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Anal. Chem. 1991, 63, 104-108
High-pressure Phase Distribution Isotherms for Supercritical Fluid Chromatographic Systems. 2. Binary Isotherms of Carbon Dioxide and Methanol Joseph R. Strubinger, Hengchang Song, and Jon F. Parcher* Department of Chemistry, University of Mississippi, University, Mississippi 38677 The binary isotherms of mixtures of carbon dioxide and 2 % methanol on silica and octadecyl-bonded silica (ODS) were measured at three temperatures over a range of pressures up to 150 bar. Binary isotherms of pure CO, and mixtures of 2-4% methanol In CO, on the same adsorbents were determined at 50 O C . The effects of temperature, pressure, and composition on the adsorption of both methanol and CO, were determined over a range of conditions with supercritical fluid mobile phases. The amounts of CO, and methanol adsorbed increased with decreasing pressure and increased dramatically at pressures close to the critical pressure of the binary mobile phase. Under the conditions normally employed for packed-column SFC, significant amounts of CO, and modifier both were adsorbed on the solid adsorbent and functioned as components of the stationary phase. Capacity factors were also measured for two probe solutes, n-hexane and benzene, concurrently with the adsorption measurements. The capacity factors decreased with Increasing density or increasing temperature but increased with concentration of methanol in the mobile phase. The partial molar enthalpies for the phasetransfer process at constant density with 2 % methanol in the fluid phase were in the range 4.7-5.7 kcai/moi, indicating a partition-like retention mechanism for the nonpolar solutes, rather than an adsorption mechanism.
INTRODUCTION One of the major problems in supercritical fluid chromatography (SFC) is the lack of a suitable mobile phase for the separation of polar solutes because most polar mobile phases have unsatisfactory critical properties. Polar additives or modifiers are often added to the supercritical fluid to enhance the solubility of polar solutes in the mobile phase. In many cases, polar modifiers, such as alcohols, significantly improve the peak shape and reduce the retention time of polar solutes. However, because the critical temperatures of the modifiers are usually very high, the mobile phase becomes a mixture with sub- and supercritical components. The critical properties, as well as the physicochemical properties, of such mixtures are complex and not well understood. Yet the chromatographic performance of SFC systems is acutely dependent upon the properties of the binary mobile phase. The critical properties of mixtures are also sensitive functions of composition, especially for mixtures of unlike components. Thus, an SFC mobile phase may become subcritical, and unstable due to liquefication of the subcritical component, at some “critical” composition that will vary with temperature and pressure. In addition, the polar modifiers could possibly affect the performance of an SFC system in a variety of other ways. For example, (i) the modifier may alter the density and solvent power of the mobile phase, (ii) the modifier can block active adsorption sites on the stationary phase, inhibiting adsorption of solutes, (iii) sorbed modifier may act as a component of the stationary phase. (iv) sorbed modifier will increase the volume of the stationary phase while 0003-2700/9 1/0363-0104$02.50/0
decreasing the volume of the mobile phase thereby changing the phase ratio, /3, for the column, and (v) the modifier may also “cluster” around a polar solute or form clusters itself in the mobile phase. The combination of all these factors could result in either enhanced or diminished retention of chromatographic solutes with variations in modifier concentration. Investigation and interpretation of the complexities of SFC retention mechanisms require much more information than can be obtained from solute partition ratio, k’,measurements alone. Numerous investigators have measured phase distribution isotherms for pure SFC mobile phase on solid adsorbents or in polymers (1-10). The general observations from these investigations are that (i) at low pressures the isotherms exhibited normal Langmuir-type adsorption with the expected phase transitions at subcritical temperatures, (ii) at supercritical temperatures the isotherms displayed a distinct maximum near the critical pressure, (iii) in the high-pressure region, the amount adsorbed decreased with increasing pressure at fixed temperature and increased as the temperature increased at fixed pressure, and (iv) density isotherms exhibited normal temperature dependence, but inverse pressure dependence, in the supercritical region. Recently, attention has focused on the exact role of polar modifiers in SFC. Several investigators have measured the adsorption or partition isotherms of such modifiers. Lochmuller and Mink ( I 1 , 1 2 ) and Schoenmakers (13) measured the adsorption of several modifiers on silica and