2336
Ind. Eng. Chem. Res. 1993,32,2336-2344
Carbon Dioxide Regeneration of Block Copolymer Micelles Used for Extraction and Concentration of Trace Organics? Gregory J. McFannt and Keith P. Johnston’ Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
Patricia N. Hurter and T. Alan Hatton Department of Chemial Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
The phase equilibria distribution of naphthalene between C02, water, and poly(ethy1ene oxide)poly(propy1ene oxidel-poly(ethy1ene oxide) block copolymer micelle phases is examined experimentally and predicted semiquantitatively using a molecular thermodynamic model. The predictions treat the poly(propy1ene oxide) micelle core as a “pseudophase” resembling an ether. The favorable distribution coefficients a t pressures as low as 70 bar suggest that C02 is appropriate for regenerating block copolymer micelles used for concentration of trace organics in dilute aqueous solutions.
Introduction The effective removal of dilute organic contaminants from wastewater streams is a problem of increasing environmental and societal concern. It is a particularly challenging one as the typically large volumes of water to be handled dictate that the cost of treatment per unit volume be very low. While there are a number of contending methods for the cleanup of contaminated water sources,all suffer from some limitation or other. Stringent purity requirements can limit the applicability of processes such as solvent extraction, for instance, since the removal of one undesirable component from the waste stream can be counterbalanced by the introduction of another, the solvent itself. Carbon adsorption, and especiallyadsorbent regeneration, is an expensive proposition, while biological treatment is inappropriate in many cases because of the large land area required, the limited ability of biological organisms to digest many organic compounds, and the difficulties of disposing of toxic sludges (Tchobanoglous, 1979). As the major problems seem to lie in the large volumes requiring processing, an initial bulk reduction step, in which the waste products are transferred from a dilute aqueous stream to a concentrated one, would be desirable if it could be achieved economically. Then a larger number of economically viable options would become available for the final recovery and concentration of the contaminant. A relatively new and promising process for initial bulk reduction and solute concentration is micellar-enhanced ultrafiltration (Christian and Scamehorn, 1989). Here, the organicsare preferentially solubilized and concentrated within the cores of micelles formed by surfactants added to the feed stream; these loaded micelles are then recovered by ultrafiltration, and the contaminant is effectively isolated from the aqueous feed stream. The tendency for free surfactant (which is always present at the critical micelle concentration) to bleed through the pores of the membrane can limit the application of this technique, however, this can be avoided, or a t least minimized, by the use of macromolecular amphiphilic block copolymer surfactants which are too large t o pass through
* Author to whom correspondence should be addressed.
We dedicate this article to Jim Fair, whose work has shown the importance of separation processes involving trace organics +
in water. t Present address: Unilever Research, 45 River Road, Edgewater, NJ 07020. 0888-588519312632-2336$04.00/0
the membranes. A related concept, but one in which the mass-separating agent is never added directly to the feed stream, is that suggested recently by Hurter and Hatton (1992). An aqueous block copolymer micellar solution is retained within the lumens of a hollow fiber membrane unit while the contaminated feed stream is introduced to the shell side of the device. The micellar solution behaves as a traditional organic solvent in that it has a high solute partition coefficient, and is essentially “immiscible” with the feed stream. The total contact area between the two “phases” attainable with commercially-available hollow fiber ultrafiltration membrane bundles more than compensates for the diffusional resistance offered by the membrane, resulting in high overall volumetric masstransfer coefficients. In both of these processes, once the separation has been achieved, and the solute has been concentrated within the micellar solution, there is still the question as to what should be done with the loaded micelles. If incineration is an unacceptable option, then it will be important to be able to regenerate the micellar solution so that it can be reused in the extraction step. Several processes could be used for this removal of the waste product from the micellar solution, as discussed by Hurter and Hatton (1992). One of these is extraction with compressed or supercritical fluids, which are attractive because their solvent strengths may be tuned with pressure to achieve highly selective extraction and easy solvent removal from the extraction product (McHugh and Krukonis, 1986; Johnston and Penninger, 1989; McNally and Bright, 1992; Kiran and Brennecke, 1993). C02 has become the solvent of choice for many supercritical processes because it is inexpensive, nontoxic, nonflammable, and has a critical temperature of 31.04 “C,just slightly above ambient temperature. C02 has also been investigated for extraction of pollutants from soils and wastewater (Yeo and Akgerman, 1990; Brady et al. 1987)where its benign nature is an important advantage. Since C02 has a low solubility parameter, or equivalently, a low polarizability per unit volume (Hyatt, 19841, it is expected to solubilizesmall organic contaminants, but not large block copolymers. In this paper, we investigateexperimentally the potential for using CO2 in the regeneration of block copolymer micelles loaded with organic contaminants. A schematic of a possible water treatment process using these ideas is shown in Figure 1, where the aqueous micellar solution acts as a recirculating extraction solvent, while the role of the supercritical COZis to regenerate the micellar solution 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Val. 32, No. 10,1993 2337 membrane extraction
micelle regeneration
organic recovery
1
syringe pump
: water
Figure 1. Proeeas for extractionof organics from water followed by micelle regeneration with carbon dioxide.
