Anal. Chem. 2005, 77, 85-92
Method for Locating the Vapor-Liquid Critical Point of Multicomponent Fluid Mixtures Using a Shear Mode Piezoelectric Sensor Jie Ke,*,† P. J. King,‡ Michael W. George,† and Martyn Poliakoff*,†
School of Chemistry and School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
A new approach to locating the critical point of fluid mixtures is reported, utilizing a shear mode piezoelectric sensor. This technique employs a single piece of quartz crystal that is installed at the bottom of a strongly stirred high-pressure vessel. The sensor response indicates whether liquid or gas is in contact with its surfaces. Thus, the sensor is able to identify vapor-liquid phase separation by registering a discontinuity in the impedance minimum of the sensor as a function of pressure. Two systems (methanol + CO2 and H2 + CO2) have been investigated using this method. The critical point data of the methanol + CO2 system were chosen to validate the approach against a wealth of literature data, and good agreement was obtained. The sensor behavior in the twophase region, as well as the effect of stirring, is discussed. The method is general and can be used with other sensors. Supercritical fluids (SCFs) have received increasing attention as environmentally acceptable replacements for toxic organic solvents.1 One broad area of use for SCFs is the carrying out of chemical reactions under super- or near-critical conditions.2-5 It has been demonstrated on both laboratory and industrial scales that performing reactions under these conditions allows good control, or even enhancement of selectivity, easy separation of products, and substantial elimination of waste.6-8 Knowledge of the phase behavior of reaction mixtures is crucial in realizing the above advantages. The importance of phase measurements in this field was recently highlighted in this journal.9 * To whom correspondence should be addressed. E-mail: Martyn.Poliakoff@ nottingham.ac.uk. E-mail:
[email protected]. Fax: +44 115 951 3058. † School of Chemistry. ‡ School of Physics and Astronomy. (1) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction, 2nd ed.; Butterworth-Heinemann: Boston, 1994. (2) Beckman, E. J. J. Supercrit. Fluids 2004, 28, 121-191. (3) DeSimone, J. D. Science 2002, 297, 799-803. (4) Poliakoff, M.; King, P. Nature 2001, 412, 125. (5) Jessop, P. G.; Leitner, W. Chemical Synthesis Using Supercritical Fluids; Wiley VCH: Weinheim, 1999. (6) Hyde, J. R.; Licence, P.; Carter, D.; Poliakoff, M. Appl. Catal., A 2001, 222, 119-131. (7) Oku, T.; Ikariya, T. Angew. Chem., Int. Ed. 2002, 41, 3476-3479. (8) Licence, P.; Ke, J.; Sokolova, M.; Ross, S. K.; Poliakoff, M. Green Chem. 2003, 5, 99-104. (9) Wells, P. S.; Zhou, S.; Parcher, J. F. Anal. Chem. 2003, 75, 18A-24A. 10.1021/ac048970i CCC: $30.25 Published on Web 11/24/2004
© 2005 American Chemical Society
The critical point of reaction mixtures is particularly important because it defines a unique point on the phase boundary where the coexisting gas and liquid phases become identical. Unlike pure substances, the critical point of multicomponent mixtures is not necessarily at either the temperature maximum or the pressure maximum on a p-T phase boundary, and the critical parameters can be quite different from those of pure substances even for very dilute solutions.10 In most cases, accurate estimates of the critical parameters cannot be obtained without at least some experimental information on the vapor-liquid equilibrium. The experimental location of critical points is usually performed either by visual methods or by analyzing the composition of small samples withdrawn from the pressure vessel. Both methods have disadvantages: accurate sampling for analysis is difficult, especially in the critical region, while determining the critical point using a view cell is labor-intensive, time-consuming, and often constrained by the subjectivity of the experimenter. There is, therefore, a considerable need to develop alternative ways of locating the critical point of the multicomponent mixtures. The shear mode piezoelectric sensor (the key element of a quartz crystal microbalance) has been widely used as a mass sensor to study the physical-chemical processes at solid-fluid interfaces, due to the advantages of its low detection limits, its low cost, and the chemical inertness of the quartz substrate.11,12 It also offers other features (such as small size and easy installation and maintenance) that make it an excellent device for working in a high-pressure environment. Such sensors have been reported as being used for studying the absorption of CO2 by polymer films,13-15 the solubility of metal complexes,16,17 and, even, molecular recognition in supercritical CO2.18 In this paper, we show that this sensor can be used to exemplify a completely new (10) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.; Butterworth: London, 1982. (11) Buttry, D. A.; Ward, M. D. Chem. Rev. 1992, 92, 1355-1379. (12) Janshoff, A.; Galla, H.-J.; Steinem, C. Angew. Chem., Int. Ed. 2000, 39, 40044032. (13) Aubert, J. H. J. Supercrit. Fluids 1998, 11, 163-172. (14) Tang, M.; Du, T.-B.; Chen, Y.-P. J. Supercrit. Fluids 2004, 28, 207-218. (15) von Solms, N.; Nielsen, J. K.; Hassager, O.; Rubin, A.; Dandekar, A. Y.; Andersen, S. I.; Stenby, E. H. J. Appl. Polym. Sci. 2004, 91, 1476-1488. (16) Guigard, S. E.; Hayward, G. L.; Zytner, R. G.; Stiver, W. H. Fluid Phase Equilib. 2001, 187-188, 233-246. (17) Park, K.; Koh, M.; Yoon, C.; Kim, H.; Kim, H. ACS Symp. Ser. 2003, No. 860, 207-222. (18) Naito, M.; Sasaki, Y.; Dewa, T.; Aoyama, Y.; Okahata, Y. J. Am. Chem. Soc. 2001, 123, 11037-11041.
