Acoustic Determination of the Helium Content of Carbon Dioxide from

The speed of sound reaches a minimum value at the critical point of a fluid. An acoustic technique is used to measure the critical pressures of mixtur...
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Anal. Chem. 1996, 68, 4436-4440

Acoustic Determination of the Helium Content of Carbon Dioxide from He Head Pressure Cylinders and FT-IR Studies of the Density of the Resulting Supercritical CO2: Implications for Reproducibility in Supercritical Experiments Andreas Kordikowski, Duncan G. Robertson, and Martyn Poliakoff*

Department of Chemistry, University of Nottingham, Nottingham, England NG7 2RD

The speed of sound reaches a minimum value at the critical point of a fluid. An acoustic technique is used to measure the critical pressures of mixtures of He + CO2 of known composition (0.1-3 mol % He). These data are then used to establish the composition of CO2 samples from commercial He head pressure cylinders. The He content of apparently similar samples of HHPCO2 is widely different. Only one sample (out of 5) showed the 3 mol % He predicted for such cylinders. These findings can only be explained if the He and CO2 within our cylinders were not fully equilibrated. If such lack of equilibrium is common, the He content of HHPCO2 from a given cylinder will be unpredictable and largely dependent on the particular history of that cylinder (i.e., its treatment during storage and handling). FT-IR measurements of the Fermi triad absorption bands of CO2 (∼5000 cm-1) were then used to quantify the difference in density between pure CO2 and HHPCO2 containing 2.2 mol % He at the same temperature and pressure. Striking differences in density were observed close to the critical point. The implications of these results for reproducibility in supercritical experiments are discussed. It is recommended that, if possible, HHPCO2 should be avoided for all studies involving CO2 close to its critical point. In most analytical applications of supercritical fluids, the composition of the fluid is a vital factor in determining reproducibility. In recent years, there have been several investigations into the effects of He on the chromatographic performance of supercritical CO2 solutions.1-4 The He derives from the so-called He head pressure cylinders, used by many analytical groups to improve the pumping efficiency of their syringe pumps. Initially, it was believed that the He pressure would have no effect on the physicochemical properties of the CO2 and that He would be completely immiscible with CO2. However, a simple analysis of available data on the liquid-vapor equilibrium shows that He is soluble in liquid CO2. Indeed, data from Burfield et al.5 show that about 3 mol % He is soluble in CO2 at room temperature and 100 * E-mail: [email protected]. (1) Rosselli, A. C.; Boyer, D. S.; Houck, R. K. J. Chromatogr. 1989, 465, 1115. (2) Raynie, D. E.; Delaney, T. E. J. Chromatogr. Sci. 1994, 32, 298-300. (3) King, J. W.; Johnson, J. H.; Eller, F. J. Anal. Chem. 1995, 67, 2288-2291. (4) Leichter, E.; Strode, J. T. B.; Taylor, L. T.; Schweighardt, F. K. Anal. Chem. 1996, 68, 894-898.

