2372
I n d . Eng. C h e m . Res. 1987,26, 2372-2377
addition of herbicides and carbon black which provides an economic advantage to the user. On the basis of the above-mentioned results and discussion, the mulch films described here contain an adequate balance of the important properties needed for an agricultural mulch film. These properties include (1)good mechanical properties, (2) the ability to retard weed growth without the incorporation of toxic chemicals such as herbicides, (3) degradability, (4)the incorporation of multinutrirional materials that can be released slowly, (5) harmless to the environments, and (6) clarity. Conclusions Various types of multinutritional, degradable, and slow-release clear agricultural mulch films containing poly(vlny1 alcohol), urea-formaldehyde, Pz05,K20, and other additives were prepared and coated with different water-resistant coating materials. The mechanical properties and the dissolution rates of these films were studied. The mechanical properties of these films are affected by the type of materials involved and the percentage of moisture present. The results also indicate that the presence of starch, ethylene glycol, and urea improves tensile strength, elongation at break, and dissolution rate of these films. The dissolution rate of the mulch film is affected by the type of coating material and its thickness, types of additives present, the temperature, and the type of water used. This information can be used to design
suitable films for any crop duration. It was also found that the prepared mulch films can prevent weed growth despite their clarity. Registry NO.PVA, 9002-89-5; U-F, 9011-05-6; TEP, 78-40-0; PVAC, 9003-20-7; EVA, 24937-78-8; EEA, 9010-86-0; VCC, 9003-22-9; KNO,, 7757-79-1; KZHPO,, 7758-11-4; starch, 9005-25-8; urea, 57-13-6; ethylene glycol, 107-21-1.
Literature Cited Agency of Industrial Sciences and Technology, Japan Kokai Tokyo Koho 81 22 324, 1981. Bryzgalov, V. A.; Sakova, T. M.; Zakharova, E. I. Plast. Mussy 1984, 2, 51-54. Clendinning, R. A. U S . Patent 3 929 937, 1975. Clendinning, R. A,; Potts, J. E.; Niegish, W. D. US. Patent 3 931068, 1976. Ingram, A. R. U S . Patent 3833401, 1974. Kuraray Co. Ltd. Japan Kokai Tokyo Koho JP 92 582, 1982. Newland, G. C.; Graecar, G . R.; Tamblyn, J. W. U S . Patent 3 454 510, 1969. Nissan Chemical Industries Ltd. Tokyo Koho J p 60 18 369, 1985. Otey, F. H.; Mark, A. M. U.S.Patent 3949145, 1976. Otey, F. H.; Westhoff, R. P.; Russel, C. R. Ind. Eng. Chem. Prod. Res. Deu. 1977, 16, 305-308. Plastopil, H. Israeli 1168 641, 1984. Reich, M.; Hudgin, D. E. U.S.Patent 3984940, 1976. Schwaar, R. H. ’Thermosetting Resins”, Report 93, 1976, p 132; Stanford Research Institute.