hydrocarbon-bonded silica. They observed Langmuir-type adsorption isotherms for the modifier as the concentration of modifier was increased at a fixed pressure of C02. In another study, mass spectrometric tracer pulse chromatogaphy (MSTPC) was used to measure the effect of the mobile-phase modifier, methanol, on the uptake of supercritical n-pentane by SE-30 and SE-54 in capillary columns (14). The methanol modifier had minimal effect on the amount of pentane sorbed. Yonker and Smith (15)used MSTPC to measure the sorption isotherms of 2-propanol from C 0 2 on an SE-54 capillary column. The amount of 2-propanol sorbed by the stationary phase decreased with increasing pressure at fixed temperature and increased with increasing temperature at fixed pressure over the range 110-140 “C and 150-400 atm. All of these studies reported the isotherms of only a single component in a multicomponent system. Tracer pulse chromatography, however, can be used to measure complete partition and adsorption isotherms for multicomponent systems (16). Experimental measurements for binary or more complex systems are needed to elucidate the complex interactions between the mobile fluid, modifier, and stationary phase in SFC systems. Thus, the primary objective of the present work was to measure the binar3 adsorption isotherms for mixtures of C 0 2 and methanol on common SFC adsorbents in order to investigate the complex phase equilibria and retention mechanisms in multicomponent SFC systems. EXPERIMENTAL SECTION The experimental technique used for these experiments was mass spectrometric tracer pulse chromatography (17, 18). The D 199 1 American Chemical Society
ANALYTICAL CHEMISTRY. VOL. 63,NO. 2, JANUARY 15. 1991 105 Table I. Column Descriptions column
ODS no. 1 ODS no. 2 silica
dimens, mm 2 2 2
X 140 mm X 150 X 150
C
B
A total surface area, m2 28.9 34.5
41.6
apparatus and procedure have been described previously (IO), and were altered only slightly for the addition of modifiers. The instrumentation was primarily a H P 5985 GC/MS system (Hewlett Packard, Palo Alto, CA) adapted for SFC. Two syringe pumps (ISCO Model SFC-500, Instrument Specialties Co., Lincoln, NB) were used-one containing pure COz and the other containing a mixture of 5% methanol in COz. The effluents from the two pumps were mixed by using a micromixing tee (The Lee Co., Westbrook, CT), and the composition of the mobile phase was analyzed at the column outlet by using a separate gas chromatograph (HP Model 5890). The concentration of the modifier was controlled by varying the relative flow rates of the two pumps. No injections were made until the postcolumn analysis agreed with the composition set by the relative delivery rate of the pumps. Several hours were sometimes required for such equilibration, but only with high concentrations of methanol near the critical point of the mixture. Otherwise,the equilibration times were in the range of 10-30 min. The experimental sample was a gaseous mixture of neon, benzene, hexane, and isotopically labeled carbon dioxide and methanol. Column temperatures varied from 50 to 100 "C, compositions varied from 2 to 4% methanol, and pressures varied from the critical pressure of the mixture up to 175 bar. The amounts of COz and methanol adsorbed were calculated from the retention times of the labeled solutes (1618).The Peng-Robinson (19) equation of state (EOS)was used to calculate the fluid density. The critical properties for mixtures of carbon dioxide and methanol were determined by using the method of Chueh and Prausnitz (20, 21) and the experimental data of Brunner (22). Neon was used for the dead-time marker, and the void volumes of the columns were measured from to and the volumetric flow rate at column conditions calculated from the EOS. Table I contains descriptions of the columns used for these experiments. The surface area for the first ODS columns was obtained by unpacking the column, weighing the material, and submitting a portion for volumetric specific surface area analysis. However, this method was expensive and resulted in the loss of the column for further experiments. In order to facilitate column surface area measurements, a new MSTPC technique was developed (23). This technique was used to measure the adsorption isotherm of nitrogen on the adsorbent within a packed column at 77 K. The total surface area of the stationary phase was calculated from the classical BET (24) method. The surface areas for the second ODS column and the silica column were obtained by using this technique. A significant advantage of this method is that the total surface area within a column can be measured in situ without unpacking the column. This allows for the repeated measurement of surface areas before and after experiments. A frequent observation in this investigation was that the surface area for the column dropped following a series of experiments. However, following extensive conditioning, the column returned to the original surface area. In this manner the column condition could be carefully monitored.