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bar pressure. It has now been shown that the presence of He substantially affects the results of chromatographic separations and supercritical extractions using He head pressure CO2 (HHPCO2).1-4 Additionally, it has been reported6 that, under some conditions, the density of HHPCO2 can be reduced by more than 25% compared to pure CO2 at the same temperature and pressure. There have been a number of indirect attempts to quantify the amount of He that is actually dissolved in the HHPCO2. For example, Taylor and co-workers4 recently weighed whole gas cylinders filled to different levels and derived the mole fraction of He from the mass of the cylinders. Their overall conclusions are summarized schematically in Figure 1, namely that the He content of HHPCO2 derived from full cylinders is higher than that from nearly empty cylinders. Although this result is consistent with the predictions of simple thermodynamics, it apparently contradicts the findings of some earlier reports.1,2 Nevertheless, all authors have agreed that increasing concentrations of He decrease chromatographic performance and, therefore, increase the observed retention time in supercritical fluid chromatography, an effect which has also been observed7 with other “negative modifiers” such as N2 or SF6. Some authors even report that He affects polymerization in supercritical CO2.8 There are few methods for measuring the amount of He in a particular sample of HHPCO2. In the first part of this paper, we describe the use acoustic measurements as a simple and reliable method for determining the He content of samples of HHPCO2 drawn directly from the gas cylinder. Our most surprising finding is that there are substantial differences in the He content of HHPCO2 obtained from apparently identical gas cylinders. In the second part, we use FT-IR spectroscopy to quantify the effect of He on the density of HHPCO2 as a function of temperature and pressure. PRINCIPLES OF MEASUREMENT Theoretical considerations9,10 and literature data11-14 on other He systems lead to the conclusion that the system He + CO2 (5) Burfield, D. W.; Richardson, H. P.; Guereca, R. A. AIChE J. 1970, 16, 97100. (6) Go ¨rner, T.; Dellacherie, J.; Perrut, M. J. Chromatogr. 1990, 514, 309-316. (7) Pickel, K. H. Proceedings of the 2nd International Symposium on Supercritical Fluids; Mc Hugh, M. A., Ed.; Johns Hopkins University: Baltimore, MD, 1991; p 457. (8) Hsiao, Y.-L.; DeSimone, J. M. Polym. Mater. Sci. Eng. 1996, 74, 260-261. (9) Streett, W. B. Can. J. Chem. Eng. 1974, 52, 92-97. (10) Schneider, G. M. Adv. Chem. Phys. 1970, 17, 1-42. (11) De Swaan Arons, J.; Diepen, G. A. M. J. Chem. Phys. 1966, 44, 2322-2330. (12) Yamanishi, T.; Okuno, K.; Naruse, Y.; Sada, E. J. Phys. Chem. 1992, 96, 2284-2289. S0003-2700(96)00573-2 CCC: $12.00

© 1996 American Chemical Society

Figure 1. Schematic summary of the results reported by Taylor et al.4 In full HHPCO2 cylinders (a), the head pressure of He is high, and so the amount of He dissolved in CO2 is correspondingly large. As the cylinder empties (b), the He head pressure falls, with a consequent reduction in the amount of dissolved He. These results imply that He and CO2 are in thermodynamic equilibrium within the cylinder. The pressure drop is not as large as implied by the shaded areas in the figure because of outgassing of He from the CO2. Using the dimensions of an average cylinder (given in the Experimental Section) and assuming that an equilibrium amount of He is dissolved in the CO2 (∼3%) and an ideal gas phase, the pressure drop on emptying the cylinder can be calculated with the ideal gas law. Assuming that the temperature is 293.15 K and the pressure inside the cylinder is 10 MPa, the pressure drops to roughly 6.5 MPa when the cylinder is almost completely emptied.

Figure 3. Variation of the critical pressure of CO2/He mixtures with mole fraction as measured acoustically. b, Calibration mixtures of known composition; [, HHPCO2 samples from (a) a “full” cylinder (filled Oct 1994), (b) the same cylinder (filled Oct 1994) after one month’s use, (c) an “empty” cylinder (filled Nov 1995), (d) a “full” cylinder (filled April 1995), and (e) an “empty” cylinder (filled Jan 1995). See also Table 1. Table 1. Summary of Acoustic Measurements of pc on He + CO2 Mixtures and Genuine Samples of HHPCO2 calibration mixtures, He + CO2

a

Figure 2. Schematic p,T diagram of the “high-temperature” part of the critical curve in the system He + CO2. O denotes data from Tsiklis,15 which show that the system exhibits gas-gas equilibrium of the first kind. Note that Tc is predicted to rise by only 6 mK/bar increase in pc.

should exhibit so-called gas-gas immiscibility of the first kind.15 Figure 2 shows a schematic representation of this rather unusual phase equilibrium; the critical curve rises continuously with a positive slope to higher pressures and temperatures, starting from the critical point of CO2. This behavior has the important consequence that a pressure can be found, for every temperature above the critical point of CO2, at which a mixture of He and CO2 will split into two phases. Since the critical curve rises monotonically to higher pressures with no extreme points in temperature or pressure, the amount of He in a particular mixture can be determined uniquely by measuring the critical point of that mixture. This means that a measurement of either the critical (13) Sretenskaya, N. G.; Sadus, R. J.; Franck, E. U. J. Phys. Chem. 1995, 99, 4273-4277. (14) Lin, H. M.; Lee, M. J.; Lee, R. J. J. Chem. Eng. Data 1995, 40, 653-656; Fluid Phase Equilib. 1995, 111, 89-99; Ind. Eng. Chem. Res. 1995, 34, 4524-4530. (15) Tsiklis, D. S. Dokl. Akad. Nauk SSSR 1952, 86, 1159-1161.

