J. Phys. Chem. 1992, 96, 8548-8552
8548
Figure 6 is equivalent to that in methanol. In order to substantiate this we have determined the fluorescence spectrum of the complex following procedures outlined in the Experimental Section. The spectrum of the complex of O-CD, shown in Figure 7, resembles remarkably closely that of AP in methanol (the emission maximum of AP appears a t 518 nm in methanol, which is the same as that for the complex). This once again confirms that the effective polarity experienced by the molecule in the complex form is equivalent to that in methanol. With a-CD, because of very little inclusion of the molecule, one expects that the probe will find a more polar environment. This has been confirmed by noticing that the emission maximum due to this complex is red-shifted with respect to that for the complex of &CD. The fluorescence quantum yield for the a-CD-AP complex is found to be only 0.02. Thus one must conclude that AP in a-CD sees an environment which is more polar than methanol.
Acknowledgment. This research was supported by a grant from the Department of Science and Technology, Government of India (NO:SR/OY/C07/90). T.S. thanks the Department of Atomic Energy, Government of India, for the award of a Dr. K. S. Krishnan Fellowship. We thank Dr. D. Chatterjee and Dr.Amit Chattopadhyay of the Centre for Cellular and Molecular Biology, Hyderabad, for providing the facility for the lifetime measurements. References and Notes (1) Kalyanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic Press: New York, 1987. (2) Ramamurthy, V.; Eaton, D. F. Acc. Chem. Res. 1988, 21, 300. (3) Duveneck, G. L.; Sitzmann, E. V.; Eisenthal, K. B.; Turro, N. J. J . Phys. Chem. 1989, 93, 7166. (4) Munoz de la Pena, A.; Ndou, T.; Zung, J. B.; Greene, K. L.; Live, D. H.; Warner, I. M. J. Am. Chem. SOC.1991, 113, 1572.
(5) Hamai, S. J. Phys. Chem. 1989,93, 6527. (6) Munoz da la Pena, A.; Ndou, T.; Zung, J. B.; Warner, I. M. J . Phys. Chem. 1991, 95, 3330. (7) Turro, N. J.; Bolt, J. D.; Kuroda, Y.; Tabushi, 1. Photochem. Photobioi. 1982, 35, 69. (8) Turro, N. J.; Okubo,T.; Chung, C. J. J. Am. Chem. SOC.1982, 104, 1789. (9) Turro, N. J.; Cox, G.S.;Li, X . Photochem. Photobiol. 1983,37, 149. (10) Cox, G. S.; Turro, N. J. J. Am. Chem. Soc. 1984,106, 422. (1 1) Turro, N. J.; Okubo, T.; Weed, G.C. Phorochem. Phorobiol. 1982, 35, 325. (12) Cox, G. S.; Hauptman, P. J.; Turro, N. J. Photochem. Photobiol. 1984, 39, 597. (13) Nag, A.; Bhattacharyya, K. J. Chem. SOC.,Faraday Trans. 1 1990, 86, 53. (14) Nag, A.; Chakraborty, T.; Bhattacharyya, K. J . Phys. Chem. 1990, 94, 4203.
(15) Nag, A,; Dutta, R.; Chattopadhyay, N.; Bhattacharyya, K. Chem. Phys. Lett. 1989, 157, 83. (16) Hoshino, M.; Imamura, M.; Ikehara, K.; Hama, Y. J . Phys. Chem. 1981,85, 1820. (17) Scypinski, S . ; Love, L. J. Anal. Chem. 1984, 56, 331. (18) Murai, H.; Mizunuma, Y.; Ashikawa, K.;Yamamato, Y.; I’Haya, Y. J. Chem. Phys. Lett. 1988, 144,417. (19) Bortolus, P.; Monti, S. J . Phys. Chem. 1987, 91, 5046. (20) Agbaria, R. A,; Gill, D. J. Phys. Chem. 1988, 92, 1052. (21) Hamai, S. J . Am. Chem. SOC.1989, 111, 3954. (22) Soujanya, T.; Krishna, T. S. R.; Samanta, A. J. Photochem. Photobioi. A : Chem. 1992, 66, 185. (23) Nagarajan, V.; Brearly, A. M.; Kanj, T. J.; Barbara, P. F. J . Chem. Phys. 1987,86, 3183. (24) Reichardt, C. Solvents and Solvent Effecrs in Organic Chemistry; VCH: Weinheim, 1988. (25) Melhuish, W . H. J . Phys. Chem. 1961, 65, 229. (26) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC.1985, 107, 3902. (27) Benesi, H. A,; Hildebrand, J. H. J. Am. Chem. SOC.1949,71,2703. (28) Kano, K.; Takenoshita, I.; Ogawa, T. Chem. Lett. 1982, 321. (29) Yorozu, T.; Hoshino, M.; Imamura, M. J. Phys. Chem. 1982, 86, 4426. (30) Szejtli, J. In Inclusion Compounds; Attwood, J. L., Davies, J. E., MacNicol, D. D., Eds.; Academic: New York, 1984; Vol. 3, p 332.
