- Email: [email protected]
Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation
G Model
ARTICLE IN PRESS
CHROMA-357892; No. of Pages 8
Journal of Chromatography A, xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation Fabrice Gritti Waters Corporation, Instrument/Core Research/Fundamental, Milford, MA 01757, USA
a r t i c l e
i n f o
Article history: Received 8 August 2016 Received in revised form 8 September 2016 Accepted 9 September 2016 Available online xxx Keywords: Supercritical fluid chromatography Sample solvent effects Retention shift Band compression Band enlargement
a b s t r a c t Experimental conditions leading to unexpected shift in retention, band compression, and to band enlargement of small molecules in supercritical fluid chromatography are reported. The stationary phase is a 3.0 mm × 150 mm column packed with 1.8 m fully porous high strength silica (HSS) StableBond (SB) C18 particles. The mobile phase is pure carbon dioxide preheated at 107 ◦ C and the column back pressure is set at 100 bar. The column was thermally insulated in a vacuum chamber at a pressure of 10−5 Torr in order to maintain the integrity of the peak symmetry. The sample solution was prepared by dissolving seven n-alkylbenzenes (from benzene to dodecylbenzene) in pure acetonitrile. The injected sample volume (1 L) was three orders of magnitude smaller than the column volume. Remarkably, the retention time of octylbenzene is found 15% smaller than that expected for this series of homologous compounds. Most strikingly, the plate counts change from about 20 000 for the three least retained analytes (benzene, ethylbenzene, and butylbenzene) to 60 000 for hexylbenzene and to only 5000 for the three most retained compounds (octylbenzene, decylbenzene, and dodecylbenzene). These unexpectedly high (reduced plate height of 1.3) and low (reduced plate height of 15) column efficiencies observed for closely related compounds are consistent with the overlap between the spatial concentration zone of the sample solvent (acetonitrile, Langmuir isotherm, k 2) and those of the analytes (competitive linear isotherms, 0 < k < 10). The present observations are fully supported by chromatogram simulations which assume that the Henry’s constants of the infinitely diluted analytes are strongly dependent on the concentration of the sample solvent in the mobile phase. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluid chromatography (SFC) possesses three main advantages over liquid chromatography (LC) and very highpressure liquid chromatography (vHPLC): (1) it is environmentfriendly (inertness of gaseous carbon dioxide), (2) it can be operated at very high linear velocities under conventional system pressures (<600 bar) due to the very low viscosity of SFC mobile phases [1–3], and (3) the strength of SFC mobile phases can be tuned over a large range of solvent strength by adjusting independently temperature, pressure, and content of organic modifier. For these reasons, its interest has been continuously growing over the last decade and supported by the manufacture of new high-performance SFC systems [1]. Among other applications, SFC is extensively used as both a high-throughput purification process and a high-resolution analytical screening tool for the preparation and discovery a new pharmaceutical drugs [4–6].
E-mail address: Fabrice [email protected]
The practice of SFC differs from that of LC due to the specific properties of mixtures of carbon dioxide with organic solvents. The proper optimization and operation of SFC-based units involves some additional knowledge with respect to those required in LC. The impact of temperature and pressure on SFC retention behavior is not similar to that observed in LC [7,8]. The efficiency of SFC columns may also be very sensitive to the surrounding thermal environment [9–11]. The reproducibility of SFC data depends strongly on the control of the inlet mass flow rate [12], the pressure set by the active back pressure regulator (BPR), the oven temperature, the nature (methanol, acetonitrile, ethanol,...) and concentration (0–40% in volume) of the organic modifier [13–15], the nature of the sample solvent [16,17], and the thermal environment in which the SFC column is placed [9–11]. SFC instruments, columns, and methods should then be well controlled for the sake of data robustness. One important difference between the separation mechanism taking place in SFC with respect to LC is that the local eluent density, its linear velocity, and the equilibrium constants of the analyte may be subject to changes during the band elution [12,14,18] as pressure
http://dx.doi.org/10.1016/j.chroma.2016.09.020 0021-9673/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
2
and temperature may vary along and across the column. First, as a general rule, the retention of the analytes is primarily controlled by the average eluent density along the column: in practice, isopycnic (constant density) conditions are then critical in SFC for the proper scale-up of purification methods. Isopycnic plots for pure carbon dioxide and its mixtures with organic modifiers are extremely useful for the experimenter [19]. Secondly, regarding the efficiency of a SFC column and similarly to what has been intensively reported in vHPLC [20–22], the experimenter has to make sure that the steepness of the radial density gradients across the column diameter are kept as small as possible. This was clearly revealed by Poe et al. [9,10,23] when low-density SFC mobile phases are used (carbon dioxide at elevated temperatures and low pressures). The heat exchanged between the column wall and the external environment should be minimized. The ultimate solution consists in placing the column in a strict adiabatic environment. This was recently achieved for air pressure below 10−4 Torr [24,25] (high vacuum). Maintaining the integrity of column efficiency in SFC is closely tied to the knowledge of the isenthalpic plots of the mobile phase because any adiabatic decompression of a fluid is performed at constant enthalpy [25,26]. These plots inform the experimenters about the required pressure and temperature that will minimize enthalpy changes during the mobile phase decompression. These adjustments are especially critical when the expansion coefficient of the SFC mobile phase is large [9]. In this work, the effect (either positive or negative) of an additional physico-chemical phenomenon on the retention and efficiency of a SFC column is revealed experimentally and explained theoretically. The efficiencies of a series of seven homologous compounds (n-alkylbenzenes from benzene to dodecylbenzene) are recorded on a 3.0 × 150 mm column packed with 1.8 m fully porous HSS-SB-C18 particles. The mobile phase (100% carbon dioxide) was preheated at 107 ◦ C and the BPR pressure was set at 100 bar. The column is fully insulated from the external thermal environment by applying a high air vacuum (10−5 Torr) in order to preserve integrity of the peak shape for such a highly expansible mobile phase. Unexpected and repeatable changes in the retention and efficiencies of the seven n-alkylbenzenes are reported. The main goal of the paper is to identify and quantify the physical origins of such behavior. Finally, simple calculations based on the equilibrium-dispersive model of chromatography accounting for the proposed relevant physical phenomena was performed in order to predict the observed retention and efficiency anomalies and confirm the separation mechanism of the seven n-alkylbenzenes. 2. Theory The adsorption system is composed of a series of homologous compounds (n-alkylbenzenes present at infinitely diluted concentrations in the mobile phase, carbon dioxide), of one organic modifier (small injection volume of the sample solvent, acetonitrile), and of carbon dioxide as the mobile phase. The next section present empirical models for the adsorption isotherms of the analytes and of the organic modifier from pure carbon dioxide onto the HSS-SB-C18 stationary phase. 2.1. Adsorption isotherms The adsorption isotherm of the organic modifier (subscript A) was assumed to be the non-competitive (the amount of analytes injected is infinitely small) Langmuir isotherm. Accordingly, KxA qA = qS 1 + KxA
(1)
where qA is the amount of organic modifier adsorbed at equilibrium onto the stationary phase, qS is the monolayer saturation capacity, xA is the volume fraction of the organic modifier in the mobile phase, and K is the adsorption–desorption equilibrium constant. The best isotherm parameters qS and b were determined unambiguously from the retention time method [27,28]. Accordingly, qS = 0.125 and K = 100. The adsorption isotherms of the seven n-alkylbenzenes is assumed to be linear (infinitesimally small amount injected) and competitive (with respect to the acetonitrile concentration CA ). The retention factor, kn , of the homologous compound Cn (n is the number of carbon atoms in the alkyl chain), is best described by a curved non-linear solvation model [13,29]: ln kn (xA ) = ln k0,n +
˛n xA 1 + ˇn xA
(2)
where ln k0,n , ˛n , and ˇn are empirical parameters. In this work, the simulation of the chromatograms was performed for 8 homologous compounds. ln k0,n is increasing regularly from 0.9 to 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, and to 3.0 (one methylene group is adding 0.3 to the intensity of ln k0,n ) with increasing n from 0 to 2, 4, 6, 8, 10, 12, and to 14. The parameters ˛n decreases from −5, to −10, −15, −20, −25, −30, −35, and to −40 (one single methylene group is adding −5 to the intensity of ˛n ). The parameters ˇn are barely increasing from 1.5 to 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, and to 2.2, respectively (one single methylene group is adding 0.1 to the intensity of ˇn ). These parameters were determined so that the predicted retention times agree qualitatively well with the observed retention times of the n-alkylbenzenes. 2.2. Simulation of band profiles The calculations of the concentration profiles of the organic modifier and of the analytes at the column outlet was performed using the equilibrium-dispersive (ED) model of chromatography [27]. This apparent model was chosen for our SFC purpose because it is relatively simple to use and requires only moderate computing time. By no means, it reflects on the exact local physical properties (density, linear velocity, equilibrium constant) along and across the SFC bed. For instance, it does not account for the compressibility of the mobile phase and the non-linear change of the flow rate as a function of position along the column. The axial non-uniformity of the column affects essentially the retention of compounds, they do not have a significant impact on the column efficiency [22]. By essence, it will reveal on the importance of the band overlap (competition for adsorption) of the analyte and sample solvent during their propagation of the chromatographic zone. This model assumes instantaneous equilibrium between the mobile and the stationary phases and a finite column efficiency characterized by an apparent axial dispersion coefficient, Da . The apparent axial dispersion coefficient is related to the apparent column efficiency through: Da =
u0 L 2N
(3)
where u0 is the chromatographic linear velocity of the mobile phase, L = 15 cm is the column length, and N is the number of theoretical plates or apparent efficiency of the column. In this model, the mass balance for any compounds (analytes and organic modifier) is written: 2
∂c ∂c 1 − t ∂q ∂ q =0 + u0 + − Da t ∂ t ∂t ∂z ∂z 2
(4)
where t is the time and z the distance along the column. q and C are the adsorbed and bulk concentrations of the organic solvent
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
in the stationary phase and in the bulk mobile phase volumes, respectively. t = 0.65 is the total porosity of the column. The amount of organic modifier injected is 1 L. For the sake of comparison, the column hold-up volume of the 3.0 mm × 150 mm column is 689 L. The selected adsorption isotherms (q(C)) were those described in the previous section. The ED model was solved using a computer program (COLCHR) available online based on an implementation of the Rouchon method [27]. The column efficiency was set at N = 7500 for the sake of accuracy of the calculation. The relative and absolute errors of the numerical calculations were 1 × 10−6 and × 10−8 , respectively. For more technical details and comparison between the different numerical methods (including the Rouchon method) used to solve the differential mass balance Eq. (4), the reader is referred to the references [27,30].
