Anal. Chem. 1996, 68, 3622-3630
Long Packed Column Supercritical Fluid Chromatography: Influence of Pressure Drop on Apparent Efficiency C. Bouigeon, D. Thie´baut,* and M. Caude
Laboratoire de Chimie Analytique de l’ESPCI (Associe´ au CNRS, No. 437), 10 rue Vauquelin, 75231 Paris Cedex 05, France
Supercritical fluid chromatography, when performed on a packed column, is a powerful and fast separation technique. To enhance the number of theoretical plates (TP) available, long packed columns (>1 m) have been used successfully, despite controversy over the effect on column efficiency of the density gradient induced by the pressure drop. Peak broadening and deformation were reported, and packings with larger particle diameter than those used in liquid chromatography (10 µm instead of 3-5 µm) were advised in order to reduce the column pressure drop. Velocity gradient induced by the density gradient was reported to reduce efficiency. This paper presents the results of investigations on the influence of density gradient on the apparent efficiency obtained on a series of four 25-cm × 4.6-mm-i.d. Nucleosil C18 columns connected in series (particle size, 5 µm). Apparent column efficiency is found to vary from less than 10 000 TP to more than 100 000 TP versus the density and the density gradient. The higher the density gradient, the higher the efficiency loss. A model is presented which accounts for the effect of linear velocity and density gradients on peak broadening. It confirms that it is the linear velocity variation rather than the variation of the density which causes band broadening and allows prediction of conditions for which apparent efficiency loss occurs. To reduce the density gradient induced by column pressure drop, one can compensate for pressure gradient by a superimposed temperature gradient (multitemperature control of the mobile phase via three column ovens). It allows one to obtain the highest efficiency and to use CO2 at lower density without any loss of efficiency. When methanol is added to the CO2, no pressure drop compensation is required in order to obtain the highest apparent efficiency. As density gradient compensation via multitemperature control of the mobile phase provides higher apparent efficiency and, consequently, higher resolution than in isothermal operation, it is especially useful for separation of complex oil samples. For separation of nonvolatile and labile solutes contained in complex mixtures, it would be very attractive to have an efficient analytical tool such as capillary gas chromatography (GC) which enables high sensitivity, high resolution, and low analysis duration. In liquid chromatography (LC), particularly in microcolumn liquid chromatography, much attention has been paid to improving the 3622 Analytical Chemistry, Vol. 68, No. 20, October 15, 1996
efficiency, which is limited to ∼20 000 theoretical plates (TP) for a 25-cm column length packed with 5-µm particles at optimum phase velocity. Unfortunately, due to the properties of liquids (high viscosity and low solute diffusion coefficient), there is a large pressure drop in the column, which severely limits the number of plates generated per unit of time; consequently, a long analysis time is needed for generating a high efficiency. An alternative could be to use capillary LC, offering a high specific permeability coefficient; however, to obtain the same number of TP per unit of time as in a packed column, the capillary column diameter must be twice the particle diameter used in packed columns. Thus, from a practical point of view, it is very difficult to use such capillary columns because, up to now, extracolumn contribution to band broadening has not been solved (for instance, a 1.3-m × 3.5-µm-i.d. column can generate 980 000 TP in 4.2 min for unretained components, but the column volume is ∼10 nL, and an 8-pL injection volume entails a 25% loss of TP!1 The use of fascinating supercritical fluids combined with capillary columns is much easier than the use of liquids. A few years ago, the chromatographer’s dream appeared to become reality: to have a robust, reproducible, selective, and very efficient separation technique that would enable one to handle very complex samples; in addition, supercritical fluid chromatography (SFC) can be coupled to LC and GC detectors to solve most of the detection problems encountered. In fact, capillary SFC can provide high efficiency when used at optimum conditions, but it has several drawbacks. The main problems occur when injecting very low volume samples to avoid band broadening and column overloading and when controlling pressure via fixed restrictors prior to GC detectors. The former leads to sophisticated and complex injection procedures with solvent removal (generally, the