Analytical Chemistry, Vol. 77, No. 1, January 1, 2005 85
approach to locating critical points. Although the sensor works well, this approach can also be used with other types of sensors, for example, a fiber-optic reflectometer.19 Our research has focused on measurement of the vapor-liquid equilibrium using sensor technology. Trying to monitor phase separation with a single sensor might appear to be impossible since the transition process is very complex and the precise way in which phases separate depends on the particular region of the phase diagram. At the onset of the transition, only a few bubbles or droplets separate from the homogeneous single phase and the sensor might not be placed correctly to detect the tiny volume of the new phase. However, we have found that this problem may be overcome using surface-sensitive sensors. Our initial attempts have involved mapping the phase boundaries of pure fluids (e.g., CHF3, CO2, and ethane) using either a fiber-optic reflectometer19 or a quartz crystal sensor.20 Very recently, this work has been extended to the location of the critical point for multicomponent mixtures using both the reflectometer and the quartz sensor.21 Our method requires that the sensors (i) respond only to the thin layer of fluid immediately contacting the sensor surface and (ii) give a significant difference in output depending on whether the sensor is in contact with gas or liquid. We have briefly reported21 that, provided these conditions are met, a single sensor can locate the critical point of a binary mixture.22 In this article, we describe our experimental technique in detail and describe the extrapolation methods for locating the critical point of multicomponent mixtures. We then present critical point and phase boundary data for five binary mixtures of MeOH + CO2 for validation against the literature data. A binary mixture of H2 + CO2 has been measured as a further system since in this case CO2 behaves as the “liquid” in the system rather than the “gas” as in the methanol system. Finally, we discuss the sensor behavior during the phase separation process and the effect of stirring, to confirm the physical basis of our new approach. EXPERIMENTAL SECTION Materials. MeOH (Acros Organics, 99.9%) was used without further purification. Carbon dioxide (BOC, 99.99%), and hydrogen, (Air Products, 99.999%) were used as supplied. High-Pressure Variable-Volume Cell. The measurements were made in a custom-built high-pressure, variable-volume cell, which provides a common platform for detecting the critical point and the phase boundary using the synthetic method.23,24 A schematic diagram of the variable-volume cell is presented in Figure 1. It mainly consists of a high-pressure chamber for the installation of different sensors and a cylinder and piston through which the pressure in the cell may be varied.20,25 The pressure (19) Avdeev, M. V.; Konovalov, A. N.; Bagratashvili, V. N.; Popov, V. K.; Tsypina, S. I.; Sokolova, M.; Ke, J.; Poliakoff, M. Phys. Chem. Chem. Phys. 2004, 6, 1258-1263. (20) Oag, R. M.; King, P. J.; Mellor, C. J.; George, M. W.; Ke, J.; Poliakoff, M. Anal. Chem. 2003, 75, 479-485. (21) Ke, J.; Oag, R. M.; King, P. J.; George, M. W.; Poliakoff, M. Angew. Chem., Int. Ed. 2004, 43, 5192-5195. (22) Inevitably, there will always be experimental uncertainties in the precise composition of the mixture in the cell. These uncertainties are likely to be much larger than the errors introduced by unrepresentative interfacial compositions, which might be found very close to the sensor surface. (23) Dohrn, D.; Brunner, G. Fluid Phase Equilib. 1995, 106, 213-282. (24) Christov, M.; Dohrn, R. Fluid Phase Equilib. 2002, 202, 153-218. (25) Oag, R. M.; King, P. J.; Mellor, C. J.; George, M. W.; Ke, J.; Poliakoff, M.; Popov, V. K.; Bagratashvili, V. N. J. Supercrit. Fluids 2004, 30, 259-272.