RESULTS AND DISCUSSION Effect of Temperature. Binary isotherms for the adsorption of COz and the modifier, methanol, on silica and ODS were measured over a range of temperatures and modifier concentrations. Figure 1shows the results for the adsorption of COzon ODS for several temperatures a t a fixed methanol concentration, 2%, in the mobile phase, along with the results from a previous investigation of pure COz (10). For all three temperatures, the adsorption of COz with methanol in the system was enhanced relative to adsorption of pure COPand the adsorption maxima were shifted to higher density. The density shift was less a t the higher temperatures, although the adsorption enhancement did not change much with tem-
p ,i
I
0.4
0
0.8
l
0.4
l
0.4
0.8
0.8
Density (g/mL) Figure 1 . Adsorption isotherms for carbon dioxide on ODS with and without 2 % methanol: (A) 50 OC with 2% MeOH; (B) 70 O C with 2 % MeOH; (C) 100 O C with 2% MeOH; (---) literature data for pure carbon dioxide ( 70). 25
6ii
E
20
1
i
3
15
'c1
-e s 'c1
4
10
c,
d
2 E
4
5
n
0
0.2
0.4
0.6
0.8
Density (g/mL) Figure 2. Binary adsorption isotherms for a 2% mixture of carbon dioxide and methanol: (0)CO, at 50 O C ; (). MeOH at 50 O C ; (0)CO, at 70 'C; (0)MeOH at 70 O C ; (A)CO, at 100 O C ; (A)MeOH at 100 0-
perature. Thus, a t least on C18-bonded silica, the presence of methanol does not inhibit adsorption of the supercritical component, COz. The adsorption process in this particular system was cooperative in nature, rather than competitive. This demonstrates that in SFC the total amount of adsorbed stationary phase may be increased significantly by the use of polar modifiers. The binary adsorption isotherms of COzand methanol with 2% methanol in COz as the mobile phase, given in Figure 2, show that at high densities the amount of methanol adsorbed was relatively independent of temperature. However, near the critical pressure the amount of methanol adsorbed a t 50 "C increased with decreasing pressure, whereas the 70 and 100 "C isotherms remained nearly constant, independent of pressure. The results clearly indicate that a disproportionate amount of methanol was adsorbed on the stationary phase; i.e. a t high densities the adsorbed layer was nearly 25% methanol even though the mobile phase contained only 2% methanol. The amount of methanol adsorbed always decreased with increasing pressure or density; i.e., no maxima
106
ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991 30 I
1
I
i
I
6 0
0
m
o 0
*
0
0
"
0
I
I
I
0 2
0 4
0 6
0 8
Density (g/mL)
0.2
0.4
0.6
0.8
Density (g/mL) Figure 4. Binary adsorption isotherms for carbon dioxide and methanol with 2 % methanol at 50 "C: (0)CO, on ODs; (H) MeOH on ODs; ( 0 )CO, on silica; ( 0 )MeOH on silica.
Flgure 3. Adsorption isotherms for carbon dioxide on silica and ODS at 50 "C: (m) pure CO, on ODs; (0)CO, with MeOH on ODS; ( 0 )pure CO, on silica; (0)CO, with MeOH on silica.
were ever observed in the adsorption of methanol. Unlike the case with the pure CO, systems, no experiments were undertaken a t subcritical conditions due to the continuous condensation of liquid methanol in the system. At 50 "C, methanol was adsorbed to an even greater extent a t pressures close to P, with an almost equal amount of CO, and methanol adsorbed a t the lowest pressures. This increase in adsorption of the modifier near the critical pressure of a binary mobile phase has been observed previously for 2propanol (12) sorbed in a polymer. Unfortunately, the sorption of CO, could not be measured, so the effect of the modifier on the sorption of CO, could not be determined. Effect of Adsorbent. Figure 3 shows the adsorption isotherms of COz on silica and ODS without a modifier and with 2 % methanol. These results are reported in units of micromoles adsorbed per square meter of adsorbent to compensate for the differences in the surface areas of the two adsorbents (Table I). The commonly used comparisons based solely on k'data cannot account for the differing surface areas of the adsorbents. The figure shows that silica adsorbed more COz than ODS a t high densities with pure CO, as the mobile phase. However, addition of 2 % methanol caused the different adsorbents to adsorb CO, to a nearly equal extent. Adsorption of COSon ODS was enhanced by the methanol modifier, whereas adsorption on silica was unaffected by the presence of methanol. Adsorbed methanol masked the effect of the CI8-bondedmaterial. Thus the use of modifiers with chemically bonded stationary phases may be redundant. In some ways, polar modifiers act as substitutes for chemically bonded phases. The binary adsorption isotherms on ODS and silica a t 50 "C with 2 % methanol are shown in Figure 4. The amount of COz adsorbed was nearly equal for the two adsorbents, as shown in Figure 3; however, the amount of methanol adsorbed was much greater on silica than ODS. This would be expected due to the greater number of free adsorption sites, which would be selective for the polar modifier, present on the surface of the untreated silica. On both adsorbents the mole fraction of methanol in the adsorbed phase on the adsorbent surface was much higher than the mole fraction in the mobile phase. Effect of Modifier Concentration. The addition of a polar modifier to supercritical fluid mobile phases has been
Density (g/mL) Figure 5 . Binary adsorption isotherms for carbon dioxide and methanol on ODS at 50 "C: (0) CO, with 2 % MeOH; (H)MeOH with 2 % MeOH; (0)CO, with 3% MeOH; (0)MeOH with 3 % MeOH; (A) CO, with 4 % MeOH; (A)MeOH with 4 % MeOH.