by removing the organic solutes. These solutes can be recovered from the supercritical COZ by reduction in pressure or variation in temperature. Our specific objective in this paper is to investigate the distribution equilibrium of naphthalene between compressed fluid solvents and three different aqueous block copolymer solutions, to complement the earlier study of Hurter and Hatton (1992) on the partitioning of naphthalene, phenanthrene, and pyrene between these block copolymer micelles and water. Most of the experiments reported here were conducted with liquid or supercritical COZas the solvent. although a few experiments used liquid propaneat ambient temperatures for comparison purposes. We describe the effect of solvent, pressure, and temperature on thephaseequilibriaand the extractionefficiency. Thethree blockcopolymersdifferprimarilyintherelative amounts of hydrophobic and hydrophilic blocks, and we investigatehow this influences thedistribution coefficients of naphthalene between the fluid, water, and micellar phases. The resulting phase equilibriumdata are analyzed using molecular thermodynamic models in order to obtain the activity coefficients of naphthalene in the micellar and water phases. Both the correlative and predictive uses for the model are discussed.
Experimental Section Three samples consisting of aqueous solutions of Pluronic (trademark, BASF) PEO-PPO-PEO (poly(ethy1ene oxide)-ply(propy1ene oxide)-poly(ethyleneoxide)) block copolymers saturated with naphthalene were prepared at 25 "C in the generating column described by Hurter and Hatton (1992). Thecoplymersused were h e a r structures designated as P103, P104, and P105, having molecular weight of 4950, 5900, and 6500 Da, respectively. The hydrophobicpropylene oxide segment content was 63 mol % for P103,52.1 mol % for P104, and only 42% for P105, the most hydrophilic of the copolymers. Prior to use, the solutions were equilibrated at 23 "C for 20 days and contained small amounts of excess naphthalene crystals, which precipitated fromsolutionat this lower temperature. Thenaphthalenecontentofasolutionwasmeasured before it was used in an experiment by diluting a 100-pLsample to 5 mL with methanol and recording the UV absorbance at the naphthalene,,A of 275 nm with a Cary 2290 spectrophotometer. Static phase equilibrium experiments were carried out in a variable-volume view cell, depicted schematically in Figure 2. The cell, the erternal sampling loop, and the
bath
sample
3phire window
.....................
n
sample collection
U
Figure 2. Variable-volume new cell apparatw for pbaae volume measurement and minosampling.
sample collection procedures were developed and refined in previous studies of the solubilization of amino acids in reversed micelles (Lemert, 1990; Lemert, et al., 1990),and of the phase behavior of a ternary surfactant/brine/ compressed liquid propane system (McFannand Johnston, 1991). Samples from each Pluronic solution (10 mL) were placed in the front part of the cell, between the movable piston and the sapphire window. C02 (10 mL at 207 bar, 23.5 "C) was added from a High Pressure Equipment syringe pump to within 0.1 g, using a vernier scale on the pump to measure the volume loaded. Additional C02 was directed from the syringe pump to the back part of the cell (behind the piston) and used to adjust the pressure on the sample in the front part of the cell. The entire assembly, consisting of theview cell, aValco six-port switchingvalve with sample loop, and the associated tubing, was placed into a water bath to provide a controlled temperature to within0.1 "C. Thesolutionswerestirred gently (toprevent foaming in the C02 phase and gelation in the block copolymer solution) at intervals over a 2-3-day span to allow naphthalene, water, and COz to partition between the upper COz-rich phase and the lower aqueous micellar phase. After the initial equilibration, duplicate pairs of samples were withdrawnat various pressures,with stirring between pressure changes, in a manner described previously (McFann and Johnston, 1991). A 44.8-pL sample loop was used for CO2-phase samples, and a 110-PL loop was used for samples from the aqueous micellar phase. In each case the sample loop contents were captured in 5 mL of methanol and the UV absorbance at 275 nm was measured with the Cary spectrophotometer. In each experiment the naphthalene concentration was measured in one of the two phases, the concentration in the other phase then being determined by mass balance (McFann and Johnston, 1991). As shown in Figure 2, a 1.6-mmrodwasattachedtothe backofthemovablepiston. The other end of the rod protruded from the back of the
2338 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 variable-volume cell and indicated the position of the piston. The opening in the back of the cell was scaled with a 1.6-mm Teflon Swagelock ferrule and a metal backup ring in a taper seal connection (High Pressure Equipment Co.). The total volume indicated by the rod could be divided between the two phases by measuring the height of the interface with a cathetometer to within 0.1 mm. The phase volumes and the masses of components were corrected to account for solvent and solute losses from previous samples. The amount of C02 in the upper phase was determined from the measured phase volume and the pure component C02 density (Din, 1962). The small amount of water in the C02 phase at equilibrium was estimated using Wiebe's (1941) data. All remaining material, including the copolymer, was assigned to the lower phase. Errors in this procedure were dominated by the error in measuring the volumes of the two phases, because of the thickness and curvature of the interface. Uncertainty in the aqueous-phase volume amounted to f0.2 mL. The reproducibility in the naphthalene concentration in the fluid phases between the pairs of samples taken at each pressure was typically within 2 5%. The two errors together produced an uncertainty of *2 in the percent extraction data. A small error in the measured fluid-phase concentration produced a large error in the calculated aqueous-phase concentration, which was determined by mass balance. This uncertainty increased as the percent extraction increased. Thus the average uncertainty in the distribution coefficient, defined as the ratio of the concentration in the fluid phase to that in the aqueous phase, was about 25 5% .