86 Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
Figure 1. Schematic diagram of the experimental setup for the measurement of the quartz and the fiber sensor properties: A, amplifier; C, pressure chamber; CY, cylinder; D, digital multimeter; FR, filter and rectifier; F, function generator; I, ISCO syringe pump; LD, luminescent diode; O, optical fiber; P, piston; PC, personal computer; PI, pressure indicator; PR, photodiode for the reference fiber; PS, photodiode for the signal fiber; PT, pressure transducer; Q, quartz sensor; S, stirrer; SE, seal; SW, sapphire window; T, thermometer (Pt100); TE, thermostated enclosure; V1, V2, V3, valves; XC, X-shape optic fiber coupler; W, water.
chamber has ports on two opposite faces for the installation of sensors: one is used by the quartz sensor (the left-hand side of Figure 1), and the other can be used for the optical fiber sensor (the right-hand side of Figure 1), allowing us to test the two different sensors simultaneously.21 The remaining two faces carry windows for visual observation; these windows are not, however, strictly necessary for the measurement described here. A magnetic stirrer bar of triangular cross section is placed at the bottom of the chamber, driven by a motor with a speed of 1000 rpm. We have found that a powerful stirrer is essential for the success of our measurements, not only because it enhances the homogeneity of fluid in the cell but also because, as explained later, it spreads liquid droplets throughout the cell allowing them to be detected by the sensor. In our configuration, the quartz sensor was installed 2 cm above the stirrer. The precise position of the sensor is not crucial, but it needs to be close to the stirrer, which in turn must be at the bottom of the cell to ensure that it agitates the liquid phase however small its volume. The cylinder contains a piston with three O-ring seals. The top of the cylinder is connected to a high-pressure syringe pump filled with a secondary fluid (e.g., water). The piston is moved downward or upward, respectively, by pumping or withdrawing the secondary fluid from the top part of the cylinder. The chamber, the cylinder, and the secondary fluid in the syringe pump are all placed in thermostated enclosures, which are held at a stable temperature, a few degrees below the measurement temperature. The temperature of the cell is sensed by a Wheatstone bridge, one arm of which contains a number of thermistors mounted on the surface of the cell. The output of the Wheatstone bridge is fed through a three-term controller, the amplified output of which feeds a number of resistive heaters distributed about the surface of the cell. The stability20,25 of the cell temperature is typically better than (0.01 K. The system temperature is measured with a calibrated platinum resistance thermometer and a digital multimeter. The cell is rated to 350 bar and a maximum temperature of 360 K. Its volume can be varied between 80 and 320 cm3. Further details of the variable-volume cell and its operation have been described by Oag et al.20,25
Shear Mode Piezoelectric Sensor. Shear mode piezoelectric sensors consist of thin piezoelectric plates with metallic coatings over the opposing faces. An alternating strain field is induced by an electrical field applied between these two metal electrodes. By choosing a suitable crystallographic orientation of the plate, usually AT-cut for quartz, the applied electric field leads to a purely transverse mechanical wave that propagates across the thickness of the crystal. At certain frequencies, the plate may be driven into mechanical resonance, affecting the electrical impedance between the two contact electrodes. When the plate is immersed in a fluid, the frequency and breadth of the resonance is affected by both the density and viscosity of the fluid contacting the sensor surface. The fluid properties can therefore be determined by monitoring the impedance of the electrical equivalent circuit of the sensor.26 The sensor was operated in the impedance minimum mode, which has been demonstrated to have a wider range of linearity than the frequency shift mode.20 An electrical circuit consisting of a function generator, a diode rectifier, and a digital multimeter was used to measure the sensor impedance, as shown in the lefthand part of Figure 1. The relationship between the impedance minimum, |Z|min, and fluid properties is given by
|Z|min ) θ0/(ωminC0K2)‚g
(1)
g ) [(Fηω)/(2CsFs)]1/2
(2)
with
where F and η are the density and viscosity of the fluid, and (CsFs)1/2 is the acoustic impedance of the sensor material.20 Equations 1 and 2 have been derived based on the assumption that the crystal has an ideally smooth surface.20,27,28 In fact, the resonance is slightly affected by a number of factors, such as the surface roughness,29,30 interfacial wetting properties,31 and adsorbed mass on the surface.32 However, we are using the shear mode crystal sensor to determine the phase separation boundary, at which the density and viscosity of the system usually undergo a substantial change. Therefore, the above factors are unlikely to affect the position of the discontinuities in the traces, which indicate phase separations, but might affect the precise numerical value of |Z|min. The sensor used in this study had a coated area of the gold electrodes of 0.145 cm2 and a nominal characteristic frequency of 6 MHz. Further details of the sensor linearity analysis and the calibration procedure has been described elsewhere.20 Sample Preparation and Measurement Strategy. Our approach involves a so-called “synthetic method”, that is, the study (26) Mason, W. P. Physical Acoustics; Academic Press: New York, 1965; Vol. 2A. (27) Muramatsu, H.; Tamiya, E.; Karube, I. Anal. Chem. 1988, 60, 2142-2146. (28) Martin, S. J.; Granstaff, V. E.; Frye, G. C. Anal. Chem. 1991, 63, 22722281. (29) Martin, S. J.; Frye, G. C.; Ricco, A. J.; Senturia, S. D. Anal. Chem. 1993, 65, 2910-2922. (30) Park, K.; Koh, M.; Yoon, C.; Kim, H.; Kim, H. J. Supercrit. Fluids 2004, 29, 203-212. (31) Theisen, L. A.; Martin, S. J.; Hillman, A. R. Anal. Chem. 2004, 76, 796804. (32) Wu, Y.-T.; Akoto-Ampaw, P.-J.; Elbaccouch, M.; Hurrey, M. L.; Wallen, S. L.; Grant, C. S. Langmuir 2004, 20, 3665-3673.