Statistical Thermodynamic Treatment of High-Pressure Phase Equilibrla in Supercritlcal Fluid Chromatography. 1. Theory Michal Roth Institute of Analytical Chemistry, Czechoslovak Academy of Sciences, 61 142 Brno, Czechoslovakia (Received: September 20, 1991)
The classical thermodynamic relationships for the pressure and temperature derivatives of solute retention in supercritical fluid chromatography (SFC) contain composition terms resulting from the effect of sorption of the mobile-phase fluid into the stationary phase (“swelling”). In this paper, the random-mixingversion of the Panayiotou-Vera lattice model has been employed to express the complicated effect of swelling on solute retention in terms of molecular parameters. The present treatment takes into account the pressure- or temperature-induced changes in both volume and composition of the stationary phase. It is believed that such an effort will contribute toward establishing SFC as a rapid and reliable technique of thermodynamic measurements in dilute supercritical mixtures. The parametrization and performance of the model will be discussed in the following paper in this issue.
Introduction Applications of supercritical fluids to industrial processes such as extraction, polymer fractionation, surface-coating technologies, or regeneration of activated carbon beds require reliable thermodynamic data on the dilute supercritical mixtures involved. The classical, static techniques of high-pressure phase-equilibrium studies are often time-consuming. In principle, supercritical fluid chromatography (SFC) may serve as an alternative, rapid technique to obtain the thermodynamic data. However, the applications of SFC to thermodynamic measurements have been impeded by a lack of adequate thermodynamic models for the effects
of pressure and temperature on solute retention in SFC. This situation in SFC contrasts sharply with the relatively well-developed thermodynamic treatments of the pressure and temperature effects on solute solubility in supercritical fluid extraction (SFE).1-4 The main reason for the contrast between SFC and SFE is that, even when the dynamic aspects of the chromatographic process are not considered, the modeling of the pressure and temperature effects on solute retention in SFC is more complicated than the similar problem in SFE. In any rigorous thermodynamic model for SFC, the stationary phase should be considered to be a
0022-3654/92/2096-8548$03.00/00 1992 American Chemical Society
Theory of Statistical Thermodynamic Treatment three-component system (solute + the principal component of the stationary phase the mobile-phase fluid sorbed into the stationary phuse), while a twmmponent system (pure crystalline solute supercriticalfluid) is usually adequate in the solid-fluid equilibria encountered in SFE. With a few notable exceptions,s-12 however, previous thermodynamic models for SFC ignored the sorption of the mobile-phase fluid into the stationary phase ('~welling").~~ Martire and BoehmSincluded the sorption of the mobile-phase fluid into their unified molecular theory of chromatography, but they assumed that the effect of swelling on solute retention was negligible in partition SFC. Considering the recent experimental results on the swelling of silicone rubber by compressed gases,7,12*14,1s such an assumption becomes questionable. Shim and employed SFC to measure the partition coefficients, infinite-dilution partial molar volumes, and infinite-dilution partial molar enthalpies of several solutes in supercritical C02. The results were corrected for the swelling-induced change in the volume of the stationary phase, but an approximation was made that the solute fugacity in the stationary phase did not vary with the absorbed amount of C02. In the particular case of polymeric stationary phases, the effect of swelling on the activity coefficient of the solute may be describedgJ2by employing the Scatchard-Hildebrand-Flory-Huggins theory of polymer solutions.16 However, ambiguities arise concerning the proper values of the partial molar volume and the solubility parameter of the mobilephase fluid dissolved in the stationary phase. The purpose of the present paper is to develop a statistical thermodynamic model to address the effect of swelling on the pressure and temperature derivatives of the solute retention in SFC. It is believed that such an effort will contribute toward establishing SFC as a rapid technique to determine the solute partial molar properties1I-l2or fluctuation integrals17 in dilute supercritical mixtures. An example of parametrization of the model will be described in the following paper in this issue.