I
1001
e L
x
80
3 1 % PI05 T-25.C
100
200
300
P (bar)
Figure 3. Naphthalene extraction from Pluronic P105 micellar solution with propane a t 26 O C . Table I. Phase Equilibria for the P1OS-Naphthalene-Prop~~water System at 26 O c a
P, vp,
bar 17 17 103 172 276
mL
V%
mL
Cg(Xl@) C$(Xl@) A(X10') 10.8 10.1 5.7 1.7 5.1 10.4 10.4 5.7 1.9 5.1 10.5 10.6 6.6 1.0 5.7 10.1 10.0 7.1 0.8 5.9 9.6 10.1 7.8 0.5 6.3 Feed composition: 5.30 g of propane and 10 mL solution with 3.1% P105 and 7.94 mM C&.
%
extr
KN
74 3.4 78 3.0 87 6.6 90 8.9 94 15.6 of aqueous
Table 11. Phase Equilibria for the P106-Naphthalene-Liquid COrWater System at 26 OC* P. vp. V k
Results We first present the experimental results for the distribution of naphthalene between the compressed fluid and aqueous micellar phases. The relevant properties for engineering design, i.e., the distribution coefficient and percent extraction, are compared over a range of pressures, and at both subcritical and supercritical conditions. The second part of the Results section offers an analysis of the influence of the PPO content on the solubilization of naphthalene by the micelles (at atmospheric pressure without C02 present). This analysis is in general agreement with the conclusions of Hurter and Hatton (1992). The results suggest a strategy for developing a molecular thermodynamic model for the micellar "pseudophase", which is presented in the Discussion section. Extraction of Naphthalene from the Micellar Solutions. The initial experiments used propane at 25 "C as the extraction solvent to provide a basis for comparison with the C02 extraction experiments. Propane was somewhat easier to work with than C02 because of the sharp interface between the propane phase and the aqueous micellar phase, which was probably a result of the immiscibility of propane and water relative to C02 and water (Kobayashi and Katz, 1953; Wiebe, 1941). The values of K N and percent extraction were calculated from the average of the two measured values for the propane-phase naphthalene concentration, which we denote as C i see (Figure 3 and Table I). The percent extraction, defined as the moles of naphthalene in the propane phase divided by the total number of moles in the system, increased from 76% at 17 bar to 94% at 276 bar. The propane-phase naphthalene concentrations,mole fractions, and KNparameters (C:/C$) all increased with pressure. Here, we have denoted the total, or overall, aqueous-phase naphthalene concentration by C$, and
69 138 207 276 345
13.0 11.7 10.3 10.1 10.0
9.5 9.7 9.9 9.7 9.5
4.6 0.9 2.8 88 5.1 5.2 1.2 2.8 86 4.3 5.7 1.0 2.6 92 5.7 5.7 1.2 2.6 86 4.8 6.0 0.9 2.8 87 6.7 O Feed composition: 9.56 g of C02 and 10 mL of aqueous solution with 3.1 % P105 and 6.9 mM C&s.
have not yet made a distinction between the naphthalene in the bulk water and that in the block copolymer micelles. The increase in K N with pressure is to be expected since the solubility parameter of propane increases from 12.0 to 13.2 (MPaW2over the pressure range of the experiment (McFann and Johnston, 1991), getting closer to the naphthalene solubility parameter of 20.3 (MPa)l/2(Barton, 1983). Liquid C02 at 25 "C behaves somewhat differently than propane (Table I1 and Figure 4). C02 is both much more compressibleand more miscible with water than is propane (Wiebe, 1941). The interfacebetween the CO2and aqueous micellar phases was thick and highly curved. There was extensive foam in the C02 phase and gel around the stir bar in the aqueous micellar phase, probably because of the closeness in density between water and liquid COz (Din, 1963). The percent extraction did not change much with pressure in liquid C02 relative to propane. C02 is as effective a solvent under supercritical conditions as in the liquid state, and possibly even a slightly better solvent at the higher temperature, as shown in Figure 4 and Tables I1 and 111. For the P105 polymer solution, the percent extraction and KNvalues were essentially the same (or possibly slightly higher) at 35 "C as at 25 "C, but no foam or gel was observed under the supercritical conditions. The results for all three polymers under supercritical conditions (Figure 5, Table 111)indicate that the percent extraction varied little with pressure or
'oor--7
C
.-0
.. . .
ti 90-
E
0 0
. O O
X
O
P105,25%
IU
100
0
200
I I
------7
E
ti 90 A
AM 0
..