of a mixture of a definite fixed composition. Therefore, the accurate preparation of samples is absolutely key to the success of the experiments. Before a sample was made, the cell was rinsed with suitable solvents several times and then evacuated using a rotary vacuum pump. For MeOH + CO2 mixtures, a measured quantity of MeOH was then introduced into the cell. For H2 + CO2, H2 was added from a high-pressure reservoir, its amount being calculated from the pressure, temperature, and total volume of the system. The cell was kept at a constant, known temperature during this process. Finally, in both cases, CO2 was expanded into the system from a high-pressure bomb. The weight difference of the bomb was used to determine the amount of CO2 that had been added to the cell. We estimate that the uncertainties in the values of the mole fractions are no more than (0.1% for MeOH and CO2 and (1% for H2. Measurements on each of the samples were made at a series of ascending temperatures at intervals of 1-3 K throughout the accessible temperature range of our apparatus. At a given temperature, the system pressure was increased to at least 10 bar above the estimated phase-transition pressure to ensure that a homogeneous phase was present in the cell. The cell was then allowed to equilibrate for 2-4 h at the desired temperature because of the large thermal mass of the cell and its thermostated housing,25 before any measurements were carried out. The volume of the cell was then decreased at a rate of 0.5 cm3 min-1 until the occurrence of a phase separation. RESULTS AND DISCUSSION Measurements of Phase Separation Near the Critical Point. We first chose a binary mixture of MeOH + CO2 with a mole fraction xMeOH ) 0.103, as our test mixture since the critical region of this mixture can be easily accessed using the apparatus described above. Figure 2a shows 18 isotherms recorded over the temperature range of 297-345 K. The measured values of |Z|min were plotted as a function of pressure at each given temperature. All the data shown in Figure 2a were collected within a period of 1 week. It can be seen from the figure that traces 1-6, which were recorded at low temperature (320 K), show a large change in |Z|min. In this paper, we use the term “jump” to describe such a sudden change or discontinuity in |Z|min. Traces 7 and 8, however, show a transition state between these two typical shapes. These traces correspond to temperatures of 317.87 and 319.00 K, both of which are close to the reported critical temperature (Tc) of this mixture.33 Both the “tick shape” and “jump shape” correspond to discontinuities in either the density or viscosity (or both) of the fluid in immediate contact with the active surface of the sensor. These discontinuities, therefore, correspond to the phase separations at the bubble point and the dew point, respectively. In addition, each trace shows a minimum along the isotherm, indicating the onset of the phase transition. The corresponding pressure at the minimum and the temperature are plotted as the p-T phase boundary, shown in Figure 2b. The data reported by Yeo et al.33 for a mixture with a similar composition (xMeOH ) 0.106) (33) Yeo, S.-D.; Park, S.-J.; Kim, J.-W.; Kim, J.-C. J. Chem. Eng. Data 2000, 45, 932-935.