+
+
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8549 the previous statistical thermodynamic models of the solute retention in SFC,Sq6,8the present treatment will focus primarily on the derivatives that make up the composition terms in eqs 1 and 2. Statistical Thermodynamic Model General Considerations. The treatment developed below will be based upon a mean-field lattice gas model similar to those described1*J9and employedZobefore. The molecules in a mixture occupy a three-dimensional cubic lattice of coordination number z and of unit cell volume h.The values of the lattice coordination number and of the unit cell volume are fixed to 10 and 1.619 X cm3/site (corresponding to 9.75 cm3/1 mol of lattice sites), r e s p e c t i ~ e l y . ~Each ~ * ~molecule ~ of component i is assumed to occupy ri lattice sites, and fractional values of ri are allowed. Distributed on the lattice are No empty sites (holes), Ni molecules of component i, Nj molecules of component j, etc. The total volume of the system (lattice), V, is then given by
V = U H [ N+ O E(riNi)l
(3)
where the summation is over all components in the mixture. An 'effective surface area", qi,is assigned to a molecule of component i in such a way that zqi = zri - 2(ri - 1)
(4)
The potential energy function between a segment of a molecule of component i and a segment of a molecule of component j is supposed to be given by a square-well potential of depth -tip Unlike the original version of the model, the present partition function does not comprise the nonrandomness correction ensuing from the quasi-chemical approximation.2'q22The total potential energy of the system, E, is then given by E = -(z / 2) CC(NjqjSjtjj) = -(z / 2) 9 [C (Niqi)]CC( a i a j e i j ) i
J
i
i
j
Definition of the Problem Treatments of the effects of pressure and temperature on solute retention in SFC by classical thermodynamics including the effects of composition were presented by several authors."12 The pressure and temperature quotients of the logarithm of the solute capacity ratio, k l , may be expressed as9si0
In eq 5, S j is the effective surface area fraction of molecules of component j
(a In kl/ap)T = (87, - e;s)/(RT) - B m T - (Vs/Vm)&T-
19 = ES,and is the effective surface area fraction of molecules of component j expressed on a hole-free basis
[ 1/(RT)I (arTs/aJ.%)T,P,",*,nz(aJ/3s/aP) 7,r (1 1
(5)
Sj = Njqj/[No + C(Niqi)I
aj
8j = N,qj/C(Niqi)
and
In eqs 1 and 2, the subscripts m and s refer to the mobile and the stationary phase, respectively, and the subscripts 1, 2, and 3 identify the solute, the principal component of the stationary phase, and the mobile-phase fluid, in that order. The symbol R refers to the molar gas constant, Tis the thermodynamic temperature, P is the pressure, V, and V ,are the volumes of the stationary and the mobile phase in the chromatographic column, respectively, and the superscript indicates the stat? of infinite dilution. Further, 8 is the partial molar volume, h is the partial molar enthalpy, ap is the isobaric expansivity, BT is the isothermal compressibility, p is the chemical potential, and n is the amount of substance (mole number). The subscript u refers to saturation of the stationary phase with the mobilephase fluid, and the general symbol 143s denotes the equilibrium proportion of the mobile-phase fluid in the stationary phase: i.e., 143s may represent the mole fraction, mass fraction, segment fraction, or molecular-surface fraction of the mobile-phase fluid in the stationary phase at equilibrium. In previous reports:-10 the composition terms in eqs 1 and 2 were expressed in different but equivalent forms; the forms given in eqs 1 and 2 are more convenient for the present p u p e . Equations 1 and 2 suggest that reliable values of and h:, cannot be obtained from the experimental data without assessing the significance of the composition terms. That is why, unlike
(6) \
(7)
To express the equation of state (EOS)and the chemical potential, the "del makes use of reduced temperature, pressure, and volume, T, P,and 5, respectively. The reducing parameters Ts and P* may be obtained from
kBT* = P*UH
(Z/2)e~
(8)
where kB is the Boltzmann constant. For a random mixture (see above) EM
= CC(8jajEjj) i
j
(9)
The reduced volume of the mixture, 5, is given by 5 = V/(nvL)
(10)