3. Experimental 3.1. Chemicals The mobile phase used was pure carbon dioxide (99.8%, with low water content). The compressed (875 psi) liquid CO2 bottle was purchased from Airgas (Worcester, MA, USA). The selected sample solvent was pure acetonitrile and the active back pressure regulator (BPR) was continuously washed with 100% isopropanol. All solvents were HPLC grade from Fisher Scientific (Fair Lawn, NJ, USA). The analytes benzene (C0 ), ethylbenzene (C2 ), butylbenzene (C4 ), hexylbenzene (C6 ), octylbenzene (C8 ), decylbenzene (C10 ), and dodecylbenzene (C12 ) were all purchased from Sigma-Aldrich (Suwannee, GA, USA) with a minimum purity of 99%.
3
3.3. Columns A 3.0 × 150 mm column packed with 1.8 m fully porous HSSSB (Stable Bond) C18 particles from Waters (Milford, MA, USA) was used in this work. 3.4. Chromatographic experiments The total flow rate was set at 2.333 mL/min. The flow rate of pure CO2 is 2.10 mL/min at a temperature of 13 ◦ C and at a pressure (inlet system pressure) of 4340 psi. The eluent temperature at the head of the column was set at 107 ◦ C by the active preheater. The BPR pressure was set at 1500 psi. The chromatographic column and the active preheater were both thermally insulated inside the vacuum chamber in order to eliminate any radial density gradients across the column diameter and to maintain excellent peak symmetry. The lab temperature was set by the air-conditioner at 24 ± 1 ◦ C. The peak profiles of the seven compounds were recorded at a wavelength of 200 nm and at a sampling rate of 20 Hz. 4. Results and discussion In the first part of this section, unexpected chromatographic behaviors are reported regarding the elution times and the efficiency of a series of n-alkylbenzenes in the above-mentioned SFC experimental conditions. In the second part, a physical explanation is provided for these observations. Finally, in the last part, the proposed underlying mechanism for these apparent retention and performance anomalies is confirmed from the simulation of the peak profiles of these n-alkylbenzenes. 4.1. The unexpected observations
3.2. Instrument and materials The ACQUITY UPC2 system (Waters, Milford, USA) was used to record the peak profiles of pure acetonitrile and of the seven alkylbenzenes. It includes a binary pump with solvent selection valves (Pump A: CO2 , Pump B: isopropanol). The two solvents were delivered separately to the injection valve (pure CO2 , 90% pump A, 2.1 mL/min) and to the BPR (pure isopropanol, 10% pump B, 0.233 mL/min). The temperature of the 40 cm × 100 m active preheater was set at 107 ◦ C. It is directly connected to the column inlet inside a vacuum chamber in which the air pressure was set to 5 × 10−6 Torr with a turbomolecular pump. All the experimental details regarding the design of the vaccum chamber and of the turbomolecular pump are given in reference [24]. The vacuum chamber is placed horizontal in still-air conditions (ambient temperature of 24 ◦ C, atmospheric pressure 1 atm). The standard post-column connectors were replaced with a 180 m i.d. fused silica glass capillaries (360 m O.D.) covered with a 20 m thick polyimide film. Each end was wrapped with a 2.5 cm × 360 m PEEK tube. A short metallic sleeve (2.0 cm long, 1/16 in. O.D.) was crimped against the PEEK tubes. Metallic nuts and ferrules were then assembled directly into the column outlet port and to the tee junction where the make-up flow of isopropanol is directed towards BPR unit. The standard 8 L TUV detection cell was bypassed and on-capillary detection was performed 5 cm downstream the column outlet. This allows to reduce to nearly zero the post-column sample dispersion. The seven n-alkylbenzenes were dissolved in pure acetonitrile. The sample volume injected to the column was 1 L. The concentrations of benzene, ethylbenzene, butylbenzene, hexylbenzene, octylbenzene, decylbenzene, and dodecylbenzene were set at 0.5, 0.7, 1.1, 1.8, 2.2, 3.4, and 4.5 g/L, respectively.
The top graph in Fig. 1 shows the experimental chromatogram of the seven homologous compounds from C0 (benzene) to C12 (dodecylbenzene). All the details for the experimental conditions are given in the experimental section. Under “normal” elution condition of a series of homologous compounds, the logarithm of the t −t0 selectivity ratio, Sn = n+2 tn −t0 , for a pair of compound containing n and n + 2 carbon atoms, is nearly constant. Sn accounts for the selectivity of two methylene groups. From the retention times measured in Fig. 1 and from the hold-up time t0 measured from the elution time of n-heptane, Sn is nearly constant for the first three pairs of alkylbenzenes (S0 = S2 = S4 = 0.54), it suddenly drops to S6 = 0.44, increases to S8 = 0.65, and finally returns to S10 = 0.55. In other words, the retention time of the compound C8 does not make sense in appearance as it elutes at a time (t8 = 1.46 min) which is smaller than that expected. Indeed, the expected retention time of C8 should be such that the coefficients Sn remain constant for all n, e.g., t8 would have been expected at exactly 1.60 min (+10%). Such a relative difference in retention time is significant. The second most striking observation pertains to the USP efficiencies of these seven homologous compounds: the efficiencies of the first three eluted compounds slowly decreases from 26 000 (C0 ) to 23 000 (C2 ) and to 20 000 (C4 ). This level of column efficiency is already quite remarkable for a 15 cm long columns packed with 1.8 m particles and run at a low BPR pressures (1500 psi) and at a high temperature (107 ◦ C at the column entrance and 57 ◦ C at the column outlet according to the isenthalpic decompression of pure CO2 under adiabatic conditions [25]). This good column performance is expected and explained by the fact that the column is well thermally insulated and, therefore, that the amplitude of the radial density gradients are minimized. Indeed, the viscosity of pure CO2 decreases from 5.0 × 10−5 Pa s (column inlet) to only 2.6 × 10−5 Pa s (column outlet). These values are typically 20 times
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model
ARTICLE IN PRESS
CHROMA-357892; No. of Pages 8
F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
4
Fig. 1. (Top graph) Experimental chromatogram of seven n-alkylbenzenes (from benzene to dodecylbenzene). The 3.0 × 150 mm column is packed with 1.8 m HSS-SB-C18 fully porous particles. The mobile phase is pure carbon dioxide. The flow rate is 2.1 mL/min at the inlet pressure of 4340 psi and at a temperature of 286 K. The inlet temperature is set by the active preheater at 380 K. The BPR pressure is fixed at 1500 psi. Note the anomalies in the retention and efficiency of the sixth and fifth compounds, respectively. (Bottom graph) Same as in the top graph, except the injection of the sample solvent (acetonitrile) only. Note the presence of an overloaded band profile from t = 1.05 to t = 1.50 min.
as small as the viscosity of usual acetonitrile/water mixtures at room temperature for which the diffusion coefficient of alkylbenzenes is around 1.5 × 10−5 cm2 /s. By simple extrapolation and by 0 .6D
m , the diffusion coefficients of assuming constant the quantity T the same alkylbenzenes in pure CO2 at such high temperature are around 1.1 × 10−4 cm2 /s. The density of pure CO2 is 1.007 g/cm3 in the high-pressure pump (flow rate 2.1 mL/min), 0.624 g/cm3 at the column inlet (flow rate 3.4 mL/min), and 0.336 g/cm3 at the column outlet (flow rate 6.3 mL/min). So, the average interstitial linear velocity along the column is about 2.86 cm/s. The corresponding reduced interstitial linear velocity is then close to 4.5. The minimum reduced plate height of well packed SFC columns with fully porous particles is usually around 2 for an optimum reduced velocity around 15 when adiabatic conditions are applied [24] (absence of transcolumn migration velocity biases due to radial temperature heterogeneities). At 5, a reduced HETP around 3 is expected, e.g., the column efficiency should be around 25 000 plates. This value is consistent with the observations for the first three eluted compounds. Most remarkably, the USP efficiency of the fourth eluted compound (hexylbenzene or C6 ) is as large as 61 000 plates, e.g., a reduced HETP of 1.35 is measured: this does not make any sense for a column packed with fully porous particles, run at a lower than optimum reduced velocity, under conditions of severe axial heterogeneities in flow velocity, temperature, and pressure [31], and operated under very challenging experimental conditions for the inlet eluent temperature (107 ◦ C) and for the BPR pressure (1500 psi). At the very best, the maximum expected efficiency of this 15 cm long column should be around 40 000 plates. Finally, the USP efficiencies of the three most retained compounds are
unusually low at 4000 (octylbenzene or C8 ), 6000 (decylbenzene or C10 ), and 5000 (dodecylbenzene or C12 ). This corresponds to reduced plate heights as large as about 15. To summarize, we are facing an unexplained riddle associated to the fact that the reduced plate heights abruptly drop from about 3 for butylbenzene to only 1.3 for hexylbenzene and then significantly increase from 1.3 to 15 for octylbenzene while the peak shape remains quasi-symmetrical (the peak asymmetry factors are equal to 1.18, 1.17, and 1.12 for C4 , C6 , and C8 , respectively). The mere addition of only two carbon atoms in the side chain of the n-alkylbenzenes cannot explain such unexpected retention and performance behavior for the HSS-SB-C18 column. Therefore, in the next section, a consistent physical explanation for the unexpected small retention time of octylbenzene, the excessively high USP efficiency of hexylbenzene, and for the poor efficiencies of the three most retained compounds (C8 , C10 , and C12 ) is proposed. 4.2. Physical origin for the unexpected observations A meticulous look at the baseline signal recorded at the UV wavelength = 200 nm (see the top graph in Fig. 1) reveals (1) a sudden discontinuity of the signal (negative step of intensity close to 1 mAU) at the elution time of 1.05 min and (2) a smooth return to its original level at about 1.50 min. Such a baseline disturbance is possibly consistent with the system peak of the sample solvent [27]. In SFC, the injected analytes are dissolved in a liquid solvent: in the present experiments, 1 L of acetonitrile used as sample solvent was inevitably injected with the analytes. In order to confirm the origin of the baseline disturbance, a blank injection (1 L of
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
acetonitrile alone) was performed. The corresponding chromatogram is shown in the bottom graph of Fig. 1 (zoom in between −2.5 mAU and 3 mAU along the y-axis, same time scale along the x-axis). Remarkably, the UV response of acetonitrile in pure carbon dioxide is negative, a concentration shock starts at 1.05 min, and a progressive return to the baseline level extends up to about 1.50 min. This demonstrates experimentally that under the current experimental conditions (BPR pressure = 1500 psi, Pinlet = 4340 psi, Tinlet = 107 ◦ C, 100% CO2 , HSS-SB-C18 stationary phase), acetonitrile is retained and the large amount injected (1 L) is enough to generate an overloaded band profile characteristic of a Langmuir adsorption behavior [27]. This observation was unambiguously confirmed by using flame ionization detection (FID) which reveals an intense positive signal with a front shock and a rear tail at the same elution times. Similar overloaded band profiles were also recorded by FID for the sample solvents methanol, ethanol, and isopropanol. In contrast, the sample solvent n-heptane used to dissolve heavier n-alkanes such as C14 and C18 shows no retention onto the non-endcapped HSS-SB-C18 stationary phase. The elution times of the front shock (1.05 min) and of the rear end (1.50 min) of the acetonitrile band profile observed at the column outlet enable us to determine unambiguously the best Langmuir adsorption parameters qS and b from the retention time method [27,28]. The retention and the langmuirian adsorption isotherm of the sample solvent acetonitrile will be the first necessary ingredients that may explain the experimental observations reported and analyzed in the previous section. Another ingredient is also critical in order to account for these unexpected observations: the retention factor of the analytes should be strongly dependent on the content of acetonitrile present in pure carbon dioxide used as the mobile phase. The relationship between the logarithm of the retention factor of the analytes and the acetonitrile content in CO2 is usually strongly non-linear when increasing the volume fraction of the organic modifier from zero to a few pecents. For instance, under isopycnic conditions, the retention factor of phenanthrene was reported to decrease from 10 to 6 and from 6 to only 5.5 when increasing the volume fraction of ethanol from 0 to 2% and from 2 to 7%, respectively [13]. This justifies the selection of a non-linear solvation retention model regarding the impact of the content of acetonitrile on the retention factor of the alkylbenzenes (see Eq. (2) in the theory section). When all the above-mentioned ingredients are gathered, then, one should distinguish between the compounds that are less retained (k < kACN ) from those that are more retained (k < kACN ) than the sample solvent (acetonitrile). Also, a specific attention has to be given to those that have the same retention time (k kACN ) as that of the front shock of the sample solvent. These three different scenarios are schematically represented in Fig. 2 in the spatial domain for three or four different elution times (t1 , t2 , t3 , and t4 ). The langmuirian overloaded band profiles of the sample solvent are represented in blue while the peak profiles of the analytes are shown in green. 