Modeling indirectly detected analyte peaks in ion-pair reversed-phase chromatography

The direction of the recorded indirectly detected analyte peaks and probe system peaks in a chromatogram can be positive or negative [1,3], depending on the type of interaction (counter-ion or co-ion interaction) and also depending on the relative retention between the probe system peak and the indirectly detected analyte peak under investigation [4]. The situations are depicted schematically in Fig. 1a–d. If the probe component acts as a co-ion towards the analyte (case 1), the first probe peak is always positive, since the first event taking place in the column top is displacement, and the second peak is always negative (see Fig. 1a and b). If the retention factor of the analyte peak is smaller than that of the co-ion probe, the first peak is the analyte and the second one is the system peak (see Fig. 1a) and if the analyte retention factor is larger than the co-ion probe the first peak is the system peak and the second one the solute (cf. Fig. 1b). When the probe component acts as a counter-ion towards the analyte, the first indirectly detected peak is always negative and the second one always positively (see Fig. 1c and d). Which peak is which depends on the relative retention between the analyte and probe system peaks, according to similar principles as outlined for case 1.

Journal of Chromatography A, Volume 1740, 11 January 2025, 465550 - Fig. 1. Schematic illustration of the sign of the indirectly detected analyte (solute) peak and system peak.jpg

The retention factor of the system peaks, for both the probe and analyte, depends on the concentration of the probe in the eluent. The current models in the literature are used to predict the retention of system peaks and are seldom useful for simulating elution profiles. The advantage of these models is that they are rather simple to use. However, if one would like to simulate the elution profiles, one needs to describe the adsorption process using an adsorption isotherm, and simulations are conducted using a column model [5]. Simulation of chromatograms based on mechanistic models is an essential research tool for gaining deeper fundamental understanding. In indirect detection, the analyte concentration is generally considered infinitesimal, however this is seldom true for the probe. Consequently, an adsorption isotherm becomes crucial for modeling purposes. In the simple case of systems without ion-pairing, Forssén and Fornstedt conducted a theoretical investigation employing competitive Langmuir and competitive bi-Langmuir adsorption isotherms to model the adsorption process in indirect detection [2]. They also estimated the elution profiles in these cases. However, to the best of the authors knowledge, elution profiles for systems in which ion-pairing is also present have not previously been modeled, which is the ambition here.

Therefore, the aim of this study is to model elution profiles under indirect detection conditions. To achieve this, indirect detection experiments were conducted using sodium 2-naphthalenesulfonate (SNS) with both anionic and cationic analytes. This led to the investigation of two scenarios: the first involving a probe and analyte with the same charge (co-ion), and the second involving a probe and analyte with opposite charges (counter-ion). In both cases, SNS was used as the probe, with alkyl-sulfonate analytes of the same charge or amine analytes of the opposite charge. In the former case, the SNS probe acts as a co-ion, and classical competitive adsorption isotherms were utilized for modeling. In the latter case, the probe acts as a counter-ion, and an adsorption isotherm considering ion-pairing on the stationary surface was derived and evaluated. The modeling results will be compared with experimentally determined areas of analyte system peaks and with calculated areas of analyte peaks under different conditions. Additionally, the sensitivity of the analytical method will be evaluated in both cases, considering the selectivity between the probe system peak and the analyte system peak.

3. Materials and methods

3.1. Chemicals and materials

All experiments were carried out on an Agilent 1200 Series HPLC System (Agilent Technologies, Palo Alto, CA, USA), which was configured with a binary pump operated in isocratic mode, a 100 μL injection loop, a diode-array UV detector, and a column thermostat. The column thermostat temperature was set to 25 °C and the flow rate to 0.4 mL min⁻¹ for all experiments. The detection wavelength was set to 254 nm. The column used was an XBridge Phenyl column (3.0 × 150 mm; 3.5 µm packing particles) obtained from Waters (Milford, MA, USA). The total porosity of the column was determined using a non-retained marker.

4. Results and discussion

4.2. Simulations of elution profiles

The determined adsorption isotherm model parameters, as seen in Table 1, were utilized alongside the ED model to simulate the elution profiles of both the probe and analytes under all conditions considered in this study. Fig. 5 presents the experimental chromatograms (blue dotted lines) and simulated elution profiles of the probe (black lines) and analyte (red lines) for analytes with the same charge as the probe, i.e., a co-ion probe (case 1). Fig. 6 presents the chromatograms and elution profiles for analytes having an oppositely charged probe component in the eluent, i.e., a counter-ion (case 2). The subplots in each row present the results for a specific analyte.

Journal of Chromatography A, Volume 1740, 11 January 2025, 465550: Fig. 5. Comparison between experimental and simulated elution profiles generated after 1 µL injections of 1 mM analyte when the probe is a co-ion (case 1). Simulated analyte (red lines), simulated probe (SNS, black lines), and experimental UV signal (blue dotted lines). The analytes are: a) and b), PenSulf; c) and d), HexSulf; and e) and f), HeptSulf. The probe concentrations are: 0.2 mM (left-hand panels: a, c, and e) and 0.4 mM (right-hand panels: b, d, and f). Note that the signal responses are normalized for improved visual comparison.

In the left-hand panels of the aforementioned figures, the subplots show the comparison between the experimental data and simulations for a 0.2 mM concentration of SNS in the eluent, while in the right-hand panels, the subplots show the same comparison for 0.4 mM SNS in the eluent. Additionally, the “Supplementary material” file presents data for SNS concentrations of 0.1 and 0.3 mM in the eluent in Figs. S1 and S2, respectively.