where n is the total number of moles of substance in the mixture and v; is the molar hard-core volume of the mixture. The molar hard-core volume of component i is related to ri by V:
= NArjVH
(11)
where N A is the Avogadro number. The total effective surface area fraction of molecules in the mixture is related to the reduced volume of the mixture by
9=
(qM/rM)/[C
+ (qM/rM) - l1
(12)
where t'M = [13(ri9i/qi)]/c(8i/qi) and q M = l/C(8j/qi). The
8550 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Roth
EOS for a mixture may be written as P/T = In [e/@ - I)] + (2/2) In
[(a
+ qM/rM - 1)/0] - 02/F (13)
The chemical potential of a component i in a mixture is - p , / ( R T ) = In X,(T) r, In (1 - 9) - In 9, In q, + (bz/2)[2q,c(9J*lJ) - (41 - rl)cc(9JskcJk)l (14)
+
+
J
J k
where /3 = l/(ke7'). The term X , ( T ) accounts for the flexibility and symmetry of the molecules of component i and, for a given component i, it is assumed to be a function of temperatureonly.18J9 Since phase-equilibriumcalculations generally involve equating chemical potentials of a component in both phases, the functional form of Al(7') need not be specified. Development of the Model. To obtain expressions for the composition terms in eqs 1 and 2, the quantity 1L3, will below be specified as Q3,, the effective molecular surface area fraction of the mobile-phase fluid (3) in the stationary phase, expressed on the hole-free basis. Before the model can be applied to calculate the composition terms in eqs 1 and 2 at some particular temperature and pressure, the equilibrium compositions of both phases have to be known. The solute, 1, is assumed to be infinitely dilute in both phases; therefore, d1, 0, a1, 0,91s 0, and a1, 0. Further, the principal component of the stationary phase, 2, is supposed to be nonvolatile and nonextractable by the mobile-phase fluid; accordingly, 92m 0 and 0. What remains then is to determine the equilibrium proportions of components 2 and 3 in the stationary phase by the following procedure: (a) At the given temperature and pressure, eqs 12 and 13 are solved for the reduced volume of the pure mobile-phase fluid, ,a, and for the total effective surface area fraction of molecules in the mobile-phase fluid, 9,. (b) The chemical potential of the pure mobile-phase fluid, p3,, IS calculated from eq 14 (except for the term In X3(T)as mentioned above). (c) A composition of the stationary phase is selected + = l), and the reducing parameters for the 2 3 mixture are determined. (d) Equations 12 and 13 are solved for the reduced volume of the stationary phase, a, and for the total effective surface area fraction of molecules in the stationary phase, 9,. (e) The chemical potential of component 3 in the stationary phase, p3,, is calculated from eq 14. (f) Steps c-e are repeated for different compositions until the condition of equilibrium, p3, = p3,, is satisfied. When the equilibrium compositions of both phases are known, the composition terms in eqs 1 and 2 may be computed from the equations to be given below. The three differential quotients that make up the composition terms will be discussed separately. It is important to note that the pressure and temperature quotients of are measurable quantities, at least in principle. Therefore, the model predictions for the two quotients may be compared with the pertinent experimental data when these become available. On the contrary, the isobaric derivative of pys with respect to Q3, is of an entirely different nature. Obviously, this quotient cannot be measured experimentally, and the theoretical analysis is the only way to estimate it. Composition Derivative of &. Functional forms of eqs 13 and 14 suggest that an isobaric derivative of p, cannot be obtained directly from eq 14. Instead, employing standard relationships between partial differential coefficient^,^^ one may write
- - - a2, -
-
+
a3,
where
The presence of the stationary-phase volume, V,, in eqs 18 and 19 does not bring problems because the Wpxntaining terms will combine to unity in the product on the rhs of eq 15. The third quotient on the rhs of eq 15 cannot be derived directly from the EOS (eq 13), but it may be expressed through another differential identity23as
Both derivatives on the rhs of eq 20 are accessible from eq 13; namely,
(a2,
a3,
and
where X3~~3/~M = s(r3a3s/q3)/(r2Q2s/q2
+ r3Q3s/43)
(23)
