A closer study of methanol adsorption and its impact on solute retentions in supercritical fluid chromatography

Journal of Chromatography A, 1442 (2016) 129–139

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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

A closer study of methanol adsorption and its impact on solute retentions in supercritical fluid chromatography Emelie Glenne a , Kristina Öhlén b , Hanna Leek b , Magnus Klarqvist b , Jörgen Samuelsson a , Torgny Fornstedt a,∗ a b

Department of Engineering and Chemical Sciences, INTERACT, Karlstad University, SE-651 88 Karlstad, Sweden Respiratory, Inflammation and Autoimmunity, Innovative Medicines, AstraZeneca R&D, Molndal, 431 83, Sweden

a r t i c l e

i n f o

Article history: Received 21 December 2015 Received in revised form 27 February 2016 Accepted 2 March 2016 Available online 5 March 2016 Keywords: Supercritical fluid chromatography SFC Excess adsorption Solvent adsorption Tracer-pulse method Solute retention

a b s t r a c t Surface excess adsorption isotherms of methanol on a diol silica adsorbent were measured in supercritical fluid chromatography (SFC) using a mixture of methanol and carbon dioxide as mobile phase. The tracer pulse method was used with deuterium labeled methanol as solute and the tracer peaks were detected using APCI-MS over the whole composition range from neat carbon dioxide to neat methanol. The results indicate that a monolayer (4 Å) of methanol is formed on the stationary phase. Moreover, the importance of using the set or the actual methanol fractions and volumetric flows in SFC was investigated by measuring the mass flow respective pressure and by calculations of the actual volume fraction of methanol. The result revealed a significant difference between the value set and the actually delivered volumetric methanol flow rate, especially at low modifier fractions. If relying only on the set methanol fraction in the calculations, the methanol layer thickness should in this system be highly overestimated. Finally, retention times for a set of solutes were measured and related to the findings summarized above concerning methanol adsorption. A strongly non-linear relationship between the logarithms of the retention factors and the modifier fraction in the mobile phase was revealed, prior to the established monolayer. At modifier fractions above that required for establishment of the methanol monolayer, this relationship turns linear which explains why the solute retention factors are less sensitive to changes in modifier content in this region. © 2016 Elsevier B.V. All rights reserved.

1. Introduction In the last years supercritical fluid chromatography (SFC) using packed columns has increased in popularity and is today considered a prime technique for a wide range of compounds offering complementary selectivity as compared to reversed phase liquid chromatography (RPLC) [1–6]. This recent revival of SFC has been strongly encouraged by both academic research groups and the pharmaceutical industry and has been facilitated by a rapid development of modern instrumentation [1,3]. The low viscosity and high diffusivity of the eluent used in SFC allows for higher mobile phase velocity as compared to HPLC, leading to shorter analysis times without reduced efficiency or loss of resolution [4–10]. The main solvent in SFC is carbon dioxide. Carbon dioxide is a linear molecule without any dipole moment; therefore, the polarity is similar to that of heptane, which is commonly used in normal

∗ Corresponding author. E-mail address: [email protected] (T. Fornstedt). http://dx.doi.org/10.1016/j.chroma.2016.03.006 0021-9673/© 2016 Elsevier B.V. All rights reserved.

phase liquid chromatography. In order to elute polar compounds from the polar stationary phases, polar solvents (such as methanol, ethanol and 2-propanol) are added to the eluent. This addition often affects the retention but also, to a lesser extent, the selectivity of the separation [11,12]. Under normal operational conditions (5–40% modifier in the eluent) significant amounts of the polar solvent are adsorbed to the stationary phase resulting in a dynamic modification of the surface [13,14]. In LC many studies have been conducted to investigate the solvent adsorption to stationary phases [15,16]. However, only a few studies have been done under SFC conditions. Most of these studies focus on the main solvent, i.e. carbon dioxide [17–22], or just cover small modifier fractions [23,24]. However, Vajda and Guiochon recently used the minor disturbance method to study the full range of modifier adsorption to a silica surface [13,14]. In the minor disturbance method, small amounts of the organic solvent are injected into a system already equilibrated with a binary eluent. The injected “disturbance” results in a perturbation peak or system peak that is used to determine the surface excess. By measuring perturbation peaks, at several different equilibrated fractions of