shown to decrease the retention of polar solutes for packed columns at low modifier concentrations, while often increasing retention of polar solutes in capillary columns at high modifier concentrations. However, many of the comparisons and conclusions drawn from such studies are deceptive due to the diverse range of experimental conditions employed. The results of experiments using very low modifier concentrations at temperatures and pressures far from the critical point are often compared with similar data from studies using high modifier concentrations near the critical point. In some cases supercritical systems have been compared with systems which were subcritical because the significant changes in the critical temperature and pressure of the mobile phase which can occur with the addition of a subcritical, polar modifier to a supercritical fluid were not recognized. Figure 5 shows the effect of modifier concentration on the adsorption isotherms of COz and MeOH a t 50 "C. At high densities the COz isotherms converged, but a t lower densities and pressures the 3 and 4% isotherms diverged significantly from the pattern observed for pure COz. The methanol isotherms show that adsorption of methanol also dramatically increased at the same density a t which the adsorption of COz increased at each mobile-phase composition. The explanation for this behavior is based on the influence of composition on the critical properties of mixtures. Table I1 lists the calculated
ANALYTICAL CHEMISTRY, VOL. 63,NO. 2, JANUARY 15, 1991
107
Table 11. Calculated Critical Parameters for Mixtures of CO, and Methanol mole fraction of methanol
T, K
P,,bar
0.00 0.02 0.03 0.04
304.2 310.9 314.3 317.5
73.8 83.5 88.1 92.4
n 35
(u
E 230
E1
-II tt
I -
O O
20
g 4 c
0
-
g
15
10
-
4
5 -
E 4
0
20
40
IO
80
104
Figure 7. Change in V 8 as a function of combined COPand methanol adsorbed on ODS and silica: (0)no MeOH; (W) 2 % MeOH; (0)3% MeOH; (A)4 % MeOH.
a 4
20
Amount Adsorbed (umol/m ’?)
-
-25 a aJ
10
nl
“0
I
I
I
50
100
150
2,J
Pressure (bar) Flgure 6. Adsorption isotherms for methanol on ODS at 50 O C : (W) with 2% MeOH in CO,; (0)with 3% MeOH in CO,; (A)with 4% MeOH in CO,; (- - -) calculated critical pressures. critical temperature and pressure for C 0 2 with 2-4% methanol. A plot of the methanol isotherms as a function of pressure, rather than density, shows that the abrupt increase in methanol and COP adsorption occurs as the pressure approaches the calculated critical pressure for the mixture. This effect is shown in Figure 6. The experimental system was almost certainly not completely at equilibrium at the lowest pressures, and the COPand methanol may have separated in the SFC column. Effect of Column Void Volumes. In the previous publication in this series (IO),the significance of the void volume of the column was discussed in detail. Briefly, the exact definition of the type of experimentally measured adsorption data is determined by the solubility of the probe solute used for the dead-time, to,measurement. If the probe is insoluble in the adsorbed phase, the measured void volume will decrease as the volume of the adsorbed phase increases. In this case, the experimental data would represent ”absolute” adsorption and the Gibbs dividing plane would be located a distance, 2, from the adsorbent surface. The change in void volume per mole of adsorbate in the condensed phase would be a measure of the molar volume of the adsorbate in the adsorbed state. If, on the other hand, the probe solute has a measurable partition coefficient in the absorbed phase, the adsorption data would have to be corrected for such solubility. Kobayashi (4) used this technique to correct for the solubility of a probe, e.g., helium, in adsorbed methane a t very low temperatures. At very high pressures, the density of the bulk phase can approach the density of the adsorbed phase, and the partition coefficient of any probe should approach unity. In this case, the measured data would be classified as ”excess” adsorption, and the void volume would remain constant independent of the amount adsorbed. The Gibbs dividing plane would then correspond to the surface of the adsorbent. Thus, the exact determination of the void volumes in this investigation was