The final expression for the isobaric derivative of pTs with respect to is then obtained by substitution of eqs 16, 17, and 20-22 into eq 15. P r d Derivative of 9%. The quotient (aa3,/aP),, may be deduced from the following argument. Suppose that, at a temperature T and pressure P, the pure mobile-phase fluid, 3, is in equilibrium with the stationary phase composed of components 2 and 3, 9%+ = 1. At equilibrium, Le., at saturation of the stationary phase with the mobile-phase fluid, the chemical potentials of component 3 in both phases are equal, p3, = p3,. Now, let the pressure be changed by dP at a constant temperature, and let the thermodynamic equilibrium be reestablished at the pressure P dP. The chemical potentials of component 3 are again equal
a,,
a3$
+
The first two quotients on the right-hand side (rhs) of eq 15 may be derived from eq 14. The first quotient is given by
+ d ~ 3 s= ~
~ 3 s
3 ,
+ d~3m
Since p3, = p3,, it follows that dp3, = dp3, and
(24)
Theory of Statistical Thermodynamic Treatment
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8551
where the subscript n2srefers to insolubility of component 2 in the mobile-phase fluid and the subscript u denotes saturation. Employing a suitable relationship between the partial deri~atives,2~ one obtains
The f m l expression for the derivative (d9,/dP),, is then obtained by substitution of q s 20-22 and 29-33 into q 28. Temperature Derivative of 9% By following an argument similar to that used in the pressure derivative of &,, one obtains (35) The left-hand side of eq 35 may be rewritten as
Substitution from eq 26 into eq 25 yields From eqs 35 and 36, it follows that
Since the mobile phase consists of pure component 3, it follows from classical thermodynamics that the first quotient on the rhs of eq 27 is equal to the molar volume of pure component 3. However, this fact will not be utilized here in order to retain consistency of the present treatment with that of the quotient (a93,/d7)p,0(seebelow). The derivatives on the rhs of eq 27 may again be recast into forms that are accessible from eqs 13 and 14. The respective rearrangements yield
For the individual derivatives on the rhs of eq 28, one obtains the following expressions:
(37) Employing the standard relationships +tween the partial deriva t i v e ~ ?one ~ may recast eq 37 into the form in which all the terms may be derived from either eq 13 or eq 14; namely
The temperature derivatives on the rhs of eq 38 are given by
(2)
= -R[ln X3(T) + r3 In (1 - 8,) - In 83s+
v,,na,33,
In q3] - R T
(
%)T
where
dT
=
and
and
In deriving eqs 39-42, it was assumed that the hard-core volumes of the components were independent of temperature, whereas the energy parameters eij were allowed to vary with temperature. The final expression for the derivative (a$,,/aT),, may be obtained
J. Phys. Chem. 1992,96,8552-8556
8552
by substitution of eqs 2&22,29-33, and 39-42 into eq 38. The functional forms of In A3(n and d In X3(n/dT in eqs 39 and 40 need not be specified, as these terms cancel out upon substitution into eq 38. Pprtirl Mohr properties In order to evaluate the performance of the model (see the following paper in this issue), it is useful to consider briefly the partial molar properties of components 1 and 3 in both phases. The infinite-dilution partial molar volume of the solute in the stationary phase, may be obtained from
cs,
c,,,
The values of and 03sare given by similar equations. An absolute value for the partial molar enthalpy of component i, hi, cannot be obtained from the model because of the term_ In in eq.14. However, one can compute the difference hi hi', where h, is the molar enthalpy of pure i in an ideal-gas state at the same temperature. For example,
X,(n
Similar relations may be obtained for
hf;,- h; and h3s - hi.
Conclusion Applications of SFC to physicochemical measurements require an intimate knowledge of the thermodynamics of solute retention in SFC. In the present contribution, a mean-field lattice model
has been employed to derive expressions for the composition terms in the classical thermodynamic relationships for the pressure and temperature quotients of solute retention in SFC with a pure (single-component) mobile phase. This model takes into account the praure or tempcratureinduced changes in both volume and composition of the stationary phase. Parametrization and performance of this model will be discussed in the following paper in this issue.