Figs. 5 and S1 display the results for the first group of analytes considered, namely, the alkyl sulfonates, which share the same charge as the probe, case 1. Here, the competitive bi-Langmuir isotherm model was employed to simulate the elution profiles. In the experimental chromatograms (blue dotted lines), two peaks are observable, aside from the initial positive and negative distortions of the baseline appearing at around two minutes. These initial distortions arise from differences between weakly adsorbed compounds in the eluent and diluent, such as differences in solvent content or buffer composition, and are eluted close to the dead volume of the column, having no significance in this context. In this case, these two mentioned main peaks on the chromatograms are always first positive and then negative. As discussed above, the probe added to the eluent adsorbs to the stationary phase. When the sample is introduced to the column equilibrated with this eluent, system peaks are generated due to disturbances in equilibrium caused by the analyte, in case 1 the probe acts as a co-ion therefore the first peak is always positive, as illustrated schematically in Fig. 1a and b. The probe system peak travels at a speed dependent on the probe adsorption strength to the stationary phase, therefore its retention time is independent on the injected analyte under linear concentration conditions (i.e., with very diluted analyte samples). This time is 12 min and 8.9 min for concentrations of the probe in the eluent of 0.2 and 0.4 mM, respectively. This can be observed by comparing Fig. 5a, c, and e with Fig. 5b, d, and f. This elution peak is called the probe system peak. The disturbance of the probe equilibrium between the mobile and stationary phases moves along the column together with the elution peak of the analyte, which can be prior (Fig. 5a-d) or after the system peak (Fig. 5e and f). Thus, it has the same retention time as the peak of the analyte eluted under linear conditions of the analyte concentration. This property is utilized in the indirect detection of analytes that are undetectable or very difficult to detect. The area of these peaks is strongly dependent on the system's sensitivity. A more sensitive system will produce larger peaks (HeptSulf), whereas a less sensitive system (PenSulf) will yield smaller elution peaks. This aspect is discussed further in Section 4.3. Through the detected system peak of the probe, we can determine the retention time of the eluted peak of the analyte, which is not visible to the detector. As seen in Figs. 5 and S1, the simulated peaks of the analytes and the probe agree very well with the experimental chromatograms. The highest relative error in the calculated retention time is 2.23 %. However, in 75 % of the considered cases, the relative error is <1 %. In calculating the error, the retention times of the peaks of the experimental and calculated elution profiles of SNS were taken into account. The retention times were determined at the apex of the peaks.

It should be noted that the peak of the analyte is eluted together with the positive peak of the probe for PenSulf and HexSulf, as shown in Figs. 5a–d and S1a–d, which corresponds to the schematic illustration in Fig. 1a. However, in the case of the injection of HeptSulf, the analyte peak is eluted together with the negative peak of the probe, as seen in Figs. 5e and f and S1e and f (cf. Fig. b). The observed difference in the direction (i.e., positive or negative) of the probe system peak connected with the analyte peak is due to the difference in the relative retention strength between the analyte and the probe. In the considered case, the competition for adsorption sites and a Langmuirian adsorption isotherm dictate the behavior: if the adsorption of the probe is stronger than the adsorption of the analyte, the analyte peak is eluted together with the positive peak of the probe, as seen in Figs. 5a–d and S1a–d. Conversely, if the adsorption of the probe is weaker than the adsorption of the analyte, the analyte peak is eluted together with the negative peak of the probe, as observed in Figs. 5e and f and S1e and f. See also the illustration of these typical case 1 chromatographic appearances in Fig. 1a and b, respectively.

5. Conclusion

For the first time, to our knowledge, the chromatograms were modeled from indirect detection experiments using sodium 2-naphthalenesulfonate (SNS) as the probe and both anionic and cationic solutes. The adsorption isotherms of the solute and the probe were determined, revealing that the probe and the anionic analytes (pentanesulfonate, hexanesulfonate, and heptanesulfonate) fitted well to a classical competitive bi-Langmuir model, which considers competition for available adsorption sites on the stationary phase between the analyte and the probe. However, for the cationic solutes (hexylamine, (dibutyl)amine, tripropylamine, and triethylamine), ion-pair formation also needed to be considered. Therefore, an expanded bi-Langmuir model that accounts for ion-pair formation was derived in this study. All these models were successfully used to predict the retention factors of the probe's system peak and the solutes' system peaks.

Furthermore, these determined adsorption isotherm parameters were utilized to successfully model elution profiles using the equilibrium dispersion model. The investigation clearly demonstrates that the ion-pair formation modified bi-Langmuir model derived in this study works well in predicting elution profiles in the case of indirect detection.

Using the adsorption isotherms and the equilibrium dispersive model, it was shown that the sensitivity (area of a peak with the same load) increases as the distance between the probe's primary system peak and the analytes' system peak decreases. Additionally, the sensitivity of the chromatographic analytical method was analyzed using the adsorption isotherm model and compared against experimental findings. This was done experimentally by determining the slope of the standard curves for all solutes under investigation. The slope of these standard curves was compared against calculated area changes with injected load, showing excellent agreement between them. This also indicates that the derived adsorption isotherm model, including the ion-pair formation, is valid under these conditions.

Finally, it is in this context worth mentioning that although this study is fundamentally aimed at modeling elution profiles, detailed simulations and determinations of adsorption isotherm models such as performed here, are not required for the practical use of the indirect detection technique. Indirect detection primarily serves as an effective method for identifying sample components that lack inherent detectable properties such as absorbance, fluorescence, or electrochemical activity. Additionally, this technique is relatively straightforward and compatible with commonly used detectors in chromatography systems, allowing researchers to circumvent the need for more complex detection methods such as mass spectrometry. But indirect detection has also the advantage, it can be used without specialized knowledge theoretical or advanced tools for mathematical modeling.