Received for review January 13, 1987 Revised manuscript received July 10, 1987 Accepted July 27, 1987
Separation of Isomers Using Retrograde Crystallization from Supercritical Fluids Keith P. Johnston,* S t e p h e n E.B a r r y , Nolan K. Read, and T y l e r R. Holcomb Department of Chemical Engineering, University of Texas, Austin, Texas 78712
Solubilities have been measured for a mixture of 2,3- and 2,6-dimethylnaphthalene in supercritical fluid carbon dioxide to identify retrograde regions, which have an inverse solubility versus temperature relationship. A retrograde crystallization process has been designed and tested for the separation of the two isomers at supercritical conditions. A thermodynamic framework has been developed which may be used to locate retrograde regions in order to evaluate the feasibility of retrograde crystallization processes. The complex effect of temperature on solubility at constant pressure has been expressed in terms of two approximately constant derivatives and the volume expansivity of the pure solvent. Supercritical fluids have several desirable properties that make them attractive for certain separation processes; e.g., the product is not contaminated with residual solvent (Paulaitis et al., 1983; Johnson, 1984; McHugh and Krukonis, 1986). A retrograde solubility region may be found near the critical pressure of the solvent where small increases in temperature cause a large decrease in the density. Chimowitz and Pennisi (1986) described recently a novel retrograde deposition process, which is a crystallization process in which the slopes of the solubility versus temperature are opposite for two solids. A crossover pressure was defined as the point where the slope of the solubility versus temperature curve changes sign. For two solids which have different crossover pressures, there exists a “crossover region ’ between the crossover pressures where an increase in the temperature precipitates only the solid with the inverse solubility versus temperature behavior. Therefore, this process has the potential to achieve infinite 088S-588~/87/2626-2372$01.50/0
selectivity in a single stage for the separation of a binary mixture. This phenomena will be explained in greater detail below. Chimowitz and Pennisi (1986) found that the process is quite successful for the separation of benzoic acid from a mixture of benzoic acid and 1,lO-decanediol, perhaps since the crossover region is large for this system. Supercritical fluid solvents have an additional degree of freedom compared with liquids, in that the solubility behavior is strongly pressure dependent as well as temperature dependent. For certain binary mixtures, it is conceivable that a pressure region may be available to perform a retrograde separation even if both components have the same solubility versus temperature slopes in liquid solvents. The objective is to achieve a fundamental understanding of the range of the crossover region for two solids, e.g., isomers, and to design and test an actual retrograde crystallization process for a system with a small crossover 0 1987 American Chemical
Society
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2373 micrometering _equilibrated valve
solution
Figure 1. Variable-volume crystallizer and sampling valve.
region. The location of the crossover pressure is described thermodynamically to provide insight for evaluating potential retrograde crystallization processes.
Experimental Section The apparatus and procedure used to obtain the solubility data have been described previously (Dobbs et al., 1986). Two saturators in series were packed with a 50-50 by weight solid mixture of 2,3-dimethylnaphthalene (DMN) and 2,6-DMN. The pressure and temperature variations were on the order of f0.4 bar and f0.2 "C, respectively. A Hewlett-Packard 5890 gas chromatograph equipped with a flame ionization detector and a 10-m X 0.53-mm poly(dimethylsi1oxane) bonded phase capillary column was used for analysis. The apparatus was modified for the retrograde crystallization experiments to include a variable volume solute collection loop or crystallizer as shown in Figure 1. The outside and inside diameters of the stainless steel crystallizer were 0.635 cm and 0.3175 cm, respectively. During crystallization, the volume was at the maximum, i.e., 1.5 cm3, in order to avoid pressure drops due to the occupied volume of the crystals. At the end of the run, the volume was reduced to 0.24 cm3 to limit the amount of precipitation of the undesired solute which contaminates the product during depressurization. It was found that the pressure drop in the crystallizer was negligible since the flow rate did not change when the valve was switched to the bypass position at the end of the run. A glass wool filter was inserted at the downstream end of the crystallizer to prevent entrainment of the solid. The temperatures of the saturator and the crystallizer were 35 and 50 "C, respectively. At the end of some of the experiments, pure carbon dioxide was used to purge part of the supercritical fluid phase in order to minimize contamination which occurs during depressurization. The amount of the purge stream was limited to avoid significant redissolution of the deposited crystals. Solubility Isotherms for the 2,3-DMN-2,6-DMN-C02 Ternary System The solubility versus pressure isotherms for the 2,6DMN-2,3-DMN-C02 ternary system are shown in Figure 2. A simple argument has been used often to explain qualitatively the effect of temperature on the solubility. At high pressures where the fluid is relatively incompressible, the solubility increases with temperature as does the vapor pressure. The effect is the same at very low pressures close to ideal gas conditions (not shown in the figure, see Prausnitz et al. (1986), p 178). In the highly compressible region at intermediate pressures, a small increase in temperature causes a large decrease in density
ioo
110
120
130
140
150
PRESSURE (BAR)
Figure 2. Solubility versus pressure isotherms for the 2,3-DMN2,6-DMN-carbon dioxide system: (+) 2,6-DMN a t 35 " C , (A)2,3DMN at 35 "C, ( X ) 2,6-DMN at 50 "C, (W) 2,3-DMN at 50 O C .
