Growth Phenomena of Single Crystals of Naphthalene in Supercritical Carbon Dioxide Hirohisa Uchida,* Atsushi Manaka, Masakuni Matsuoka, and Hiroshi Takiyama Department of Chemical Engineering, Faculty of Technology, Tokyo University of Agriculture and Technology (TUAT), 24-16 Nakacho-2, Koganei, Tokyo 184-8588, Japan Received November 11, 2003;
CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 5 937-942
Revised Manuscript Received July 4, 2004
ABSTRACT: The growth behavior and growth rates of naphthalene single crystals in supercritical carbon dioxide were observed and measured at temperatures 307.7, 312.7, and 317.7 K and pressures 15, 17.5, and 20 MPa to highlight the behavior of crystal growth in the supercritical phase. The morphology of naphthalene crystals did not change during the steady growth in the supercritical phase. The crystal growth rates from the supercritical phase were almost independent of pressure and higher with increasing temperature or supersaturation and were approximately between 4 × 10-9 and 2.5 × 10-8 m s-1 as supersaturation varied from 0.018 to 0.073, values which were found to be intermediate between those from a liquid or vapor phase at the same supersaturation. The activation energy for crystal growth from the supercritical phase was determined as 70.9 kJ mol-1, which showed that the crystal growth mechanism in the supercritical phase is almost similar to that in the liquid or vapor phase and that the growth rates were governed by the surface integration step. Introduction Supercritical fluids have been thought to be a new type of attractive solvent and have been applied in various fields of industries such as in separations, reactions, and material processing because their solvent power is moderate, and their transport properties are favorable in mass transfer rates. In particular, several crystallization techniques using supercritical fluids such as rapid expansion of supercritical solutions (RESS),1-3 supercritical antisolvent recrystallization (SAS),4-6 and particles from gas saturated solutions (PGSS)7,8 processes have been proposed recently, which have garnered much attention and have been expected as effective and environmentally friendly separation or particle design methods.9-11 Knowledge of the crystal growth phenomena in supercritical fluids is of importance and is essential for the design and development of the process using supercritical crystallization techniques and establishing optimum operation conditions for the process. Moreover, crystal growth phenomena in supercritical fluids have not been elucidated sufficiently despite their importance and also are of much interest and are attractive since they may be more complex than those in liquid or vapor phases. Preliminary elucidation of the crystal growth phenomena of an organic compound in a supercritical fluid has been performed in the present work. Specifically, the crystal growth rates of naphthalene single crystals in supercritical carbon dioxide were measured under various temperatures, pressures, and supersaturation to investigate the behavior of the crystal growth specific to the supercritical phase growth. Carbon dioxide has been usually used as a supercritical solvent for many industrial applications because it is environmentally * To whom correspondence should be addressed. Current address: Department of Chemical Engineering, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan. Tel and Fax: +81-72-254-9301. E-mail: uchida@ chemeng.osakafu-u.ac.jp.
