Phase equilibria, partial molar enthalpies, and partial molar volumes

Jan 1, 1991 - Solution Properties of C60 and C70 Fullerenes and C21 to C40 n-Alkanes at Infinite Dilution in Carbon Dioxide from Supercritical Fluid ...
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J . Phys. Chem. 1991, 95, 353-360

353

Phase Equilibria, Partial Molar Enthalpies, and Partial Molar Volumes Determined by Supercritical Fluid Chromatography Jae-Jin Shim and Keith P. Johnston* Department of Chemical Engineering, University of Texas, Austin, Texas 78712 (Received: April 12, 1990) A variety of types of thermodynamic properties have been determined at infinite dilution by supercritical fluid chromatography. A key challenge is to identify clearly the retention mechanism. An experimental technique is presented for the measurement of retention due to absorption into a bulk c18 liquid (stationary) phase, independently of the adsorption on the support. The important effect of the swelling of the liquid phase by the fluid phase is included. Distribution coefficients are presented for naphthalene and phenanthrene between C02and the C,*liquid phase, and used to determine Henry's constants in the liquid phase and solute partial molar volumes and enthalpies in the fluid phase. In the highly compressible region of C02 at 35 O C , solute partial molar enthalpies have been found to reach negative values of hundreds of kJ/mol, indicating strongly exothermic solute-solvent clustering.

Introduction A number of recent studies have focused on the influence of a supercritical fluid on a condensed phase such as a polymer, biomolecule, or growing crystal.' For example, additives may be impregnated into a polymer rapidly and in a controlled manner with carbon dioxidee2 In addition, C 0 2 may be used to extract monomers, oligomers, and solvents from polymers.' The success of these potential applications depends upon the understanding of a fundamental issue, the distribution of a solute between a polymer phase and a supercritical fluid phase. This presents a significant experimental challenge; however, it can be addressed very effectively with supercritical fluid chromatography (SFC). Although SFC is used commonly for analytical separations, it has been used to determine thermodynamic properties in only a few instances. Thermodynamic properties in a polymeric stationary phase may be determined by inverse gas chromatography! In SFC, the phase equilibrium is considerably more complex due to two reasons: (1) the interactions in the dense fluid (mobile) phase are highly nonideal, and (2) the carrier fluid may swell the liquid (stationary) phase. In order to determine a thermodynamic property in the fluid-phase chromatographically, it is necessary to describe independently an analogous property in the liquid phase, and vice versa. Because the interactions are complex in both phases, special techniques are required to measure and interpret retention data, in order to obtain reliable thermodynamic properties. The primary objective of this article is to develop these techniques, in order to determine a variety of properties. Secondly, these properties are analyzed theoretically in order to describe supercritical fluid-phase behavior and clustering of the supercritical fluid about the solute. Solutesolvent clustering has been observed spectroscopically with several UV-vis and fluorescence probes, as reviewed el~ewhere.~ Four key types of thermodynamic properties which may be measured by SFC include the following: (1) phase equilibria properties such as the distribution coefficient, K2 = c2L/c2F,where czL and c2Fare the concentrations of species 2 in the liquid and fluid phases, respectively; (2) solute properties such as the Henry constant or Flory interaction parameter in the liquid phase, and the fugacity coefficient in the fluid phase; ( 3 ) partial molar properties of a solute in the fluid phase at infinite dilution, such ( I ) Johnston, K. P.; Penninger, J. M. L., Eds. Supercritical Fluid Science und Technology: ACS Symposium Series No. 406; American Chemical So-

ciety: Washington, DC, 1989. (2) (a) Berens, A. R.; Huvard, G. S. In ref I, p 207. (b) Berens, A. R.; Huvard, G. S.; Korsmeyer, R. US Patent 4820752, April 1989. (3) McHugh, M.; Krukonis, V. Supercriticul Fluid Extrartion: Principles und Prurtice; Butterworths: Boston, 1986. (4) Lloyd, D. R.; Ward, T. C.; Schreiber, H. P., Eds. Inuerse Gas Chromatography; ACS Symposium Series No. 391; American Chemical Society: Washington, DC, 1989. ( 5 ) (a) Brennecke, J. F.; Eckert, C. A. AIChE J . 1989, 35, 1409. (b) Johnston, K. P.; Kim, S . ; Combes, J. ACS Symp. Ser. 1989, No. 406, 52.

0022-3654J9 1/2095-0353$02.50/0

as ozmand h2-, (4) partial molar properties of a solute in the liquid phase, such as 02- and h2-. Previous SFC studies have addressed primarily types 3 and 4, while types 1 and 2 have received very little attention due to experimental challenges. The distribution coefficient of a solute, K2 (type I ) , is the key thermodynamic property for calculating all of the properties listed above. Normally, SFC is used to measure only the capacity factor, k2 = ( t 2 - t o ) / t o ,where t2 and to are the retention times of the solute and an unretained marker, respectively. K2is the product of the capacity factor and the ratio of the amounts of the two phases in the column. Whereas k2 is an extensive property, K2 is intensive, that is, independent of the amounts of the two phases. Olesik et aL6 measured K2over a wide range of temperature and pressure for phenanthrene between C 0 2 and a polydimethylsiloxane stationary phase on a capillary column. An approximation was made that the amount of the stationary phase did not change with pressure. Shim and Johnston7 determined K2 for toluene between C 0 2 and silicone rubber by a frontal analysis technique. The large volume change of silicone rubber with pressure was measured independently, in order to determine K 2 from the chromatographic data. A model was developed to predict the behavior of K2 by using information only from the binary systems. An SFC technique has been developed to determine type 2 properties from ratios of capacity factoms Each property was determined relative to that of a reference substance, naphthalene. The above frontal analysis technique7 was used to determine another type 2 property, the Flory interaction parameter for a solute in the polymer phase. van Wasen and Schneider9 used SFC to determine D2- in the fluid phase ( t y p 3), based on an adsorption retention mechanism. Both 02- and h2- are key properties for understanding and describing the large pressure and temperature effects in S C F phenomena, for example, on solubilities and selectivities in S C F extractionsJOand on reaction rate constants and reaction selectivities." Unfortunately, only a few other measurements of o2I2 and h2I3are available. These studies were made with techniques other than SFC. The study of h2 did not focus on the infinite dilution limit, which is of interest in the present study. There have (6) Olesik, S. V.; Steger, J. L.; Kiba, N.; Roth, M.; Novotny, M. V. J . Chromatogr. 1987, 392, 165. (7) Shim, J.-J.; Johnston, K. P. AIChE J . 1989, 35 (7), 1097. (8) Brown, B. 0.; Kischbaugh, A. J.; Paulaitis, M. E.Fluid Phuse Equilib. 1987, 247. (9) (a) van Wasen, U.;Schneider, G. M.J . Phys. Chem. 1980,81,229. (b) van Wasen, U.;Swaid, 1.; Schneider, G. M. Angew. Chem., Inr. Ed. Engl. 1980, 19, 575. (IO) Johnston, K.P.; Peck, D. G.; Kim, S. Ind. Eng. Chem. Res. 1989, 28, 1 3 3 1