results from HHPCO2 cylinders

x(He)/%

pc/bar

samplea

pc/bar

x(He)/%

0.1 0.4 1.12 1.99 3.0

74.0 74.1 76.6 79.4 81.4

a b c d e

78.6 79.4 80.2 80.8 81.6

1.87 2.16 2.46 2.68 2.98

See Figure 3 for details of HHPCO2 cylinders.

temperature, Tc, or the critical pressure, pc, of a mixture can be used to quantify the composition of the sample. In this study, however, we have measured pc rather than Tc because, over the composition ranges found in HHPCO2, the absolute value of pc is much more sensitive to the presence of He. Indeed, a mixture of 3% He in CO2 had a value of Tc identical to that of pure CO2 within the accuracy of our measurement ((0.05 °C, see below). EXPERIMENTAL SECTION The critical points of He/CO2 mixtures were measured by acoustic methods. Since published acoustic measurements16 only cover the speed of sound in He/CO2 mixtures in their homogeneous region, we have calibrated our measurements using mixtures of He/CO2 of known composition. The He content of genuine samples of HHPCO2 was then derived from this calibration curve. Warning: These experiments involve high pressures and should, therefore, only be carried out with equipment with the appropriate pressure rating. Preparation of Gas Mixtures for Calibration. Both He and CO2 were supplied by BOC, with a purity of 99.99%. He + CO2 mixtures were prepared in a high-pressure bomb, 150-mL capacity (Whitey HDF4-150). The bomb was weighed empty and was then cooled with liquid nitrogen. A certain amount of CO2 was frozen (16) Pitayevskaya, L. L.; Popov, A. A. Dokl. Akad. Nauk 1991, 316, 1112-1116.

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Figure 4. Rationalization of our analysis of He in HHPCO2, assuming that the He and CO2 are not thoroughly equilibrated. Diagram a shows density stratification in a full cylinder with a low He content at the bottom of the cylinder from where the HHPCO2 is drawn off. Diagrams b and c show how, as the the cylinder is drained, Herich CO2 gradually reaches the dip tube.

Figure 5. Calculated diffusion of He in water at 293 K as a model for He in liquid CO2. Assuming that the behaviors of water and CO2 are similar, the calculation suggests that it would take more than 2 years for all of the He to dissipate.

in the bomb, thawed, and reweighed. The procedure was repeated to add a known amount of He into the bomb although, of course, He does not actually liquefy at 77 K. The mass differences were then used to calculate the mole fractions of the system; the accuracy depended only on the balance (Mettler PM4000). The uncertainty in reading the balance was 0.01 g, which for our synthetic compositions resulted in an error of ∆x ) (0.15 for the mole percentage. Five different mixtures were prepared with mole fractions of He in the range 0.001-0.03. However, for consistency with previous papers in this area, all compositions are quoted as mol % He in the mixture (i.e., 0.1-3 mol % He). After the gases were mixed, the system was allowed to equilibrate for at least 30 min at the desired temperature (above Tc of pure CO2, 304.2 K) before any acoustic measurements were made. Measurement of pc. A detailed description of the Nottingham acoustic equipment and its filling and safety procedures has been given elsewhere.17 The acoustic cell was constructed from a standard stainless steel 1/4-in. cross-piece (Swagelok 400-4), forming an acoustic cavity of ∼2-mL volume. Pressure was generated by a hand pump (High Pressure Equipment Co., Model 62-6-10) and monitored with a solid-state pressure transducer (17) Kordikowski, A.; Robertson, D. G.; Aguiar-Ricardo, A. I.; Popov, V. K.; Howdle, S. M.; Poliakoff, M. J. Phys. Chem. 1996, 100, 9522-9526. This paper also discusses the implications of a two-phase system on the acoustic signal.

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Figure 6. Representative FT-IR spectra of pure CO2 in the region of the Fermi triad. The individual spectra correspond to densities of the fluid of ∼0.1, 0.3, 0.5, 0.7, and 0.9 g cm-3 at 304.6 K. For a more quantitative analysis, the peak areas were integrated between the limits 5170 and 4750 cm-1 (the end points of the region illustrated; see Experimental Section for more details). The inset diagram shows the linear dependence of the integrated area with fluid density for three different temperatures.