and thus a decrease in solubility. A more quantitative description of the temperature effect on solubility will be presented below in terms of the partial molar enthalpy of the solute. Kurnik and Reid (1982) measured the solubility of each isomer in carbon dioxide, along with the solubilities for a mixture of the two solids, over a wide pressure range. The present study supplements these data with a large number of points in the crossover region. In most cases, the data agree within several percent. In the ternary system, the solubility of each solid is increased due to the presence of the other solid, since it is more polarizable than COP. An additional theoretical description of this effect has been published (Dobbs and Johnston, 1987). The crossover pressure where the isotherms intersect is 119 f 2 bar for 2,6-DMN, while that of 2,3-DMN is 125 f 2 bar as shown in Figure 2. The uncertainty in the crossover pressure is due primarily to the uncertainty in the solubilities which is due primarily to the chromatographic analysis. Between these pressures, an increase in the temperature of a saturated solution containing both solutes from 35 to 50 "C raises the solubility of 2,6-DMN and lowers that of 2,3-DMN. As a result, this increase in temperature should precipitate pure 2,3-DMN. A retrograde crystallization process would be performed in a region between the two crossover pressures, the crossover region. Chimowitz and Pennisi (1986) interpolated the solubility data of Kurnik and Reid (1982) to obtain crossover pressures of 107 bar for 2,6-DMN and 126 bar for 2,3-DMN for a temperature range of 35-45 "C. The more detailed solubility measurements of the present study indicate that the range of the crossover region is only about 6 bar instead of 19 bar. Although the high temperature is slightly different for the two studies, it would not be expected to cause such a large difference in the range of the crossover region based on a large amount of solubility data in the literature (Johnston et al., 1982; Schmitt, 1984). A large number of solubility measurements are required to locate the retrograde region with sufficient accuracy, since it is influenced
2374 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 Table I. Results for the Retrograde Crystallization Process actual results 2,3-DMN, 2,6-DMN, pressure, bar COZ?g mg/g coz mg/g coz 16.5 2.13 0.63 115 llSnb 15 1.41 0.62 0.141 120 36.9 0.52 70.9 0.85 0.231 120 121c 47.9 0.70 0.188 0.055 124 54.8 0.11 Denotes run without plunger.
12
14
ratio 2,3/2,6 3.4 2.3 3.7 3.7 3.7 2.0
* 1 residence volume (0.76 cm3) pure C 0 2 purge.
16
18
DENSITY (MOUL)
Figure 3. Solubility versus density isotherms for the 2,3-DMN2,6-DMN-carbon dioxide system: (0) 2,6-DMN a t 35 "C, ( 0 ) 2,3DMN at 35 "C, (m) 2,6-DMN a t 50 OC, (+) 2,3-DMN a t 50 "C.
by the difference in a derivative property, Le., the slope of solubility versus preasure, as is evident in Figure 2. The crossover pressure for a solute in carbon dioxide changes with the addition of a second solute, so that ternary solubility data will be required to locate the crossover region in systems with narrow crossover regions. For a given temperature, the solubility versus pressure curves of the two isomers have a similar shape. For each solid, the 50 "C isotherm has a significantly greater slope than the 35 "C isotherm since the fluid is more compressible at 50 "C for this pressure range. Another reason for the difference in slopes can be determined by an examination of the solubility isotherms versus the solvent density (see Figure 3). The solvent density is within less than 1% of the density of the solution since the solubilities are low (Eckert et al., 1986). The isotherms do not intersect since the effect of pressure on density has been removed. The slopes are greater for the 50 "C isotherms than the 35 "C isotherms. This may be attributed to the fact that the density range is lower for the 50 "C isotherms so that the effects of the repulsive forces are less significant.