1. In the first retention configuration (top drawings, k < kACN ), the front of the analyte zone propagates at a faster rate than the front zone of acetonitrile. This drives the spatial resolution of the analyte and acetonitrile zones. For a little while, initially, the rear part of the analyte zone overlaps with the front part of the acetonitrile zone. As a result, the rear part of the analyte zone progresses faster than its front part (because the retention factor of the analytes are decreasing with increasing even so slightly the content of acetonitrile in the CO2 mobile phase) which causes a certain degree of spatial compression for the analyte peak and a slight drop in retention. Because the front zone of the analyte always progresses at its own rate in absence of acetonitrile, the retention times of these compounds are very
5
Fig. 2. Representation of the evolution of the spatial concentration zones of the analyte (thick solid green line) and of the sample solvent acetonitrile (thick solid blue line) for several fixed elution times (t1 , t2 , t3 , and t4 ). The analyte is nearly nonretained when the two concentration zones interfere. (Top) The retention time of the compound is smaller than the elution time of the acetonitrile shock. (Middle) The retention time of the compound is very close to the elution time of the acetonitrile shock. (Bottom) The retention time of the compound is larger than the elution time of the acetonitrile shock.
close to those expected. The smaller the difference kACN − k is, the longer the distance along which the two zones will overlap and the more intense the band compression will be. The efficiencies of such compounds are then at least equal to the expected ones in complete absence of acetonitrile. In conclusion, no particular anomalies are expected for the least retained compounds unless their retention factor become extremely close (from below) to the retention of the front shock of acetonitrile. This situation will be described as a third case scenario (k kACN ). 2. In the second retention configuration (bottom drawings, k > kACN ), the front of the analyte zone is now initially overlapping with the rear part of the acetonitrile zone, which propagates at a faster rate than the analyte. Therefore, the front part propagates at a higher speed than the rear part (again because the retention of the well retained analytes is severely decreasing with increasing the content of acetonitrile in the mobile phase) generating a certain spatial enlargement of the analyte zone. The spatial resolution of the analyte and acetonitrile zones is essentially driven by the axial dispersion of acetonitrile at the front part of the analyte zone. This contributes to progressively lower its concentration as the sample zones are progressing. Because the speed of the sample zone is always in between the speed of the front shock of acetonitrile and its own intrinsic speed in absence of acetonitrile, the retention time of such compound is necessarily smaller than expected. Accordingly, this scenario should lead to lower than expected retention times and efficiencies. This is particularly true when the retention factor of the analyte is barely larger than the retention of the front shock of acetonitrile. At the limit, this retention configuration will be categorized as the third case scenario (k kACN ). 3. In the third case scenario, the retention factor of the analyte is very close to the retention of the front shock of acetonitrile (k kACN ). This means that the analyte zone propagates nearly unretained (the retention factor of the analyte drops dramatically in the presence of even a very small amount of acetonitrile in pure CO2 ) with the acetonitrile zone as it exits the column. The retention time is equal to the elution time of the acetonitrile shock and the apparent efficiency measured is much higher than expected due to band compression: the peak width of this particular analyte is roughly equal to the peakwidth of a non-retained
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8 6
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
compound. The difference with a non-retained compound is that it elutes at a larger elution time, which is imposed by the elution time of the front shock of the sample solvent. In conclusion, it is proposed that the combination of (1) the retention of the sample solvent, (2) the langmuirian overloaded band profiles of the sample solvent, and (3) the strong dependence of the retention factor of the analyte on the content of the sample solvent in pure carbon dioxide are the necessary ingredients responsible for the unexpected retention and efficiency behaviors reported and discussed in the first section. Such a phenomenon related to the dissolution of the sample in a solvent in which it is more soluble than in the mobile phase has previously been described in non-linear preparative liquid chromatography. The deformation and splitting of the band profiles of proteins have been observed and predicted by dynamic models [32,33]. For the sake of experimental validation of the proposed mechanism, n-heptane was used as the sample solvent in order to dissolve heavier n-alkanes such as C14 and C18 . n-heptane is non-retained under the same experimental conditions as those applied in Fig. 1 while the retention factor of C14 and C18 are close to 20 and 70, respectively. This corresponds to the second retention configuration for which the efficiency is expected to be smaller than the benchmark column efficiency around 20 000. Indeed, the recorded plate counts of C14 and C18 were measured at only 4500 and 1500, respectively. In order to fully confirm this proposed hypothesis, the simulation of chromatograms for a series of homologous compounds is performed in the next section.
Fig. 3. Calculation of the individual concentration profiles of eight homologous compounds in presence of the sample solvent. Same column dimension as in Fig. 1. 1 L sample volume injected. The adsorption isotherm is a Langmuir model and its parameters were best estimated from the retention time method using the data in the bottom graph of Fig. 1 (tshock = 63 s, tR = 92 s). The Henry’s constants of the eight compounds and their dependence on the sample solvent composition in the mobile phase are listed in the theoretical section.
4.3. Confirmation of the proposed physical origin from numerical simulation All the numerical details (adsorption isotherms and column properties) regarding the calculations of the band profiles of the sample solvent and of the compounds belonging to the same homologous series are given in the theory section. Let us recall that the adsorption isotherm of the sample solvent is a Langmuir model in full agreement with the observation (see bottom graph in Fig. 1). The volume of sample solvent injected is 1 L. The competitive adsorption isotherms of all analytes are linear with a Henry’s constant that depends strongly on the content of the sample solvent. For the sake of computer resources and convergence of numerical calculations, the column efficiency in the ED model of chromatography was set at 7500. Figs. 3 and 4 show the calculated peak profiles of the analytes (colored solid lines) in the presence and in the absence of sample solvent (black solid lines), respectively. Fig. 4 superimposes the two chromatograms and reveals clearly the predicted relative changes in retention times (these changes are marked by arrows) and peak widths of the analytes. The units are seconds for the x-axis (elution time) and arbitrary for the y-axis (analyte concentration). Remarkably, the efficiencies of the least retained compounds are all similar but slightly larger than 7500. These compounds propagate at a faster linear velocity than that of the shock of the sample solvent, which elutes exactly at t = 65 s. As explained in the previous section, the retention and efficiencies are those expected. Note that, due to the initial overlap of the rear part of the spatial sample zone and the front part of the sample eluent, the calculated retention times in the presence of sample solvent are slightly smaller than those expected without the 1 L injection of the sample solvent. Remarkably, the calculations confirm that the efficiencies (2500 only) of the two most retained compounds (brown and pink colors) are about three times as low as the expected efficiency (7500). This is consistent with the observations in the top graph of Fig. 1. The spatial zone of these two compounds is stretched because their rear part
Fig. 4. Same calculated chromatogram as in Fig. 3. For the sake of comparison, the same chromatogram was calculated in absence of sample solvent and superimposed to it. The solid arrows indicate the relative changes in the elution times of the eight compounds resulting from the interference between the analyte and sample solvent concentration zones. Note the diminution of the retention times, the strong compression of the peak for compound # 6, and the significant enlargement of the peak width for compound # 7 and #8.
progresses at a lower pace than their front part which is drained by the sample solvent zone. The retention of these two compounds is also strongly decreasing in the presence of the sample solvent. Finally, one intermediate compound shows the singular behavior proposed in the third scenario: most of the mass of this compound remains confined with the sample solvent front even though it is intrinsically more retained than the shock of the sample solvent. In contrast to the two most retained compounds, axial dispersion does not allow this analyte to leave the sample solvent zone by its rear. It is because the difference in retention factor kAnalyte − kACN is too small. Finally, a deeper look at the calculated concentration profiles of the analytes and sample solvent reveals a clear peak splitting for the three most retained compounds (see Fig. 5): most of the sample mass is drained by the acetonitrile zone and elutes before the remaining mass, which is eventually separated from the solvent zone by a combined effect of axial dispersion and retention difference. This was already reported in preparative liquid chromatography of proteins [32,33]. The peak splitting obviously does
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
7
it elutes with a peak width equivalent to that of a non-retained compound while its elution time is that of the retained sample solvent. The present work also elucidated this complex interference between the chromatographic bands of the analytes and of the sample solvent in SFC from simple modeling (equilibrium-dispersive model of chromatography). It is important to mention that the present observations are not systematic in SFC when using significant amounts of organic modifier in the mobile phase, low temperatures, and high BPR pressure. In such experimental conditions, the injection of a small volume of sample solvent does not affect much the local retention factor of the analytes during their migration along the column. Obviously, no anomalies can be expected and the experimenter will not be facing severe changes in retention and performance. Acknowledgements
Fig. 5. Same plots as in Fig. 4, except the zoom at the base of the peak profiles. Note the peak splitting for compounds # 6, 7, and 8.