(RDP Electronics, Series TJE). Pressure readings were constant within (0.01 MPa. The acoustic cavity and hand pump were thermostated with a circulating water thermostat (Haake, F3K), which held the temperature constant (0.02 K. Temperature was measured by a thermocouple and digital multimeter (ThurlbyThandar TTI-1906) with an accuracy of (0.05 K. The acoustic signal was obtained by using a pulse generator (Wayne Kerr CT500) to feed a microsecond pulse into the acoustic cavity via a ceramic transducer. A second, identical transducer monitored the signal at the other end of the cavity, and after amplification, the signal was displayed on an oscilloscope (Gould DSO 475), from which the transit time of the pulse across the acoustic cavity was obtained. The transit time, which is proportional to the reciprocal of the speed of sound, reaches a maximum at the critical point. After equilibration of the gas mixture (see above), the pressure was slowly decreased, and for each pressure the corresponding transit time was measured. The pressure was lowered until a maximum in the transit time was observed. FT-IR Measurements. IR spectra were recorded using a miniature high-pressure cell, as described previously,18,19 fitted with temperature and pressure monitors similar to those on the acoustic cavity. The optical path length was 3 mm, and spectra were recorded on a Perkin-Elmer Model 2000 FT-IR interferometer with 16 scans at 2-cm-1 resolution with a TGS detector. The integrated areas of the IR bands were obtained using the integrate as a single peak function in the Galactic GRAMS Research 2000 software package. HHPCO2. Test measurements were made on a series of cylinders of HHPCO2 (BOC SFC grade), each labeled with the month of filling by the manufacturer; the oldest was October 1994, and the newest November 1995. All relevant acoustic measure(18) Poliakoff, M.; Howdle, S. M.; Kazarian, S. G. Angew. Chem., Int. Ed. Engl. 1995, 34, 1275-1295. (19) Howdle, S. M.; Poliakoff, M. In Supercritical FluidssFundamentals for Applications; Kiran, E., Levelt Sengers, J. M. H., Eds.; NATO ASI Series E 273; Kluwer Academic Publications, Dordrecht, The Netherlands, 1994; pp 527-537.

Figure 7. Plots of the area of the FT-IR Fermi triad bands of pure CO2 and a HHPCO2 sample (2.2 mol % He) against pressure for three different temperatures. The traces are labeled as follows: (304.6 K) b, CO2; O, HHPCO2; (309.5 K) [, CO2; ], HHPCO2; (324.3 K) 2, CO2; 4, HHPCO2. The right-hand ordinates axis has been recalibrated in density using data from the inset diagram in Figure 6. It can be seen that the HHPCO2 sample always has a lower density and a higher critical pressure at a given temperature.

ments were made in March 1996. The cylinders were 1.47 m high, with an external diameter of 22.9 cm; the dip tube had an internal diameter of 8 mm and was ∼1.5 m long (i.e., 75 mL of CO2 was contained within the dip tube). Full cylinders contained a nominal 20 kg of CO2. Each acoustic determination of pc required removal of only 150 mL (∼100 g) of HHPCO2 from the cylinder and, therefore, had no significant effect on the overall composition of the contents. RESULTS AND DISCUSSION Acoustic Measurements. Figure 3 shows a plot of pc as a function of He concentration for He/CO2 mixtures of known composition, and Table 1 summarizes the data. As expected, the relationship over this composition range is linear within experimental error. The values of pc measured for five genuine samples of HHPCO2 are also shown in Figure 3. These samples were taken from four different cylinders, two newly opened and two nearly empty. The He contents of the HHPCO2 samples were calculated from these critical pressures as shown in Figure 3 and Table 1. The following points are clear: (i) no two samples contained the same mole fraction of He; (ii) the only sample found to have the expected 3% He was from a nominally empty cylinder; (iii) both full cylinders yielded samples with less He than this empty cylinder; (iv) the He concentrations from the two full cylinders were substantially different, 1.8 and 2.65% He, respectively, although the cylinders were apparently identical; and (v) the He content of HHPCO2 from one of the full cylinders was found to have increased, from 1.8 to 2.1%, when second sample was taken ∼1 month later, after the cylinder had been in regular use for chromatography. Not only are these observations inconsistent, but they are impossible from a thermodynamic point of view. One is, therefore, forced to conclude that the contents of the cylinders were not in thermodynamic equilibrium after the initial filling of the cylinder by the gas suppliers. Our observations can then be rationalized by assuming that the CO2 near the bottom of the cylinder is relatively poor in He (see Figure 4).