benign, nonhazardous, and inexpensive, and has a low critical temperature and a moderate critical pressure. Naphthalene was chosen as the model solute, although it has been important but not so special of a compound in chemical industries, because it has often been used for many studies related to supercritical fluids because of its relatively high solubility in supercritical carbon dioxide12 and the availability of sufficient data on the phase equilibria13-16 and transport properties.17,18 Moreover, hitherto the growth phenomena of naphthalene crystals grown from liquid,19-23 vapor,24,25 melt,26-30 and supercritical phases31,32 have been investigated by several researchers. For example, the crystal growth phenomena, especially the kinetic roughening, of naphthalene crystals growing from liquid solutions were studied, in which the linear growth rates of naphthalene single crystals in stagnant toluene or n-hexane solutions at various temperatures were reported.19-21 The growth rates at 312.2 K were reported to be approximately between 10-7 and 10-4 m s-1 in the supersaturation range from 0.01 to 1.0. The rates of solid condensation of naphthalene from vapors, which are not strictly the same as the growth rates of naphthalene single crystals, were reported.24,25 For instance, Matsuoka24 reported the rates of solid condensation on a cold surface of naphthalene from vapors in inert nitrogen gas. The solid condensation rates were found to be increased with supersaturation by a power of 2 and are governed by the surface integration step. Comparing the crystal growth from a vapor phase and that from a liquid phase, the crystal growth rates from a vapor phase at 309.7 K were approximately between 10-9 and 10-7 m s-1 as supersaturation varied from 1.0 to 10, which showed that the growth rates from a vapor phase are much slower than those from a liquid phase at the same conditions. The melt growth of naphthalene crystals were studied by van den Berg,30 and the growth rates of the face (110) of naphthalene crystals at 353.2 K were reported to be approximately between 10-6 and 10-5 m s-1 at the supersaturation from 0.0001 to 0.005
10.1021/cg034212u CCC: $27.50 © 2004 American Chemical Society Published on Web 07/28/2004
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and were correlated as a function of the supersaturation, σ, evaluated from supercooling as R(110) ) 5.5 × 10-2 σ1.6 (m s-1). Considering the above studies, it can be said that the crystal growth rates of naphthalene are higher in the order of those from melt, liquid, and vapor phases at the same experimental conditions. Recently, the growth phenomena, mechanism, and kinetics of naphthalene single crystals in supercritical carbon dioxide at 318.2 K and pressures from 7.7 to 9.1 MPa were studied by Tai and Cheng.31 It was reported that the growth rates of naphthalene single crystals were higher with increasing pressure at the same supersaturation and were approximately between 10-9 and 10-7 m s-1 as supersaturation varied from 0.01 to 1.0, and they concluded that, compared with the conventional crystallization processes such as those from liquid solutions and vapor phases, the crystal growth of naphthalene single crystals in supercritical fluids showed characteristics similar to liquid solution growth rather than vapor growth as far as the growth mechanism and kinetics were concerned. This would be a notable study to investigate the crystal growth phenomenon from a supercritical phase, but unfortunately the experiments were performed at the lower pressure regions near the critical pressure of carbon dioxide, although most techniques using supercritical carbon dioxide have been performed in the higher pressure regions above 10 MPa because of the excellent solvent characteristics such as high solubility in these regions. The crystal growth phenomena at the higher pressures are different from those at the lower pressures because of the difference in solvent characteristics. In the present work, we measured the growth rates of naphthalene single crystals from supercritical carbon dioxide solutions at pressures 15, 17.5, and 20 MPa and temperatures 307.7, 312.7, and 317.7 K. Then, the growth rates obtained in the present work were compared with those at the lower pressures reported by Tai and Cheng.31 Moreover, a comparison of growth rates of naphthalene crystals growing from supercritical, liquid, vapor, and melt phases have been performed and their differences of the growth phenomena and the growth mechanism have been discussed in detail. Experimental Section Materials. Reagent-grade naphthalene (supplied from Kanto Kagaku Co.; the purity is more than 98%) was used as a solute. After impurity components in the solute were extracted with supercritical carbon dioxide in the present apparatus, the remaining high-purity components were used for the measurement of crystal growth rates. High-purity carbon dioxide (more than 99.990%, supplied by Showa Tansan Co.) was used as received. Preparation of Seed Crystals. Seed crystals of naphthalene were prepared by slow evaporation at 293.2 K from ethanol-acetone 50/50 vol % solutions saturated with naphthalene. The seed crystals thus obtained were bounded by (001), (201 h ), and (110) crystallographic faces as reported by Wells,33 and the dimension of the seed crystals was about 5 mm as shown in Figure 1. Apparatus and Procedures. An experimental apparatus equipped with a crystal growth cell was newly constructed to investigate the crystal growth behaviors in supercritical fluids. This apparatus is basically a flow-type and consists of a section of preparing supercritical solutions saturated with solutes and that of growing the solute in the supersaturated supercritical solutions. The apparatus is shown schematically in Figure 2.
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Figure 1. Photographs of a naphthalene single crystal: (a) a seed crystal; (b) a crystal after the steady growth for 4 h.