0)
0
L
C
Q
2
2 9 % P103
80
.
Q
n
0 32% T
P'
0
-
A
35'C
200
PI04
3 1 % P105
300
400
P (bar) Figure 5. Comparison of naphthalene extraction efficiency from Pluronic P103,P104,and P105micellar solutions using COz at 35 "C.
Table 111. Phase Equilibria for Block Copolymer-Naphthalenesupercritical COrWater Systems at 38 "C,
P,
v,
V%
5%
CL(Xl0S) C$(XlO') y;(XlO') extr KN 3.1% P105O 124 11.4 10.3 5.2 7.0 3.0 88 7.4 5.5 7.0 3.1 88 7.8 138 10.5 10.8 207 9.7 10.8 6.1 7.0 3.1 89 8.7 276 9.0 10.8 6.5 7.0 3.1 89 9.3 345 8.8 10.6 6.6 7.0 3.0 88 9.4 3.2% P104b 124 10.8 10.7 6.5 1.0 3.8 86 6.5 138 10.2 10.8 6.7 1.1 3.8 84 6.1 207 9.9 10.2 7.2 0.8 3.5 89 9.0 276 9.3 10.4 1.4 1.1 3.5 88 6.7 2.9% P103c 96 12.1 10.5 5.8 1.7 4.2 18 3.4 110 11.4 10.4 6.3 1.4 3.8 82 4.5 124 11.2 10.3 6.6 1.4 3.9 83 4.7 138 10.8 10.4 7.2 1.0 4.0 88 1.2 207 9.7 10.5 7.6 1.1 3.8 87 6.9 90 10.9 276 9.1 10.6 8.7 0.8 4.2 a Feed composition: 9.22g of COz and 10 mL of aqueous solution with 3.1% P105 and 6.6 mM naphthalene. Feed composition: 9.43 g of CO2 and 10mL of aqueous solution with 3.27% P104 and 8.0 mM naphthalene. Feed composition: 9.19 g of COzand 10mL of aqueous solution with 2.9% P103 and 8.9 mM naphthalene. bar
mL
4
H measured directly
0
calculated from mass balance
'
3-
0
.-0
E
4-
0
0
Figure 4. Comparison of naphthalene extraction efficiency from Pluronic P105 micellar solutions using liquid COz at 25 "C and supercritical COz at 35 "C.
c. X
I
100
200
300
400
300
P (bar)
100
-5 E
0
0 P105.35C
Ind. Eng. Chem. Res., Vol. 32,No. 10,1993 2339
mL
polymer type above 124 bar, being generally between 85 and 90%. At pressures below 124 bar there was a slight drop in extraction efficiency. The concentration of
P (bar) Figure 6. Comparison of directly measured aqueous-phase naphthalene concentration with that determined by masa balance from the COaphase naphthaleneconcentrationfor PluronicP103solutions.
naphthalene in the supercritical C02 phase, C i , did increase with pressure, but because this increasewas largely offset by a significant decrease in C02 volume (Din, 1962), the mole fractions of naphthalene in the C02 phase changed little above 124 bar. Since the lower phase was incompressible, C? also changed little with pressure. The increases in naphthalene concentration with pressure did, however, lead to significant increases in KN,since it was based on the concentration ratio and not the mole-fraction ratio. Two experiments with the P103 polymer solution were run under the same experimental conditions, but different sampling conditions, to test for mass balance closure. In one experiment the sample was taken from the C02 phase using a 44.8pL sample loop, while in the other the aqueous micellar phase was sampled using a 110-pLsample loop. As shown in Figure 6,the measured values of C$ were found to be consistent with those determined by mass balance. The agreement is good, particularly considering that the concentrations determined by mass balance are subject to considerable uncertainty, due to the small values of C? compared to C i . The direct measurement of C? is subject to some uncertainty also, primarily because of the small amounts of naphthalene present, which lead to small UV absorbances. The modest effects of pressure on the percent extraction and KN are somewhat surprising in view of the fact that the solubility parameter of C02, like that of propane, increases significantlywith pressure (Johnston et al., 1989). However, the trends in naphthalene solubility for this liquid-fluid system are strikingly similar to those in the solid naphthalene-supercritical fluid C02 system at the same temperature (Mackay and Paulaitis, 1979). There the solubility is relatively constant above 120 bar, and decreases sharply below 120bar. Thus it would seem that the interactions which govern the fugacity of naphthalene in the supercritical solvent cause similar behavior in the solid-fluid and micelle-fluid equilibria. KN and the percent extraction are extensive properties of the system. They both depend upon the polymer concentration and the naphthalene loading, while the percent extraction also depends on the phase-volumeratio. The percent extraction was similar for the three polymers, even though the initial naphthalene concentration in the aqueous micellar solutions was substantially greater with higher polymer PPO content. The mole fractions of naphthalene measured in the CO2phasewere significantly less than those for saturated C02 in equilibriumwith excess pure naphthalene crystals (Tsekhanskaya et al., 1964; Paulaitis and McHugh, 1980). There are several ways to
2340 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 Table IV. Phase Equilibria for the NaphthalendOzWater System at 35 "Ca
v,
P, VF, bar mL mL CL(XIOs) cE(X106) y~O(10') 4.2 6.8 6.0 110 11.4 10.8 4.0 7.4 7.1 138 10.5 10.7 4.0 3.9 7.8 207 9.9 10.4 3.5 3.9 8.1 276 9.0 10.9 3.9 3.8 8.2 345 9.1 10.3
#(x1o8) 1.1 1.4 0.7 0.6 0.7
KN 113 96 195 231 210
Feed composition: 9.34g of COz, 10 mL of water, and 12 mg of naphthalene. O.O810/