I I I>.

( I I ) Johnston, K. P. In ref 1, Chapter I . (12) (a) Eckert, C. A.; Ziger, D. H.;Johnston, K. P.; Kim, S. J. Phys. Chem. 1986, 90 (12), 2738. (b) Wu, P. C.; Ehrlich, P. AIChE J . 1973.19, 533. (c) Foster, N. R.; Macnaughton, S. J.; Chaplin, R. P.;Wells, P. T. Ind. Eng. Chem. Res. 1989,28, 1903. (13) Christiansen, J. J.; Walker, A. C.; Schofield, R. S. J . Chem. Thermodyn. 1984, 16, 445.

0 1991 American Chemical Society

Shim and Johnston

354 The Journal of Physical Chemistry, Vol. 95, No. 1. 1991 been several theoretical treatments of partial molar properties of dilute solutes in supercritical fluid solvent^.'^^,^^ In the highly compressible near-critical region, SCF solvent molecules cluster about a solute over many coordination shells as demonstrated with studies of D~~~ solvatochromic shifts of spectroscopic probe^,^.'^ and more recently radial distribution functions calculated by computer simulation and integral equations.16 A knowledge of the energetics of this clustering could be obtained from h2" data. An SFC technique has been developed specifically to determine type 4 derivative properties in the stationary phase from slopes of k 2 versus pressure and temperature. This gives insight into the retention mechanism. Yonker et al." found that the solute is in a more solvated environment, indicative of bulk absorption, as the film thickness of the stationary phase increases. Brown et aL8 determined ij2 (stationary phase) and enthalpies of transfer between the phases for five polynuclear aromatic hydrocarbons on an octadecylsilica stationary phase. These D2 data were used to evaluate two contributions to the retention mechanism, adsorption onto the surface and absorption into the bulk stationary phase. The above studies indicate that it is important to be able to distinguish between surface adsorption and bulk absorption for determining thermodynamic properties. Adsorption on the support can be influenced by the pore size and structure, surface area, and concentration of silanol groups. To remove the effect of surface adsorption, we chose to subtract the capacity factor on the bare silica support from the total capacity factor. The resulting retention is due primarily to bulk absorption into the C18liquid coating. The usefulness of this technique has been demonstrated previously for inverse gas chromatography,'* particularly for nonpolar solutes. The change in the phase ratio (due to swelling of the stationary phase) with pressure and temperature has been included for the first time for the determination of K2 by elution SFC. Given a well-defined K 2 , it becomes possible to obtain accurate values of each of the other types of thermodynamic properties, as described in the Theory section. Specifically, we discuss distribution coefficients (type 1 ), Henry's constants in the liquid phase (type 2), and solute partial molar volume and enthalpies in the fluid phase (type 3). The results are examined in terms of the molecular interactions in each phase and the large effect of temperature and pressure on the density of the solvent.

Theory Partial molar properties have been determined previously from slopes of capacity factors versus pressure and temperature as described above. The purpose of this section is to derive relationships for type 2-4 thermodynamic properties from the distribution coefficient, K 2 , instead of the capacity factor. This is advantageous since K 2 is an intensive thermodynamic property. The capacity factor of the solute, k2, is defined as the molar ratio of solute between the liquid (stationary) and fluid (mobile) phasesI9

where VL and are the volumes of the liquid and fluid phases, respectively, t2 is the retention time of the solute, and to is that of a marker that has minimal retention. For a regular solution the volume of mixing vanishes, so that the partial molar volume of the solute, D2L is equal to the molar volume of a hypothetical (14) (a) Kim, S.;Wong, J . M.; Johnston, K. P. In Supercritical Fluid Technology;Penninger, J. M. L., Radosz, M., McHugh, M. A,, Krukonis, V. J., Eds.; Elsevier: New York, 1985; p 45. (b) Debenedetti, P. G. Chem. Eng. Sci. 1987,42, 2203. (c) Chang, R. F.; Morrison, G.; Levelt Sengers, J. M. H. J . Phys. Chem. 1984, 88, 3389. (d) Chimowitz, E. H.; Kelley, F. D.; Munoz, F. M. Fluid Phase Equilib. 1988, 44, 23. (15) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206. (16) Lee, L. L.; Debenedetti, P. G. Recent Adu. Sep. Sci., in press. (17) (a) Yonker, C. R.; Gale, R. W.; Smith, R. D. J . Phys. Chem. 1987, 91, 3333. (b) Yonker, C. R.; Smith, R . D. J . Phys. Chem. 1988, 92, 1664. (18) Card, T.W.; AI-Saigh, 2.Y.; Munk, P. Macromolecules 1985, 18, 1030. (19) Conder, J . R.; Young, C. L. Physicochemical Measurement by Gas Chromarography; Wiley: Chichester, 1979.

pure liquid, vZL. Therefore, the volume fraction of solute in the liquid phase is given by

a2= n2Lv2L/V

(2)

so that eq 1 may be rewritten as

(3) where y2 is the mole fraction of solute in the fluid phase and vF is the molar volume. The distribution coefficient of solute may be defined as K2 = c ~ ~ / c ~ ~