solvent of the sample must be evaporated, using nitrogen venting for instance, in order to detect the first eluting compounds); the latter is not yet solved despite the number of various restrictors advocated in the literature. Fused silica capillary restrictors are generally used with capillary columns; unfortunately, they have a major shortcoming because they change the flow depending on the pressure of the supercritical fluid. This is bad for chromatography due to the influence of the mobile phase velocity on column efficiency. Moreover, the lower the restrictor internal diameter, the higher the plugging frequency of the restrictor due to precipitation and, during the mobile phase expansion, deposition of non volatile compounds to the walls of the restrictor. Keeping in mind these data, Smith’s statements are not surprising: “Although generally ignored by (1) Manz, A.; Simon, W. J. Chromatogr. 1987, 387, 187. S0003-2700(96)00205-3 CCC: $12.00
© 1996 American Chemical Society
those unfamililar with SFC, the restrictor provides crucial control of SFC fluid flow by decompression through a small orifice capillary or porous medium and constitutes a potential Achilles’ heel for SFC” 2 and, more recently, “Capillary columns are not the right tools for this powerful and very promising technique. Forget all you learned from your experiences with capillary GC”.3 As a consequence, capillary SFC is a technique complementary to packed column SFC, and it did not fulfill all the features it was expected to. Recent work by Berger and Wilson4 demonstrated that another way to reach very high efficiency in SFC is to combine several conventional columns or packed microcolumns: it was shown that 200 000 TP efficiency could be obtained using a series of 11 columns (200 mm × 4.6 mm i.d.), while the pressure drop was not greater than 160 bar. Thus, high efficiency and selectivity can be obtained in a reproducible manner via an apparatus offering full control over flow rate, temperature, mobile phase composition, and pressure. Although it has been shown that high efficiency could be obtained in packed column SFC using small particles,4-6 such a high pressure drop in SFC is questionable, because many studies7-12 have concluded that a pressure drop greater than 20 bar generates a density drop, leading to a density gradient in the column, which affects column efficiency; band broadening and severe peak deformation were described10 and attributed to the density gradient. Thus, it was proposed to use larger diameter particles in SFC than those used in LC to minimize the pressure/ density drop in the column.7 This paper contributes to the understanding of the effect of the density gradient in the column on efficiency in packed column SFC. A model has been derived to describe the influence of density gradient on efficiency, and the model has been verified using a 1-m-long column comprised of four 4.6-mm × 25-cm packed columns. The apparent efficiency of the column was measured on test solutes as a function of the operating conditions. To overcome the effect of CO2 density gradient, the influence of a combined temperature gradient is investigated in order to minimize the density variation along the column: the temperature will be higher at the column inlet than at the column outlet to balance the CO2 density variation due to the pressure drop through the long column. The results are used to advantage for separation and quantitation of polyaromatic hydrocarbons from raw petroleum fractions. THEORETICAL PART: MODELING OF PEAK BROADENING INDUCED BY DENSITY GRADIENTS IN SFC Because of pressure drop (dP/dx < 0 according to Figure 1), a density gradient (dF/dx < 0) exists along the column in SFC. This density gradient induces two other gradients: a mobile phase gradient of linear velocity and a solute retention factor gradient. (2) Smith, R. D.; Wright, B. W.; Yonker, C. R. Anal. Chem. 1988, 60, 1323A. (3) Smits, R. LC-GC Int. 1994, 7, 505. (4) Berger, T. A.; Wilson, W. H. Anal. Chem. 1993, 65, 1451. (5) Malik, A.; Li, W.; Bartle, K. D. J. Microcolumn Sep. 1993, 5, 361. (6) Gere, D. R.; Board, R.; McManigill, D. Anal. Chem. 1982, 54, 736. (7) Schoenmakers, P. J.; Uunk, L. G. M. Chromatographia 1987, 24, 51. (8) Berger, T. A.; Deye, J. F. Chromatographia 1990, 30, 57. (9) Janssen, H. G.; Snidjers, H.; Cramers, C.; Schoenmakers, P. J. J. High Resolut. Chromatogr. 1992, 15, 458. (10) Mourier, P. A.; Caude, M. H.; Rosset, R. H. Chromatographia 1987, 23, 21. (11) Janssen, H. G.; Snidjers, H.; Rijks, J. A.; Cramers, C.; Schoenmakers, P. J. J. High Resolut. Chromatogr. 1991, 14, 438. (12) Berger, T. A.; Blumberg, L. M. Chromatographia 1994, 38, 5.
Figure 1. Notations used for the description of a negative density gradient per unit of length.