exploit these findings in process design optimization. The pressure or solvent-to-feed ratio may be lowered, or polymers with a higher capacity for naphthalene could be used in the extraction stage, with no loss of efficiency in the micellar regeneration step. Such process design options may be evaluated using the thermodynamic models presented below. Experiments were conducted on a system composed of water, naphthalene, and C02 only, to obtain the concentration of naphthalene in the bulk water phase in the absence of micelles (Table IV). The quantities of the three components loaded into the cell were essentially equivalent to those used in the experiments with block copolymer present. For this feed composition, the amount of naphthalene in the water phase in equilibrium with the C02 phase was about an order of magnitude less than the reported naphthalene solubility in water of 2.5 X lo4 M (Stephen and Stephen, 1963). These values are significantly lower than the overall concentrations (C?) reported in Table 111, confirming the expectation that the vast majority of the naphthalene in the system was associated with the block copolymer micelles and the supercritical C02 phase, and not with the water itself. When the K N values in Table IV are expressed as a ratio of mole fractions instead of concentrations, they are in agreement with the trends established by the experiments of Yeo and Akgerman (1990). Another noteworthy feature of the COZdata at supercritical conditions is that the aqueous micellar phase volume was consistently larger than the loaded volume of 10 mL, and that the C02 phase volume was consistently smaller than would be expected from the pure CO2 density at the temperatures and pressures used in these experiments. These results indicate a net transfer of C02 to the aqueous micellar phase, as anticipated on the basis of the CO2-water phase equilibrium dataof Wiebe (1941). Wiebe reported a mole fraction of COZin water of about 0.025, and of water in C02 of about 0.005 at 35 OC and 276 bar, which is quantitatively consistent with our measured phase volumes at these conditions. The volume measurements on the system water-naphthalene-C02 shown in Table IV are indistinguishable from those made with block copolymer present (Table 111). More accurate measurements of the C02 solubility could be made by other techniques (Daneshvar and Gulari, 1989; Dixon and Johnston, 1991)to investigate the possibility of using CO2 to shrink or swell block copolymer micelles as a means of controlling their interior polarity; such controllable micelles could be of interest in practial applications (Lemert al., 1990). Solubilizationof Naphthalene in Block Copolymer Micelles at Atmospheric Pressure. Before proceeding to thermodynamic modeling, it is instructive to examine more closely the distribution of solute between the block copolymer micelles themselves and the surrounding water, in the absence of C02. It would be reasonable to assume that the naphthalene is located only within the nonpolar
'
0 .' 5
'
1 .' o
'
1 .' 5
'
'
2.0
nP0 1 4 0
Figure 7. Influence of block copolymer structure on the number of moles of naphthalene in the micelle core at atmospheric pressure.
PPO blocks, but the actual situation could be more complicated. Reports in the literature have discussed solubilizationmechanisms and have noted block copolymer micelles preferentially solubilize aromatic solutes over aliphatic ones (Nagarajan et al., 1986; Cao et al., 1991), a feature shared by other,families of surfactants (Mukerjee and Cardinal, 1978; Christensen and Friberg, 1980; Nagarajan and Ruckenstein, 1991). In the case of block copolymer surfactants the increased solubilizationhas been linked to the small size and polarizability of the aromatic molecules, which could allow them to interact with the PEO coronas of the micelles,as well as with the PPO cores. The results of Hurter and Hatton (1992)are not consistent with this hypothesis; however, and they concluded that the solute was associated only with the PPO core and not with the PEO corona. It was also shown that with increasing PEO content, for constant PPO molecular weight blocks, there was a decrease in the solubilization capacity of the PPO core. This was attributed to structural changes in themicelle caused by the changes in the polymer composition,with asmaller PPO core leadingto a reduction in solubilization efficiency. This conclusion has been supported by a detailed mean-field theoretical analysis of micellization and solubilization in block copolymer solutions (Hurter et al., 1993). The naphthalene concentration increases with the number of PPO blocks in the three copolymers, indicating the importance of the PPO blocks as the primary solubilization sites (Hurter and Hatton, 1992). To characterize the naphthalene distribution in the micellar solution, we adopt the suggestion of Mackay (1987) and assume that the ratio of moles of naphthalene per mole of propylene oxide, ni'tnpo, is the same in the three polymers, since they each have the same arrangement of PEO and PPO blocks as well as similar molecular weights. We define an analogous ratio, nio/nEo,for the naphthalene in the PEO part of the micelles. As shown above, the amount of naphthalene in the bulk water is negligible compared to that in the micelles. Thus the total number of moles in the micelles is given by nt= which can be rearranged to yield
The slope of this line is n~o;O/npo and the intercept is .io/nEO. The actual plot (Figure 7) is indeed reasonably linear and passes close to the origin, which means the first-
Ind. Eng. Chem. Res., Vol. 32, No. 10,1993 2341 order assumption that the naphthalene is almost entirely associated with the PPO core isjustified for these polymers. To first order, this result is similar to that used by Hurter and Hatton (19921, except that somewhat different parameters have been considered. However, they found that nLo/npo changes on the order of 20% for the PPO range investigated. It can be anticipated that, in the presence of a C02 phase, interactions between the dissolved C02 and the PEO corona would tend to displace naphthalene even further toward the PPO core.