(4)

thus

The fugacity of the solute in the fluid phase may be written asZo

fiF= Y242P where 42is the fugacity coefficient of solute (unity for an ideal gas). For the liquid phase f2L

= @2H2(P0)exp

(

- PO)

D2L*"(P

RT

)

(7)

where H 2 ( P )is the Henry constant at the reference pressure (P). It may be assumed that is constant with respect to pressure. At equilibrium the fugacity of each component is equal in the fluid and liquid phases. The Henry constant may be obtained from eqs 5-1 OzL9"

Derivative properties may be obtained by equating differentials of the logarithm of the fugacity of the solute in each phase d In fZF = d In fiL (9) The total derivative may be expressed in terms of partial derivatives with respect to pressure, temperature, and composition

D2F d P RT

- h21G dT+(-) RT2

dy2=

RZF

T.P

where the superscript IG means ideal gas. It is assumed thatf2L for the solute depends only on the concentration of the solute in the liquid phase and not on the concentrations of the other two components, in our case C02and c18. It may be shown that this implies that H 2 is the same for the solute in each of the other two components in the liquid phase,21which is reasonable for many nonpolar systems. If an additional composition variable were added to this equation, the analysis would become more complex and may require other simplifying assumptions.22 Henry's law is applicable for the liquid phase near infinite dilution so that (8 Inf2L/8@2)T,P = 1 / @ 2 Differentiation of eq 6 yields (8 Inf2F/L3Y2)T,P = 1/Y2

+ (8 In

42/8Y2)T,P

(1 1)

(12)

(20) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G.Molecular Thermodynamics of Fluid Phase Equilibria, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1986. (21) Reference 20, p 398. (22) Modell, M.; Reid, R. C. Thermodynamics and Its Applications, 2nd ed.; Prentice-Hall: Englewocd Cliffs, NJ, 1983.

The Journal of Physical Chemistry, Vol. 95, No. I , 1991 355

Thermodynamic Properties Determined by SFC

(COMPUTER)

c

Marker L A

1001

Vent 4

A

'

'

'

'

'

'

'

1

SFC OVEN PUMP

Figure 1. Schematic diagram of the supercritical fluid chromatograph equipped with timed-split injection system: A, solute saturator, P, pressure transducer; S, Valco sampling valve; V, Valco switching valvc.

Based on a previous study of c $ ~near the infinite dilution the second term is small enough compared with the first term so that Henry's law applies. At constant temperature, eqs 5, 11, and 12 may be substituted into eq 10 to yield

where K is the isothermal compressibility -( l / u ) ( d ~ / d P )It~ will be shown that K 2 is a much simpler function of density than pressure, so it is useful to rewrite eq 13 as o2F,-

+

+

= BZL*OD ~ R q 1 p ( a In K Z / d p ) T ]

An analogous derivation at constant pressure yields h2F.- - h IG = (h2L.- - h IG 2 2 1 - R7.W In K2/aT)/J- PI

(14)

(15)

where is_thevolume expansivity, -( 1 / p ) ( d p / d T ) p . For an ideal solution, h2L*"is equal to the molar enthalpy of the pure (subcooled) liquid. As will be shown in the next section, it is useful to express the temperature derivative at constant density instead of constant pressure. With these two modifications eq 15 becomes h2F.- - h IG = 2 -AhTp - R P [ ( aIn K 2 / a T ) , - a{l + p(d In K 2 / d p ) A ] (16)

Expressions are given in the Appendix for the calculation of BZF*.' and hZFlmfrom the Peng-Robinson equation of state. Experimental Section The apparatus consists of a supercritical fluid chromatograph (Lee Scientific Inc., Model 501), which was modified to include a packed column and a computer-controlled time-split injection system actuated with helium (see Figure 1). The stainless steel column was 25 cm long with an i.d. of 1 mm, and both ends were plugged with pressed frits containing 2-pm pores (Alltech Associates). The stationary phase was C18-bondedVYDAC TP wide pore silica (300-A pore size, 20-30-pm particle size). To correct for interactions with the support, additional experiments were performed with bare VYDAC TP silica of the same size, which was deactivated with dimethylchlorosilane (DMCS).24 For thermodynamic measurements by packed column SFC, it is important to inject the solute with the carrier fluid, as liquid solvents may influence solute retention. The solute was dissolved with C 0 2 in a I-mL vessel, which contained a small amount of ethane. Ethane was used as a marker to determine to, since its retention was negligible. This solution was added to a 0.2-pL internal sample loop in the injection valve (Valco instruments). By opening this timed-split injection system for 20 ms, approximately 5-1076 of the sample was injected, typically 0.1 pg. The purpose of the timed-split injection was to lower the solute and marker concentrations in the column toward infinite dilution. (23) Debenedetti, P. G.; Kumar, S. K. AfChE J . 1986, 32, 1253. (24) (a) Ottenstein, D. M. J . Gas Chromatogr. 1963, I (4). 11. (b) Dabe, S.Personal communication, Manville Filtration and Minerals, Lompoc, CA, 1989.

'd.1

0.3

0.5

0.7

0.9

Density (g/ml)

Figure 2. Capacity factor of phenanthrene on bare silica and on C18bonded silica. B, CI8-bondedsilica at 35 OC; 0,bare silica at 35 "C; A, C18-bondedsilica at 100 OC; A, bare silica at 100 "C.