Figure 2. Schematic diagram of experimental apparatus: (1) gas cylinder; (2) dryer; (3) filter; (4) cooling unit; (5) feed pump; (6) pressure indicator; (7) preheater; (8) stopper; (9) preequilibrium cell; (10) equilibrium cell; (11) thermostated water bath (temp ) T); (12) temperature indicator; (13) crystal growth cell; (14) temperature indicatior; (15) pressure indicator; (16) thermostated water bath (temp ) T*); (17) trap; (18) wet gas meter; (V1) back-pressure regulator; (V2-V7) stop valves; (V8) micrometering valve. From the gas cylinder (1), carbon dioxide was supplied and was liquefied through the cooling unit (4). The liquefied carbon dioxide was sent to the preheater (7) by the feed pump (5) (GL Sciences, Co., APS-5L). When the carbon dioxide passed through the preheater in the thermostated water bath (11) at an experimental temperature (temp ) T) which was controlled within ( 0.1 K, it became a supercritical fluid. We used the preequilibrium cell (9) and the equilibrium cell (10) (Taiatsu Techno Co., TVS-N2), which were made of SUS316, and an inner diameter, height, and volume of 30 mm, 150 mm, and 120 cm3, respectively. The preequilibrium cell was equipped to obtain sufficient equilibrium conditions. Solid solute was packed into the cells with glass beads to prevent channeling. The cells were immersed into the thermostated water bath.
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Table 1. Experimental Conditions and Crystal Growth Rates at the Constant Temperature 308.2 K and the Supercooling 0.5 K run no.
p (MPa)
T (K)
T* (K)
∆T (K)
y2
y/2
σ
G (m s-1)
1-1 1-2 2-1 2-2 3-1 3-2
15.1 15.1 17.6 17.5 20.0 20.0
308.2 308.2 308.2 308.2 308.2 308.2
307.7 307.7 307.7 307.7 307.7 307.7
0.5 0.5 0.5 0.5 0.5 0.5
1.504 × 10-2 1.504 × 10-2 1.618 × 10-2 1.615 × 10-2 1.686 × 10-2 1.686 × 10-2
1.476 × 10-2 1.476 × 10-2 1.584 × 10-2 1.581 × 10-2 1.648 × 10-2 1.648 × 10-2
0.0188 0.0188 0.0212 0.0213 0.0228 0.0228
4.22 × 10-9 4.09 × 10-9 4.25 × 10-9 4.81 × 10-9 5.91 × 10-9 5.49 × 10-9
Figure 3. Schematic drawing of the crystal growth cell: (1) crystal growth cell, (2) seed crystal, (3) sapphire observation windows, (4) stirrer, (5) CCD camera. Valve V3 was closed, and valve V4 was opened to admit supercritical carbon dioxide into the preequilibrium cell and the equilibrium cell. When supercritical carbon dioxide passed through the preequilibrium cell and the equilibrium cell, the supercritical carbon dioxide was in contact with the solid solutes in the cells under an equilibrium pressure. The equilibrium pressure was measured by the pressure transducer (6) (Setra Systems, Inc., Model 280E) with accuracy of ( 0.04 MPa. To observe the growth behavior and to measure the growth rates of a fixed crystal at a constant pressure and temperature, the crystal growth cell (13) (Taiatsu Techno Co.), as shown in Figure 3, was newly constructed. The cell was made of SUS316 and designed for pressures up to 30 MPa and for temperatures up to 373.2 K. The volume of the cell is 28 cm3, and the cell has two sapphire observation windows with a diameter of 20 mm. By opening valve V6, the supercritical carbon dioxide saturated with the solutes was admitted into the cell through a heated pipe at the equilibrium temperature. The fluid temperature in the pipe was measured and checked with the Pt-100 thermometer (12). The cell was immersed in the thermostated water bath (16) controlled within ( 0.1 K, the temperature (temp ) T*) of which was different from that (temp ) T) of the thermostated water bath (11). Supersaturation was controlled by using the difference in temperatures between T and T*. Temperature and pressure in the cell were measured with