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modifier of the binary eluent, the excess adsorption isotherm over the whole modifier fraction range can be determined; however, it is not easy to distinguish the perturbation peaks from the general front disturbances. In this study we are going to use the tracer pulse (TP) method to determine the excess adsorption isotherm of deuterium-labeled methanol to a Kromasil diol silica surface [25–27]. More than fifty years ago Helfferich and Peterson published an article in Science regarding a “paradoxical” behavior in nonlinear chromatography [26]. In that study they theoretically showed that when an excess of sample molecules is injected into a chromatographic column that is equilibrated with a constant stream of identical molecules, the observed peak will not contain the injected molecules. Instead, the observed peak will only contain molecules from the stream whereas the injected molecules will exit the column in a slower moving, invisible peak. The general visible peak is known as the perturbation peak or system peak [28], and the invisible peak is the tracer peak [29]. To detect the injected molecules, we used stable isotopes (e.g. deuterium labeled) and mass spectrometric detection [29]. The aim of this study is twofold. Firstly, we aim at a deeper understanding of how methanol adsorbs to a diol stationary phase in SFC conditions. For this purpose, the tracer pulse method was used to determine surface excess adsorption isotherms of methanol from carbon dioxide on a diol silica adsorbent. Secondly, we aim at relating these findings to actual solute retention times to understand in more detail how this solvent adsorption affects retention times for various solutes injected at different fractions of methanol. By taking this approach, we hope to gain better unified knowledge on how the solute retention is affected by the solvent surface excess isotherm, in this particular model system.

2. Theory Gibbs surface excess () could be used to describe the adsorbed layer formed on a surface in contact with a binary mixture. Gibbs surface excess according to IUPAC, is defined as “the difference between the amount of component actually present in the system, and that which would be present (in a reference system) if the bulk concentration in the adjoining phases were maintained up to a chosen geometrical dividing surface (Gibbs dividing surface)” [30]. The surface excess could be positive, i.e. representing an accumulation, or negative, representing a deficiency of the compound on the surface compared to in the bulk solution. Surface excess () respective surface concentration (q) depends on the fraction of organic modifier in the eluent (); the concept is illustrated in Fig. 1, where the fraction of organic modifier spans from neat carbon dioxide to neat modifier. In Fig. 1a, phase systems at different  are drawn; molecules adsorbed to the surface are represented by gray and black circles, gray circles represent the excess molecules, black circles represent the molecules that would be present in the reference system and white circles are molecules in the bulk. At low modifier concentrations in the bulk, most adsorption sites are available and it is highly favorable for molecules to adsorb (see Fig. 1a, I). At this point the surface excess (solid lines) and the surface concentration (dashed lines) are more or less identical (see Fig. 1b). At further increased bulk concentration, the number of available adsorption sites on the surface decreases, which results in a slower increase of the surface concentration. The excess reaches a maximum at point II, when the increase in the surface concentration is equal to the increase of the bulk eluent. After this point, the excess will decrease. Note that the surface concentration is still increasing at this point. Point III represents the point at which the monolayer is formed on the surface. Finally, neat methanol is used in the bulk, with the result that the

surface and bulk concentration are identical and we have no excess (see Fig. 1a, IV). In this study the excess adsorption isotherm () is determined using the tracer pulse method and could be expressed as [25]:  () =

(VR () − V0 ) , S

(1)

where VR is the retention volume of the tracer peak, S is the specific surface area of the stationary phase, V0 is the total volume of the mobile phase in the column, and  is the fraction of modifier in the eluent. The total adsorbed amount of modifier on the stationary phase (q) (see dashed line in Fig. 1b) could be expressed as [31]:

 

q  =  () + Va ,

(2)

where Va is the surface-specific volume of the adsorbed phase. To be able to estimate the surface-specific volume we need to define the Gibbs dividing plane over the surface. In the region surrounding the inflection point (point III in Fig. 1b), a further increase of the bulk concentration does not result in additional adsorption to the stationary phase. This point could be used to estimate the layer thickness according to [14,31]:  () = qmax − 

d () = qmax − Va , d

(3)

where qmax is the maximum amount of modifier which could be adsorbed per square meter of stationary phase [31]. In the minor disturbance method, retention volumes of the perturbation peaks (VR,Pert ) are used instead of tracer peaks to determine the adsorption data. Here the established equilibria is disturbed, generating perturbation peaks, therefore the method is called the perturbation method and used to determine general isotherms [29]. The perturbation peaks propagates through the column at another velocity than that of the tracer peak, as describe in the Introduction (see Section 1). The excess adsorption isotherm using the minor disturbance method could be expressed as [14,32]:

  () = 0



(VR,pert () − V0 ) d, S

(4)

Deriving Eqs. (1) and (4) assumes that the volumetric flowrate is constant or at least that the temperature, pressure and density gradient over the column does not significantly affect the retention of the tracer or the perturbation peaks. 3. Experimental 3.1. Materials Carbon dioxide (99.99%, AGA Gas AB, Lidingö, Sweden), HPLC graded methanol (> 99.9%, Sigma-Aldrich, St. Louis, MO, USA) and methanol-d4 99.8 atom%D, Sigma-Aldrich, St. Louis, MO, USA) were used. The seven analyzed solutes were adenine, caffeine, theophylline, antipyrine, theobromine, bromacil and deoxyadenosine; purchased at Sigma-Aldrich (St. Louis, MO, USA). The SFC system was a Waters UPC2 system (Waters Corporation, Milford, MA, USA) equipped with a PDA detector and a Waters SQD single quadrupole mass spectrometer, using either APCI or ESI in positive mode. The mobile phase flow to the mass spectrometer was split with a passive splitter and diluted with 0.2 mL/min methanol for APCI mode and with 0.45 mL/min of a mixture of 95/5% (v/v) methanol/10 mM HCOONH4 for ESI mode, respectively. The extra column volume was measured as the retention volume of methanol-d4 without the column in the system and was 0.074 cm3 from injection loop to the PDA detector and 0.109 cm3 from the loop to the MS detector. All retention volumes were corrected with the extra column volume. Two absolute pressure transmitters (EJX530A, Yokogawa Electric

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Fig. 1. Schematic illustrations of the concepts surface concentration and surface excess, respectively. In a) we see the molecular level at the surface, corresponding to different modifier fractions, , (I–IV). Here white circles are molecules in the bulk and gray/black ones are molecules on the surface; gray circles indicate excess molecules. In b) the surface excess,  (gray solid line) and the solvent surface concentration, q (black dashed line) respectively are plotted versus the fraction organic modifier in the eluent (). Here, the gray dash-dotted line shows an extrapolation of the slope of the linear decrease of the excess adsorption around the inflection point marked with a vertical dotted line. The intercept of this slope gives the maximum adsorbate capacity per square meter of stationary phase qmax (gray line). The vertical dashed line denotes the maximum of the excess.

Corporation, Tokyo, Japan) were connected to the inlet and the outlet of the column, respectively. The pressure in the column was estimated as an average of these two sensors; a Pico Technology data logger was used to record the pressure. The total and modifier mass flow was measured directly after the mobile phase mixer and between the solvent pump and the vent valve, respectively using a Bronkhorst mini CORI-FLOW model M12 (Bronkhorst High-TechB.V., Ruurlo, Netherlands). The modifier flow was measured during each experiment. The total mass flow was measured at three different times for each experimental condition, the average measure for each condition were used in the calculations. The mini CORI-FLOW model M12 is tested at pressures up to 340 bar and flow rates greater than 0.1 g/h. To obtain accurate flow rate measurement for low fraction of the modifier (below 0.5% (v/v)) the flow rate was determined by weighing the amount of methanol pumped for 15 h using an analytical balance +/− 0.1 mg (AX504, Mettler Toledo, Greifensee, Switzerland). Columns: The columns used were a Kromasil Diol (150 × 4.6 mm) and a Kromasil Silica (100 × 4.6 mm) with 5 ␮m particles and 60 Å pore size (AkzoNobel, Bohus, Sweden). The diol column had a surface area of 540 m2 / g and contained 0.992 g stationary phase [33].