Indeed, if we assume that the mass flow rate (Fm) is constant, we observe a volumic flow rate (Fv) gradient due to the density gradient and, hence, a gradient of linear velocity (du/dx > 0 according to eq 3):
Fm ) Fv(T,P)F(P,T)
(1)
u ) Fv/S
(2)
u is the linear velocity of the mobile phase, S is the column cross section, and is the column porosity. So,
u ) Fm/FS
(3)
Moreover, the retention factor of the solute i in the system increases when the mobile phase density decreases according to relation 4:13,14
log(k′) ) aF + b
(4)
Consequently, a negative density gradient along the column induces a retention factor gradient along the column (dk′/dx > 0).15,16 Influence of Gradient of Linear Velocity on Peak Broadening in SFC. We can estimate the variation of peak width along the column in the presence of a gradient of linear velocity: du/ dx > 0. In a prime time, we will neglect the k′ gradient. Peak width measured at 32.4% of peak height is equal to 3σ and is defined by the abscissa x1 and x2 at time t: x1 + ∆x1 and x2 + ∆x2 at time t′ (t′ - t ) ∆t) (Figure 2). Moreover, we assume u1 and u2 are constant during ∆t because ∆x1,∆x2 , x2 - x1. Because u2 > u1, we have ∆x2 > ∆x1, which involves dσ/dt > 0. So, a positive value of du/dx induces an increase of peak width (negative effect). (13) Peaden, P. A.; Lee, M. L. J. Liq. Chromatogr. 1982, 5, 179. (14) Peaden, P. A.; Lee, M. L. J. Chromatogr. 1983, 259, 1. (15) Schoenmakers, P. J.; Verhoeven, F. C. C. J. G. J. Chromatogr. 1986, 352, 315. (16) Bartle, K. D.; Boddington, T.; Clifford, A. A.; Shilstone, G. F. J. Chromatogr. 1989, 471, 347.
Analytical Chemistry, Vol. 68, No. 20, October 15, 1996
3623
retention factor gradient, which reduces peak widthswe obtain the following: Using the eqs 5 and 6 in the general case, we have
∆t )
∆x1 (1 + k1′) u1
(8)
∆t )
∆x2 (1 + k2′) u2
(9)
with u ) Fm/FS (eq 3) and k′ ) exp(aF + b) (eq 4), where F is the fluid density at abscissa x1 and F + r the fluid density at abscissa x2 (r < 0 represents the density gradient). We obtain by combination of eqs 3, 4, 8, and 9, Figure 2. Notations used for the description of a positive gradient of linear velocity per unit of length.
3∆σ ) ∆x2 - ∆x1 Fm {1/(F + r)[1 + exp(a(F + r) + b)] S 1/F[1 + exp(aF + b)]}
) ∆t
(10)
After reducing to the same denominator and developing, eq 10 gives
Fm 1 3∆σ ) ∆t × S (F[1 + exp(aF + b)])2 {F + F exp(aF + b) - F - F exp[a(F + r) + b] r - r exp[a(F + r) + b]} (11) As r ≈ 0, exp(ar) ≈ 1 + ar. Neglecting second-order terms, this leads, after developing, to Figure 3. Notations used for the description of a positive retention factor gradient per unit of length.
Influence of Retention Factor Gradient on Peak Broadening in SFC. Using the notations defined in Figure 3, if we consider dk′/dx > 0, and if we neglect the gradient of linear velocity, we will find the following situation: u being constant, we can notice that
∆x1 (1 + k1′) u
(5)
∆x2 (1 + k2′) ∆t ) u
(6)
∆t )
)
1 1 3∆σ ) u∆t 1 + k2′ 1 + k1′
(7)
and since k2′ > k1′, ∆σ/∆t is negative, and the peak width decreases. We can relate this to the use in LC of elution gradient (∆k′/dt > 0, which corresponds to ∆k′/∆x < 0 in the column, which is the same case as the one observed in SFC) to improve peak width. Influence of Density Gradient on Peak Broadening in SFC. Now, considering both gradients (Figure 4)sthe gradient of linear velocity, which increases the peak width, and the 3624
[1 + exp(aF + b) + (aF) exp(aF + b)] (12) Let
B(F) )
1 + exp(aF + b) + (aF)exp(aF + b) (F[1 + exp(aF + b)])2
(13)
then
Thus,
(
Fm -r × S (F[1 + exp(aF + b)])2
3∆σ ) ∆t
Analytical Chemistry, Vol. 68, No. 20, October 15, 1996
Fm 3∆σ ) ∆t B(F)(-r) S
(14)
There is a linear variation of peak width versus the variation of fluid density within the elution peak, r. If B > 0, then ∆σ and peak width increase as the solute migrates in the column due to the decrease of the density (since r < 0). The negative effect of gradient of linear velocity overcomes the positive effect of retention factor gradient in the column and vice versa if B < 0. If the variation of k′ versus F is known (i.e., if a and b in eq 4 are known), B(F), the prediction of peak width variation along the column due to the fluid density gradient in SFC, may be calculated. EXPERIMENTAL SECTION Apparatus. We used a home-made SFC chromatograph based on a Varian Series 2500 liquid chromatograph (Varian, Palo
Figure 4. Notations used for the description of a negative density gradient per unit of length.