Table V. Interaction Parameters for COa (F), Ha0 (W), and Naphthalene (N) at 36 OC k F W N F -0.2104 0.0856 W 0.162' 0.4W N 0.085b -0.llOE 0 PanagiotopoulosandReid(1986). MackayandPaulaitis (1979). Yeo and Akgerman (1990).
Discussion Determination of the Activity Coefficient of a Solute in a Block Copolymer Micelle from Phase Equilibria. Micellar and microemulsion systems have often been modeled by assuming that the interior of the micelle is a "pseudophase" in equilibrium with the continuous phase (Overbeek et al., 1987; Bourrel and Schechter, 1988; Peck et al., 1991). In the present case, the three phases in equilibrium, Le., the fluid (F),water (W), and micelle interior (M) phases, each contain naphthalene. To regress the activity coefficients of naphthalene from the experimentally determined phase equilibria, we begin by setting the fugacity of naphthalene (N)equal in the three phases:
f;=#=f:
(3)
In the C02 phase, the fugacity may be expressed as
& =YN~NP
(4)
where the fugacity coefficient, +N, can be obtained from the Peng-Robinson equation of state (Prausnitz et al., 1986):
a
&('--' :) .( + + + u u
2(2)'12bRT The mixing rules are
(1 2'/')b) (1- 2'12)b
a = CCY&Uij
(6)
b = Cyibi
(7)
+ + (kij - kji)yi)
( ~ p j ) ' / ~ (kij l
(8)
The aij parameters reduce to aij
(apj)'I2(l - kij)
As shown in the previous section, the bulk of the naphthalene in the micelle phase resides in the micelle cores; thus we define xf as the mole fraction of naphthalene based on moles of monomer propylene oxide units of molecular weight 57 in the cores of the micelles. The number of propylene oxide units in the micelles is known from the given molecular weight and PEOIPPO ratio of the surfactants. The reference fugacity, fiL,is defined as the vapor pressure of a hypothetical subcooled liquid naphthalene at the temperature of the system. The fugacity is corrected to the system pressure by means of the Poynting correction (the exponential term). We consider pNL, UN, and the Poynting correction to be the same for the micelle phase and the water phase, since the system pressure is far greater than any Laplace pressure that might exist in the micelles. The vapor pressure of subcooled liquid naphthalene is found from the DIPPR database (Daubert and Danner, 1988) to be 7.03 X 10-4 bar at 35 "C,and the sublimation pressure of solid naphthalene is 2.78 X 10-4 bar at the same temperature. The ratio of the two, is 2.53, which is practically identical to the value of 2.56 predicted by the thermodynamic relation (Prausnitz et al., 1986)
(5)
where the cross-attraction term may be determined by the expression of Panagiotopoulos and Reid (1986): aij =
and
(9)
when kij = kji. This type of equation has often been used for systemscontaining C02,naphthalene, or water (Kurnik and Reid, 1982; Mackay and Paulaitis, 1979; Panagiotopoulos and Reid, 1986; Yeo and Akgerman, 1990). Values for kij are listed in Table V. In the micelle core and water phases, we use a pure liquid standard state along with activity coefficients, so that
(12) The thermodynamic parameters Ahf, Tt, and Acp for naphthalene are listed in the DIPPR database. A negligible volume change term in eq 12 has been neglected. We now have all the data needed to calculate the YN. The P103 system was chosen for the calculations because naphthalene concentrations were directly measured in both phases for this system. The naphthalene concentrations in the water phase may be taken from the data for the system without micelles present in Table IV, since the fluid-phase mole fractions of naphthalene are essentially the same as in Table 111. This assumption is quite reasonable for a dilute surfactant system, because the naphthalene in the bulk water encounters few micelles. The number of moles of naphthalene in the micelles was determined from the known water-phase and overall micellar solution concentrations, :C and C$ and their respective volumes by simple material balance. All the mole fractions used in the calculations of YN were derived from experimental data. The fugacity coefficients of naphthalene in the C02 phase were calculated using eq 5 assuming either a water-free CO2 phase or a watersaturated CO2 phase in accordance with Wiebe's (1941)