Results for the Retrograde Crystallization Process Table I shows the results of the retrograde crystallization experiments for a series of pressures. The best results were obtained for the runs at 120 and 121 bar in which 79% pure 2,3-DMN was recovered from a 50% mixture by
expected results 2,3-DMN, 2,6-DMN, mg/g mg/g 3.45 1.33 2.20 0.34 1.30 0.048 1.30 0.0025 0.85 0.037 0.74 0.033
1 residence volume (0.24 cm3) pure C 0 2 purge.
weight, which corresponds to an increase in the mass ratio from 1/1to 3.7/1. Theoretically, it should be possible to recover absolutely pure 2,3-DMN, although, in actuality, 2,6-DMN contaminates the product during depressurization. The expected results were determined by using the equilibrium concentration at each temperature, which was obtained from Figure 2. The amount of each solid that precipitates upon depressurization was calculated based on the volume of the crystallizer loop at the time of depressurization. The data indicate that it is difficult to obtain a high yield and purity when the retrograde region is narrow. The yield was relatively high at 115 and 118 bar, which is well below the crossover pressure of 2,3-DMN (125 bar). The purity was relatively low since these pressures are also in the retrograde region for 2,6-DMN, i.e., below the crossover pressure. At the high-pressure end of the crossover region at 124 bar, only a small amount of 2,3-DMN was deposited. The best results were obtained 1-2 bar above the crossover pressure of 2,6-DMN, which is 119 bar. In most cases, the purities of 2,3-DMN were limited more by an unexpectedly large amount of 2,6-DMN than by the yield of 2,3-DMN. This indicates the possibility that the width of the retrograde region, which is defined by crossover pressures of 119 f 2 and 125 f 2 bar, may be less than 6 bar, perhaps as little as 2 bar.
Thermodynamic Analysis In order to evaluate potential retrograde crystallization processes, it would be useful to have a way to gauge a priori the range of a crossover region for two solids as a function of their properties. The crossover pressure may be related thermodynamically to the enthalpy of sublimation and the partial molar enthalpy of the solute in the supercritical fluid phase. The starting point is the criterion for equilibrium d In f; = d In f;
(1)
A t constant pressure, the total derivative may be written for each phase as p d In f i = -(hi- h $ ) / R T 2 d T + (8 In f i / d x i ) ~ dxi
(2)
The second term is zero for the solid phase if it is pure, which is the case for the systems of interest. Substitution of eq 2 into eq 1 for each phase gives ( d x z / d T ) p , , = -(ha -
h)/tRT2 (8 In f 2 / a x 2 ) T p 1 (3)
where component 2 is the solute and u denotes saturation conditions. The temperature effect on the solubility may be explained quantitatively by using eq 3. According to the criteria of stability, (8 In f 2 / d x 2 ) T , p is always positive. Equation 3 indicates that the slope of the solubility versus temperature changes sign at a crossover pressure where
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2375
h, = h;. To locate the crossover pressure, it is convenient to relate the partial molar enthalpies to the ideal gas state by
hzS- 62 = (hZs- big) - (h2 - hip)
(4)
where the first term is by definition the configurational enthalpy of the solid and the second term is the partial molar configurational enthalpy of the solute in the fluid phase. The configurational enthalpy of the solid is essentially the same as the negative of the enthalpy of sublimation since the vapor phase is ideal at the triple point, and hzsis relatively insensitive with respect to pressure. As a result, the crossover pressure is located at the point where the partial molar configurational enthalpy equals the negative of the enthalpy of sublimation, i.e.,
h2 - h2k = -Ah 2eub
(5)
I t has been shown that the partial molar enthalpy of a solute is related to the partial molar volume at the limit of the critical point of the pure solvent by (Chang and Levelt-Sengers, 1986)
-600 0
100
200
PRESSSURE (BAR)
where u denotes the coexistence curve. The partial molar volume may be extremely pronounced in the critical region; e.g., it is on the order of -10000 cm3/mol for naphthalene in supercritical carbon dioxide at 35 OC and 79.7 bar (Eckert et al., 1986). According to eq 6, the behavior of the partial molar enthalpy is closely related to the partial molar volume and should also be pronounced in the critical region. The pronounced values for D2 in the highly compressible near-critical region may be understood by using the thermodynamic relationship Di =
U ~ nT (aP/ani)T,V,n,
(7)