Integral restrictors were made from 100-pm i.d. by 375-pm 0.d. fused silica tubing (Polymicro Technologies, Inc.) .25 A chromatographic switching valve was used to choose between one of two restrictors to vary the flow rate from 0.1 to 0.3 mL/min at column conditions. k2 varied less than 1% for this increase in flow rate. Flow rate fluctuations were less than fO.l pL/min and pressure fluctuations less than fO.l bar. Retention times were measured to within 0.001 min with a Hewlett-Packard Model 3392A integrator, and the typical reproducibility in the capacity factor was within 1%. High-purity carbon dioxide (99.99%, Liquid Carbonic) was used as the carrier fluid and ethane (99.076, Big Three Industrieq, Inc.) as the marker. The solutes naphthalene (Aldrich, 99+%) and phenanthrene (Aldrich, 98+%) were used as received. Results and Discussion Capacity Factor. The typical packing size is 3-10 pm for analytical SFC. For 10-pm Whatman Partisil particles, the pressure drop is up to 1.7 bar for a 25-cm-long, 4.6-mm-i.d. column with a flow rate of 0.5 mL/min.8 At most conditions this pressure drop would produce a negligible effect on K2, except in the highly compressible near critical region, which is of interest in the present study. We found that pressure drops were below 0.3 bar for a particle size range of 20-30 pm. This larger particle size decreased the number of theoretical plates modestly, although this is not an important concern since only a single analyte is injected for each experiment. In some cases, similar resolution is observed with 5- and 37-50-pm particles;26however, the resolution decreases significantly for 100-pm particles. We also observed a large reduction in the number of theoretical plates for 130-pm Chromosorb W particles. Therefore, a particle size of 20-30 pm offers a good compromise between pressure drop and number of theoretical plates. In a previous SFC study of the toluene-silicone rubber-C02 system by frontal analy~is,~ 250-pm-thick strips of pure silicone rubber were placed in a column without a support, to avoid potential errors due to adsorption on a support. In the present study, the thickness to surface area of the polymer is much smaller because of the support. This reduces substantially the time for equilibration, and the results are corrected for the retention due to adsorption on the support. The capacity factors of phenanthrene are given both for CI8-bondedVYDAC TP silica and the DMCS-treated bare silica support in Figure 2. In each case, log k decreases fairly linearly with density. A significant fraction of the total retention on the C18-bondedsilica is due to the support. At 35 OC, approximately 15-20% of k is due to the support, while this increases to 50-5576 at 100 "C. The actual retention due to absorption in the liquid c 1 8 phase is the difference between the total k2 and k2 on the bare support. The liquid c18 is called "polymeric" in that the c18 groups (25) Guthrie, E. J.; Schwartz, H. E. J . Chromatogr. Sci. 1986, 24, 236. (26) Dean, T. A.; Poole, C. F. J . Chromatogr. 1989,468, 127.

356 The Journal of Physical Chemistry, Vol. 95, No. I, 1991 TABLE I: Thermodvnamic Prowrties of Nanhthalene at Infinite Dilution from SFC (Liquid Phase, CIS;Fluid Phase, C02)

Dress.. bar

K

k

17~9".

Lhol

Shim and Johnston TABLE 11: Thermodynamic Properties of Phenanthrene at Infinite Dilution from SFC (Liquid Phase, (2,"; Fluid Phase, COI)

hF9-. kJ/mol

press., bar

K

k

17~9".

L/mol

24.8 9.64 7.62 6.43 5.52 3.85 2.98 2.22 1.73 1.33 1.1 1

-8.40 -5.06 -2.97 -2.03 -1.39 -0.548 -0.266 -0.082 0.01 1 0.069 0.095

-440 -318 -221 -173 -1 39 -91.5 -73.7 -60.6 -52.5 -47.0 -42.6

95.6 105.8 116.0 126.2 156.7 207.6 258.5

60.3 13.9 5.57 3.35 1.74 1.06 0.8 I

50 OC 734 163 63.7 37.7 18.8 10.8 8.1

-2.87 -2.38 -1.26 -0.670 -0.164 -0.001 0.049

-1 27

80.4 82.4 83.9 85.5 87.5 95.6 105.8 126.2 156.7 207.6 258.5

2.56 1.12 0.927 0.807 0.706 0.5 10 0.434 0.354 0.321 0.265 0.235

95.6 105.8 116.0 126.2 156.7 207.6 258.5

4.28 1.41 0.692 0.467 0.288 0. I86 0. I46

50 O 52.1 16.5 7.91 5.25 3.10 1.90 1.45

105.8 126.2 141.4 156.7 207.6 258.5

3.78 I .24 0.684 0.338 0.174 0.105

70 OC 49.8 15.5 8.22 3.93 1.90 1.10

-1.04 -0.983 -0.710 -0.461 -0.126 -0.038

-44.0 -63.1 -63.9 -58.6 -41.3 -34.7

105.8 126.2 141.4 156.7 207.6 258.5

60.9 13.5 5.53 2.60 0.95 0.58

70 OC 800 168 66.4 30.2 10.3 6.1

-1.53 -1.47 -1.06 -0.668 -0.141 -0.011

105.8 126.2 156.7 177.1 207.6 258.5 258.5 258.5

I .80 0.972 0.406 0.244 0. I37 0.086 0.086 0.086

100 OC 25.5 13.3 5.33 3.1 1 1.69 1 .OO 1.00 1 .oo

-0.418 -0.500 -0.487 -0.383 -0.192 -0.192 -0.192 0.01I

1.9 -3.5 -19.5 -23.1 -24.4 -24.4 -24.4 -22.6

105.8 126.2 156.7 177.1 207.6 258.5

35.3 14.5 4.1 1 2.08 0.97 0.42

100 OC 498 198 53.9 26.5 11.9 4.9

-0.879 -0.886 -0.748 -0.583 -0.359 -0.157

-7.59 -4.12 -2.32 -1.54 -1.02 -0.368 -0.157 -0.024 0.041 0.079 0.096

-416 -301 -204 -1 56 -121 -77.0 -57.9 -42.0 -29.7 -19.6

80.4 82.4 83.9 85.5 87.5 95.6 105.8 126.2 156.7 207.6 258.5

-2.09 -1.67 -0.870 -0.471 -0.129 -0.016 0.020

-106 -121 -93.6 -73.3 -50.4 -38.0 -31.1

-1 1 .o

C

l

are cross-linked with siloxanes. It is likely that the retention is modestly different than for pure octadecane. This correction will improve the accuracy of thermodynamic properties significantly. The actual k , isotherms are listed in Tables I and 11. The logarithm of the actual k 2 versus density is also fairly linear in density. The results suggest that adsorption was minimal for two reasons. The peaks were symmetric without tailing, and k2 changed only 1% as the sample size increased from 0.02 to 0.3 pg. For polar solutes, the degree of adsorption can be much larger due to interaction with silanol groups on the silica. Phase Equilibria. The distribution coefficient was calculated from the actual (corrected) capacity factor and the ratio of volumes of the phases according to eq 5. The fluid to liquid volume ratio, p/r",may be calculated in terms of the swelling of the liquid phase Ar"/VoL by the relationship