Alto, CA). It includes two Model 2510 pumps allowing the addition of polar modifiers [one supplies the liquid CO2 using cooling of the pump heat at 0 °C, and the other supplies the modifiers via a Gilson Model 811 dynamic mixer (Gilson, Villiers le Bel, France)], a Valco Model N60 injection valve, equipped with a 20-µL loop, three Croco-cil ovens (Cluzeau Info Labo, France) in series in which are placed the columns (the first oven containing two columns), a Varian Model 2550 UV detector, and a Tescom pressure control valve heated at 40 °C to avoid freezing of the CO2 during expansion. Data were collected on a Shimadzu CR4A integrator (Touzart et Matignon, Les Ulis, France). Stationary Phases. We have implemented four Spherisorb ODS 2 columns, 25 cm × 4.6 mm, 5 µm (Colochrom, Gagny, France). Samples. Test solutes were polyaromatic hydrocarbons (PAHs) purchased from Aldrich (Saint-Quentin Fallavier, France). Hydrocracking oil samples were kindly provided by Institut Franc¸ais du Pe´trole (Rueil-Malmaison, France). The samples were dissolved in the modifier added to the CO2 (methanol or dichloromethane). Fluids. The CO2 was of industrial quality from L’Air Liquide (Nanterre, France). Methanol and dichloromethane were of HPLC grade and were purchased from Prolabo (Fontenay-sousBois, France) and from SDS (Peypin, France), respectively. RESULTS AND DISCUSSION Existence of a Density Gradient in Packed Column SFC. According to Darcy’s law, the flow of the mobile phase through a packed column entails a pressure drop which is, for a given packing, a function of column length, mobile phase velocity, and viscosity. Owing to their nature, supercritical fluids exhibit compressibility; as a consequence, pressure drop also means density drop or density gradient in a given column, as can be seen in Figure 5, where the density (A) and the density gradient (density drop) of carbon dioxide for a pressure drop equal to 100 bar (B) are plotted as a function of column outlet pressure (P) for various temperatures (T) (these data are obtained using IUPAC equation of state). The shape of the isotherms (Figure 5A) indicates that there are some conditions where the variation of density versus the pressure is low (the compressibility is low),
Figure 5. Pressure-density diagram of the CO2 for different temperatures (A: s, 40; ‚‚‚, 55; and - - -, 70 °C), and 3D plot of density gradient versus pressure and temperature (B).
i.e., at low temperature and pressure higher than 130 bar. On the other hand, reducing the pressure at low temperatures (going toward the critical point) gives a tremendous rise in the CO2 compressibility, and the isotherms exhibit a kind of plateau (for example, around 40 °C and 90 bar). Depending on the pressure drop in the column, density will vary from column inlet to column outlet: as the pressure decreases, the density will decrease, and the higher the compressibility of the fluid in the conditions of the analysis, the higher the pressure drop-induced density gradient in the column. In fact, the density gradient will depend on the pressure drop, the temperature, and the outlet pressure: for a temperature equal to 35 °C and an outlet pressure equal to 150 bar, the density gradient entailed by a pressure drop equal to 100 bar is lower than 0.1 g cm-3 m-1; at 40 °C and for a column outlet pressure of 120 bar, a pressure drop of 100 bar generates a density gradient greater than 0.4 g cm-3 m-1. As described in the Theoretical Part, the CO2 density gradient in the column induces both positive linear velocity and negative retention factor gradients. Thus, the influence of the mobile phase density (F) in the column, the temperature, and the density gradient on column apparent efficiency is investigated and checked with our model. Analytical Chemistry, Vol. 68, No. 20, October 15, 1996
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Figure 6. Plot of apparent efficiency versus the mean density of the CO2 in a 1-m-long packed column. Stationary phase, Spherisorb ODS2, 5-µm packed in four 25-cm × 4.6-mm-i.d. columns connected in series; mobile phase, neat CO2 at 40 (0), 55 (2), and 70 °C (9), flow rate 2.5 mL/min. The curve (O) is obtained using multitemperature control; conditions are given for each point in Table 4. Pressure drop, 120 bar; solute, fluoranthene; UV detection at 254 nm. Flim is determined by the intercept of the three curves with 80 000 TP on plot A (it corresponds to a loss of 20% of maximum efficiency).
“Apparent efficiency” is preferred to “efficiency” because linear velocity and retention factor gradients exist in the column. Apparent efficiency (N) is calculated using
N ) 5.54(tR/δ)2
with tR the retention time and δ the peak width at half the peak height of the test solute (fluoranthene). Influence of CO2 Density and CO2 Density Gradient on Apparent Efficiency (Neat CO2). The effect of CO2 density gradient on apparent efficiency was studied by varying the fluid density from 0.55 to 0.88 g cm-3 via pressure control using the Tescom valve (the density was expressed as the mean value between column inlet and outlet densities); apparent efficiency was measured at 40, 55, and 70 °C (Figure 6) using the four Spherisorb columns in series. Apparent efficiency decreases from 100 000 TP (corresponding to a reduced plate height (h) equal to 2) to