The authors would like to acknowledge and thank Michael Fogwill (Waters, Milford, MA, USA) for providing us with the Acquity UPC2 equipment and the external active preheater. References
not occur for the least retained analytes because their mass is rapidly separated from the sample solvent zone by a strict thermodynamic process. 5. Conclusion In this work, unexpected retention and efficiency behaviors were observed and discussed in SFC for a series of homologous compounds (n-alkylbenzenes). Even though the injected sample volume (1 L) was three orders of magnitude smaller than the column volume (3.0 × 150 mm, 1060 L), it was unambiguously shown experimentally that this even so small amount of sample solvent (0.79 mg of acetonitrile) was enough to cause unpredictable shifts in the retention times and inconsistently high or low column efficiencies. In fact, these apparent chromatographic anomalies can be fully explained from the basic fundamentals of adsorption and mass transfer in SFC. The fundamental explanation behind these observations is that the equilibrium distribution of the analytes between pure carbon dioxide and conventional silica-C18 stationary phases is highly sensitive to the amount of sample solvent present in the mobile phase. As a result, during the time the spatial band of the analyte overlaps and interferes with that of the sample solvent, the analyte propagates along the column at a faster linear velocity than that it experiences in absence or organic solvent in the mobile phase. Retention times are then smaller than expected. Such analyte/sample solvent interaction also induces either band compression or band enlargement. Interestingly, when the sample solvent is significantly retained, three different SFC performances are then expected depending on the intensity of the analyte retention: if the analyte is more retained than the sample solvent then column efficiencies are dramatically low due to the enlargement of the spatial peak zone in the column. Inversely, if the analyte is less retained than the sample solvent, then, column efficiencies remain close to what they should be in the absence of analyte/sample solvent band interference. Most remarkably, if the retention of the analyte happens to match closely that of the sample solvent, such compound will ceaselessly interfere with the sample solvent during its migration along the column. This analyte/sample solvent “co-elution train” generate extremely high column efficiencies due to band compression. Note that these high column efficiencies are only apparent: the compound is confined inside the sample solvent zone, its band is continuously compressed on its rear part, so,
[1] G. Guiochon, A. Tarafder, Fundamental challenges and opportunities for preparative supercritical fluid chromatography, J. Chromatogr. A 1218 (2011) 1037–1114. [2] T.A. Berger, B.K. Berger, K. Fogleman, Chromatographic separations and analysis: supercritical fluid chromatography for chiral analysis and semi-preparative purification, Ref. Module Chem. Mol. Sci. Chem. Eng. 8 (2014) 354–392. [3] M. McNally, Supercritical fluid chromatography, Compr. Anal. Chem. 47 (2006) 561–574. [4] T.A. Berger, Preparative supercritical fluid chromatography–chromatography supercritical fluid, Encycl. Sep. Sci. (2007) 1–15. [5] J. Blehaut, P. Franco, T. Zhang, E. Lang, E. Valery, J.-F. Marcoux, Industrial applications of chiral chromatography, Ref. Module Chem. Mol. Sci. Chem. Eng. 47 (2012) 400–456. [6] W. Ren-Qi, O. Teng-Teng, N. Siu-Choon, T. Weihua, Recent advances in pharmaceutical separations with supercritical fluid chromatography using chiral stationary phases, TrAC 37 (2012) 83–100. [7] E. Leselier, Retention mechanisms in super/subcritical fluid chromatography on packed columns, J. Chromatogr. A 1216 (2009) 1881–1890. [8] T. Berger, Packed Column SFC, 1st ed., Royal Society of Chemistry, London, UK, 1995. [9] D.P. Poe, J.J. Schroden, Effects of pressure drop, particle size and thermal conditions on retention and efficiency in supercritical fluid chromatography, J. Chromatogr. A 1216 (2009) 7915–7926. [10] K. Kaczmarski, D. Poe, A. Tarafder, G. Guiochon, Efficiency of supercritical fluid chromatography columns in different thermal environments, J. Chromatogr. A 1291 (2013) 155–173. [11] K. Kaczmarski, D. Poe, A. Tarafder, G. Guiochon, Efficiency of supercritical fluid chromatography columns in different thermal environments, J. Chromatogr. A 1291 (2013) 155–173. [12] F. Gritti, A. Tarafder, G. Guiochon, Interpretation of dynamic frontal analysis data in solid/supercritical fluid adsorption systems. I: Theory, J. Chromatogr. A 1290 (2013) 73–81. [13] A. Rajendran, T. Gilkison, M. Mazzotti, Effect of pressure drop on solute retention and column efficiency in supercritical fluid chromatography. Part 2: Modified carbon dioxide as mobile phase, J. Sep. Sci. 31 (2008) 1279–1289. [14] F. Gritti, G. Guiochon, Effect of methanol concentration on the speed-resolution properties in adiabatic supercritical fluid chromatography, J. Chromatogr. A 1314 (2013) 255–265. [15] M. Enmark, D. Asberg, H. Leek, K. Ohlen, M. Klarqvist, J. Samuelsson, T. Fornstedt, Evaluation of scale-up from analytical to preparative supercritical fluid chromatography, J. Chromatogr. A 1425 (2015) 280–286. [16] J. Fairchild, P. Iraneta, J. Hill, Influence of sample solvent composition for SFC separations, LCGC North America 31 (2013) 326–333. [17] J. Fairchild, D. Brousmiche, J. Hill, M. Morris, C. Boissel, K. Wyndham, Chromatographic evidence of silyl ether formation (SEF) in supercritical fluid chromatography, Anal. Chem. 87 (2015) 1735–1742. [18] F. Gritti, G. Guiochon, Limit of the speed-resolution properties in adiabatic supercritical fluid chromatography, J. Chromatogr. A 1295 (2013) 114–127. [19] A. Tarafder, G. Guiochon, Use of isopycnic plots in designing operations of supercritical fluid chromatography: II. The isopycnic plots and the selection of the operating pressure–temperature zone in supercritical fluid chromatography, J. Chromatogr. A 1218 (2011) 4576–4585. [20] F. Gritti, M. Martin, G. Guiochon, Influence of viscous friction heating on the efficiency of columns operated under very high pressures, Anal. Chem. 81 (2009) 3365–3384.
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
[21] F. Gritti, G. Guiochon, Complete temperature profiles in ultra-high- pressure liquid chromatography columns, Anal. Chem. 80 (2008) 5009–5020. [22] F. Gritti, G. Guiochon, Optimization of the thermal environment of columns packed with very fine particles, J. Chromatogr. A 1216 (2009) 1353–1362. [23] K. Kaczmarski, D. Poe, G. Guiochon, Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography, J. Chromatogr. A 1217 (2010) 6578. [24] F. Gritti, M. Gilar, J.A. Jarrell, Achieving quasi-adiabatic thermal environment to maximize resolution power in very high-pressure liquid chromatography: theory, models, and experiments, J. Chromatogr. A 1444 (2016) 86–98. [25] F. Gritti, M. Gilar, J.A. Jarrell, Quasi-adiabatic vacuum-based column housing for very high-pressure liquid chromatography, J. Chromatogr. A 1456 (2016) 226–234. [26] F. Gritti, T. McDonald, M. Gilar, Intrinsic advantages of short packed capillaries over narrow-bore columns in very high-pressure gradient liquid chromatography, J. Chromatogr. A 1451 (2016) 107–119. [27] G. Guiochon, A. Felinger, A. Katti, D. Shirazi, Fundamentals of Preparative and Nonlinear Chromatography, 2nd ed., Academic Press, Boston, MA, 2006.
[28] F. Gritti, G. Guiochon, Analytical solution of the ideal model of chromatography for a bi-Langmuir adsorption isotherm, Anal. Chem. 85 (2013) 8552–8558. [29] M. Gilar, T. McDonald, J. Johnson, J. Murphy, J. Jorgenson, Wide injection zone compression in gradient reversed-phase liquid chromatography, J. Chromatogr. A 1390 (2015) 86–94. [30] K. Kaczmarski, Estimation of adsorption isotherm parameters with inverse method: possible problems, J. Chromatogr. A 1176 (2007) 57–68. [31] J. Giddings, Dynamics of Chromatography, Marcel Dekker, New York, NY, 1965. [32] W. Feng, X. Zhu, L. Zhang, X. Geng, Retention behaviour of proteins under conditions of column overload in hydrophobic interaction chromatography, J. Chromatogr. A 729 (1996) 43–47. [33] R. Muca, W. Marek, W. Piatkowski, D. Antos, Influence of the sample-solvent on protein retention, mass transfer and unfolding kinetics in hydrophobic interaction chromatography, J. Chromatogr. A 1217 (2010) 2812–2820.