- -r"

VoF - A r " VoL+ A r "

-

VoF/VOL - Ar"/VoL 1

+ Ar"/VoL

(17)

where the subscript 0 refers to a reference state at atmospheric pressure and the column temperature. Because the degree of swelling has not been measured for bonded CI8,it was estimated very accurately from swelling data for silicone rubber' and eicosane,*' as discussed in detail elsewhere.2s For silicone rubber and eicosane, the plots of swelling versus activity of C 0 2varied by a constant ratio up to 76 bar, the highest pressure where data were available for eicosane. The eicosane data were extrapolated to higher pressures, based on the silicone rubber data. A correction was made for the difference in swelling between octadecane and eicosane. At 35 O C , the swelling reached nearly 60%at 300 bar. (27) Chai, C.-P.; Paulaitis, M. E. J . Chem. Eng. Dum 1981, 26 (3), 277. (28) Shim, J.-J. Ph.D. Dissertation, University of Texas, Austin, 1990.

hF", kJ/mol

35 oc 285 110 86.9 73.2 62.7 43.0 32.9 24.1 18.2 13.6 11.3

35 OC 29.5 12.9 10.6 9.19 8.02 5.70 4.80 3.83 3.38 2.7 1 2.37

o

o

-141 -1 IO

-88.7 -66.7 -57.8 -54.3 -62.2. -79.4 -81.9 -75.0 -59.5 -53.9 -4.9 -1 6.9

-35.3 -33.8 -40.2 -34.8 t

KZ

Pressure (bar) Figure 3. Complex behavior of the distribution coefficient of naphthalene between Cis and C02 versus pressure: 0,35 OC:0 , 50 " C ; A, 70 OC; A, 100 "6;-, calculated by eq 8.

Consequently, the ratio of p/r" changed significantly with pressure, from 10.8 to 8.4 as pressure increased from 80 to 258 bar. In Figure 3 and Tables I and 11, K2 isotherms are presented for naphthalene and phenanthrene as a function of pressure. At a given T and P,K2 is about an order of magnitude larger for phenanthrene, which is consistent with its lower volatility. At 35 O C , only 4 OC above the critical temperature of C02, K2 decreases sharply with pressure, near the critical pressure. Here, it is important that pressure drops in the column are minimal, less than 0.5 bar. In contrast, these data may be represented much more clearly as a function of density as shown in Figure 4 for naphthalene and phenanthrene. It is well-known that density is a better indicator of solvent strength than pressure, based on solubility isotherms of solids in supercritical fluids. It has been demonstrated theoretically that the logarithm of solubility is related approximately linearly to log p.29 A similar relationship has been de-

Thermodynamic Properties Determined by SFC 100

A A

-

The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 357

*

1 .1

I

1

3.0

3.5

1000/T(K)

Density (glml)

Figure 5. Comparison of distribution coefficients of naphthalene as a function of temperature at constant density (0.45 g/mL) and at constant

1

pressure (100 bar) at 35,OC: m, constant density; 0 , constant pressure.

K2

L 1

l. 1

Density (g/ml)

Figure 4. Distribution coefficients of naphthalene (A) and phenanthrene (B) versus density: 0, 35 OC;0 , 50 O C ; A, 70 'c; A, 100 O C ; -, calculated by eq 8.

veloped for the logarithm of the capacity factor.30 A similar procedure may be used for the distribution coefficient to show that

a In p

l--

R TK

Since B z " / ~ is relatively constant in the vicinity of the solvent critical point,z9 In K2 is approximately linear in In p. The data in Tables I and 11 were regressed with this relationship, and the correlation coefficients ranged from 0.997 to 1.OOO. The complex nature of the pressure representation of K2 is due to the two competing effects of temperature on the density of the solvent and the volatility of the solute. These two effects may be considered separately as shown in Figure 5 by plotting log K2 versus 1/ T a t constant density. At constant density, the behavior is nearly linear, as the volatility increases with temperature. At constant pressure, K2 goes through a maximum. At the highest pressures where the fluid is relatively incompressible, Kz decreases with temperature as the volatility increases. At lower pressures, the decrease in density with temperature can dominate the volatility effect, causing K2 to increase. This is a retrograde effect and has been observed previously for kz.30 The temperature derivative of K 2 at constant pressure is related thermodynamically to the derivative at constant density:

We have shown that (a In K 2 / t 3 ( l / T ) ) pand (a In K z / a p ) T are relatively constant. Therefore, the complex behavior of ( a In Kz/t3( I/T)),, is related to the large effect of temperature on density, (ap/a( l / T ) ) p This presents a useful method to model ( a In K 2 / d ( 1 / T ) ) psince two of the derivatives in eq 19 are rel(29) Kumar, S. K.; Johnston, K. P. J . Supercrit. Fluids 1988, I , 15. (30) (a) Leyendecker, D.:Fhmitz, F. P.; Klesper, E. J. Chromatogr. 1984, 315, 19. (b) Kelly, F. D.; Chimowitz, E. H. Submitted to AIChE J . (c) Chimowitz, E. H.; Kelly, F. D. J . Supercrit. FIuids 1989, 2, 106.