References rad Notes (1) Johnston, K. P.; Eckert, C. A. AIChE J . 1981, 27, 773. (2) Gitterman, R. B.; Procaccia, I. J. Chem. Phys. 1983, 78, 2648. (3) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice; Butterworths: Boston, 1986. (4) Debenedetti, P. G.; Kumar, S.K. AIChE J. 1988, 34, 645. (5) Martire, D.E.; Bahm, R. E. J. Phys. Chem. 1987, 91, 2433. (6) Martire, D. E. J . Chromatop. 1988, 452, 17. (7) Shim, J.-J.; Johnston, K.P. AIChE J . 1989, 35, 1097. (8) Kelley, F. D.; Chimowitz, E. H.AIChE J . 1990, 36, 1163. (9) Roth, M.J . Phys. Chem. 1990, 94,4309.
(IO) Roth, M.J. Supcrcrit. Fluids 1990, 3, 108. ( 1 1 ) Shim, J.-J.; Johnston, K. P. J . Phys. Chem. 1991, 95, 353. (12) Shim, J.-J.; Johnston, K. P. AIChE J. 1991, 37, 607. (13) Roth, M.J . Microcol. Sep. 1991, 3, 173. (14) Fleming, G. K.; Koros, W.J. Macromolecules 1986, 19, 2285. (15) Pope, D. S.; Sanchez, I. C.; Koros, W.J.; Fleming, G. K. Macromolecules 1991, 24, 1779. ( 1 6 ) Tompa, H. Polymer Solutions; Butterworth: London, 1956; Chapter 4. (17) Roth, M.J . Phys. Chem. 1991, 95, 8 . (18) Panayiotou, C.; Vera, J. H. Polym. J . 1982, 14, 681. (19) Kumar, S. K.; Suter, U. W.; Reid, R. C. Ind. Eng. Chem. Res. 1987, 26, 2532. (20) Daneshvar, M.;Kim, S.;Gulari, E. J . Phys. Chem. 1990,94,2124. (21) Guggenheim, E. A. Mixtures; Clarendon Ress: Oxford, U.K., 1954. (22) Panayiotou, C.; Vera, J. H.Can. J. Chem. Eng. 1981, 59, 501. (23) Guggenheim, E. A. Thermodynamics. An Advanced Treatment for Chemists and Physicists, 3rd 4.; North-Holland: Amsterdam, 1957; Chapter 3, pp 83-95.
Statistical Thermodynamic Treatment of HigkPressure Phase Equillbria in Supercritical Fluid Chromatography. 2. Parametrization and Testing of the Model Michal Roth Institute of Analytical Chemistry, Czechoslovak Academy of Sciences, 61142 Brno, Czechoslovakia (Received: February 6, 1992)
In a typical capillary-columnsupercritical fluid chromatography (SFC)system [naphthalentpoly(dimethylsiloxane)-carbon dioxide], the random-mixing version of the Panayiotou-Vera lattice model is shown to yield moderately successful reproductions of experimental data on supercritical solubility, polymer swelling, and solute partition coefficients with a unique set of purecomponent parameters and one adjustable parameter per binary. With the parameters fixed by fitting the above data, the treatment described in part 1 of this series (preceding paper in this issue) provides reasonable predictions for the partial molar properties of the solute and for the effect of compositionon the chemical potential of the solute in the stationary phase. In the present system, swelling of the stationary phase by the supercritical fluid is predicted to make a positive contribution to (a In kl/aP)Tand a negative contribution to (a In kl/a7')p It appears that relative contributions of the stationary-phase composition changes t o (a In k,/aP),and (a In k,/aT), generally decrease with increasing isothermal compressibility and isobaric expansivity of the mobile-phase fluid, respectively.
Introduction In part 1 of this series,' the random-mixing version of the Panayioutou-Vera lattice model2 has been used to derive expressions for the effect of swelling on the presure and temperature derivatives of solute mention in supercritical fluid chromatography (SFC).In the present part, an example of parametrization of the model will be given in order to evaluate the performance of the model. It will be shown how the complicated effect of mobilephase sorption into the stationaryphase on the solute retention in SFC may be addressed by employing information on the re-
spective binary subsystems involved. The system to test the theoretical treatment will be naphthalene (1)-poly(dimethylsiloxane) (PDMS)(2)-carbon dioxide (3). For this particular system, nearly all necessary experimental data are available. This (second) part of the series may roughly be divided into two sections. In the first section, the sour- and calculations of the purecomponent and unlike interaction-energy parameters will be described. At the same time, this section will illustrate the capability of the model to reproduce the experimental data used
0022-3654/92/2096-8552S03.00/00 1992 American Chemical Society
