3018
J. Phys. Chem. 1982, 86, 3016-3021
to the dynamic process of the phase transition, where the dynamics of the total system were assumed to be described by two characteristic processes, a nucleation (or vanishing) process and a successive growth (or shrinking) process. In their theoretical development, the former was considered as a process where a certain lipid of state A appears (or vanishes) in the sea of the lipids of state B. The latter was the process of growth (or shrinking) of the cluster consisting of the lipids of state A. The time constants of the nucleation process and the growth process were distinguished from each other. If this cluster model is assumed to be applicable to our system, we dare to suppose that the rapid and slow proceases observed in the single lamellar
liposomes correspond to the nucleation and growth processes, respectively, because it is likely that the growth process does depend on the liposome size, but the nucleation does not. If it is the case, the original feature of the nucleation process provided by Kanehisa and Tsong should be modified as the nucleation itself occurs cooperatively, because the rapid process as well as the slow process exhibits the slowing down at the midpoint of the phase transition with a time constant of about 20 ns. If the nucleation process occurs independently, the time constant of the process should be a few nanoseconds which corresponds to the time constant of the configurational change between trans and cis on a specific C-C bond.
Solubility of Solids and Liquids in Supercritical Gases Josef Chrastll F'hyslcal Chemical mepartment, Technlcal Center, General Foods Corporation, Tanytown, New York 1059 1 (Received: December
IO, 1981; In Flnal Form: March 1, 1982)
An apparatus for the determination of the solubilities of solids and liquids in dense gases is described. The solubilities of stearic acid, oleic acid, behenic acid, tributyrin, tripalmitin, triolein, trilinolein, palmityl behenate, behenyl behenate, a-tocopherol, cholesterol, water, and cafestol in supercritical carbon dioxide at different temperatures and pressures were determined. An equation was derived from the association laws and/or from the entropies of the components and was compared with these experimental results. The equation agreed with experimental results over a wide range of pressures and temperatures. Some experimental results from the literature (naphthalene, anthraquinone,p-chloroiodobenzene) were also reproduced by means of this equation. Very good agreement with these experimentalresults was found, as in previous examples. The association number, heats of solution, and other thermodynamicalcharacteristics of compounds dissolved in dense gases are discussed. The separation of a-tocopherol and tripalmitin by the supercritical carbon dioxide extraction was measured experimentally at different pressures and temperatures. The equation describing the ideal separation of two independent components by means of a dense gas extraction is described.
Introduction The quantitative determinations of the solubilities of different solutes in dense gases (naphthalene in and carbon dioxide,2 anthraquinone in ether,3 p-chloroiodobenzene in ethylene; water in nitrogen>6 anthracene in ethylene,' amino acids and sugars in carbon dioxide,* etc.) proved that the solubility profile of solids or liquids in supercritical gases changes significantly with pressure and temperature, and the isobars have a maximum and/or a minimum on the temperature-solubility curve (Figures 6 9 ) . From Dalton's law, we expect that the mole fraction of a dissolved solute in a gas is given by P J P , where P, is the vapor pressure of the solute at a given temperature. But P, is normally very small vs. P, and experiments show large deviations from that law when higher pressures are used. The concentration of an extracted component is often lo5, and up to 10l2, times higher than if it were calculated from the vapor pressure of a dissolved compound.g (1)Diepen, G. A. M.; Scheffer, F. E. C. J. Am. Chem. SOC.1948,70,
Recent attempts try to relate the solubility directly to the pressure and temperature, based on fugacities: solubility parameters,1° and virial These equations usually do not describe the solubilities of different compounds in supercritical gases over a wide range of pressures and temperatures, and in many cases the estimation of the constants in these equations is very difficult or impossible. Additionally, the complexity of virial equations increases substantially with increased accuracy. In this work, we have related the solubilities directly to the density (concentration) of a gas, avoiding the complexity of the equations of state which all show significant differences from experimental results. Experimental Section We have determined the solubilities of different solids and liquids in dense gases by means of an apparatus described in Figure l. The solid or liquid compound (2-5 g) was placed on the bottom of high-pressuretubing A, and on the top of a magnetic stirrer (1-2 g), which moved in
40~.5-9. _ _ -_. _
(2) Tsekhanskaya, Yu. V.; Iomtev, M. B.; Mushkina, E. V. Zh. Fit. Khrm. 1984,38, 2166-71. (3)Smita, A. 2.Phys. Chem. 1905,52,587-601. (4)Ewald, A. H.Trans. Faraday SOC.1953,1401-5. 1927, 49, 65-78. (5)Bartlett, E.P. J. Am. Chem. SOC. (6)Saddington, A. W.;Krause, N. W. J . Am. Chem. SOC.1934 56, 353-61. (7) Gunst, C. A. J. Phys. Chem. 1953,57,578-83. ( 8 ) Stahl, E.; Schilz, W. Chem.-Zng.--Tech. 1978,50,535-7.
(9) Franck, E. U. 'Physical Chemistry"; Academic Press: New York, 1971;Vol. I. (10)Czubryt, J. J.;Myers, M.N.; Giddings, J. C. J. Phys. Chem. 1970, 74,4260-5. (11)Franck, E. U. Z . Phys. Chem. 1956,6,345-55. (12)Rowlinson, J. S.;Richardson, M. J. Adu. Chem. Phys. 1959,2, 85-118. (13)Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. "The Properties of Gases and Liquids"; McGraw-Hill: New York, 1977.
0 1982 American Chemical Society
7
Solids and Liquids in Supercritical Gases
The Journal of Physical Chemistry, Vol. 86, No. 15, 1982 3017
In K + In [A] + k In [B] = In [ABk] (2b) where [A] is the molar vapor concentration of a solute, [B] is the molar concentration of a gas, and [AB,] is the molar concentration of the solute in a gas. K is the equilibrium constant, which can be expressed as In K = AHwlv/RT+ qe,where AHwlvis the heat of solvation, and qs is a constant. The vapor concentration of the solute [A] can be approximated by the Clapeyron-Clausiusequation: In [A] = AH,,/RT + qv,where AHvapis the heat of vaporization of the solute, and qv is a constant. Usually [A]