2342 Ind. Eng. Chem. Res., V O ~32, . No. 10, 1993 Table VI. Thermodynamic Parameters for P103-NaphthaleneCOzwater System at 35 OC
P,
bar
110 124 138 207 276
X:
(XI@) 0.97 0.91 1.30 0.70 0.61
XN ( XI@)
3.9 3.9 2.7 3.1 2.3
&(XI@) @N(X1@) 3.9 3.8 3.4 3.9 2.8 4.0 3.8 2.0 4.2 2.0
*I M
1.4 1.4 0.8 1.2 1.4
3.4 3.2 4.1 2.6 3.7
Table VII. Estimated Activity Coefficient of Naphthalene in Various Solvents E~(30)~ solvent XN 4 T,"C YN 2.1 31 14.9 0.189 hexane 33 19.2 0.9 tetrachloroethylene 0.441 30.0 1.0 33 16.0 0.377 42.6 butyl ether 0.271 29.9 1.5 34 15.9 ethyl propyl ether 0.427 35.0 0.9 39 19.0 chloroform 50 23.3 4.2 0.094 34.7 butanol 52 26.0 0.046 30.0 8.6 ethanol 12.0 55 29.6 0.037 37.6 methanol 63 47.9 0.003 12,000 water 0 Stephenand Stephen(1963). Reichardt (1988). Barton (1983).
*
data; the C#JNvalues were found to differ by only lo%,and the water-saturated values were selected for the determination of the YN. Poynting corrections were calculated from published data (Daubert and Danner, 1988). Activity coefficientsdetermined by combining eq 3 with eqs 4, 10, and 11, shown in Table VI, are constant with pressure within the limits of experimental error, as expected. Pressure effects on the fugacity are treated successfully by the Poynting correction, since water, naphthalene, and the micelles are essentially incompressible. It is the compressible fluid phase that experiences large pressure effects. The activity coefficients of naphthalene in the water phase are enormously larger than the activity coefficients in the micelles, confirming the large thermodynamic driving force for naphthalene to leave water and enter the micelles, as demonstrated experimentally by Hurter and Hatton (1992). The previously determined values of GLand f$ can be used to calculate the activity coefficients of saturated solutions of naphthalene in various organic solvents. Solid-liquid phase equilibria may be expressed as XNYNG~ =
f$
PI 03
YN
(13)
The results are tabulated in Table VII, with the solvents ranked in polarity according to the E ~ ( 3 0solvent ) polarity scale (Reichardt, 1988). The calculated activity coefficients of naphthalene in the micellar core are roughly equivalent to those in slightly polar solvents, which would be expected for a PPO environment. This correspondence between experiment and theory gives credibility to the calculated naphthalene activity coefficients. Prediction of the Distribution of Naphthalene between a Block Copolymer Micelle and COz. Since the mole fractions of naphthalene in the micelle core do not change much from one Pluronic surfactant to another, the activity coefficients should also be invariant and could be used for predicting phase equilibria. The amount of naphthalene in the water phase is negligible, and thus the relevant equilibrium naphthalene distribution to be predicted is that between the micelles and the fluid phase. The C02 and the surfactant are essentially immiscible, with only naphthalene distributing between them. In this case we specify the amount of surfactant, C02, and naphthalene to be distributed, in analogy to a liquid-liquid equilibrium flash calculation.
P104
T
f o0
-
35.C
300
200
400
P (bar)
Figure 8. Measured w predicted naphthalene mole fractions in the COz phase in equilibrium with Pluronic micellar solutions.