crucial for the definition and interpretation of the experimental data. Figure 7 shows the experimentally determined void volumes for all of the adsorption experiments at one temperature, 50 OC. The figure also illustrates the problems encountered with this type of measurement. The scatter in the experimental void volume data is much greater than that observed for the adsorption data for several reasons. The two major difficulties were the accuracy of the Peng-Robinson EOS for mixtures close to the critical point and mechanical control of the mobile-phase flow rate during injection. Accurate measurement of the void volume requires a constant and known (calculated) flow rate from the time of injection to the retention time of the neon probe. These conditions are hard to achieve experimentally. Thus, it is impossible to calculate any thermodynamic parameters from the type of data shown in Figure 7. However, it is obvious that the void volume was reduced by adsorption of either methanol or COz. This leads to the conclusion that the type of adsorption measured was “absolute” adsorption with > 0. The most likely probability, however, is that the neon was slightly soluble in the condensed phase, and the adsorption data should be corrected for this effect. However, such a correction would require accurate data for the solubility of neon in supercritical fluid mixtures of methanol and COPover a range of temperature, pressures, and compositions. Retention of Probe Solutes. The retention times of two probe solutes, benzene and hexane, were monitored at m l e = 78 and 86 while the adsorption isotherms were measured. These nonpolar, low molecular weight probes are not representative of the typical solutes separated by SFC but were the most practical for the experimental conditions, i.e. very low flow rates. The probe solutes displayed the usual decrease in retention as the density increased, which can be attributed to the increased solvating power, which is proportional to density, of the mobile phase. However, Figure 8 shows that adding methanol to the mobile phase increased the retention of benzene on ODS at fixed density. The solvating power of the mobile phase would be increased by the addition of methanol which should decrease the retention of benzene if this were the primary factor affecting retention. However, as shown previously, large amounts of methanol were absorbed on the stationary phase and this could lead to increased retention in several ways: (i) the adsorbed methanol could increase the volume of the stationary phase while decreasing the volume of the mobile phase (decreasing p), resulting in an increase in k ’ ( k ’ = KIP) if the partition coefficient, K , was constant, (ii) the partition coefficients of the probe solutes in methanol may be higher than octadecane or C02,and (iii) the increase in the volume of the stationary phase would lead directly to increased retention if partitioning of the probe solute in the adsorbed phases was significant. All of these
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991
3
1 -
0 ' 0
2
0 2
04
Density (g/mL)
Figure 8. Retention of benzene on ODS at 50
06
08
OC:
(0) no MeOH: (W)
0
2 % MeOH; ( 0 )3 % MeOH; (A)4 % MeOH.
factors probably operate in making the retention mechanism extremely complicated. The effect of temperature on the capacity factor of benzene with 2% methanol in the mobile phase was also investigated. The van't Hoff plots for benzene retention a t fixed densities are shown in the inset to Figure 9. The enthalpies calculated from the slopes of the lines ranged from -5.8 kcal/mol at the lowest density (0.2 mL/g) to -4.7 kcal/mol a t 0.5 mL/g. However, because of the complicated retention mechanism(s) and the multicomponent, multiphase nature of the stationary phase, it is difficult to asses the thermodynamic significance of the enthalpy data. The experimental data for n-hexane as the probe solute mimicked the results shown for benzene.