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
ARTICLE IN PRESS
CHROMA-357892; No. of Pages 8
Journal of Chromatography A, xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation Fabrice Gritti Waters Corporation, Instrument/Core Research/Fundamental, Milford, MA 01757, USA
a r t i c l e
i n f o
Article history: Received 8 August 2016 Received in revised form 8 September 2016 Accepted 9 September 2016 Available online xxx Keywords: Supercritical fluid chromatography Sample solvent effects Retention shift Band compression Band enlargement
a b s t r a c t Experimental conditions leading to unexpected shift in retention, band compression, and to band enlargement of small molecules in supercritical fluid chromatography are reported. The stationary phase is a 3.0 mm × 150 mm column packed with 1.8 m fully porous high strength silica (HSS) StableBond (SB) C18 particles. The mobile phase is pure carbon dioxide preheated at 107 ◦ C and the column back pressure is set at 100 bar. The column was thermally insulated in a vacuum chamber at a pressure of 10−5 Torr in order to maintain the integrity of the peak symmetry. The sample solution was prepared by dissolving seven n-alkylbenzenes (from benzene to dodecylbenzene) in pure acetonitrile. The injected sample volume (1 L) was three orders of magnitude smaller than the column volume. Remarkably, the retention time of octylbenzene is found 15% smaller than that expected for this series of homologous compounds. Most strikingly, the plate counts change from about 20 000 for the three least retained analytes (benzene, ethylbenzene, and butylbenzene) to 60 000 for hexylbenzene and to only 5000 for the three most retained compounds (octylbenzene, decylbenzene, and dodecylbenzene). These unexpectedly high (reduced plate height of 1.3) and low (reduced plate height of 15) column efficiencies observed for closely related compounds are consistent with the overlap between the spatial concentration zone of the sample solvent (acetonitrile, Langmuir isotherm, k 2) and those of the analytes (competitive linear isotherms, 0 < k < 10). The present observations are fully supported by chromatogram simulations which assume that the Henry’s constants of the infinitely diluted analytes are strongly dependent on the concentration of the sample solvent in the mobile phase. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluid chromatography (SFC) possesses three main advantages over liquid chromatography (LC) and very highpressure liquid chromatography (vHPLC): (1) it is environmentfriendly (inertness of gaseous carbon dioxide), (2) it can be operated at very high linear velocities under conventional system pressures (<600 bar) due to the very low viscosity of SFC mobile phases [1–3], and (3) the strength of SFC mobile phases can be tuned over a large range of solvent strength by adjusting independently temperature, pressure, and content of organic modifier. For these reasons, its interest has been continuously growing over the last decade and supported by the manufacture of new high-performance SFC systems [1]. Among other applications, SFC is extensively used as both a high-throughput purification process and a high-resolution analytical screening tool for the preparation and discovery a new pharmaceutical drugs [4–6].
E-mail address: Fabrice [email protected]
The practice of SFC differs from that of LC due to the specific properties of mixtures of carbon dioxide with organic solvents. The proper optimization and operation of SFC-based units involves some additional knowledge with respect to those required in LC. The impact of temperature and pressure on SFC retention behavior is not similar to that observed in LC [7,8]. The efficiency of SFC columns may also be very sensitive to the surrounding thermal environment [9–11]. The reproducibility of SFC data depends strongly on the control of the inlet mass flow rate [12], the pressure set by the active back pressure regulator (BPR), the oven temperature, the nature (methanol, acetonitrile, ethanol,...) and concentration (0–40% in volume) of the organic modifier [13–15], the nature of the sample solvent [16,17], and the thermal environment in which the SFC column is placed [9–11]. SFC instruments, columns, and methods should then be well controlled for the sake of data robustness. One important difference between the separation mechanism taking place in SFC with respect to LC is that the local eluent density, its linear velocity, and the equilibrium constants of the analyte may be subject to changes during the band elution [12,14,18] as pressure
http://dx.doi.org/10.1016/j.chroma.2016.09.020 0021-9673/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
2
and temperature may vary along and across the column. First, as a general rule, the retention of the analytes is primarily controlled by the average eluent density along the column: in practice, isopycnic (constant density) conditions are then critical in SFC for the proper scale-up of purification methods. Isopycnic plots for pure carbon dioxide and its mixtures with organic modifiers are extremely useful for the experimenter [19]. Secondly, regarding the efficiency of a SFC column and similarly to what has been intensively reported in vHPLC [20–22], the experimenter has to make sure that the steepness of the radial density gradients across the column diameter are kept as small as possible. This was clearly revealed by Poe et al. [9,10,23] when low-density SFC mobile phases are used (carbon dioxide at elevated temperatures and low pressures). The heat exchanged between the column wall and the external environment should be minimized. The ultimate solution consists in placing the column in a strict adiabatic environment. This was recently achieved for air pressure below 10−4 Torr [24,25] (high vacuum). Maintaining the integrity of column efficiency in SFC is closely tied to the knowledge of the isenthalpic plots of the mobile phase because any adiabatic decompression of a fluid is performed at constant enthalpy [25,26]. These plots inform the experimenters about the required pressure and temperature that will minimize enthalpy changes during the mobile phase decompression. These adjustments are especially critical when the expansion coefficient of the SFC mobile phase is large [9]. In this work, the effect (either positive or negative) of an additional physico-chemical phenomenon on the retention and efficiency of a SFC column is revealed experimentally and explained theoretically. The efficiencies of a series of seven homologous compounds (n-alkylbenzenes from benzene to dodecylbenzene) are recorded on a 3.0 × 150 mm column packed with 1.8 m fully porous HSS-SB-C18 particles. The mobile phase (100% carbon dioxide) was preheated at 107 ◦ C and the BPR pressure was set at 100 bar. The column is fully insulated from the external thermal environment by applying a high air vacuum (10−5 Torr) in order to preserve integrity of the peak shape for such a highly expansible mobile phase. Unexpected and repeatable changes in the retention and efficiencies of the seven n-alkylbenzenes are reported. The main goal of the paper is to identify and quantify the physical origins of such behavior. Finally, simple calculations based on the equilibrium-dispersive model of chromatography accounting for the proposed relevant physical phenomena was performed in order to predict the observed retention and efficiency anomalies and confirm the separation mechanism of the seven n-alkylbenzenes. 2. Theory The adsorption system is composed of a series of homologous compounds (n-alkylbenzenes present at infinitely diluted concentrations in the mobile phase, carbon dioxide), of one organic modifier (small injection volume of the sample solvent, acetonitrile), and of carbon dioxide as the mobile phase. The next section present empirical models for the adsorption isotherms of the analytes and of the organic modifier from pure carbon dioxide onto the HSS-SB-C18 stationary phase. 2.1. Adsorption isotherms The adsorption isotherm of the organic modifier (subscript A) was assumed to be the non-competitive (the amount of analytes injected is infinitely small) Langmuir isotherm. Accordingly, KxA qA = qS 1 + KxA
(1)
where qA is the amount of organic modifier adsorbed at equilibrium onto the stationary phase, qS is the monolayer saturation capacity, xA is the volume fraction of the organic modifier in the mobile phase, and K is the adsorption–desorption equilibrium constant. The best isotherm parameters qS and b were determined unambiguously from the retention time method [27,28]. Accordingly, qS = 0.125 and K = 100. The adsorption isotherms of the seven n-alkylbenzenes is assumed to be linear (infinitesimally small amount injected) and competitive (with respect to the acetonitrile concentration CA ). The retention factor, kn , of the homologous compound Cn (n is the number of carbon atoms in the alkyl chain), is best described by a curved non-linear solvation model [13,29]: ln kn (xA ) = ln k0,n +
˛n xA 1 + ˇn xA
(2)
where ln k0,n , ˛n , and ˇn are empirical parameters. In this work, the simulation of the chromatograms was performed for 8 homologous compounds. ln k0,n is increasing regularly from 0.9 to 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, and to 3.0 (one methylene group is adding 0.3 to the intensity of ln k0,n ) with increasing n from 0 to 2, 4, 6, 8, 10, 12, and to 14. The parameters ˛n decreases from −5, to −10, −15, −20, −25, −30, −35, and to −40 (one single methylene group is adding −5 to the intensity of ˛n ). The parameters ˇn are barely increasing from 1.5 to 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, and to 2.2, respectively (one single methylene group is adding 0.1 to the intensity of ˇn ). These parameters were determined so that the predicted retention times agree qualitatively well with the observed retention times of the n-alkylbenzenes. 2.2. Simulation of band profiles The calculations of the concentration profiles of the organic modifier and of the analytes at the column outlet was performed using the equilibrium-dispersive (ED) model of chromatography [27]. This apparent model was chosen for our SFC purpose because it is relatively simple to use and requires only moderate computing time. By no means, it reflects on the exact local physical properties (density, linear velocity, equilibrium constant) along and across the SFC bed. For instance, it does not account for the compressibility of the mobile phase and the non-linear change of the flow rate as a function of position along the column. The axial non-uniformity of the column affects essentially the retention of compounds, they do not have a significant impact on the column efficiency [22]. By essence, it will reveal on the importance of the band overlap (competition for adsorption) of the analyte and sample solvent during their propagation of the chromatographic zone. This model assumes instantaneous equilibrium between the mobile and the stationary phases and a finite column efficiency characterized by an apparent axial dispersion coefficient, Da . The apparent axial dispersion coefficient is related to the apparent column efficiency through: Da =
u0 L 2N
(3)
where u0 is the chromatographic linear velocity of the mobile phase, L = 15 cm is the column length, and N is the number of theoretical plates or apparent efficiency of the column. In this model, the mass balance for any compounds (analytes and organic modifier) is written: 2
∂c ∂c 1 − t ∂q ∂ q =0 + u0 + − Da t ∂ t ∂t ∂z ∂z 2
(4)
where t is the time and z the distance along the column. q and C are the adsorbed and bulk concentrations of the organic solvent
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
in the stationary phase and in the bulk mobile phase volumes, respectively. t = 0.65 is the total porosity of the column. The amount of organic modifier injected is 1 L. For the sake of comparison, the column hold-up volume of the 3.0 mm × 150 mm column is 689 L. The selected adsorption isotherms (q(C)) were those described in the previous section. The ED model was solved using a computer program (COLCHR) available online based on an implementation of the Rouchon method [27]. The column efficiency was set at N = 7500 for the sake of accuracy of the calculation. The relative and absolute errors of the numerical calculations were 1 × 10−6 and × 10−8 , respectively. For more technical details and comparison between the different numerical methods (including the Rouchon method) used to solve the differential mass balance Eq. (4), the reader is referred to the references [27,30].