the Pt-100 thermometer (14) and the pressure transducer (15) (Setra Systems, Inc., Model 280E) with accuracy of (0.04 MPa, respectively. A single piece of naphthalene seed crystals mounted at the tip of a platinum wire (0.3 mm in diameter) was suspended and placed horizontally at a fixed position in the cell. The fixed seed crystal was allowed to be grown in a supersaturated supercritical solution of naphthalene. It was then washed by supercritical carbon dioxide undersaturated with naphthalene before each experiment to prevent initial breeding. A magnetic stirrer was employed in the cell, which gently mixed the solution during the growth measurements. The flow rate of carbon dioxide was adjusted to be about 3.3 cm3 s-1 by the micrometering valve V8 (Hoke Inc., 1666G4Y). The volume of carbon dioxide was measured by the wet gas meter (18) (Shinagawa Co., W-NK0.5A). The growth of the crystal was continuously observed with a CCD camera and recorded on a video recorder. The change in the crystal dimension was measured from the images on the monitor screen where the crystal was placed so that the base plane (001) face was parallel to the screen. The growth rates were measured parallel to the supercritical solution flow. The reliability of the part of preparing saturated supercritical solutions in the apparatus was preliminarily verified by
Figure 4. Solubility of naphthalene in supercritical carbon dioxide: (O) 308.2 K;12 (4) 318.2 K;12 (0) 328.2 K;12 (s) calculated results. measuring the solubility of naphthalene in supercritical carbon dioxide at 308.2 K and several pressures and then comparing these results with literature data reported by Tsekhanskaya et al.12 The results obtained were in good agreement with the literature data with an average absolute deviation of 8.9%. The measurements of crystal growth rates were performed at pressures of 15, 17.5, and 20 MPa, a constant temperature of 307.7 K and constant supercooling of 0.5 K to examine the pressure effects on the crystal growth phenomena. Moreover, the measurements were performed at the temperatures of 307.7, 312.7, and 317.7 K, the supercoolings of 0.5, 1.0, and 2.0 K, and constant pressure of 15 MPa to investigate the effects of temperature and supersaturation on the crystal growth phenomena. The experimental conditions are listed in Table 1. Here supersaturation as the driving force for crystal growth, σ, was thermodynamically defined by34,35
σ ) ∆µ/RT ) ln(γ2 y2/γ/2 y/2) ≈ ln(y2/y/2)
(1)
where the ratio of activity coefficients, γ/2 and γ2 of solutes at the equilibrium and the supersaturated states were approximated by unity. In the above equation, ∆µ is the difference of the chemical potential between solutes in an equilibrium state and solutes in the supersaturated state, R is the gas constant, T is the absolute temperature, y2 is the solubility of naphthalene in supercritical carbon dioxide in mole fraction, and the superscript * shows the equilibrium state. The solubility was obtained from the correlation using the equation of state proposed by Yu and Lu36 based on the data reported by Tsekhanskaya et al.12 as shown in Figure 4. The detailed description for calculating the solubility is provided in the appendix.
Results and Discussion Linear Growth Rates. In the present experiments, observations were made normal to the (001) face, and the growth rates was measured as shown in Figure 1. The linear growth rate was defined as follows:
G ) dL/dθ ) (L(θ2) - L(θ1))/(θ2 - θ1)
(2)
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Table 2. Experimental Conditions and Crystal Growth Rates at the Constant Pressure 15 MPa and the Supercoolings 0.5, 1.0, and 2.0 K run no.