At constant volume, the addition of a small amount of a highly polarizable solute to a supercritical fluid decreases the pressure due to the attractive forces. In the highly compressible supercritical region, an extremely large volume contraction is required to return to the original pressure. As a result, the partial molar volume of a solute at infinite dilution becomes negative infinity as the compressibility of the solvent diverges at the critical point. The minimum in the partial molar volume occurs at the same pressure as the maximum in the isothermal compressibility, a result that was described theoretically (Kim et al., 1985). Partial molar configurational enthalpies were obtained by using the Peng-Robinson equation of state since experimental values are unavailable. To simplify the analysis, infinite dilution was assumed since the actual solubilities were on the order of At infinite dilution, the ternary system may be described by two binary ones; i.e., solute-solute interactions are insignificant. The combining rules were
Figure 4. Calculated partial molar configurational enthalpy for 2,3-DMN in carbon dioxide a t 35 "C by using the Peng-Robinson equation of state (horizontal line is -AhZBUb). Table 11. Partial Molar Configurational Enthalpy of 2,3-Dimethylnaphthalene in Supercritical C02 at 35 "C Calculated by Using the Peng-Robinson Eauation of State h z - hie, hz - big, P, bar kJ/mol P. bar kJ/mol 109 -104.0 119 -93.21 111 -101.4 121 -91.59 113 -99.04 123 -90.10 115 -96.91 125 -88.72 117 -94.97 127 -87.44
the configurational enthalpy with respect to composition with the result
h2 - hip = P dV/an2 - R T + T aa/aT - a( z - 0.414B)( 2(2lI2)b z + 2.44B
.[
(Z
- 0.414B) X
+ 2.44 a(nB)/an, - 0.414
(z
- 0.414B),)
([
+ In
d(nB)/an,
(
+
z 2.44B z - 0.414B
2(2ll2)b( T n dTdn,
)
ndn,1
and
Quadratic mixing rules were used for the attractive parameter, a, and for the repulsive parameter, b. Kwak and Mansoori (1986) demonstrated that the quadratic mixing rule for b is superior to the linear one. The partial molar configurational enthalpy is obtained by differentiation of
The calculated partial molar configurational enthalpies are shown for 2,3-DMN in carbon dioxide in Figures 4 and 5. The values are shown in Table I1 near the upper crossover pressure. The binary interaction parameter, k12, was regressed from one experimental point, the crossover pressure at 125 bar. In the ideal gas limit, the partial molar
2376 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 -1
-2
>
4 -3
100
1
-4
3.0
3.1
3.3
3.2
3.4
3.5
36
i l f r (lOOO/K)
-120'
0
100
200
PRESSURE (BAR)
Figure 5. Calculated partial molar configurational enthalpy for 2,3-DMN in carbon dioxide at 50 "C by using the Peng-Robinson equation of state (horizontal line is -Ahzaub).
configurational enthalpy is zero. At higher pressures, its behavior resembles that of the partial molar volume. As a highly polarizable solute molecule is added to the solvent at constant pressure, the configurational enthalpy decreases due to the attractive forces. The minimum occurs at the maximum in the isothermal compressibility, which was also the case for the partial molar volume (Kim et al., 1985). This would be expected according to eq 6. As the pressure increases, the isothermal compressibility and likewise the partial molar Configurational enthalpy become less pronounced. The partial molar configurational enthalpy of 2,3-DMN is shown at 323 K in Figure 5. The curve is less sharply peaked at 323 K compared with 308 K, which is consistent with the behavior of the isothermal compressibility and the partial molar volume. As the temperature increases, the minimum in the partial molar configurational enthalpy shifts to higher pressures, as does the maximum in the isothermal compressibility according to the relationship that describes the critical isochore
( P - P c ) / P c= constant(T - T c ) / T c This relationship also defines the minimum in the partial molar volume of the solute at infinite dilution (Kim et al., 1985). The enthalpy of sublimation was obtained for each isomer using vapor pressure data available from the literature (Osborn and Douslin, 1975). At 35 "C, the enthalpies of sublimation are 88.16 and 92.22 kJ/mol for 2,3and 2,6-DMN, respectively. It is larger for the 2,6 isomer since it is more symmetric and thus packs more efficiently in the solid phase. As shown in Figure 4, there are two crossover pressures where the partial molar configurational enthalpy equals the negative of the enthalpy of sublimation. This work focuses only on the upper crossover pressure. The difference in the upper crossover pressures for the two isomers is a key property that governs the performance of a retrograde separation process. It may be due to differences in the heats of sublimation, the partial molar configurational enthalpies, or both. The equation of state is not accurate enough to evaluate the difference in the
Figure 6. Logarithm of solubility verms 1/T at constant density for naphthalene in ethylene at 10 g-mol/L (data from Diepen and Scheffer (1953)).