Figure 8. Plot of the density differences between pure CO2 and HHPCO2 as a function of pressure at different temperatures: (a) 304.6, (b) 309.5, and (c) 324.3 K. Note that the maximum difference occurs close to the critical isochore of the mixture and that the absolute difference increases as the critical temperature is approached.

Usually, a cylinder with a dip tube is filled first with CO2, and He is then flushed into the cylinder until the desired head pressure is reached. Since pressurizing a cylinder takes only a few seconds, He is flushed through the CO2 very rapidly with only a short contact time between the He and the bulk of the CO2. If the freshly filled cylinder is not in equilibrium, subsequent equilibration can occur only through diffusion, but the precise rate of equilibration cannot be calculated without knowing the diffusion coefficient of He in CO2 under the appropriate temperature and pressure conditions. However, an estimate can be made using the appropriate data for H2O, since the density of CO2 at 293 K and 100 bar is 904.4 kg m-3, close to that of water. Figure 5 shows the distribution of He in H2O at different time intervals calculated using D12 ) 6.5 × 10-9 m2 s-1, the literature value20 for He in H2O at 293 K. The mean-square distance for diffusion is only 0.64 m per year. All four cylinders were filled less than 18 months prior to our acoustic measurements, but Figure 5 shows that more than 2 years at 293 K is needed for an initial concentration pulse of He to be largely dissipated over a distance of 1.5 m. Repeating the calculations for 303 K (D12 ) 8.4 × 10-9 m2 s-1) shows that the mean-square distance increases, compared to that calculated for 293 K, but only from 0.64 to 0.73 m/year, a distance still smaller than the height of our cylinders (see Experimental Section). This temperature dependence of diffusion provides a plausible explanation why HHPCO2 from otherwise identical cylinders can contain different amounts of He. Even if the filling procedure at the gas supplier were the same for every cylinder, small differences in temperature during storage or handling would have a significant effect on the diffusion of He into the liquid CO2. It might be supposed that convection within the liquid phase would equilibrate the CO2 and He much more rapidly than suggested by the calculations in Figure 5. However, as shown below, dissolution of He in supercritical CO2 causes a significant reduction in density compared to pure CO2 at these pressures. It seems reasonable to suppose that some reduction in density will (20) Verhallen, P. T. H. M.; Oomen, C. J. P. Chem. Eng. Sci. 1984, 39, 15351541.