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Figure 2. Experimental data for the binary mixture MeOH + CO2 with xMeOH ) 0.103: (a) impedance minimum (|Z|min) versus pressure along 18 isotherms between 297.55 and 344.09 K. Traces are number 1-18 from low to high temperature. O represents the value of |Z|min from the coexisting liquid-phase at the dew point. (b) The p-T phase boundary, 0, obtained from (a) (xMeOH ) 0.103), 9, data reported by Yeo et al. (xMeOH ) 0.106).33
are also depicted with solid circles in the figure. We note that the standard deviation for the phase-separation pressure between our data and the literature data is ∼0.7 bar. Considering the slightly different composition of the two mixtures (0.103 vs 0.106), there is a good agreement between our data and those of Yeo et al.33 Location of the Critical Point. Unlike a pure substance, where the critical point is at the end point of the vapor-pressuretemperature curve, the critical point of a multicomponent mixture is not necessarily at either the temperature maximum or the pressure maximum on a p-T phase boundary.10 Hence, the critical point of a mixture cannot be identified from any simple characteristic points present on p-T the boundary. However, the critical point can be defined as the point where the bubble point and dew point lines meet on the p-T phase boundary. As has been discussed in the previous section, a shear mode sensor can indicate whether the vapor-liquid phase transition is a bubble point or dew point from the shape of the isotherms (|Z|min-p traces). The critical point may therefore be estimated by recording a number of isotherms in the critical region and by noting their shape. For example, we can conclude that Tc must lie be between 316 and 320 K from the data shown in Figure 2a. However, there are two drawbacks to using this direct inspection method: (1) accurate determination of critical points would require a very considerable number of measurements in the critical region, and (2) the isotherms have similar shapes near the critical point, leading to uncertainty in identifying the critical isotherm. In what follows, we use the data shown in Figure 2a to demonstrate the advantage of an extrapolation method for locating the critical point. It can be seen from Figure 2a that each trace with a jump shows two characteristic points. The first is the minimum in |Z|min, which has been identified as the phase-transition point. The 88 Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
Figure 3. Locating the critical point using the extrapolation method. (a) the |Z|min-T curve: curve A, the top point of the jump shown in Figure 2; curve B, the phase-transition point for each isotherm. Curve A was fit using the quadratic formula and was extrapolated to the left of the datum points. Curves A and B are intersected at the critical temperature C. (b) The more convenient |Z|min-T curve: this curve was fitted with a cubic polynomial and extrapolated to |Z|min ) 0 (the dashed line) to find Tc.
other is the top point of the jump (marked as circles in Figure 2a), which represents the properties of the coexisting liquid phase just after the phase separation. Figure 3a shows a plot of the top point of the jump and the phase-transition point (the bottom point) as a function of temperature (curves A and B). For curve A, |Z|min is fitted using a quadratic formula in temperature; this fitted curve extrapolated to the left of the data points. For curve B, |Z|min is fitted with a cubic spline in temperature. The point where the two curves intersect is taken to be Tc. The extrapolation may be further simplified by introducing ∆|Z|min, which represents the height of the jump at the dew point. Because all intensive properties of two coexisting phases are identical at the critical point, a jump with a zero height must indicate the position of the critical point. ∆|Z|min can be obtained from the corresponding points on curves A and B (Figure 3a) and then can be plotted as a function of temperature (Figure 3b). Tc is found at the temperature where ∆|Z|min extrapolates to zero. The two methods give very similar values of Tc for this mixture. However, the ∆|Z|min method is also suitable for those systems with a complex curvature21 of the Z-T lines and usually reduces errors caused by curve-fitting processes. Using the example given in Figure 3, which describes a mixture with xMeOH ) 0.103, Tc is 318.0 ( 0.2 K. Once Tc is obtained, the critical pressure (pc) may be interpolated from the p-T phase boundary derived from the |Z|min traces, e.g., as shown in Figure 2b. In the method just described, the critical point is located by extrapolating from a few dew points in the critical region. The accuracy of Tc depends on the number of data points measured and how close they are to the critical point. In the case of the MeOH + CO2, five to eight data points at intervals of 3 K along the dew point line would be sufficient to give an accuracy better than (0.5 K. One advantage of our extrapolation method over the conventional visual methods is that it gives numerical values
Table 1. Experimental Critical Parameters for the Binary System MeOH + CO2
a
xMeOH
Tc/K
pc/bar
0.205 0.139 0.103 0.078 0.040 0a
328.2 320.9 318.0 316.6 312.5 304.21
104.9 93.0 88.6 86.9 82.4 73.825
Literature value for pure CO2.44
Figure 4. Superimposed pT phase boundaries for the binary system MeOH + CO2 at five different xMeOH: ], 0.040; 0, 0.078; O, 0.103; ×, 0.139; +, 0.205.