partial molar configurational enthalpies for the two isomers. It is not expected that they should differ significantly since they are each nonpolar with similar sizes and polarizabilities and therefore should interact similarly with
coz.
In order to evaluate the effect of the difference in the heats of sublimation of the two isomers, suppose that the difference in the partial molar configurational enthalpies is insignificant. The crossover pressure for the 2,3 isomer is 125 bar. Since the heat of sublimation of the 2,6 isomer is 92.22 kJ/mol at 35 "C, the crossover pressure would be 120 bar according to the partial molar configurational enthalpy values shown in Table 11. This is consistent with the experimental crossover pressure of 119 bar. This suggests, although it does not prove, that the difference in the heats of sublimation is primarily responsible for the difference in the crossover pressures for this system. An alternative explanation of the temperature effect on solubility may be made by using the thermodynamic relationship
(
=
-)p
(
-)p
+
(
%?)T
(&),
(11)
Although (a In ~ ~ / a ( l / Tis) a) ~strong function of pressure and temperature in the critical region (see Figure 4 and eq 3), the same derivative at constant density is well-behaved as shown in Figure 6 for naphthalene in ethylene at 10 g-mol/L. This derivative is also linear for densities of 5 and 14 g-mol/L, except near the upper critical end point. The partial molar enthalpy is defined as a function of the slope at constant pressure, not at constant density. At concentrations which are sufficiently low to fall in the Henry's law region, eq 3 may be simplified with the result
(a In x2/aT)p,u=
- h,)/RT2
(12)
An alternative energy may be defined by using this relationship with a modification such that the slope is taken at constant density. This energy is 60 kJ/mol for naphthalene in ethylene at 10 g-mol/L. The derivative a In x2/dp is approximately constant and positive for solids in supercritical fluids as shown by several
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2377 authors (Johnston and Eckert, 1981; Schmitt, 1984), at least at reduced densities from 0.5 to 2. The expression in eq 11 is useful, as it describes a complicated function, (a In xz/d(l/T))p, in terms of two approximately constant derivatives and a property of the pure solvent, dp/d(l/T), which is closely related to the volume expansivity, -(l/p) dp/dT. This provides a convenient method to calculate the partial molar enthalpy. The complicated behavior of hz in the critical region arises directly from the large value of the volume expansivity of the solvent in this region. The crossover pressure is located at the point where the two terms in eq 11cancel out each other. The derivative (a In xZ/d(l/T)), is negative for the conditions of interest. At reduced densities up to at least 2, both of the derivatives in the second term in eq 11are positive. At a given temperature, the volume expansivity is a much stronger function of pressure than are the other two derivatives on the right-hand side. For this reason, it would be expected that crossover pressures for systems of the type in this study would be located in compressible regions where the volume expansivity is significant, e.g., at reduced pressures less than about 3.
behavior similar to the partial molar volume and becomes on the order of -lo3 kJ/mol in the highly compressible near-critical region where the volume expansivity is large. As a result, the slope of the solubility versus temperature is quite large in this near-critical part of the retrograde region, so that a relatively large amount of solid may be deposited with a small temperature change. For the mixture of DMN isomers, the crossover region was narrow and did not extend down into the near-critical region. As a consequence,the purity and yield of product were limited in the experimental crystallization process. It is expected that retrograde crystallization processes should produce higher purities and yields for a mixture with a wider crossover region, especially if it includes the near-critical region.