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also occur when He dissolves in near-critical liquid CO2, and this will lead to density stratification in the liquid phase in our cylinder. Such stratification is well documented in H2O and can lead to almost total suppression of convection, for example, in solar-heated brine pools21 with depths similar to that of the CO2 in our cylinders.22 Larger-scale stratification has been invoked to explain the tragic buildup of CO2 in Lake Nyos in Cameroon.23 FT-IR Measurements: Effects of He on Fluid Density. In the first part of this paper, we showed that HHPCO2 withdrawn from a fresh cylinder contains a variable amount of He, typically ∼2% He. Here we use FT-IR to investigate the effect of such a concentration of He on the density of the fluid. Our measurements are based on the integrated area of the the so-called “Fermi triad” IR bands of CO2 at ∼5000 cm-1 (see Figure 6). Buback and co-workers24 have shown that these bands have extinction coefficients which are largely independent of density, and therefore the intensity of these bands should provide a convenient means for probing the density of supercritical CO2. FT-IR measurements were made on pure CO2 and on a sample of HHPCO2 containing 2.2 mol % He as determined by our acoustic method. Spectra were recorded at three different temperatures (304.4, 309.5, and 324.2 K) and over the pressure range of 5-330 bar. The total area of the Fermi triad was obtained by integration (see Experimental Section), and the areas were plotted against pressure as shown in Figure 7. As expected, the curves show a steep increase when the pressure is in the vicinity of the critical isochore, and this increase is enhanced the closer the temperature is to Tc. Figure 7 also shows that, at each temperature, the critical isochore of the HHPCO2 sample is at higher pressures than that of pure CO2. The IUPAC equation of state25 was then used to calculate the density of pure CO2 for the appropriate pressures at all three temperatures. The integrated area of the bands was found to be linearly dependent on the fluid density (see inset plot in Figure 6). Helium does not absorb IR, and the presence of 2.2% He will add little to the mass of the fluid. Therefore, we can use the same intensity-density relationship to estimate the density of HHPCO2 as shown on the right-hand ordinate scale in Figure 7. The data from Figure 7 can then be used to quantify the difference in density between this sample of HHPCO2 and pure CO2 at the same temperature and pressure. The results are plotted in Figure 8. It is clear that the density differences are large and unlikely to be affected by our neglecting the contribution of the mass of the He to the density. The plots show that the maximum difference (21) Bronicki, Y. L. CHEMTECH 1981, 494-498. (22) Amusingly, the stratification of gaseous CO2 has been featured in the semiserious Daedalus Column of Nature (Jones, D. E. H. Nature 1990, 346, 1294). (23) Kling, G. W.; Clark, M. A.; Compton, H. R.; Devine, J. D.; Evans, W. C.; Humphrey, A. M.; Koenigsberg, E. J.; Lockwood, J. P.; Tuttle, M. L.; Wagner, G. N. Science 1987, 236, 169-175. (24) Buback, M.; Schweer, J.; Tups, H. Z. Naturforsch. 1985, 41a, 505-518. (25) Carbon Dioxide International Thermodynamic Tables of the Fluid State 3; Pergamon Press: Oxford, UK, 1976.

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occurs at a pressure close to the extension of the critical isochore, but even 20 °C above Tc, the differences between HHPCO2 and CO2 are still significant. This means that separations or extractions at low temperatures will be adversely affected by the extremely low density of the HHPCO2. Although one could compensate for the density differences by applying a higher pressure, there may be uncertainty in the amount of He actually dissolved in the CO2, and hence a wrong correction might be made. Finally, it should be remembered that the plots in Figure 8 refer to a sample of HHPCO2 containing only 2.2% He rather than the 3% He expected for a fully equilibrated sample. CONCLUSION We have shown that acoustic measurements offer a simple and precise method for quantifying the He content of HHPCO2. Applying this technique to the cylinders in our laboratory, we have been forced to conclude that the He and CO2 are not necessarily in thermodynamic equilibrium. Most chemists are unused to systems which are not in equilibrium. The properties of such systems depend on their history as well as their current state. Therefore, these properties are largely unpredictable. Furthermore, by use of FT-IR, we have confirmed earlier reports6 that the presence of He can have a very substantial effect on the density of HHPCO2 compared to pure CO2 particularly in the region close to the critical point. Irreproducibility in SF chromatography and extraction has sometimes been attributed to a variety of shortcomings in the instrumentation. However, the substantial effect of He on fluid density suggests that many of these cases may be associated with variability in the He content of HHPCO2. Although cylinders could presumably be equilibrated by suitable agitation, our recommendation is that HHPCO2 should be used with caution whenever precision or long-term reproducibility is required. The use of HHPCO2 should definitely be avoided in any study involving temperatures and pressures close to critical (i.e., measurements of solubility, solvent clustering, etc.). Our studies underline yet again the fundamental importance of phase behavior in the study of supercritical fluids. ACKNOWLEDGMENT We are grateful to the EPSRC (ROPA Grant No. GR/K34764), BP Chemicals Ltd., the EPSRC Clean Technology Unit, and the Royal Academy of Engineering for their financial support. We thank Dr. D. E. H. Jones for drawing our attention to refs 21-23, and Prof. V. N. Bagratashvili, Dr. M. W. George, Dr. S. M. Howdle, Dr. V. K. Popov, Mr. E. Shervington, Mr. K. Stanley, and Dr. R. J. Watt for their help and advice. Received for review June 11, 1996. Accepted September 23, 1996.X AC960573N X

Abstract published in Advance ACS Abstracts, November 1, 1996.