The results of the predictions are shown in Figure 8, for a constant YN of 3.4. As expected, the agreement is good. The calculation procedure is to guess a y i , determine xf by mass balance, calculate using eq 4 and from eq 10, and iterate until the naphthalene fugacities in the two phases are equal. We used measured phase volumes, but the entire calculation could be done without these volumes by using Wiebe's (1941) data to calculate the distribution of C02 and water between the upper and lower phases. Many possible extraction conditions could be examined in this way using activity coefficient data from a limited set of experiments. It may be possible to predict distribution coefficients for systems with other types of block copolymer surfactants or other nonpolar solutes, by incorporating a structural and compositional dependence into the activity coefficients. One way to do this is by means of regular solution theory (Prausnitz et al., 1986). The activity coefficient would be written as
ft
&
where U N is the molar volume of naphthalene, @PO is the volume fraction of the hydrophobic moiety in the micelle core, and Bpo and 6~ are the solubility parameters of the micelle core and of naphthalene, respectively. For all but the most highly loaded micelles, @poshould be essentially equal to 1, showing what was previously demonstrated in Figure 8; Le., YN is not particularly sensitive to composition for these dilute conditions. The solubility parameter of naphthalene, 6 ~ is, defined for a hypothetical subcooled liquid as 6, = (15) (Prausnitz, et al., 1986), where AUNis defined as Ahv*P RT. Using the DIPPR data, BN a t 35 "C is 20.1 (MPa)1/2, which is close to the value of 20.3 (MPa)1/2 listed in the published tables (Barton, 1983). If we set @poequal to 1, 6p0 is 15.5 (MPa)'/2 for a # of 3.4, which is comparable to the solubility parameters of higher alcohols and ethers (see Table VII). Since a micelle core composed of chains of propylene oxide units would be expected to have the characteristics of an ether, this is a satisfying result. This conclusion also concurs with the observations of Hurter and Hatton (1992) that the micelle water partition coefficient for a series of polycyclic aromatic hydrocarbons is correlated almost quantitatively with the octanol-water
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2343 partition coefficient. Thus, in the Pluronic systems the 7 : could be calculated by a direct application of regular : and distribution cosolution theory. Consequently, 7 efficients should be able to be predicted for other block copolymer systems. Several other methods are potentially useful for calculations of the activity coefficients of solutes inside block copolymer micelles. Spectroscopic studies have been conducted in the past to determine the environment experienced by aromatic solutes in micelles (Mukerjeeand Cardinal, 1978; Christensen and Friberg, 1980; Cao et al., 1991; Nagarajan and Ruckenstein, 19911, and the data could be used to define a polarity index for different types of block copolymers and solutes, which could then be correlated to activity coefficients. The data could also be used in conjunction with an infinite dilution activity coefficient model such as in the MOSCED approach (Thomas and Eckert, 1984). Fundamental insight on the details of the molecular structure of the core and interfacial regions of the micelle and their influence on solubilization may be described by self-consistent field theory (Scheutjens and Fleer, 1979; Cogan and Gast, 1990; Cogan et al., 1992; Hurter et al., 1993). Just as with the predictive model for phase equilibria discussedabove, a large number of systems could be investigated with a limited number of experiments. Such predictive models would be extremely important for industrial design and scaleup of the proposed wastewater treatment process.
Conclusions Pluronic block copolymer micelles loaded with naphthalene can be regenerated efficiently using compressible fluids such as sub- and supercritical C02 and propane. Pressures as low as 70 bar were sufficient to achieve a 90% removal of naphthalene from the micellar solutions in a single-stage operation, and COZcould likely regenerate micelleswith even larger naphthalene loadings than those used in this study. The success a t the lower pressures is satisfying given the significant capital costs in supercritical fluid extraction processes. These results indicate that the concept of a membrane extraction process using block copolymer micelles,followed by micelle regeneration using C02, as suggested by Hurter and Hatton (19921, could provide an effective method for recovering organics in concentrated form, without contamination of the feed stream by the C02 or the block copolymer. A molecular thermodynamic model was developed which successfully correlates and even predicts the phase equilibria both between the micelle and fluid phases and between the micelle and water phases. Only a minimal amount of experimental data is needed to predict a wide range of conditions. The enormous change in YN between the water and micellar phases confirms the large driving force for the membrane part of the process described by Hurter and Hatton (1992). The model indicates that the micelle core environment resembles that of an ether or a higher alcohol, with relatively little penetration by water. Furthermore, the activity coefficient of naphthalene in the micelle may be calculated semiquantitatively with regular solution theory. Further work is needed to investigate the phase behavior for other solutes and polymer surfactants, as is more quantification of overall mass-transfer rates in these systems. Acknowledgment This material is based on work supported by the National Science Foundation under Grant No. CTS8900819, the Separations Research Program a t The
University of Texas, the State of Texas Energy Research in Applications Program, and a Camille and Henry Dreyfus Foundation Teacher-Scholar Grant to K.P.J. T.A.H. was supported by the Department of Energy under Grant No. DE-FG02-92-ER14262.
Nomenclature a = attractive parameter for Peng-Robinson equationof state b = repulsive parameter for Peng-Robinson equation of state C = concentration, mol/L Ac, = heat capacity of liquid - heat capacity of solid EO = ethylene oxide unit within block copolymer f = fugacity Ah' = enthalpy of fusion Ahvap = enthalpy of vaporization K = distribution coefficient k = interaction parameter n = number of moles P = pressure P a t = vapor pressure R = universal gas constant T = temperature Tt = triple point temperature Auv*P = internal energy of vaporization V = volume u = molar volume W = bulk water phase x = mole fraction in W and M phases y = mole fraction in F phase Greek Letters y = activity coefficient
6 = solubility parameter 9 = volume fraction rp = fugacity coefficient Subscripts and Superscripts
Aq = aqueous micellar phase (W F = propane or COZphase
+ M phases)
N = naphthalene L = hypothetical subcooled liquid M = block copolymer micelles OL = liquid reference state OS= solid reference state PO = propylene oxideunit within polytpropylene oxide) block
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Received for review February 12, 1993 Accepted June 23,1993. ~
e Abstract
15, 1993.
~~~~
~~
published in Advance ACS Abstracts, September