Conclusions A large number of solubility measurements are required to locate the crossover pressure with sufficient accuracy, since it is influenced by a difference in the slopes of the solubility versus pressure for two temperatures. The crossover pressures are 119 f 2 and 125 f 2 bar for 2,6and 2,3-DMN, respectively, although the difference in the crossover pressures was earlier thought to be much larger. An actual process was designed that was used to recover 79% pure 2,3-DMN from a 50-50 mixture of 2,3- and 2,6-DMN, by weight. The derivative (a In xz/d(l/T)), is constant for naphthalene in ethylene for a density range of 5-14 g-mol/L except near the upper critical end point. The same derivative at constant pressure, and hence the partial molar enthalpy of the solute, is strongly varying in the critical region because it is a direct function of the volume expansivity. A method has been developed to obtain the partial molar enthalpy as a function of two constants, (a In xz/d(l/T)), and (a In X ~ / B P along ) ~ , with the volume expansivity of the pure solvent. The crossover pressure, where axz/aT = 0, is located at the point where the partial molar configurational enthalpy of the solute equals the negative of the enthalpy of sublimation. For two solids, the size of the crossover region depends on the difference in the heats of sublimation, partial molar configurational enthalpies, or both. For the two isomers, 2,3- and 2,6-DMN, the difference in the heats of sublimation is consistent with the size of the crossover region. The partial molar configurational enthalpy exhibits
Literature Cited
Acknowledgment This work was supported by the Separations Research Program at the University of Texas. Registry No. COz, 124-38-9;2,3-dimethylnaphthalene, 58140-8;2,6-dimethylnaphthalene,581-42-0.
Chang, R. F.; Levelt-Sengers, J. M. H. J.Phys. Chem. 1986,90,5921. Chimowitz, E. H.; Pennisi, K. J. AZChE J. 1986,32, 1665. Diepen, G. A.; Scheffer, F. E. J. Phys. Chem. 1953,57,575. Dobbs, J. M.; Johnston, K. P. Znd. Eng. Chem. Res. 1987,26,56. Dobbs, J. M.; Wong,J. M.; Johnaton, K. P. J.Chem. Eng. Data 1986, 31,303-308. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. Phys. Chem. 1986,90,2738. Johnston, K. P.; Eckert, C. A. AIChE J. 1981,27,773. Johnston, K. P. ”Supercritical Fluids” In Kirk-Othmer Encyclopedia of Chemical Technology, 3rd ed.; Wiley: New York, 1984. Johnston, K. P.; Ziger, D. H.; Eckert, C. A. Znd. Eng. Chem. Fundam. 1982,21,191-197. Kim, S.; Wong, J. M.; Johnston, K. P. “Theory of the Pressure Effect in Dense Gas Extraction”, In Supercritical Fluid Technology; Penninger, J., Ed.; Elsevier: New York, 1985. Kurnik, R. T.; Reid, R. C. Fluid Phase Equilib. 1982,8, 93. Kwak, T. Y.; Mansoori, G. A. Chem. Eng. Sci. 1986,41, 1303. McHugh, M. A.;Krukonis, V. J.; Supercritical Fluid Extraction Principles and Practice, Butterworths, Boston (1986). Osborn, A. G.; Douslin, D. R. J. Chem. Eng. Data, (1975),20, 229. Paulaitis, M.E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Reu. Chem. Eng. (1983),1, 179. Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice-HalE Englewood Cliff, NJ, 1986. Schmitt, W. J. “The Solubility of Monofunctional Organic Compounds in Chemically Diverse Supercritical Fluids”, Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, 1984.
Received for review February 20, 1987 Revised manuscript received July 7, 1987 Accepted August 4, 1987