3.2. Experimental procedures All experiments were conducted with a set instrumental back pressure at 120 bar, a column temperature of 40 ◦ C and a flow rate at 1.0 mL/min. The void volumes of the columns were estimated by repeated injections of methanol-d4 with neat methanol as eluent. Before each experiment starting at neat carbon dioxide the column was equilibrated with neat carbon dioxide for approximately 65 h at 60 ◦ C to wash out all residues of methanol. To avoid uptake of water the methanol was exchanged every day and purged with nitrogen gas. The labeling effect was determined by triplicate injections of methanol and methanol-d4 with neat carbon dioxide as eluent, the peaks were detected at 196 nm.

3.2.1. Tracer pulse method The excess adsorption isotherm was measured with the tracer pulse method. Experiments were carried out over the full range of eluent compositions from 0 to 100% (v/v) of methanol, with both increasing and decreasing methanol fractions. After 60 min equilibration for a certain eluent composition, 1 ␮L of the isotope labeled tracer was injected in triplicate at each composition (using a 2 ␮L loop). The retention volumes were calculated using average retention times for the tracer pulses. The samples were detected using

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Table 1 Structures of solute components used in the study. Name

Adenine

Caffeine

Theophylline

Antipyrine

Structure MW [g/mol]

135.1

194.2

180.2

188.2

Name

Theobromine

Bromacil

Deoxyadenosine

Structure MW [g/mol]

180.2

261.2

251.2

MS in APCI mode, which was tuned manually for positive single ion monitoring (SIM) at 37 m/z, with a probe temperature of 350 ◦ C and a cone voltage of 30 V.

˙ of carbon dioxide and molar volume and measured mass flows m methanol: v%MeOH =

3.2.2. Effect on retention factor Table 1 shows the seven different solutes analyzed on the silica respective diol column using mobile phases with set methanol fractions ranging from 1 to 60% (v/v). The samples were diluted in methanol to a concentration of 2 mg/mL and 10 ␮L were injected in triplicate (using a 10 ␮L loop). The peaks were detected with UV (␭ = 220 nm) and MS in the ESI mode. 3.2.2. Calculation of volume fractions To verify the set conditions of the system the real volume fraction of methanol in carbon dioxide was calculated using measured mass flow, pressure and temperature. Initially the molar volume of the fluid (V) was calculated according to Kato et al. [34]: V=

M 

,

(5)

M = xCO2 MCO2 + xMeOH MMeOH

VCO2 = V + xMeOH VMeOH

˙ MeOH m V MMeOH MeOH

+

˙ C0 m 2 MC0

2

· 100

(7)

VC02

4. Results and discussion In this study, we are investigating in more detail how the adsorption of the co-solvent to the stationary phase in SFC affects the retention and equilibration time of the separation system. First, in Section 4.1, the system is validated by measuring flow, pressure, and evaluation of volume fractions of methanol in the mobile phase. Thereafter, the selection of method for adsorption data acquisition is discussed and evaluated. In Section 4.2 the solvent excess adsorption isotherm is determined. Finally, in Section 4.3, we measure the retention factors for test solutes at different fractions of modifier in the eluent to study the impact of methanol adsorption on solute retention. 4.1. System validation

where M is the molecular weight of the fluid,  is the density of the fluid and x is the mole fraction. The mass fractions of carbon dioxide and methanol, pressure and temperature were used as input values in REFPROP v 9.1 from National Institute of Standards and Technologies (NIST) [35] to calculate the density of the fluids using the Kunz and Wagner [36] equation of state implementation. The molar fractions were determined from measurements of mass flow of methanol and total fluid: The partial molar volume (Vi ) was then calculated according to:

∂V ∂xCO2 ∂V = V − xCO2 ∂xCO2

˙ MeOH m V MMeOH MeOH

(6)

A Python 3 x wrapper integration of REFPROP database in CoolProp [37] was used to numerically estimate ∂V/∂x. Then the volumetric fraction of methanol could be calculated from the

For reliable determination of adsorption data we must know the actual volumetric flow rate in our system as well as the modifier fraction of the eluent. To do this the mass flows (methanol and total) as well as pressure were measured, and from these measurements, the density, volumetric flow and volume fractions were calculated as an average flow over the column. The densities were calculated using REFPROP from NIST; see Section 3.2 for volumetric flow rate and volume fraction of modifier calculations. All measurements were conducted in triplicate. The eluent used in SFC is a compressible fluid [6]. Therefore, the volumetric flow of the fluid increases toward the end of the column, especially when the organic modifier fraction is low. To reduce this effect the system was operated at a flow rate of 1 mL/min. Fig. 2a shows the actual flow rate for a set flow rate of 1 mL/min (gray line), at different methanol fractions in the eluent. The deviation from the set flow rate value decreases as the methanol fraction increases (see Fig. 2a), an observation consistent with previous

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Fig. 2. a) Measured volumetric flow rate at different actual volume fractions of methanol (␪) (circles). The set flow rate of 1 mL/min is indicated by the horizontal gray line. b) Difference between set and actual volume fraction of methanol (␪) at different actual volume fractions of methanol is plotted.

studies [13,38,39]. That is, the largest difference between set and actual flow rate is at low fractions of modifier. Previous studies have shown that calculations with set flow rate give lower adsorption isotherms as compared to calculations using measured values [13]. The observed difference between set and actual flow rates is system dependent, because all separation system manufactures have different approaches to control the carbon dioxide flow rate. We also noted a volumetric flow of 1.02 mL/min for neat methanol in the column. However, there is a temperature difference in the conditions between the pump and the column as the fluid is heated in the column. At a temperature of 22 ◦ C, the measured mass flow for neat methanol is consistent with a flow of 1.00 mL/min. This clearly shows the importance of measuring the flow rate in the column for conducting accurate adsorption studies. Fig. 2b shows the difference between the set volume fraction of methanol and the actual fraction (␪) against the actual volume fractions (␪) of methanol. As far as we know, no one has investigated how this error is manifested in the acquired adsorption isotherm. In Fig. 2b, one can see that the set values of the modifier fractions were consistently larger than the actual values. Later, in Section 4.2, we will investigate how this affects the adsorption isotherm. As discussed in the introduction, an injection of methanol into a column already equilibrated with an eluent containing methanol will give rise to a perturbation peak used in the minor disturbance method and a tracer peak used in the TP method. In this study our determined perturbation peak was very noisy and contained extra peaks. At higher methanol fractions the peak was not even detectable using UV (see Fig. 3a). The corresponding tracer peak (see Fig. 3b) did not have these issues. Therefore, the TP method was selected for our adsorption isotherm studies. Using isotope labeled compounds could result in the labeled compounds interacting differently with the stationary phase in the separation system as compared to the unlabeled compounds, in what is known as the labeling effect. Previously, we investigated how this affects the estimated adsorption isotherm and found that it primarily affected the estimated monolayer saturation capacity [29].

