better results were observed for peak width where a decreased peak width after the regeneration was observed for about 40% of the compounds. The regeneration procedure had slightly better effect in case of 2-PIC. Indeed, the retention was quite stable on this stationary phase and thus, the regeneration procedure did not bring significant change in the t<sub>R</sub> for most of the compounds. The peak width then improved for about 40% of the compounds. In contrast, t<sub>R</sub> closer to the t<sub>R</sub> of the first injection were observed after regeneration on 1-AA column for > 60% of the compounds using MeOH and MeOH+NH<sub>3</sub>. For MeOH+H<sub>2</sub>O, the t<sub>R</sub> was mostly unaffected by the regeneration procedure and/or additional shift of the t<sub>R</sub> was observed. Regeneration improved the peak width for > 50% of the compounds eluting on 1-AA. Regeneration also positively affected the t<sub>R</sub> and peak width of about 20% and 50% of the compounds on DEA, respectively.
<figure><img src="image_13.png" /><figcaption>Figure 10. Comparison of changes in retention time and peak width after regeneration procedure. k' closer to the value of the first injection after regeneration (blue) vs. after 12 months (grey). Changes within ± 1% are marked in purple. (A) 2-EP, (B) 2-PIC, (C) 1-AA, (D) DEA.</figcaption></figure>

4. CONCLUSIONS

Molecular descriptors as parameters defining individual compounds were explored by ANN to describe
the retention mechanisms of four SFC-dedicated stationary phases with 2-ethylpyridine, 2-picolylamine,
1-aminoanthracene, and diethylamine functional groups. A total of 226 molecular descriptors of each
individual compound allowed to define the specific parameters, including molecular characteristics,
increasing and/or decreasing the retention on each column using three tested organic modifiers. The
effect of the additive on the retention mechanism was quite small in the case of the 2-EP, 2-PIC, and DEA
columns as also confirmed by the high correlation of tR observed using pure MeOH and MeOH with NH3
and/or H2O. Thus, the main advantage of the organic modifier with additive on 2-EP is the possibility to
elute some specific analytes and/or to affect peak width and shape. In contrast to 2-EP, the change in
organic modifier did not result in the elution of additional analytes from 2-PIC. Basically the same weights
were assigned to the molecular descriptors on the DEA column regardless of the organic modifier used. Here, the use of MeOH+NH₃ allowed the elution of several acids. The greatest differences in retention mechanism caused by used organic modifier were observed on the 1-AA column. While MeOH and MeOH+H₂O resulted in similar patterns, the use of MeOH+NH₃ caused significant changes in molecular descriptor weights, reflecting different properties of the analytes playing a role in the interaction with the stationary phase. Furthermore, the formation of pseudo-stationary phase caused by the adsorption of acidic mobile phase on positively charged amine moieties in case of 2-EP, 2-PIC, and 1-AA was described.

2-EP stationary phase had the most stable t<sub>R</sub> when MeOH+H₂O was used, while the highest fluctuation of t<sub>R</sub> was observed with MeOH+NH₃. These results confirmed the positive effect of water on t<sub>R</sub> stability and silyl ether formation prevention. Higher t<sub>R</sub> stability was observed for 2-PIC with propanediol linker shielding residual silanols. The same stability over time was observed when MeOH and MeOH+H₂O were used. A fluctuation was observed with NH₃ as an additive, but this phenomenon can be explained by the additional interactions of ammonia with free silanol groups. On the other hand, 1-AA stationary phase showed the highest stability with MeOH+NH₃. The DEA stationary phase was characterized by the largest changes in t<sub>R</sub> over time. The instability was observed especially when MeOH and MeOH+NH₃ were used, while MeOH+H₂O resulted in increased retention stability. These results suggest changes in the stationary phase surface caused by the silyl ether formation and/or additional interactions of the additive with free silanols. The tested regeneration procedure had no significant effect on 2-PIC where the retention over time was quite stable. Unfortunately, the same is true for 2-EP and DEA where beneficial effect on k' was observed only for about 20% of the analytes, with slightly better results in the case of peak width. A more pronounced effect of regeneration was observed for 1-AA. Indeed, k' values closer to the original one was observed after regeneration for > 60% compounds on 1-AA using MeOH and MeOH+NH₃. Nevertheless, the regeneration procedure did not provide an unambiguous beneficial effect and did not meet the expectation as the surface of the stationary phases did not return to the original state. Therefore, further research is needed to develop more effective regeneration conditions.

CRediT authorship contribution statement

**Veronika Pilařová:** Conceptualization, Investigation, Methodology, Writing – Original Draft, **Kateřina**

**Plachká:** Conceptualization, Methodology, Formal Analysis, Visualization, Writing – Original Draft, **Taťána**

**Gazárková:** Investigation, Writing – Review & Editing, **František Švec:** Supervision, Writing – Review & Editing, **Jean-Christophe Garrigues:** Software, Writing – Review & Editing, **Lucie Nováková:** Conceptualization, Supervision, Project administration, Funding acquisition, Writing – Review & Editing.
**Data availability**

Data will be made available on request.

**Acknowledgments**

The authors gratefully acknowledge the financial support of the Project of the Czech Science Foundation (GAČR n. 21-27270S), the Projects of Specific Research SVV 260 662, and the project New Technologies for Translational Research in Pharmaceutical Sciences (NETPHARM, CZ.02.01.01/00/ 22_008/0004607) co-funded by the European Union.

**Appendix A. Supplementary Material**

**Supplementary Material (PDF):** List of analytes; List of molecular descriptors; LSER parameters; Compounds eluting on 2-EP; Heatmaps of molecular descriptor weights; Molecular descriptors with the highest SD in weights based on used organic modifier; Comparison of $t_R$ on 2-EP and 2-PIC; Molecular descriptors with the highest SD in weights over time.
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**Declaration of interests**

[x] The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[ ] The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
CRediT authorship contribution statement

**Veronika Pilařová:** Conceptualization, Investigation, Methodology, Writing – Original Draft, **Kateřina**

**Plachká:** Conceptualization, Methodology, Formal Analysis, Visualization, Writing – Original Draft, **Taťána**

**Gazárková:** Investigation, Writing – Review & Editing, **František Švec:** Supervision, Writing – Review & Editing, **Jean-Christophe Garrigues:** Software, Writing – Review & Editing, **Lucie Nováková:**

Conceptualization, Supervision, Project administration, Funding acquisition, Writing – Review & Editing.