CONCLUSIONS Mass spectrometric tracer pulse chromatography can be used to measure binary adsorption isotherms for supercritical fluids and modifiers. The capability of this experimental technique to measure adsorption of the mobile phase as well as the retention of solutes is a significant advantage in the study of phase equilibria and retention mechanisms in SFC. The commonly used polar modifiers, such as methanol, adsorb to a considerable extent onto SFC stationary phases. Sub- and supercritical C 0 2also adsorbs onto SFC adsorbents at the high pressures routinely used in SFC. The total amount of methanol and COPadsorbed as well as the mole fraction of each component in the adsorbed phase (on the stationary phase) are important factors in the retention mechanisms for chromatographic solutes in SFC. Another important factor is the critical properties of the binary mobile phase when a modifier is used in SFC. The addition of small amounts of modifier can cause unexpectedly large changes in the critical parameters for the mobile-phase mixture. Precise methods for calculating the critical properties of mixtures are not available, especially for mixtures containing low concentrations of one component. The most likely sources of error in this investigation occur in the calculations of the critical properties and density of the mixed mobile phase. Many investigations have shown that polar modifiers do change the density and solvating power of the mobile phase, which affects solute retention. However, a second important aspect in the use of modifiers is the influence of the modifiers and supercritical fluids on the physical and chemical properties of the stationary phase. The most dramatic effects on solute behavior were observed when the modifier concentration was high enough to significantly alter the critical properties of the mobile phase.
, L -
0
0 4
0 2
0 6
08
Density ( g / m L ) Figure 9. Retention of benzene on ODS with 2 % methanol: (W) 50 OC;
( 0 )70
OC;
(A)100
OC.
Of the five possible influences of polar modifiers listed in the Introduction, this work has shown that it is possible, if not probable, that all five effects may operate in any given SFC procedure involving the use of subcritical, polar modifiers. This study concentrated on the experimental regime close to the critical temperature and pressure. These conditions are usually avoided in practical SFC. Thus, the effects observed were magnified. However, these studies reveal fascinating physicochemical phenomenon in the adsorbed 2-dimensional stationary phase for both sub- and supercritical systems. Registry No. C02, 124-38-9; MeOH, 67-56-1.
LITERATURE CITED Findenegg, G. H. In Fundamentals of Adsorption; Engineering Foundation: New York. 1983; pp 207-218. Blumel, S.;Koster, F.; Findenegg. G. H. J . Chem. Soc., Faraday Trans. 2 1982, 78,1753-1764. Findenegg, G. H.; Loring, R. J . Chem. Phys. 1984, 87, 3270-3276. Hori, Y.; Kobayashi, R. J . Chem. Phys. 1971, 5 4 , 1226-1236. Selim, M. I . ; Strubinger. J. R. fresenius' Z . Anal. Chem. 1988, 330, 246-249. Yonker, C. R.; Smith, R. D. J . Chromatogr. 1990, 505, 139-146. Gilmer, H. 6.; Kobayashi, R. AIChE J . 1964, 70,797-803. Strubinger, J. R.; Parcher, J. F. Anal. Chem. 1989, 6 1 , 951-955. Parcher, J. F.; Strubinger, J. R. J . Chromatogr. 1989, 479, 251-259, Strubinger. J. R.; Song, H.; Parcher, J. F. Anal. Chem., preceding article in this issue. Lochmuller, C. H.; Mink, L. P. J . Chromatogr. 1987, 409, 55-60. Lochmuller, C. H.; Mink, L. P. J . Chromatogr. 1989, 477, 357-366. Janssen, J.; Schoenmakers, P. J.; Cramers, C. A. JHRC 8 CC 1989, 72, 645-651. Strubinger, J. R.; Selim, M. I . J . Chromatogr. Sci. 1988, 2 6 , 579-583. Yonker, C. R.; Smith, R. D. Anal. Chem. 1989, 67, 1348-1353. Parcher, J. F.; Hyver, K. J. J . Chromatogr. 1984, 302, 195-204. Parcher, J. F.: Selim, M. I. Anal. Chem. 1979, 57. 2154-2156. Parcher, J. F. J . Chromatogr. 1982, 252. 281-288. Peng. D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59-64. Chueh, P. L.; Prausnitz, J. M. AZChE J 1967, 73, 1099-1 107. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977; Chapter 5. Brunner. E. J . Chem. Thermcdyn. 1985, 77,671-679. Song, H.; Strubinger, J. R.; Parcher, J. F. J . Chromatogr. 1990, 578, 319-328. Brunauer. S.;Emmett, P. H.: Teller, E. J . Am. Chem. Soc. 1938, 60, 309-319.
RECEIVED for review June 12,1990. Accepted October 8,1990. Acknowledgment is made to the National Science Foundation and to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