The labeling effect was investigated by injecting either methanol or deuterium labeled methanol (methanol-d4) using neat carbon dioxide as eluent (see Fig. 4a). We noted that the areas of the eluted peaks were smaller for labeled methanol than for unlabeled. The reason for this is that, in the region of 163–220 nm, the spectra for methanol-d4 shifts its absorption maxima towards smaller wavelengths as compared to methanol [40]. This shift is associated with stretching O (D) and results in a lower molar attenuation coefficient for methanol-d4 than for methanol at 196 nm, where the peaks were detected. Therefore, the UV response from methanol and methanol-d4 was normalized (see Fig. 4b). The estimated maximum labeling effect results in an increased retention time of 0.33%. Therefore, the labeling effect can be considered to be more or less negligible in this study. 4.2. Adsorption isotherms The excess adsorption isotherm for methanol on a diol column was measured in the full range from neat carbon dioxide to neat methanol as eluent. This was repeated three times; twice with increasing methanol fractions and once by decreasing the fraction of methanol. All injections of methanol-d4, except when neat carbon dioxide was used as eluent, resulted in symmetrical peaks. Fig. 5a and b shows the injections of methanol-d4 in an eluent comprising 20% (v/v) methanol in carbon dioxide and neat carbon dioxide, respectively. In the latter case the eluted peak is strongly tailed whereas in the former case the peak is sharp and symmetrical. To predict the retention volume at neat carbon dioxide, raw adsorption isotherms were determined from the overloaded methanol elution profiles using the elution by characteristic points [38]. The raw adsorption isotherm data were fitted to the Langmuir adsorption isotherm[41]. The retention volume of methanol using neat carbon dioxide as mobile phase was estimated from the adsorption isotherm using this expression:



VR = V0 1 + F

dq | dC C=C0

 ,

(8)

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a)

(b)

Fig. 3. Perturbation and tracer peak from a 1 ␮L injection of neat methanol-d4 into a eluent containing 3% (v/v) methanol in carbon dioxide at a set flow rate of 1 mL/min. a) Perturbation peak (detected using UV) and b) the corresponding tracer peak (detected using MS-APCI). For more details, see Experimental section.

a)

b)

Fig. 4. a) Overlaid elution zones from a 1 ␮L injection of methanol (solid) or methanol-d4 (dashed) into a stream of neat carbon dioxide at a set flow rate of 1 mL/min. b) same elution as in a) but with normalized response.

where VR is the estimated retention volume, V0 is the holdup volume, F is the phase ratio (ratio between stationary phase and mobile phase volume), and dq/dC at C = C0 is the initial slope of the adsorption, also known as the Henry constant or the equilibrium ratio. Cavazzini et al. used a similar approach to estimate the methanol adsorption in dichloromethane surface excess adsorption isotherms of methanol from dichloromethane on a polymeric DACH-ACR adsorbent [42]. In that study, the authors used the inverse method to estimate the adsorption isotherm of methanol at neat dichloromethane.

When the retention volumes of methanol-d4 were compared for the experiments conducted three times only small differences between replicates were found. The retention volumes were then calculated as a mean of all injections with same methanol fraction in the eluent (see Fig. 6). At values of the methanol fraction lower than (␪ < 0.1), the retention volumes increased rapidly with a decreasing fraction of methanol in the eluent, and at higher methanol fractions, the retention volume was more or less equal to the void volume. In Fig. 7 the excess adsorption isotherms (circles) and surface concentration (black dashed line) are presented. At an actual methanol fraction of 0.13 the excess adsorption has reached its

E. Glenne et al. / J. Chromatogr. A 1442 (2016) 129–139

a)

135

b)

Fig. 5. Tracer peaks of 1 ␮L methanol-d4 injected at methanol fractions in the eluent of a) 20 or b) 0% (v/v) at a set flow rate of 1 mL/min.

Fig. 6. The retention volumes for methanol-d4 at different actual fractions of methanol (circles), calculated as a mean value of experiments conducted three times.

maximum (see vertical dashed line) and the inflection point of the adsorption isotherm is reached at a methanol fraction of 0.28 (vertical dotted line in Fig. 7). The surface specific volume Va was estimated to 0.402 ␮L/m2 using Eq. (3) at the linear decrease of the excess isotherm at methanol fractions between 0.17 and 0.38. This corresponds to a layer thickness of about 4 Å. Methanol has a volume of 67 Å3 [32]; if we assume that the methanol is spherical, the diameter could be estimated to ≈5 Å. From this we could conclude that a monolayer of methanol is formed on the column. For methanol fractions above 50% (v/v) (cf. Fig. 7) the adsorption isotherm increase and this might be an indication of multilayer behavior. This increment is though weak and there might be deviations in the layer estimation at fractions above the linear region.