p (MPa)
T (K)
T* (K)
∆T (K)
y2
y/2
σ
G (m s-1)
1-1 1-2 2-1 2-2 3-1 3-2
15.1 15.1 15.0 15.0 15.1 15.1
308.2 308.2 308.7 308.7 309.7 309.7
307.7 307.7 307.7 307.7 307.7 307.7
0.5 0.5 1.0 1.0 2.0 2.0
1.504 × 10-2 1.504 × 10-2 1.527 × 10-2 1.527 × 10-2 1.591 × 10-2 1.591 × 10-2
1.476 × 10-2 1.476 × 10-2 1.471 × 10-2 1.471 × 10-2 1.476 × 10-2 1.476 × 10-2
0.0188 0.0188 0.0374 0.0374 0.0750 0.0750
4.22 × 10-9 4.09 × 10-9 7.94 × 10-9 8.01 × 10-9 1.39 × 10-8 1.49 × 10-8
4-1 4-2 5-1 5-2 5-3 6-1 6-2
15.0 15.2 15.2 15.2 15.2 15.0 15.1
313.2 313.2 313.7 313.7 313.7 314.7 314.7
312.7 312.7 312.7 312.7 312.7 312.7 312.7
0.5 0.5 1.0 1.0 1.0 2.0 2.0
1.794 × 10-2 1.814 × 10-2 1.846 × 10-2 1.846 × 10-2 1.846 × 10-2 1.889 × 10-2 1.901 × 10-2
1.763 × 10-2 1.782 × 10-2 1.782 × 10-2 1.782 × 10-2 1.782 × 10-2 1.763 × 10-2 1.772 × 10-2
0.0174 0.0178 0.0353 0.0353 0.0353 0.0690 0.0703
6.29 × 10-9 6.56 × 10-9 9.55 × 10-9 9.54 × 10-9 1.02 × 10-8 2.53 × 10-8 2.05 × 10-8
7-1 7-2 8-1 8-2
15.2 15.0 15.1 15.1
318.2 318.2 318.7 318.7
317.7 317.7 317.7 317.7
0.5 0.5 1.0 1.0
2.155 × 10-2 2.123 × 10-2 2.175 × 10-2 2.175 × 10-2
2.119 × 10-2 2.089 × 10-2 2.104 × 10-2 2.104 × 10-2
0.0168 0.0161 0.0332 0.0332
9.77 × 10-9 9.78 × 10-9 1.33 × 10-8 1.56 × 10-8
Figure 5. Comparison of the crystal growth rates of naphthalene single crystals grown from supercritical, liquid, vapor, and melt phases: (O) from supercritical phase at 15.1 MPa and 307.7 K; (4) from supercritical phase at 15.1 MPa and 312.7 K; (0) from supercritical phase at 15.1 MPa and 317.7 K; (3) from supercritical phase at 17.5 MPa and 307.7 K; (]) from supercritical phase at 20.0 MPa and 307.7 K; (b) from supercritical phase at 7.7 MPa and 318.2 K;31 (2) from supercritical phase at 8.4 MPa and 318.2 K;31 (9) from supercritical phase at 9.1 MPa and 318.2 K;31 (g) from vapor phase at 309.7 K;24 (f) from vapor phase at 318.2 K;24 (1) from liquid phase at 298.2 K;19,21 ([) from liquid phase at 318.2 K;19,21 (×) from melt phase at 353.2 K;30 (s) calculated by eq 3 for the present results; (- - -) calculated by eq 3 for the literature data.
where θ denotes growth time (θ2 > θ1) and L(θ) is the crystal length along the (001) face at time θ. Figure 1 shows a seed crystal and the crystal after the steady growth for 4 h. From these figures, the morphology of the crystal growing in supercritical carbon dioxide was found to be the same as that of the seed crystal. The experimental crystal growth rates obtained are listed in Tables 1 and 2 and shown in Figure 5. Effects of Pressure on Crystal Growth Rates. The experimental crystal growth rates obtained were about 4 × 10-9-6 × 10-9 m s-1 at the pressures 15-20 MPa and the constant temperature 307.7 K and ∆T ) 0.5 K. The crystal growth rates slightly increased with pressure, and the effects of pressure on the growth rates were less than those at the lower pressures (7-9 MPa) reported by Tai and Cheng.31 This would be because at the lower pressure regions, especially in the vicinity of the critical pressure of carbon dioxide, the pressure
dependency of physical properties such as phase equilibria and transport properties, in particular, the pressure dependency of solubility in supercritical carbon dioxide, is much larger compared with that at the higher pressure regions. Effects of Temperature and Supersaturation on Crystal Growth Rates. The crystal growth rates obtained experimentally varied from 4 × 10-9 to 2.5 × 10-8 m s-1 at the temperatures 307.7, 312.7, and 317.7 K and the supersaturation from 0.018 to 0.073 and the constant pressure of 15 MPa. The crystal growth rates were higher with increasing temperature or supersaturation. The magnitude and the supersaturation dependency of the crystal growth rates were almost the same as those reported by Tai and Cheng31 as shown in Figure 5. Crystal growth rates are generally correlated as a function of supersaturation and temperature using a power law model of the following form:34,35
G ) Kσg
(3)