2.6

2.9

3.2

1000/T( K )

Figure 6. Henry's constants of naphthalene and phenanthrene as a function of temperature in CI8over a pressure range of 80-260 bar. (The error bars indicate a slight variation with pressure.) A, naphthalene; m,

phenanthrene. atively constant, and accurate equations of state are available for the pure fluid property (ap/a( 1/ 7'))p The Henry constants were obtained from K 2 according to eq 8, as shown in Figure 6 . The binary interaction parameter, kI2, was regressed for each isotherm, in order to cause H2 to be nearly constant with pressure; further details are given elsewhere.28 At a given temperature, Hzis about 2 orders of magnitude larger for naphthalene than for phenanthrene, which is primarily due to the difference of their vapor pressures. This result is consistent with the previously measured relative ratios of Henry's constants of these two materials, which were determined from ratios of capacity factors.8 The temperature dependence of the regressed values of k12may be represented by a linear relationship

k12 = c

+ d ( T - 308.2 K)

(20)

where c and d are constants, 0.17 and -0.001 1, respectively, for naphthalene and 0.20and -0.0014, respectively, for phenanthrene. Based on Hzfor each isotherm in Figure 6 and eq 20, Kz was calculated and was nearly within experimental error for naphthalene and phenanthrene as shown in Figures 3 and 4. Solute Partial Molar Volumes at Infinite Dilution in the Fluid Phase. The partial molar volumes of naphthalene and phenanthrene were calculated from K2 with eq 14. Because of the simple behavior of log K versus p, each isotherm was regressed very accurately with a cubic polynomial. The isothermal compressibility, K,and density of pure C 0 2 were calculated from an extremely accurate equation of state." It is reasonable to assume regular solution behavior; that is, ij2Lis the molar volume of the pure subcooled liquid for two reasons. The retention is only by absorption, not adsorption, and each of the components is nonpolar. (31) Reynolds, W.C. Thermodynamic Properties in SI: Graphs, Tables, and Computational Equations for Forty Substances, Stanford University, 1979.

358

Johnston

The Journal of Physical Chemistry, Vol. 95, No. 1 , 1991 0.0

0.5

1 .o

t

1.5

(L

-'8!0

0:2 '0:4

'

0:6

'

0:8

i I

ann

-OW

IiO

8.0

0.2

0.4

0.6

0.8

1.0

Density (g/ml)

Density (giml) Figure 7. Partial molar volumes of naphthalene at infinite dilution in C 0 2and isothermal compressibility ( P K ) versus density at 35 OC: B,this work: 0, Eckert et al.:'" A, van Wasen and S~hneider:~ -, P K .

Density (glml) Figure 9. Partial molar enthalpy of naphthalene (A) and phenanthrene

Density (glml) Figure 8. Partial molar volume of naphthalene in the fluid phase from thc experimental distribution coefficient according to eq 14: 0,35 OC; 0, 50 "C;A, 70 OC;A, 100 OC;-, predicted by eq A3. This approximation is known to be accurate for the sorption of fluids such as C 0 2 into rubbery polymers.32 As shown in Figure 7, the new Bzm data for naphthalene in fluid C 0 2 agree very closely with those of Eckert et al.,lZBwhich were measured directly with a densitometer. This agreement supports the validity of the SFC technique, particularly the assumption of a simplc absorption mechanism in the liquid phase. Additional data are given in Figure 8 in Tables I and 11. An advantage of the SFC technique is that it takes about 10 min to obtain a data point, compared with 12 h for the densitometer technique. In addition, several solutes could be investigated simultaneously if the peaks are resolved to a degree such that solute-solute interactions are minimized. For polar solutes, there may be nonideal interactions in the liquid phase and the densitometer technique may be more reliable. A spectroscopic technique has been developed to determine Agrxn for the reversible reaction of the tautomers 2-hydroxypyridine and 2-pyrid0ne.~~This is a convenient method for exploring differences in ut" for two species. To shed insight into the nature of DZm, we examine a thermodynamic triple-product relationship ij2-

= uKn(aP/an,)-T,v+,,

(21)

Two factors influence D2-, Le., K of the pure solvent and the factor n(aP/an2)which is a function of the strength of the solutesolvent interactions. Both the present data and a previous study'" indicate that n(aP/an2)mdoes not diverge near the critical point of the solvent. For a van der Waals mixture, the attractive part of aP/an2 is given by

(B) in the fluid phase from the experimental distribution coefficient according to eq 16: 0, 35 OC;0, 50 OC;A, 70 O C ; A, 100 O C ; -, predicted by eq A4.

Therefore, D2- scales as PK, as shown in Figure In the near-critical region at a given p and K , B20Dis more negative for phenanthrene than naphthalene due to its larger polarizability and thus larger aI2.%At higher pressures, repulsive forces become more important and the situation is more complicated. An interesting feature of the new SFC technique is that the properties n(aP/anz)-and K are treated separately. This may be seen by a comparison of eqs 14 and 2 1. The experimental technique actually measures n(dP/an2)",thus providing insight into the solutesolvent intermolecular interactions. Since K of the pure solvent is calculated accurately, the shape of Dzm(p)is correct and the minimum is in the right place. A limitation in the SFC technique is that very long times would be needed to determine k 2 at lower pressures than those listed in Table 11. In Figure 8 , ~ is~ determined by calculating n(dP/an2) with the Peng-Robinson equation of state (eq A3), with the same values of k 1 2listed above in eq 20 and K and p from the above highly precise equation of state for pure C02.31 Although the agreement is good at most conditions, the calculated values are more pronounced in the regions where 9" is most extreme. It is likely that this difference is due to limitations in the equation of state and simple van der Waals 1 (quadratic) mixing rules. The experimental data provide a means to develop and test improved theories, which treat clustering of the solvent about the solute as discussed below. These results may be used to examine previous studies of stationary-phase properties such as D ~ An~equation . ~ similar ~ to eq 13 was used to calculate 82Lfrom the slope of k2. The PengRobinson equation was used to calculate the other properties, p , K , and OzF. The accuracy of this equation of state has been shown to be limited for the latter two ~ r o p e r t i e s . ~Because ~ the magnitude of the other terms in eq 14 is usually much larger than 7.12a914

where a12 is the interaction constant between the solute and C02. (32) Fleming, G. K.;Koros, W.J. Macromolecules 1986, 19 (E), 2285. (33) Peck, D. G.; Mehta, A. J.; Johnston, K. P. J . Phys. Chem. 1989, 93, 4297.

(34) Wong, J. M.; Pearlman, R. S.; Johnston, K. P. J . Phys. Chem. 1985, 89. 2671, (35) Ziger, D. H. Ph.D. Dissertation, University of Illinois, UrbanaChampaign, 1983.

The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 359

Thermodynamic Properties Determined by SFC

7

t

0

1001

-58!1'

.