3. Experimental 3.1. Chemicals The mobile phase used was pure carbon dioxide (99.8%, with low water content). The compressed (875 psi) liquid CO2 bottle was purchased from Airgas (Worcester, MA, USA). The selected sample solvent was pure acetonitrile and the active back pressure regulator (BPR) was continuously washed with 100% isopropanol. All solvents were HPLC grade from Fisher Scientific (Fair Lawn, NJ, USA). The analytes benzene (C0 ), ethylbenzene (C2 ), butylbenzene (C4 ), hexylbenzene (C6 ), octylbenzene (C8 ), decylbenzene (C10 ), and dodecylbenzene (C12 ) were all purchased from Sigma-Aldrich (Suwannee, GA, USA) with a minimum purity of 99%.
3
3.3. Columns A 3.0 × 150 mm column packed with 1.8 m fully porous HSSSB (Stable Bond) C18 particles from Waters (Milford, MA, USA) was used in this work. 3.4. Chromatographic experiments The total flow rate was set at 2.333 mL/min. The flow rate of pure CO2 is 2.10 mL/min at a temperature of 13 ◦ C and at a pressure (inlet system pressure) of 4340 psi. The eluent temperature at the head of the column was set at 107 ◦ C by the active preheater. The BPR pressure was set at 1500 psi. The chromatographic column and the active preheater were both thermally insulated inside the vacuum chamber in order to eliminate any radial density gradients across the column diameter and to maintain excellent peak symmetry. The lab temperature was set by the air-conditioner at 24 ± 1 ◦ C. The peak profiles of the seven compounds were recorded at a wavelength of 200 nm and at a sampling rate of 20 Hz. 4. Results and discussion In the first part of this section, unexpected chromatographic behaviors are reported regarding the elution times and the efficiency of a series of n-alkylbenzenes in the above-mentioned SFC experimental conditions. In the second part, a physical explanation is provided for these observations. Finally, in the last part, the proposed underlying mechanism for these apparent retention and performance anomalies is confirmed from the simulation of the peak profiles of these n-alkylbenzenes. 4.1. The unexpected observations
3.2. Instrument and materials The ACQUITY UPC2 system (Waters, Milford, USA) was used to record the peak profiles of pure acetonitrile and of the seven alkylbenzenes. It includes a binary pump with solvent selection valves (Pump A: CO2 , Pump B: isopropanol). The two solvents were delivered separately to the injection valve (pure CO2 , 90% pump A, 2.1 mL/min) and to the BPR (pure isopropanol, 10% pump B, 0.233 mL/min). The temperature of the 40 cm × 100 m active preheater was set at 107 ◦ C. It is directly connected to the column inlet inside a vacuum chamber in which the air pressure was set to 5 × 10−6 Torr with a turbomolecular pump. All the experimental details regarding the design of the vaccum chamber and of the turbomolecular pump are given in reference [24]. The vacuum chamber is placed horizontal in still-air conditions (ambient temperature of 24 ◦ C, atmospheric pressure 1 atm). The standard post-column connectors were replaced with a 180 m i.d. fused silica glass capillaries (360 m O.D.) covered with a 20 m thick polyimide film. Each end was wrapped with a 2.5 cm × 360 m PEEK tube. A short metallic sleeve (2.0 cm long, 1/16 in. O.D.) was crimped against the PEEK tubes. Metallic nuts and ferrules were then assembled directly into the column outlet port and to the tee junction where the make-up flow of isopropanol is directed towards BPR unit. The standard 8 L TUV detection cell was bypassed and on-capillary detection was performed 5 cm downstream the column outlet. This allows to reduce to nearly zero the post-column sample dispersion. The seven n-alkylbenzenes were dissolved in pure acetonitrile. The sample volume injected to the column was 1 L. The concentrations of benzene, ethylbenzene, butylbenzene, hexylbenzene, octylbenzene, decylbenzene, and dodecylbenzene were set at 0.5, 0.7, 1.1, 1.8, 2.2, 3.4, and 4.5 g/L, respectively.
The top graph in Fig. 1 shows the experimental chromatogram of the seven homologous compounds from C0 (benzene) to C12 (dodecylbenzene). All the details for the experimental conditions are given in the experimental section. Under “normal” elution condition of a series of homologous compounds, the logarithm of the t −t0 selectivity ratio, Sn = n+2 tn −t0 , for a pair of compound containing n and n + 2 carbon atoms, is nearly constant. Sn accounts for the selectivity of two methylene groups. From the retention times measured in Fig. 1 and from the hold-up time t0 measured from the elution time of n-heptane, Sn is nearly constant for the first three pairs of alkylbenzenes (S0 = S2 = S4 = 0.54), it suddenly drops to S6 = 0.44, increases to S8 = 0.65, and finally returns to S10 = 0.55. In other words, the retention time of the compound C8 does not make sense in appearance as it elutes at a time (t8 = 1.46 min) which is smaller than that expected. Indeed, the expected retention time of C8 should be such that the coefficients Sn remain constant for all n, e.g., t8 would have been expected at exactly 1.60 min (+10%). Such a relative difference in retention time is significant. The second most striking observation pertains to the USP efficiencies of these seven homologous compounds: the efficiencies of the first three eluted compounds slowly decreases from 26 000 (C0 ) to 23 000 (C2 ) and to 20 000 (C4 ). This level of column efficiency is already quite remarkable for a 15 cm long columns packed with 1.8 m particles and run at a low BPR pressures (1500 psi) and at a high temperature (107 ◦ C at the column entrance and 57 ◦ C at the column outlet according to the isenthalpic decompression of pure CO2 under adiabatic conditions [25]). This good column performance is expected and explained by the fact that the column is well thermally insulated and, therefore, that the amplitude of the radial density gradients are minimized. Indeed, the viscosity of pure CO2 decreases from 5.0 × 10−5 Pa s (column inlet) to only 2.6 × 10−5 Pa s (column outlet). These values are typically 20 times
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model
ARTICLE IN PRESS
CHROMA-357892; No. of Pages 8
F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
4
Fig. 1. (Top graph) Experimental chromatogram of seven n-alkylbenzenes (from benzene to dodecylbenzene). The 3.0 × 150 mm column is packed with 1.8 m HSS-SB-C18 fully porous particles. The mobile phase is pure carbon dioxide. The flow rate is 2.1 mL/min at the inlet pressure of 4340 psi and at a temperature of 286 K. The inlet temperature is set by the active preheater at 380 K. The BPR pressure is fixed at 1500 psi. Note the anomalies in the retention and efficiency of the sixth and fifth compounds, respectively. (Bottom graph) Same as in the top graph, except the injection of the sample solvent (acetonitrile) only. Note the presence of an overloaded band profile from t = 1.05 to t = 1.50 min.
as small as the viscosity of usual acetonitrile/water mixtures at room temperature for which the diffusion coefficient of alkylbenzenes is around 1.5 × 10−5 cm2 /s. By simple extrapolation and by 0 .6D
m , the diffusion coefficients of assuming constant the quantity T the same alkylbenzenes in pure CO2 at such high temperature are around 1.1 × 10−4 cm2 /s. The density of pure CO2 is 1.007 g/cm3 in the high-pressure pump (flow rate 2.1 mL/min), 0.624 g/cm3 at the column inlet (flow rate 3.4 mL/min), and 0.336 g/cm3 at the column outlet (flow rate 6.3 mL/min). So, the average interstitial linear velocity along the column is about 2.86 cm/s. The corresponding reduced interstitial linear velocity is then close to 4.5. The minimum reduced plate height of well packed SFC columns with fully porous particles is usually around 2 for an optimum reduced velocity around 15 when adiabatic conditions are applied [24] (absence of transcolumn migration velocity biases due to radial temperature heterogeneities). At 5, a reduced HETP around 3 is expected, e.g., the column efficiency should be around 25 000 plates. This value is consistent with the observations for the first three eluted compounds. Most remarkably, the USP efficiency of the fourth eluted compound (hexylbenzene or C6 ) is as large as 61 000 plates, e.g., a reduced HETP of 1.35 is measured: this does not make any sense for a column packed with fully porous particles, run at a lower than optimum reduced velocity, under conditions of severe axial heterogeneities in flow velocity, temperature, and pressure [31], and operated under very challenging experimental conditions for the inlet eluent temperature (107 ◦ C) and for the BPR pressure (1500 psi). At the very best, the maximum expected efficiency of this 15 cm long column should be around 40 000 plates. Finally, the USP efficiencies of the three most retained compounds are
unusually low at 4000 (octylbenzene or C8 ), 6000 (decylbenzene or C10 ), and 5000 (dodecylbenzene or C12 ). This corresponds to reduced plate heights as large as about 15. To summarize, we are facing an unexplained riddle associated to the fact that the reduced plate heights abruptly drop from about 3 for butylbenzene to only 1.3 for hexylbenzene and then significantly increase from 1.3 to 15 for octylbenzene while the peak shape remains quasi-symmetrical (the peak asymmetry factors are equal to 1.18, 1.17, and 1.12 for C4 , C6 , and C8 , respectively). The mere addition of only two carbon atoms in the side chain of the n-alkylbenzenes cannot explain such unexpected retention and performance behavior for the HSS-SB-C18 column. Therefore, in the next section, a consistent physical explanation for the unexpected small retention time of octylbenzene, the excessively high USP efficiency of hexylbenzene, and for the poor efficiencies of the three most retained compounds (C8 , C10 , and C12 ) is proposed. 4.2. Physical origin for the unexpected observations A meticulous look at the baseline signal recorded at the UV wavelength = 200 nm (see the top graph in Fig. 1) reveals (1) a sudden discontinuity of the signal (negative step of intensity close to 1 mAU) at the elution time of 1.05 min and (2) a smooth return to its original level at about 1.50 min. Such a baseline disturbance is possibly consistent with the system peak of the sample solvent [27]. In SFC, the injected analytes are dissolved in a liquid solvent: in the present experiments, 1 L of acetonitrile used as sample solvent was inevitably injected with the analytes. In order to confirm the origin of the baseline disturbance, a blank injection (1 L of
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
acetonitrile alone) was performed. The corresponding chromatogram is shown in the bottom graph of Fig. 1 (zoom in between −2.5 mAU and 3 mAU along the y-axis, same time scale along the x-axis). Remarkably, the UV response of acetonitrile in pure carbon dioxide is negative, a concentration shock starts at 1.05 min, and a progressive return to the baseline level extends up to about 1.50 min. This demonstrates experimentally that under the current experimental conditions (BPR pressure = 1500 psi, Pinlet = 4340 psi, Tinlet = 107 ◦ C, 100% CO2 , HSS-SB-C18 stationary phase), acetonitrile is retained and the large amount injected (1 L) is enough to generate an overloaded band profile characteristic of a Langmuir adsorption behavior [27]. This observation was unambiguously confirmed by using flame ionization detection (FID) which reveals an intense positive signal with a front shock and a rear tail at the same elution times. Similar overloaded band profiles were also recorded by FID for the sample solvents methanol, ethanol, and isopropanol. In contrast, the sample solvent n-heptane used to dissolve heavier n-alkanes such as C14 and C18 shows no retention onto the non-endcapped HSS-SB-C18 stationary phase. The elution times of the front shock (1.05 min) and of the rear end (1.50 min) of the acetonitrile band profile observed at the column outlet enable us to determine unambiguously the best Langmuir adsorption parameters qS and b from the retention time method [27,28]. The retention and the langmuirian adsorption isotherm of the sample solvent acetonitrile will be the first necessary ingredients that may explain the experimental observations reported and analyzed in the previous section. Another ingredient is also critical in order to account for these unexpected observations: the retention factor of the analytes should be strongly dependent on the content of acetonitrile present in pure carbon dioxide used as the mobile phase. The relationship between the logarithm of the retention factor of the analytes and the acetonitrile content in CO2 is usually strongly non-linear when increasing the volume fraction of the organic modifier from zero to a few pecents. For instance, under isopycnic conditions, the retention factor of phenanthrene was reported to decrease from 10 to 6 and from 6 to only 5.5 when increasing the volume fraction of ethanol from 0 to 2% and from 2 to 7%, respectively [13]. This justifies the selection of a non-linear solvation retention model regarding the impact of the content of acetonitrile on the retention factor of the alkylbenzenes (see Eq. (2) in the theory section). When all the above-mentioned ingredients are gathered, then, one should distinguish between the compounds that are less retained (k < kACN ) from those that are more retained (k < kACN ) than the sample solvent (acetonitrile). Also, a specific attention has to be given to those that have the same retention time (k kACN ) as that of the front shock of the sample solvent. These three different scenarios are schematically represented in Fig. 2 in the spatial domain for three or four different elution times (t1 , t2 , t3 , and t4 ). The langmuirian overloaded band profiles of the sample solvent are represented in blue while the peak profiles of the analytes are shown in green. 