Figure 6. Experimental critical points for the system MeOH + CO2. b, This work; 0, Yeo et al.;33 ], Leu et al.;36 +, Brunner et al.;35 ×, Brunner et al.34
Figure 5. |Z|min-T diagram for the binary system of MeOH + CO2 showing the extrapolation for obtaining values of Tc for different mole fractions MeOH: (a) 0.040; (b) 0.078; (c) 0.103; (d) 0.139; (e) 0.205.
of the critical parameters even when only a few measurements have been made. This is particularly important in studying chemical reactions in supercritical fluids, where a “quick” answer is often required for the critical parameters of reaction mixtures. Measurements of |Z|min against pressure were made between 297 and 345 K for four further mixtures of MeOH + CO2 with xMeOH ) 0.040, 0.078, 0.139, 0.205. The p-T phase boundaries for all five mixtures are shown in Figure 4. Each datum point in this figure was obtained from a single isotherm similar to those shown in Figure 2a. To locate the critical points, the height of the jump (∆|Z|min) was determined using the method just noted in the previous section. Figure 5 shows that ∆|Z|min increase monotonically as a function of T for all five mixtures. It also shows that ∆|Z|min increases more rapidly for the dilute solution (xMeOH ) 0.040) than for the most concentrated solution (xMeOH ) 0.205). All curves in this figure were fitted using quadratic or cubic polynomials. Tc was found by extrapolation to ∆|Z|min ) 0. As expected, Tc is found to increase with xMeOH. Again, pc was interpolated from the p-T phase boundaries shown in Figure 4, and the results are summarized in Table 1. The critical points of the MeOH + CO2 system have been measured by various investigators using a range of different methods and equipment, including variable-volume view cells,33 static optical cells,34 and sampling methods.35,36 Figure 6 compares the critical point data
from our study with data from the literature. It can be seen that the quartz sensor values agree well with those determined using more conventional techniques. Our data cover a smaller temperature range than the literature values, merely because of temperature limitations on our variable-volume cell. The only limitation on our method will be the operating temperature range of the particular sensor used. H2 + CO2. We are particularly interested in hydrogenation of organic compounds in scCO2 due to their industrial importance.37,38 Nearly all organic substrates are heavier molecules than CO2, so that their mixture with CO2 leads to a large increase in Tc. By contrast, H2 has the opposite effect on Tc because H2 is a permanent gas with a very low value of Tc (33 K). The mixture H2 + CO2 is therefore an interesting test of our method because CO2 is the “liquid” phase component. In a classic experimental study from 220 to 290 K by Tsang and Streett,39 H2 + CO2 was shown to exhibit type III phase behavior in the Scott and van Konynenburg classification.40 This implies that three phases can exist in equilibrium at low temperatures. However, our measurements has been preformed in the temperature region of 293-313 K, where only two phases (vapor + liquid) coexist. Measurements of |Z|min as a function of pressure were made on the mixture with xH2 ) 0.091 along 14 isotherms in the critical (34) Brunner, E. J. Chem. Thermodyn. 1985, 17, 671-679. (35) Brunner, E.; Hueltenschmidt, W.; Schlichthaerle, G. J. Chem. Thermodyn. 1987, 19, 273-291. (36) Leu, A. D.; Chung, S. Y. K.; Robinson, D. B. J. Chem. Thermodyn. 1991, 23, 979-985. (37) Machado, R. M.; Heier, K. R.; Broekhuis, R. R. Curr. Opin. Drug Discovery Dev. 2001, 4, 745-755. (38) Nishimura, S. Handbook of Heterogeneous Catalytic Hydrogenation for Organic Synthesis; Wiley-Interscience: New York, 2001. (39) Tsang, C. Y.; Streett, W. B. J. Eng. Sci. 1981, 36, 993-1000. (40) van Konynenburg, P. H.; Scott, R. L. Philos. Trans. R. Soc. London, Ser. A 1980, 298, 495-540.
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Figure 8. Plots of |Z|min versus T for the dew points of the binary mixture H2 + CO2 with xH2 ) 0.091 (see Figure 7 for the original data). The curve was fitted with a cubic polynomial and extrapolated to |Z|min ) 0 (the dashed line) to find Tc.
Figure 7. Experimental data for the binary mixture H2 + CO2 with xH2 ) 0.091: (a) impedance minimum (|Z|min) versus pressure along 14 isotherms between 293.02 and 312.21 K. Traces are number 1-14 from low to high temperature. The inset diagram shows the details of the jump from trace 8. (b) The p-T phase boundary. The error bars represent the estimated error on the measured bubble/dew point pressure. The arrow indicates the position of the critical point.