0.4

"

0.7

"

'

'

'

1 .o

Density (giml)

Excess number of solvent molecules clustered about a solute molecule calculated from the experimental partial molar volume data according to eq 2 5 : 0,35 'c; 0 , 50 'C; A, 70 'C; A, 100 'C. Figure IO.

D2L, these inaccuracies lead to errors in ij2L. This could explain the large variations in D2L in the stationary phase,I7 for example,

-200 mL/mol for naphthalene and +4000 mL/mol for biphenyl at 35 "C. In the present study, it is assumed that ijZL = uzL, and the resulting values of DZF agree with the literature as explained above. Solute Partial Molar Enthalpies at Infinite Di_lution in the Fluid Phase. In Figure 9, experimental values of hZm- h21G are shown for naphthalene and phenanthrene for several temperatures, based on eq 16. The AhZnp was determined at each temperature from the literature.35 At high density, where K and (3 are small, the magnitude of h2" is small. The shape of hz' versus p is similar to that of -8. In the density range 0.40-0.44 g/mL, h," goes through a minimum much like D2-. The minimum is due primarily to the maximum in 0, which occurs near, but not exactly at, the point where K is a maximum. Here the solvent condenses about the solute very e_xothermically. Because phenanthrene is more polarizable, its hzmis more exothermic. The partial molar enthalpy was calculated from eq 3 I , along with an accurate equation for K and p of pure CO2.j1 The calculated values are somewhat smaller than the experimental values, which may be due to limitations in the Peng-Robinson equation of state or to a nonvanishing heat of mixing in the liquid phase. The partial molar enthalpy of trapfer of a solute from the fluid phase to the liquid phase, h2L3m- h2"", may be calculated directly from the data with eq 15. Therefore, its behavior is similar to that of in Figure 9, but shifted by AhvaP. The similar behavior of Dzm and hzmmay be explained theoretically. At the limit of the critical point of the ~ o l v e n t l ~

Since nze is related to Dzm, it is clear from eq 23 that nzc and h2" are related as is apparent in Figures 9 and IO. A typical energy for a van der Waals force is 5 kJ/mol. Therefore, the minimum hzmof -500 kJ/mol indicates that about 100 exothermic interactions are caused by each solute molecule, which is consistent with Figure 10. Many of these interactions are solvent-solvent interactions which are due to the presence of the solute. Because the solvent is highly compressible, attractive forces move solvent molecules into energetically favorable_locations. As K approaches that of a typical liquid, the values of h2- become ordinary, so that nze becomes small for a nonpolar mixture. The boundaries of a cluster are not discrete but are characterized by long-range fluctuations over many coordination shells. In addition, the local solvent density near the solute is augmented over the bulk density, although it must remain finite at the critical point. Similar results were obtained for the Ahrxnfor the reversible reaction between 2-hydroxypyridine and 2 - p ~ r i d o n e .For ~ ~ a reduced temperature of 1.003, there were up to 100 more exothermic interactions about the more polar reactant. This clustering is of practical interest as it influences the chemical potential of a solute and thus phase behavior5.I0as well as reaction rate and equilibrium constants.37 Partial Molar Enthalpy and Retrograde Solubility Phenomena. An important application of h2- data is the prediction of retrograde solubility phenomena, which may be used for separations of ~ o l i d s . ~ ~The ~ * slope ~ * of the solubility of a solid in a fluid, y 2 , is given by (aY2/dT)P,, = -(h," - fi,)/[R7-Yd

Inf2/aY2)T,PI

(26)

where u denotes the saturation curve and h; is the enthalpy of the pure solid. According to the criteria of stability, (a lnf2/r3y2)Tg is always positive.22 Therefore the slope of y 2 changes sign at a pressure called the "crossover pressure" where the numerator is zero. For a binary solid mixture, there may be a region where only one of the solids is in the retrograde region. Here a temperature increase may be used to precipitate this solid, potentially in pure form. The efficiency of the process is strongly dependent upon the difference in the crossover pressures. Therefore, SFC, which provides a convenient means to determine the difference in h2 for the two substances, could be used to evaluate this efficiency.

Conclusions A variety of thermodynamic properties may be obtained rapidly from SFC;however, special techniques are required. The swelling of the liquid phase is considerable for CISand must be included. The retention mechanism must be well-defined, which is usually not ~ ~ ~the case for SFC. This has been accomplished by correcting for adsorption on the support. The retention mechanism appears lim h2- = T(BP/aT), D2- + const (23) to be absorption into a bulk ideal liquid stationary phase based T~IJ'CI on the experimental procedure, the shape of the peaks, the agreement with the D2- data of Eckert, and the Henry constants. where ( d P / a T ) , is the slope of the vapor pressure curve of the Although the distribution coefficient is a complex function of pure so_lvent extrapolated at the critical point. Since 8," scales pressure and temperature, approximately linear relationships have as PK, hzmscales as P K . The minimum in f i 2 - and hzmoccur near been identified as a function of log p at constant T and of 1/T the maximum in P K , which is near the critical isochore. at constant p. Solvent Clustering about a Solute at Infinite Dilution. We The distribution coefficient is the key chromatographic property present a brief summary of the theoretical relationship between for describing phase equilibria. It has been modeled accurately solute-solvent clustering and the partial molar properties, 02-, and by using a Henry constant to describe interactions in the liquid hz". The number of solvent molecules about a solute in excess phase and the Peng-Robinson equation of state to calculate the of the bulk amount may be defined as fugacity coefficient in the fluid phase. Infinite dilution properties provide an important basis for calculating phase behavior at finite n2e = p J " * ~ r ) - 11 dr (24) concentration.' This work provides a basis for a subsequent study, in which the support is coated with a polymer of interest and not where g12is the radial distribution function and r I 2is the radius just a commercial chromatographic stationary phase. This type over which solvent and solute molecules are correlated. A very of phase equilibria is important in practical applications including simple and useful result may be obtained for a solute at infinite dilution from eq 24 along with Kirkwood-Buff solution t h e ~ r y l ~ ~ s ' ~polymer impregnation and purification. In the highly compressible near-critical region, solute partial nZe = K I M - ~ ( ~ P / ~ ) T , v , J (25) molar volumes and enthalpies reach very large negative values. hzF9"

At the critical point of the pure solvent, K , r12,and n2ediverge. (36) Debenedetti, P. G.;Kumar, S. K. AIChE J . 1988, 34 (4). 645

~

(37) See references cited in ref 11. (38) Johnston, K. P.; Barry, S. E.; Read, N. K.; Holocomb, T. R. Ind. Eng. Chem. Res. 1987, 26, 2372.