1. In the first retention configuration (top drawings, k < kACN ), the front of the analyte zone propagates at a faster rate than the front zone of acetonitrile. This drives the spatial resolution of the analyte and acetonitrile zones. For a little while, initially, the rear part of the analyte zone overlaps with the front part of the acetonitrile zone. As a result, the rear part of the analyte zone progresses faster than its front part (because the retention factor of the analytes are decreasing with increasing even so slightly the content of acetonitrile in the CO2 mobile phase) which causes a certain degree of spatial compression for the analyte peak and a slight drop in retention. Because the front zone of the analyte always progresses at its own rate in absence of acetonitrile, the retention times of these compounds are very
5
Fig. 2. Representation of the evolution of the spatial concentration zones of the analyte (thick solid green line) and of the sample solvent acetonitrile (thick solid blue line) for several fixed elution times (t1 , t2 , t3 , and t4 ). The analyte is nearly nonretained when the two concentration zones interfere. (Top) The retention time of the compound is smaller than the elution time of the acetonitrile shock. (Middle) The retention time of the compound is very close to the elution time of the acetonitrile shock. (Bottom) The retention time of the compound is larger than the elution time of the acetonitrile shock.
close to those expected. The smaller the difference kACN − k is, the longer the distance along which the two zones will overlap and the more intense the band compression will be. The efficiencies of such compounds are then at least equal to the expected ones in complete absence of acetonitrile. In conclusion, no particular anomalies are expected for the least retained compounds unless their retention factor become extremely close (from below) to the retention of the front shock of acetonitrile. This situation will be described as a third case scenario (k kACN ). 2. In the second retention configuration (bottom drawings, k > kACN ), the front of the analyte zone is now initially overlapping with the rear part of the acetonitrile zone, which propagates at a faster rate than the analyte. Therefore, the front part propagates at a higher speed than the rear part (again because the retention of the well retained analytes is severely decreasing with increasing the content of acetonitrile in the mobile phase) generating a certain spatial enlargement of the analyte zone. The spatial resolution of the analyte and acetonitrile zones is essentially driven by the axial dispersion of acetonitrile at the front part of the analyte zone. This contributes to progressively lower its concentration as the sample zones are progressing. Because the speed of the sample zone is always in between the speed of the front shock of acetonitrile and its own intrinsic speed in absence of acetonitrile, the retention time of such compound is necessarily smaller than expected. Accordingly, this scenario should lead to lower than expected retention times and efficiencies. This is particularly true when the retention factor of the analyte is barely larger than the retention of the front shock of acetonitrile. At the limit, this retention configuration will be categorized as the third case scenario (k kACN ). 3. In the third case scenario, the retention factor of the analyte is very close to the retention of the front shock of acetonitrile (k kACN ). This means that the analyte zone propagates nearly unretained (the retention factor of the analyte drops dramatically in the presence of even a very small amount of acetonitrile in pure CO2 ) with the acetonitrile zone as it exits the column. The retention time is equal to the elution time of the acetonitrile shock and the apparent efficiency measured is much higher than expected due to band compression: the peak width of this particular analyte is roughly equal to the peakwidth of a non-retained
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8 6
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
compound. The difference with a non-retained compound is that it elutes at a larger elution time, which is imposed by the elution time of the front shock of the sample solvent. In conclusion, it is proposed that the combination of (1) the retention of the sample solvent, (2) the langmuirian overloaded band profiles of the sample solvent, and (3) the strong dependence of the retention factor of the analyte on the content of the sample solvent in pure carbon dioxide are the necessary ingredients responsible for the unexpected retention and efficiency behaviors reported and discussed in the first section. Such a phenomenon related to the dissolution of the sample in a solvent in which it is more soluble than in the mobile phase has previously been described in non-linear preparative liquid chromatography. The deformation and splitting of the band profiles of proteins have been observed and predicted by dynamic models [32,33]. For the sake of experimental validation of the proposed mechanism, n-heptane was used as the sample solvent in order to dissolve heavier n-alkanes such as C14 and C18 . n-heptane is non-retained under the same experimental conditions as those applied in Fig. 1 while the retention factor of C14 and C18 are close to 20 and 70, respectively. This corresponds to the second retention configuration for which the efficiency is expected to be smaller than the benchmark column efficiency around 20 000. Indeed, the recorded plate counts of C14 and C18 were measured at only 4500 and 1500, respectively. In order to fully confirm this proposed hypothesis, the simulation of chromatograms for a series of homologous compounds is performed in the next section.
Fig. 3. Calculation of the individual concentration profiles of eight homologous compounds in presence of the sample solvent. Same column dimension as in Fig. 1. 1 L sample volume injected. The adsorption isotherm is a Langmuir model and its parameters were best estimated from the retention time method using the data in the bottom graph of Fig. 1 (tshock = 63 s, tR = 92 s). The Henry’s constants of the eight compounds and their dependence on the sample solvent composition in the mobile phase are listed in the theoretical section.
4.3. Confirmation of the proposed physical origin from numerical simulation All the numerical details (adsorption isotherms and column properties) regarding the calculations of the band profiles of the sample solvent and of the compounds belonging to the same homologous series are given in the theory section. Let us recall that the adsorption isotherm of the sample solvent is a Langmuir model in full agreement with the observation (see bottom graph in Fig. 1). The volume of sample solvent injected is 1 L. The competitive adsorption isotherms of all analytes are linear with a Henry’s constant that depends strongly on the content of the sample solvent. For the sake of computer resources and convergence of numerical calculations, the column efficiency in the ED model of chromatography was set at 7500. Figs. 3 and 4 show the calculated peak profiles of the analytes (colored solid lines) in the presence and in the absence of sample solvent (black solid lines), respectively. Fig. 4 superimposes the two chromatograms and reveals clearly the predicted relative changes in retention times (these changes are marked by arrows) and peak widths of the analytes. The units are seconds for the x-axis (elution time) and arbitrary for the y-axis (analyte concentration). Remarkably, the efficiencies of the least retained compounds are all similar but slightly larger than 7500. These compounds propagate at a faster linear velocity than that of the shock of the sample solvent, which elutes exactly at t = 65 s. As explained in the previous section, the retention and efficiencies are those expected. Note that, due to the initial overlap of the rear part of the spatial sample zone and the front part of the sample eluent, the calculated retention times in the presence of sample solvent are slightly smaller than those expected without the 1 L injection of the sample solvent. Remarkably, the calculations confirm that the efficiencies (2500 only) of the two most retained compounds (brown and pink colors) are about three times as low as the expected efficiency (7500). This is consistent with the observations in the top graph of Fig. 1. The spatial zone of these two compounds is stretched because their rear part
Fig. 4. Same calculated chromatogram as in Fig. 3. For the sake of comparison, the same chromatogram was calculated in absence of sample solvent and superimposed to it. The solid arrows indicate the relative changes in the elution times of the eight compounds resulting from the interference between the analyte and sample solvent concentration zones. Note the diminution of the retention times, the strong compression of the peak for compound # 6, and the significant enlargement of the peak width for compound # 7 and #8.
progresses at a lower pace than their front part which is drained by the sample solvent zone. The retention of these two compounds is also strongly decreasing in the presence of the sample solvent. Finally, one intermediate compound shows the singular behavior proposed in the third scenario: most of the mass of this compound remains confined with the sample solvent front even though it is intrinsically more retained than the shock of the sample solvent. In contrast to the two most retained compounds, axial dispersion does not allow this analyte to leave the sample solvent zone by its rear. It is because the difference in retention factor kAnalyte − kACN is too small. Finally, a deeper look at the calculated concentration profiles of the analytes and sample solvent reveals a clear peak splitting for the three most retained compounds (see Fig. 5): most of the sample mass is drained by the acetonitrile zone and elutes before the remaining mass, which is eventually separated from the solvent zone by a combined effect of axial dispersion and retention difference. This was already reported in preparative liquid chromatography of proteins [32,33]. The peak splitting obviously does
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
7
it elutes with a peak width equivalent to that of a non-retained compound while its elution time is that of the retained sample solvent. The present work also elucidated this complex interference between the chromatographic bands of the analytes and of the sample solvent in SFC from simple modeling (equilibrium-dispersive model of chromatography). It is important to mention that the present observations are not systematic in SFC when using significant amounts of organic modifier in the mobile phase, low temperatures, and high BPR pressure. In such experimental conditions, the injection of a small volume of sample solvent does not affect much the local retention factor of the analytes during their migration along the column. Obviously, no anomalies can be expected and the experimenter will not be facing severe changes in retention and performance. Acknowledgements
Fig. 5. Same plots as in Fig. 4, except the zoom at the base of the peak profiles. Note the peak splitting for compounds # 6, 7, and 8.