Vajda and Guiochon showed that they had a multilayer formation of 10.2 Å of methanol on a silica column [14]. In their study the maximum of the excess isotherm for methanol was estimated to be just under 0.1 and the inflection point was at 0.28. The multilayer formation combined with a steeper initial slope on the silica column compared to the diol column indicates a stronger interaction with methanol on the silica surface. Further, a comparison between the retention factor for methanol on these two phases, where the retention factor is 42 on the silica column and only 12 on the diol column, indicates that methanol adsorbs much weaker on the diol column as compared to the silica column. This is expected and can be explained by a more polar nature of the silica column.

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Fig. 7. Determined surface excess (circles) and estimated surface concentration (dashed black line). The gray dash-dotted line shows the extrapolated negative linear slope in the excess adsorption. The excess adsorption maximum is shown with vertical dashed line and inflection point with vertical dotted line.

Fig. 8. Comparison between excess adsorption isotherms calculated using set flow rate and methanol fraction (dashed gray line), actual flow rate and set methanol fraction (dash dotted gray line) or both actual flow rate and methanol fraction in the eluent.

The excess adsorption isotherm in Fig. 8 is calculated in three different ways; (i) with set volume fractions and set flow rate (gray dashed lines), (ii) with set volume fractions and measured flow rate (gray dash dotted line) and with (iii) both actual volume fractions and measured flow rates (black line). It is clear from a visual inspection that the excess adsorption based on the set values of volume fractions (gray lines) increases when the flow rate is corrected (dash dotted line). Correction for both flow and volume fractions (black line) results in an excess adsorption that has a lover and later maximum of the excess adsorption isotherm. Further, the

excess adsorption isotherm based on set volume fractions has a steeper linear decrease of the excess isotherm around the inflection points as compared to the one with corrected volume fractions. This steeper decrease results in an overestimation in the surface specific volume and an estimated solvent layer thickness of 7.3 Å, for set volume fractions with corrected flow and 6.4 Å, set volume fractions and flow. This corresponds to 1.5 and 1.4 layers of methanol. Thus, calculations based on the set values on the instruments, results in wrong assumptions about the adsorbed layer volume and even

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a)

b)

Fig. 9. Natural logarithms of the retention factors for caffeine, antipyrin, bromacil, theopylline, theobromine, adenine and deoxyadenosine (symbols, see figure caption) versos different actual fractions of methanol on a) diol or b) silica column. The dashed vertical line marks the maximum of the excess adsorption and the dotted vertical line shows the inflection point, respectively.

about the number of layers. Therefore is it important to measure both the total flow rate and flow of the volume fractions.

4.3. Impact of methanol adsorption on solute retentions With the gained detailed knowledge about the methanol adsorption on the diol surface, it was possible to investigate how this layer influenced the solute retention factors. To make the observation more general, solutes retention behavior on a silica column were also investigated. The methanol adsorption data on the silica column were taken from an already published article by Vajda and Guiochon [14]. The retention factors were measured for seven different small ( < 300 g/mole) neutral solutes see Table 1) on both the silica and diol columns using different mobile phase compositions. In Fig. 9, the natural logarithms of the solutes retention times were plotted for separations performed on the diol (Fig. 9a) and the silica (Fig. 9b) column. In RPLC, the retention factor (k) dependency on modifier fraction can be described using the linear solvent strength model [43]. This relationship is often linear within a limited range of modifier fraction. From Fig. 9a it is clear that at low modifier fractions of 0–0.28 on the diol column the relationship log k vs methanol fraction is non-linear and very sensitive to methanol changes in the eluent. This methanol fraction range corresponds to the initial part of the solvent adsorption isotherm prior to the formation of the monolayer. After the monolayer formation the log k vs methanol fraction becomes more or less linear and the retention is much less sensitive to methanol changes in the eluent. On the silica column (Fig. 9b) the same trend as for the diol column was observed, with nonlinear relationships at low fractions of methanol, which gets more and more linear as the solvent layer is formed on the stationary phase. This clearly indicates that the linear solvent strength model is usable over a wide modifier fraction as long as the solvent adsorption layer is saturated. At low fractions, the linear solvent strength model is only valid over a very narrow range of modifier fraction.