region (see Figure 7a). Five low-temperature isotherms (traces 1-5) show the tick shape, indicating a bubble point on the phase boundary. Traces 6-9 show two jumps as the pressure is decreased isothermally. The first jump at high pressure is relatively small. The details of such a small jump is shown in the inset diagram in Figure 7a using trace 8 as an example. The second jump at lower pressure is more abrupt than the first one because it is further away from the critical point. In this case, the two separated phases have large differences in both density and viscosity. As a result, the sensor produces a large decrease in the output signal when it is brought from the two-phase region to a homogeneous gas. Nevertheless, both of these jumps are ascribed to dew points on the phase boundary. Traces 10-14 change smoothly from high to low pressure because there is no phase transition at these temperatures. Based on these data, a p-T phase boundary for the binary mixture can be drawn up, as shown in Figure 7b. To locate the critical point, we identified seven dew points from four isotherms (traces 6-9), and the corresponding plot of ∆|Z|min versus T is given in Figure 8. This curve shows a maximum at ∼301 K. Four points with a high ∆|Z|min value (>40 Ω) are normal dew points; the other three (∆|Z|min < 40 Ω) are dew points indicating retrograde condensation. All seven points could be satisfactorily fitted with a cubic polynomial, even though the curvature of the line is more complicated than for the MeOH + CO2 system. The value obtained for Tc was 299.0 ( 0.3 K. Finally, pc was interpolated from the p-T phase boundary (Figure 7b) as 113 bar. In practice, this mixture is a very difficult system to study because its critical temperature (∼299 K) is only 2 K below the maximum temperature (∼301 K) of the phase envelope (the “maxcondentherm” point). However, by applying our sensor technique, the critical point and the maxcondentherm point can 90 Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
be easily distinguished using the shape of the |Z|min-p traces. Furthermore, the retrograde condensation has been observed and identified without any difficulty (traces 6-9 in Figure 7a). We now consider why our approach to locating critical points actually works. Sensor Behavior in the Fluid Mixtures. The vapor-liquid phase transition manifests itself in different ways depending on how the system crosses the phase boundary. When a mixture with a given composition is taken from a single phase into twophase region across the bubble point line, gas bubbles will form in the liquid phase and then rise up to the top of the vessel. At a dew point, liquid droplets will form from the gas phase and fall to the bottom of the vessel.41 At the critical point, bubbles and droplets form simultaneously in the vessel since bubbles and droplets become indistinguishable. Gravity causes droplets to fall downward, and a meniscus eventually appears at the center of the vessel. In what follows we will describe in detail how a single sensor can monitor such a complicated process of phase separation in the critical region. Figure 9 shows the dependence of |Z|min and the cell pressure as a function of the cell volume (V) for MeOH + CO2 at three different temperatures. It can be seen from Figure 9b that the |Z|min trace corresponding to the bubble point has the form of a tick. |Z|min decreases as volume increases when the system is in a homogeneous one-phase state. After the occurrence of the phase transition, |Z|min increases as volume increases. The minimum on the trace is marked as the bubble point where the gradient changes from negative to positive. The trace also shows that the sensor measures only the properties of the liquid phase; otherwise, the value of |Z|min recorded after phase separation would be much smaller than that in the liquid phase. This is understandable because the sensor is placed close to the bottom of the vessel, while the bubble point meniscus is near the top, well above the sensor. Even so, phase separation leads to a change in composition of the liquid phase,42 with proportionally more MeOH remaining in the liquid phase. As a result, both density and viscosity of the liquid phase increases after the phase separation, and it is to these increases that the sensor responds. A trace corresponding to a dew point is shown in Figure 9f. Initially, |Z|min decreases with the increase of volume in the single(41) In theory, surface tension could cause the internal pressure within sufficiently small droplets to differ appreciably from the mean of the system pressure. However, in practice, this error is negligible compared to other uncertainties in measurements. Furthermore, surface tension is very low near and at the critical point. (42) This would apply to mixtures that are not exactly at an azeotropic point.
Figure 9. Comparison of pressure traces (top) and impedance minimum traces (bottom) as a function of the cell volume for the mixture of MeOH + CO2 (xMeOH ) 0.103). (a, b) Bubble point; (c, d), slightly above the critical point; and (e, f), dew point. Note that the direction of volume scale has been reversed (large volume on the left) so that the |Z|min traces are shown in the same orientation as in the earlier figures.