The authors would like to acknowledge and thank Michael Fogwill (Waters, Milford, MA, USA) for providing us with the Acquity UPC2 equipment and the external active preheater. References
not occur for the least retained analytes because their mass is rapidly separated from the sample solvent zone by a strict thermodynamic process. 5. Conclusion In this work, unexpected retention and efficiency behaviors were observed and discussed in SFC for a series of homologous compounds (n-alkylbenzenes). Even though the injected sample volume (1 L) was three orders of magnitude smaller than the column volume (3.0 × 150 mm, 1060 L), it was unambiguously shown experimentally that this even so small amount of sample solvent (0.79 mg of acetonitrile) was enough to cause unpredictable shifts in the retention times and inconsistently high or low column efficiencies. In fact, these apparent chromatographic anomalies can be fully explained from the basic fundamentals of adsorption and mass transfer in SFC. The fundamental explanation behind these observations is that the equilibrium distribution of the analytes between pure carbon dioxide and conventional silica-C18 stationary phases is highly sensitive to the amount of sample solvent present in the mobile phase. As a result, during the time the spatial band of the analyte overlaps and interferes with that of the sample solvent, the analyte propagates along the column at a faster linear velocity than that it experiences in absence or organic solvent in the mobile phase. Retention times are then smaller than expected. Such analyte/sample solvent interaction also induces either band compression or band enlargement. Interestingly, when the sample solvent is significantly retained, three different SFC performances are then expected depending on the intensity of the analyte retention: if the analyte is more retained than the sample solvent then column efficiencies are dramatically low due to the enlargement of the spatial peak zone in the column. Inversely, if the analyte is less retained than the sample solvent, then, column efficiencies remain close to what they should be in the absence of analyte/sample solvent band interference. Most remarkably, if the retention of the analyte happens to match closely that of the sample solvent, such compound will ceaselessly interfere with the sample solvent during its migration along the column. This analyte/sample solvent “co-elution train” generate extremely high column efficiencies due to band compression. Note that these high column efficiencies are only apparent: the compound is confined inside the sample solvent zone, its band is continuously compressed on its rear part, so,
[1] G. Guiochon, A. Tarafder, Fundamental challenges and opportunities for preparative supercritical fluid chromatography, J. Chromatogr. A 1218 (2011) 1037–1114. [2] T.A. Berger, B.K. Berger, K. Fogleman, Chromatographic separations and analysis: supercritical fluid chromatography for chiral analysis and semi-preparative purification, Ref. Module Chem. Mol. Sci. Chem. Eng. 8 (2014) 354–392. [3] M. McNally, Supercritical fluid chromatography, Compr. Anal. Chem. 47 (2006) 561–574. [4] T.A. Berger, Preparative supercritical fluid chromatography–chromatography supercritical fluid, Encycl. Sep. Sci. (2007) 1–15. [5] J. Blehaut, P. Franco, T. Zhang, E. Lang, E. Valery, J.-F. Marcoux, Industrial applications of chiral chromatography, Ref. Module Chem. Mol. Sci. Chem. Eng. 47 (2012) 400–456. [6] W. Ren-Qi, O. Teng-Teng, N. Siu-Choon, T. Weihua, Recent advances in pharmaceutical separations with supercritical fluid chromatography using chiral stationary phases, TrAC 37 (2012) 83–100. [7] E. Leselier, Retention mechanisms in super/subcritical fluid chromatography on packed columns, J. Chromatogr. A 1216 (2009) 1881–1890. [8] T. Berger, Packed Column SFC, 1st ed., Royal Society of Chemistry, London, UK, 1995. [9] D.P. Poe, J.J. Schroden, Effects of pressure drop, particle size and thermal conditions on retention and efficiency in supercritical fluid chromatography, J. Chromatogr. A 1216 (2009) 7915–7926. [10] K. Kaczmarski, D. Poe, A. Tarafder, G. Guiochon, Efficiency of supercritical fluid chromatography columns in different thermal environments, J. Chromatogr. A 1291 (2013) 155–173. [11] K. Kaczmarski, D. Poe, A. Tarafder, G. Guiochon, Efficiency of supercritical fluid chromatography columns in different thermal environments, J. Chromatogr. A 1291 (2013) 155–173. [12] F. Gritti, A. Tarafder, G. Guiochon, Interpretation of dynamic frontal analysis data in solid/supercritical fluid adsorption systems. I: Theory, J. Chromatogr. A 1290 (2013) 73–81. [13] A. Rajendran, T. Gilkison, M. Mazzotti, Effect of pressure drop on solute retention and column efficiency in supercritical fluid chromatography. Part 2: Modified carbon dioxide as mobile phase, J. Sep. Sci. 31 (2008) 1279–1289. [14] F. Gritti, G. Guiochon, Effect of methanol concentration on the speed-resolution properties in adiabatic supercritical fluid chromatography, J. Chromatogr. A 1314 (2013) 255–265. [15] M. Enmark, D. Asberg, H. Leek, K. Ohlen, M. Klarqvist, J. Samuelsson, T. Fornstedt, Evaluation of scale-up from analytical to preparative supercritical fluid chromatography, J. Chromatogr. A 1425 (2015) 280–286. [16] J. Fairchild, P. Iraneta, J. Hill, Influence of sample solvent composition for SFC separations, LCGC North America 31 (2013) 326–333. [17] J. Fairchild, D. Brousmiche, J. Hill, M. Morris, C. Boissel, K. Wyndham, Chromatographic evidence of silyl ether formation (SEF) in supercritical fluid chromatography, Anal. Chem. 87 (2015) 1735–1742. [18] F. Gritti, G. Guiochon, Limit of the speed-resolution properties in adiabatic supercritical fluid chromatography, J. Chromatogr. A 1295 (2013) 114–127. [19] A. Tarafder, G. Guiochon, Use of isopycnic plots in designing operations of supercritical fluid chromatography: II. The isopycnic plots and the selection of the operating pressure–temperature zone in supercritical fluid chromatography, J. Chromatogr. A 1218 (2011) 4576–4585. [20] F. Gritti, M. Martin, G. Guiochon, Influence of viscous friction heating on the efficiency of columns operated under very high pressures, Anal. Chem. 81 (2009) 3365–3384.
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020
G Model CHROMA-357892; No. of Pages 8 8
ARTICLE IN PRESS F. Gritti / J. Chromatogr. A xxx (2016) xxx–xxx
[21] F. Gritti, G. Guiochon, Complete temperature profiles in ultra-high- pressure liquid chromatography columns, Anal. Chem. 80 (2008) 5009–5020. [22] F. Gritti, G. Guiochon, Optimization of the thermal environment of columns packed with very fine particles, J. Chromatogr. A 1216 (2009) 1353–1362. [23] K. Kaczmarski, D. Poe, G. Guiochon, Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography, J. Chromatogr. A 1217 (2010) 6578. [24] F. Gritti, M. Gilar, J.A. Jarrell, Achieving quasi-adiabatic thermal environment to maximize resolution power in very high-pressure liquid chromatography: theory, models, and experiments, J. Chromatogr. A 1444 (2016) 86–98. [25] F. Gritti, M. Gilar, J.A. Jarrell, Quasi-adiabatic vacuum-based column housing for very high-pressure liquid chromatography, J. Chromatogr. A 1456 (2016) 226–234. [26] F. Gritti, T. McDonald, M. Gilar, Intrinsic advantages of short packed capillaries over narrow-bore columns in very high-pressure gradient liquid chromatography, J. Chromatogr. A 1451 (2016) 107–119. [27] G. Guiochon, A. Felinger, A. Katti, D. Shirazi, Fundamentals of Preparative and Nonlinear Chromatography, 2nd ed., Academic Press, Boston, MA, 2006.
[28] F. Gritti, G. Guiochon, Analytical solution of the ideal model of chromatography for a bi-Langmuir adsorption isotherm, Anal. Chem. 85 (2013) 8552–8558. [29] M. Gilar, T. McDonald, J. Johnson, J. Murphy, J. Jorgenson, Wide injection zone compression in gradient reversed-phase liquid chromatography, J. Chromatogr. A 1390 (2015) 86–94. [30] K. Kaczmarski, Estimation of adsorption isotherm parameters with inverse method: possible problems, J. Chromatogr. A 1176 (2007) 57–68. [31] J. Giddings, Dynamics of Chromatography, Marcel Dekker, New York, NY, 1965. [32] W. Feng, X. Zhu, L. Zhang, X. Geng, Retention behaviour of proteins under conditions of column overload in hydrophobic interaction chromatography, J. Chromatogr. A 729 (1996) 43–47. [33] R. Muca, W. Marek, W. Piatkowski, D. Antos, Influence of the sample-solvent on protein retention, mass transfer and unfolding kinetics in hydrophobic interaction chromatography, J. Chromatogr. A 1217 (2010) 2812–2820.
Please cite this article in press as: F. Gritti, Unexpected retention and efficiency behaviors in supercritical fluid chromatography: A thermodynamic interpretation, J. Chromatogr. A (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.020