where K denotes the overall crystal growth rate coefficient. In the present supersaturation ranges, the experimental linear growth rates were approximately proportional to supersaturataion, that is, g ) 1 in eq 3. The overall crystal growth rate coefficients obtained are listed in Table 3. The temperature effects of both the diffusion and integration steps can be examined by calculating activation energies, E, with the Arrhenius equation:34,35
K ) K0 exp(-E/RT)
(4)
where K0 is a constant. The activation energy for the crystal growth of naphthalene single crystals from supercritical carbon dioxide solutions was determined as 70.9 kJ mol-1, and this suggests that the growth rates were governed by the surface integration step. Comparison of Crystal Growth Rates from Supercritical, Liquid, Vapor, and Melt Phases. Figure 5 shows a comparison among the crystal growth rates from supercritical, liquid, vapor, and melt phases, in which the growth rates from toluene liquid solutions reported by Elwenspoek,19,21 the condensation rates on a cold disk from a vapor in an inert nitrogen gas
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Table 3. Overall Crystal Growth Rate Coefficients for Crystal Growth of Naphthalene Single Crystals Grown from Supercritical, Liquid, Vapor, and Melt Phases crystal growth phase
p (MPa)
T (K)
g
K (m s-1)
ref
supercritical carbon dioxide solution
15.1 15.1 15.1 7.7 8.4 9.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
307.7 312.7 317.7 318.2 318.2 318.2 283.2 298.2 318.2 327.2 280.7 286.7 299.2 303.2 309.7 318.2 353.2
1 1 1 1 1 1 1.7 1.7 1.7 1.7 2 2 2 2 2 2 1.6
2.0 × 10-7 3.2 × 10-7 4.7 × 10-7 6.5 × 10-8 1.2 × 10-7 1.9 × 10-7 1.1 × 10-4 8.8 × 10-4 1.9 × 10-3 2.3 × 10-2 4.4 × 10-11 8.1 × 10-11 3.1 × 10-10 4.3 × 10-10 1.8 × 10-9 4.1 × 10-9 5.5 × 10-2
this work this work this work a a a b b b b c c c c c c d
liquid toluene solution vapor
melt
a Determined in this work from the crystal growth rates reported by Tai and Cheng.31 b Determined in this work from the crystal growth rates reported by Elwenspoek.19,21 c Determined in this work from the solid condensation rates reported by Matsuoka.24 d Reported by van den Berg.30
Table 4. Activation Energies for Crystal Growth of Naphthalene Single Crystals Grown from Supercritical, Liquid, and Vapor Phases crystal growth phase
E (kJ mol-1)
supercritical carbon dioxide solution liquid toluene solution vapor
70.9 88.7 90.9
reported by Matsuoka,24 and the growth rates from the melt reported by van den Berg30 are shown together. From this figure, the crystal growth rates in the supercritical phase were found to be intermediate between those in liquid and vapor phases. The crystal growth rates from supercritical, liquid, vapor, and melt phases can also be correlated by eq 3. The overall crystal growth rate coefficients, K, and the exponents, g, determined in the present work or reported in the literature are shown in Table 3, respectively. Then the activation energies for crystal growth from liquid and vapor phases were determined using the eq 4 and are compared in Table 4. The values of g determined for the supercritical, liquid, vapor, and melt growth were different from each other, which were between 1 and 2. The activation energies determined for the supercritical, liquid, and vapor growth were found to be from 70 to 91 kJ mol-1. Considering these results, the crystal growth mechanism in a supercritical phase is not so special or strange and is almost similar to that in liquid or vapor phases, and the surface integration step is the rate-controlling step, although the activation energy is slightly lower than that of liquid or vapor growth. Conclusions The growth rates of naphthalene single crystals in supercritical carbon dioxide were measured under various temperatures, pressures, and supersaturations to investigate their effects on the crystal growth phenomena. The crystal growth rates obtained were almost independent of pressure. This can be explained by the