phase region. Then a large increase in |Z|min is observed along the trace, and finally,|Z|min increases steadily with the increase of volume, as is found on the bubble point trace (Figure 9b). The large increase in |Z|min can be explained as follows. When the system reaches the dew point, liquid droplets start to condense on the surface of the sensor; they then coalesce to form a thin film of liquid, which provides a liquidlike environment for the sensor. We note that the effective thickness (δ) of the fluid that is driven by the vibrating crystal is only 70-110 nm for supercritical CO2.32 Any fluid beyond this distance from the sensor surface, whether it be liquid or gas, does not have any effect on the response of the sensor. Thus it follows, for our sensor, that the volume of liquid in the space that affects the sensor is only ∼3 nL. Therefore, even a tiny amount of liquid condensed on the surface of the sensor will dramatically change the output. At the onset of the dew formation, liquid droplets tend to appear first on the surfaces of the equipment (including the internal walls of the cell, the sensor, and the stirrer surfaces) because surfaces provide nucleation sites for condensation. No meniscus is formed at this stage. As the volume increases further, a small quantity of liquid phase will collect at the bottom of the cell, apparently leaving the sensor, which is higher up the cell, in a gas phase. However, we have a high-speed stirrer at the bottom of the cell, which splashes the liquid to the sensor. The liquid stays on the sensor surface for a substantial period of time because of surface tension. (The role of the stirrer is discussed further below.) The trace shown Figure 9d represents a transition from the traces of the bubble point to the dew point. Only a very small jump in |Z|min (indicated by the arrow) can be observed from the trace, which suggests that the temperature of this isotherm is just above Tc for the mixture. If temperature were exactly at Tc, no sudden increase would be seen in the |Z|min trace because both densities and viscosities of two phases are necessarily identical. The p-V traces for the three corresponding temperatures are also shown in Figure 9. The bubble point determined from the break point in the pressure curve (Figure 9a) coincides with the turning point in |Z|min. This provides a cross check of our method. However, no similar break points can be seen from the pressure
Figure 10. Striking effect of stirring on the |Z|min-p traces for MeOH + CO2. The stirrer is alternatively on and off for each 30 min. The arrows indicate where the stirrer was switched on (v) and off (V). The traces were recorded (a) while increasing and (b) while decreasing the system pressure.
traces for the critical and dew points (Figure 9c and e), whereas the quartz sensor clearly indicates the occurrence of the phase transition. The quartz sensor is providing more information about the phase separation than conventional pVT measurements, particularly in the critical region. As discussed above, the stirrer is believed to play an important role in our measurements. Therefore, we have examined the effect of stirring on |Z|min in some detail. The measurements were performed under conditions of increasing pressure as well as conditions of decreasing pressure, which we have used up until now. Some results for MeOH + CO2 are shown in Figure 10a and b. During the measurements, the stirrer was switched on and off repeatedly at 30-min intervals while |Z|min was recorded continuously. It is clear from Figure 10a that the value of |Z|min is strikingly affected by the stirrer, just as is predicted by our postulated explanation. In particular, the top part of Figure 10a (|Z|min > 250 Ω), corresponding to the times when the stirrer was on, shows that the sensor gives a signal indicating the liquid phase. Each time the stirrer was switched off, the liquid drained from the surface of the sensor, and the signal switched to the gaslike value (see the lower part of the trace) until the stirrer was restarted. These traces were recorded under conditions of increasing pressure so fluid remaining upon the sensor can quickly “redissolve” into the gas phase. As expected, no effect was observed in the single-phase region, when the on/off of the stirrer could not affect the fluid. We also observed sharp spikes just after the stirrer was restarted, which we believe indicate nonequilibrium liquid droplets being splashed onto the surface of the sensor. These droplets might contain a high concentration of MeOH or trace contamination from the secondary fluid in the pump. Nevertheless, equilibrium is achieved after a few minutes, and subsequently, the output from the sensor shows the expected liquidlike values. When the experiment was repeated under conditions of decreasing pressure, the effects of the stirrer were smaller, Figure Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
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10b. Although no liquid was being splashed onto the surface of the sensor when the stirrer was off, the sensor was still not surrounded by gas, because the liquid droplets continually condense on the surface of the sensor as the pressure decreases, and once formed, surface tension helps them adhere to the sensor. It must be stressed that when the sample is stirred vigorously, the |Z|min-p traces show no difference between increasing or decreasing the system pressure. Finally, it should be stressed that our method for detecting phase separation does not require the mixture to display retrograde condensation. However, if retrograde condensation does not occur under the conditions being studied, it is unlikely that a critical point will exist in that part of phase space. CONCLUSIONS We have shown that the vapor-liquid critical point of multicomponent mixtures can be located in an objective manner by use of a single, shear mode quartz sensor. Our approach relies on the fact that the phase separation occurring at the bubble and dew points has different characteristics, which we are able to distinguish using a surface-sensitive sensor. Hence the critical point may be located from the intersection of the bubble point and dew point curves of the mixture. To locate the critical point, two extrapolation methods have been demonstrated using a MeOH + CO2 system. The results show that extrapolating the ∆|Z|min versus T curve to zero offers a simple way of obtaining Tc with an error of