We could speculate that at low fractions of modifier the solvent and solute compete for the available surface area. In other words, we have a two-component system where methanol should be treated as a component in exactly the same way as the solute is treated [42]. At fractions around and above the point where the solvent layer is formed, methanol just modifies the interaction. In other words, it only affects the adsorption process (equilibrium constant) and does not compete about adsorption sites on the surface. The linear solvent strength theory assumes that the solvent just affects the partition, and this could be the reason for the poor model agreement (very narrow linear windows, see Fig. 9) at low fractions of modifier. 5. Conclusions Excess adsorption isotherms of methanol in carbon dioxide on a diol column were measured in the whole composition range, from neat carbon dioxide to neat methanol, using the tracer pulse method. Our result shows that methanol forms monolayers with a thickness of 4 Å and that the monolayers are formed at a methanol fraction of 0.28. For methanol fractions above 50% (v/v) the adsorption isotherm increase and this might be an indication of multilayer behavior. This could be compared with methanol adsorption to silica columns where methanol exhibits multilayer formation with a thickness of 10.2 Å [14]. The minor disturbance method was first tested but deemed unsuitable for these measurements, due to noisy signals containing extra peaks, and at higher methanol fractions, the peak was not even detectable. Therefore, the more tedious tracer peak (TP) method was used in this study. In this study special attention was made to determine both the actual flow rate respective the actual fraction of modifier instead of relying on the instrumental set conditions. Previously it was observed that special attention must be paid to the determination of the actual volumetric flow rate, especially when the mobile phase contains a low fraction of methanol [13]. We could confirm this but found that it also of crucial importance to accurate measure the actual delivered volume fraction of methanol for reliable calcula-

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tions of the excess adsorption isotherms. Using the set value of the modifier fraction led to an overestimated layer thickness of 7 Å. We therefore advise to measure both the total flow rate and the flow of modifier, as the actual volume fractions is an important factor. Finally, the establishment of the methanol layer formation was related to the observed retentions of seven different solutes (see Table 1) on a silica respective a diol column (see Fig. 9). The retention factor for the solutes revealed a nonlinear relationship between log k and the modifier fraction at low fractions of modifier, corresponding to the initial part of the methanol adsorption isotherm prior to full formation of the monolayer. The curvature then decreased at higher fractions of modifier, and at methanol fractions corresponding to established solvent layers, the relationship flattened out and finally became more or less linear. This indicates that the linear solvent strength model which assumes that the solvent should be described as a modifier (just modifying the solutes equilibrium between stationary and mobile phase) may not be valid at low fractions of modifier in the eluent. The findings concerning the uncertainties of mobile phase compositions found especially at low modifier concentrations are important also for practicing chromatographer. This may have consequences for chromatographic performance if methods are transferred between laboratories/instruments or when scaling up to preparative chromatography. Further studies are needed and currently ongoing in our laboratories to investigate how general these findings are for the SFC technique. Acknowledgments This work was supported by the Swedish Knowledge Foundation for the KK HÖG 2014 project “SOMI: Studies of Molecular Interactions for Quality Assurance, Bio-Specific Measurement & Reliable Supercritical Purification” (grant number 20140179) and by the Swedish Research Council (VR) in the project “Fundamental Studies on Molecular Interactions aimed at Preparative Separations and Biospecific Measurements” (grant number 2015-04627).

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