pressure dependency of physical properties such as phase equilibria and transport properties. The crystal growth rates from a supercritical phase were found to be intermediate between those from a liquid or vapor phase. On the other hand, the activation energies for the crystal growth from supercritical, liquid, and vapor phases showed that the crystal growth mechanism in the supercritical phase is almost similar to that in the liquid or vapor phase and the surface integration step is the rate-controlling step. Considering the supercritical crystallization techniques such as RESS, GAS, and PGSS, the crystal growth phenomena are thought to be different from the present situation, in which the crystal growth rates of single crystals from a supercritical phase have been measured, because the crystal growth for the supercritical crystallization are performed under complex conditions which are suspension conditions with changing temperature and pressure. This study, however, is the beginning of the elucidation of crystal growth of organic compounds under supercritical conditions. Acknowledgment. The authors are grateful to Taiatsu Techno Co. for a gift of the equilibrium cells. This study was carried out under the 21st Century COE program of “Future Nano-Materials” in Tokyo University of Agriculture and Technology. Appendix: Calculation of Solubility of Naphthalene in Supercritical Carbon Dioxide The solubility of supercritical fluids in a solid phase is usually almost zero, the pressure effect on the solidstate molar volume is negligible, and the fugacity coefficient of pure solid components under their saturation pressure (very low) at temperature T can be approximated by unity. On the basis of these assumptions, the solubility, y2 of solid component 2 in a supercritical fluid is given by the following equation:37
y2 )
[
]
sat psat voS 1 2 2 (p - p2 ) exp p φG RT 2
(A1)
where p is the total pressure, psat is the saturated 2 vapor pressure of solid component 2, voS 2 is the solidstate molar volume of solid component 2, superscript S means the solid state and φG 2 is the fugacity coefficient of solid component 2 in the supercritical fluid, R is the gas constant, and T is the temperature. The fugacity coefficient of the solute in a pressurized gas phase φG 2 was evaluated by adopting the equation of state proposed by Yu and Lu:36
p)
a RT v - b v(v + c) + b(3v - c)
(A2)
where a, b, and c are pure component parameters which can be calculated with the critical properties and the Pitzer’s acentric factor. To apply eq A2 to a binary system, the conventional mixing rules are used for the parameters,
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Table 5. The Properties of Carbon Dioxide and Naphthalene compound
TC (K)
pC (MPa)
ω
vS × 103 (m3 mol-1)
carbon dioxide naphthalene
304.1a 748.4a
7.38a 4.05a
0.239a 0.302a
0.1119b
a
b
Ref 39. Ref 40.
a, b, and c as follows:
a)
∑i ∑j yiyjaij
aij ) (1 - kij)xaiaj
b)
∑i ∑j
bij ) (1 - lij)
c)
∑i ∑j
yiyjbij
yiyjcij
bi + bj 2
c i + cj
cij ) (1 - lij)
2
(A3)
(A4)
(A5)
where kij and lij denote the binary interaction parameters between unlike molecules i and j. When eqs A1A5 are utilized, the fugacity coefficient φG 2 will be thermodynamically derived. The saturated vapor pressures of naphthalene were calculated by the equation proposed by Fowler et al.,38 and the other physical properties used are listed in Table 5. The binary interaction parameters k12 and l12 for carbon dioxide (1)-naphthalene (2) system were determined to give a good representation of the solubilities of naphthalene in supercritical carbon dioxide at 308.2, 318.2, and 328.2 K and were approximated by simple linear functions of absolute temperature as follows:
k12 ) 0.4268 - 1.2 × 10-3T
(A6)
l12 ) 0.2450 - 1.1 × 10-3T
(A7)
The present model gave good correlation results for the solubility with a maximum average absolute relative deviation (AARD) of 2.6%. References (1) Matson, D. W.; Petersen, R. C.; Smith, R. D. Adv. Ceram. Mater. 1986, 1, 242-246. (2) Matson, D. W.; Petersen, R. C.; Smith, R. D. Mater. Lett. 1986, 4, 429-432. (3) Petersen, R. C.; Matson, D. W.; Smith, R. D. J. Am. Chem. Soc. 1986, 108, 2100-2102. (4) Bleich, J.; Mu¨ller, B. W.; Waβmus, W. Int. J. Pharm. 1993, 97, 111-117. (5) Dixon, D. J.; Johnston, K. P. J. Appl. Polym. Sci. 1993, 50, 1929-1942.