360

J. Phys. Chem. 1991, 95, 360-365

Both of these properties scale as the isothermal compressibility. Here, each solute molecule can induce on the order of 100 exothermic solute-solvent and solvent-solvent interactions over many coordination shells. The large magnitudes of hlDdescribe large temperature effects on the chemical potential of the solute, which can lead to large temperature effects on phase behavior and chemical reactions.

anb ~ - b + =

fi2

an2 KV

(V

- b)2

Acknowledgment is made to the Separations Research Program at the University of Texas, the Shell Development Company, and the Camille and Henry Dreyfus Foundation for a Teacher-Scholar Grant. We are grateful for helpful discussions with Petr Munk, Ray West, and Jerry King.

( T $ ,- a)( v - hZrG= PO2 - R T

A2

Appendix The fugacity coefficient may be calculated from the PengRobinson equation with quadratic mixing rules for the attractive and repulsive parameters, a and b, respectively. The combining rules are

aij = ( 1 - kij)(aiiajj)1/2

(‘41)

+

(A21

b, = (bii1/3 b , j 1 / 3 ) 3 / 8

where k , is an adjustable binary interaction parameter. The expressions for B2 and h2 in the fluid phase are

RT-

+

z - bD,)

+

bh2 + 2bv - b21

1

+

v 2.4146 v - 0.4146 At infinite dilution, the best results are obtained by calculating v and K from a highly accurate equation of state for the pure fluid. Registry No. COz, 124-38-9; naphthalene, 91-20-3; phenanthrene, 85-01 -8.

Substituent Group Effects on the Solubilization of Polar Aromatic Solutes (Phenols, Anilines, and Benzaldehydes) by N-Hexadecylpyridinium Chloride Byung-Hwan Lee,+ Sherril D. Christian,**+Edwin E. Tucker,+and John F. Scamehornt Institute for Applied Surfactant Research, The University of Oklahoma, Norman, Oklahoma 73019, Department of Chemistry and Biochemistry, The University of Oklahoma, Norman, Oklahoma 73019, and School of Chemical Engineering and Materials Science, The University of Oklahoma, Norman, Oklahoma 7301 9 (Received: April 13, 1990; In Final Form: July 10, 1990)

Solubilization isotherms of polar aromatic solutes (phenols, anilines, and benzaldehydes) in N-hexadecylpyridiniumchloride micelles have been determined at 25 OC by using the semiequilibrium dialysis method. Effects of various substituent groups (H, F, CI,Br, CH30, NO2,CH3, Et, i-Pr, and CF3) have been studied for the solubilization of phenol, aniline, and benzaldehyde derivatives in aqueous solutions of the surfactant. Both hydrophobic and electrostatic effects are shown to be important in influencing the solubilization behavior. The simple expression, K = KO(1 - B a 2 , is used to correlate the solubilization equilibrium constant ( K ) with the mole fraction of solute in the micelles ( X ) . Linear free energy relationships can be used to correlate the solubilization results for the different classes of compounds.

Introduction The ability of micelles to solubilize organic compounds is one of the remarkable properties of aqueous surfactant systems. Many investigators have used various physical methods to study the solubilization of polar and nonpolar organic solutes in ionic and nonionic surfactant micelles.’-* Studies of the solubilization of organic solutes have been made to determine the effects of micellar structure and changes in the environment at the site of solubilization. However, the effects of physical properties of the solute (including polarity, inductive effects, branching, and locus of substitution) on complete solubilization isotherms have not been extensively studied for aqueous surfactant systems. Such factors are known to be important,9J0 but little has been done to include them in solubilization models. Micelles of ionic surfactants can interact electrostatically with highly polar solutes because the large surface charge densities of these aggregates lead to strong ion-dipole i n t e r a c t i o n ~ . ~In J~ ‘Department of Chemistry and Biochemistry. f School of Chemical Engineering and Materials Science.

addition, ionic micelles ordinarily have an extensive hydrophobic core region, which can interact strongly with hydrocarbon and halogenated hydrocarbon groups of solutes. Hydrophobic effects have often been considered to be dominant in determining the locus of solubilization.6,1’J2but the effects of electrostatic interactions ( 1 ) Mukerjee, P. In Solution Chemistry of Surfactants; Plenum Press: New York, 1979; Vol. 1, p 153. ( 2 ) Nagarajan, R.; Chaiko, M. A,; Rukenstein, E. J . Phys. Chem. 1984,

.~

88. 2916.

(3) Kandori, K.; McGreey, R. J.; Schechter, R. S. J . Phys. Chem.1989, 93, 1506. (4) Muto, Y.; Asada, M.; Takasawa, A.; Esumi, K.;Meguro, K.J . Colloid Interface Sci. 1988, 124, 632. ( 5 ) Sepulveda, L.; Lissi, E.; Quina, F. Adu. Colloid Inrerfuce Sci. 1986, 25,

1.

( 6 ) Moroi, Y.; Matuura, Y. J . Colloid Inferface Sci. 1988, 125, 456. (7) Greiser, F.; Drummond, C. J . J . Phys. Chem. 1988, 92, 5580. (8) Moroi, Y.; Sato, K.,Motuura, R. J . Phys. Chem. 1982, 86, 2463. (9) Treiner, C.; Chattopadhyay, A. K. J . Phys. Chem. 1986, 109, 101. (IO) Malliaris, A. Ado. Colloid Interface Sci. 1987, 27, 153. ( I I ) Bunton, C. A.; Sepulveda, L. J . Phys. Chem. 1979, 83, 680.

0022-3654191 12095-0360%02.50/0 0 1991 American Chemical Society