(6) Dixon, D. J.; Johnston, K. P.; Bodmeier, R. A. AIChE J. 1993, 39, 127-139. (7) Weidner, E.; Knez, Z.; Novak, Z. Proceedings of the 3rd International Symposium on Supercritical Fluids, Strasbourg, France, 1994; pp 229-234. (8) Weidner, E.; Knez, Z.; Novak, Z. WO Patent 95/21688, 1995. (9) Bungert, B.; Sadowski, G.; Arlt, W. Ind. Eng. Chem. Res. 1998, 37, 3208-3220. (10) Jung, J.; Perrut, M. J. Supercrit. Fluids 2001, 20, 179-219. (11) Palakodaty, S.; York, P. Pharm. Res. 1999, 16, 976-985. (12) Tsekhanskaya, Yu. V.; Iomtev, M. B.; Mushkina, E. V. Russ. J. Phys. Chem. 1964, 38, 1173-1176. (13) Bartle, K. D.; Clifford, A. A.; Jafar, S. A.; Shilstone, G. F. J. Phys. Chem. Ref. Data 1991, 20, 713-756. (14) Christov, M.; Dohrn, R. Fluid Phase Equilib. 2002, 202, 153-218. (15) Dohrn, R.; Brunner, G. Fluid Phase Equilib. 1995, 106, 213282. (16) Lucien, F. P.; Foster, N. R. J. Supercrit. Fluids 2000, 17, 111-134. (17) Liong, K. K.; Wells, P. A.; Foster, N. R. J. Supercrit. Fluids 1991, 4, 91-108. (18) Sua´rez, J. J.; Medina, I.; Bueno, J. L. Fluid Phase Equilib. 1998, 153, 167-212. (19) Elwenspoek, M. Appl. Phys. A 1986, A41, 123-125. (20) Elwenspoek, M. Mol. Phys. 1988, 64, 229-245. (21) Elwenspoek, M.; van der Eerden, J. P. J. Phys. A: Math. Gen. 1987, 20, 669-678. (22) Elwenspoek, M.; Bennema, P.; van der Eerden, J. P. J. Cryst. Growth 1987, 83, 297-305. (23) Jetten, L. A. M. J.; Human, H. J.; Bennema, P.; van der Eerden, J. P. J. Cryst. Growth 1984, 68, 503-516. (24) Matsuoka, M. J. Chem. Eng. Jpn. 1982, 15, 194-199. (25) Volmer, M.; Schultze, W. Z. Phys. Chem. 1931, 156, 1-22. (26) Datt, S. C.; Verma, J. K. D. Indian J. Pure Appl. Phys. 1968, 6, 96-97. (27) Gordon, R. B. Acta Metall. 1965, 13, 199-203. (28) Robinson, P. M.; Scott, H. G. Acta Metall. 1967, 15, 12301231. (29) Schreiner, A.; Ko¨nig, A. Chem. Eng. Technol. 2002, 25, 181187. (30) van den Berg, E. P. G. Ph.D. Thesis, The University of Nijmegen, Nijmegen, The Netherlands, 1997. (31) Tai, C. Y.; Cheng, C.-S. AIChE J. 1995, 41, 2227-2236. (32) Tai, C. Y.; Cheng, C.-S. Trans. 1. Chem. E. 1997, 75, 228232. (33) Wells, A. F. Philos. Mag. 1946, 37, 184-199. (34) Mullin, J. W. Crystallization, 4th ed.; Butterworth Heinemann: Oxford, 2001. (35) Davey, R.; Garside, J. From Molecules to Crystallizers-An Introduction to Crystallization, Oxford Science: Oxford, 2000. (36) Yu, J.-M.; Lu, B. C.-Y. Fluid Phase Equilib. 1987, 34, 1-19. (37) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall PTR: New Jersey, 1999. (38) Fowler, L.; Trump, W. N.; Vogler, C. E. J. Chem. Eng. Data 1968, 13, 209-210. (39) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (40) Perry, R. H.; Green, D. W.; Maloney, J. O., Eds. Perry’s Chemical Engineers’ Handbook, 6th ed.; McGraw-Hill: New York, 1984.
CG034212U
