Ind. Eng. Chem. Res. 1994,33, 1984-1988
1984
Fractionation of Polystyrene with Supercritical Propane and Ethane: Characterization, Semibatch Solubility Experiments, and SAFT Simulations Debjeet Pradhan, Chang-keng Chen, and Maciej Radosz’ Exron Research and Engineering Company, Annandale, New Jersey 08801 Polystyrene is characterized as a mixture of a finite number of discrete pseudocomponents. Solubilities and partition coefficients of the pseudocomponents in propane and in ethane are measured in semibatch experiments at temperatures ranging from 323 to 453 K and pressures up to 67 MPa. An equation of state based on the statistical associating fluid theory (SAFT) is used to correlate the data. Increasing temperature and pressure are found to increase the solubilities and partition coefficients, but decrease selectivities. The solubility of pseudocomponents is also found to depend on the molecular weight distribution of the polymer.
Introduction Supercritical fluids (SCF) are applicable in selective separations, such as extraction (SFE), fractionation (McHugh and Krukonis, 1986; Eckert et. al., 1992; Daneshvar et. al., 1992), and chromatography (SFC) (Westwood, 1993). Applications range from the smallscale sample preparation techniques using SFE, e.g., in the analysis of food, agricultural, and pharmaceutical products, to large-scale processes such as deasphalting of heavy oils, decaffeination of coffee beans, extraction of edible oils, and dehydration of alcohol. Regardless of the application, our ability to evaluate its economic feasibility and to design proper equipment depends on the availability of thermodynamic and mass-transfer data. Cygnarowicz and Seider (1991) have reviewed various methods that are used in the design of SFE equipment. These methods, which are based on mass-transfer and equation-of-state correlations, are primarily from small molecules and their well-defined mixtures. Such correlations are usually not available for large molecules and polydisperse mixtures like heavy oils and polymers. Kumar et al.’s (1986,1987) work on the distribution of polystyrene (PS) chains (oligomers) between a polymerrich and a solvent-rich phase in supercritical ethane solutions is one of the exceptions. By treating a polymer as a multicomponent system consisting of a mixture of n-mers (chains of length n) and by expressing the distribution of each n-mer in the two phases as a massthey have shown that a based partition coefficient, K’,,, polymer-supercritical fluid solution behaves as a mixture of independent quasi-binaries of the SCF and the individual chains (n-mers). Kumar et al. (1986, 1987) concluded on the basis of their experiments that the equilibrium solubility of an oligomer in a SCF solvent is not affected by the presence of other oligomers in solution. This conclusion greatly simplifies the multicomponent equilibrium calculations. Our goal is to extend Kumar et al.’s work to much larger, and polydisperse, polystyrene molecules, and to quantify the results of supercritical fluid fractionation. Our approach is to measure the polystyrene partition coefficients in semibatch experiments and to correlate them with the SAFT equation of state.
Experimental Section The apparatus used in this study, referred to as the polymer fractionation unit (PFU), is represented sche-
* To whom correspondence should be addressed.
matically in Figure 1. A batch of polymer (usually 10-15 g) is placed in a long tubular extraction cell (20 OOO psi HiP nipples, usually 12 and 8 in. long, in series), and the solvent is pumped through it using a set of syringe pumps (Isco, 100D) which operate in a constant-pressure, continuous-flow mode. The pressure in the extraction cell is maintained by means of either a Jasco back-pressure regulator (for P < 35 MPa) or a restrictor (for P > 35 MPa). Downstream of the restrictor, a Valco switching valve enables the collection of samples in ice-cooled U-tubes with minimal interruption of the flow. The volume of solvent used per sample is determined with a wet test meter (WTM). All tubing external to the oven is heat traced to prevent precipitation of the polymer from the flowing solution and to avoid plugging. Pressure is maintained with an accuracy to within f0.05 MPa and temperature to within f l K. The WTM has a least count of 0.01 L, and the thermocouple a t the inlet to the WTM can measure temperature to within f l K. The extract collected in the U-tubes is weighed with a Mettler balance with a least count of 0.0001 g and analyzed using a gel permeation chromatograph (Waters 150 C ALC/GPC). The experimental approach is to minimize the change in polymer composition over time due to the preferential extraction of light fractions by the solvent and to approximate a state of thermodynamic equilibrium between the flowing solvent and the static polymer feed. This is accomplished by (i) allowing for low extract yields, that is, using a large amount of polymer feed (10-15 g), but extracting only a small fraction (-0.1 g), (ii) using low flow rates (0.02-0.1 standard L of gas/min; in comparison, Kumar et al. used a flow rate of 1.0 standard L of gas/ min), and (iii) rejecting the samples collected during the initial transient state. Figure 2 shows a typical plot of overall solubility of polystyrene in supercritical propane as a function of time. A similar plot can be obtained for each pseudocomponent. The solubility curve increases up to a certain maximum during the transient state, and then it levels off (steady state). The average of all the points after the curve levels off is reported as the equilibrium solubility. By operating above the glass transition temperature (Tg) of polystyrene and by allowing long times for diffusion, we allow for sufficient mobility in the polystyrene molecules to overcome any mass-transfer resistance in the polymer-SCF system. Moreover, the use of a supercritical solvent (or diluent) has a plasticizing effect that further reduces the mass-transfer resistance between the poly-
0888-5885/94/2633-1984$04.50/0@ 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 8, 1994 1985 polystyrene (PS45000) Mw = 45000
TUBING
-tl
SYRINGE
CELL
t?
PS3250
PUMP
GAS
CYLINDER
- 18
24
30
36
42
48
Minutes Figuret. Gel permeationchromatograph (GPC)trace of polystyrene PS46ooo showingthe bimodal distribution of molecularweights, and pseudocomponents (slices) demarcated by dotted lines. tl and t Z denote the time interval during which pseudocomponent 3 elutes out of the GPC columns.
9
-51
0.08 0.06
;0.04 0.02
for the residual Helmholtz energy is a combination of a reference part, made up of contributions from the hard sphere (hs),chain, and association (assoc) terms, and a dispersion (disp) part.
I 1
/
0 0
50
100 150 200 Time (minutes)
250
300
Figure 2. Typical plot of solubilityvs time in a semibatchextraction process. The Y-axis corresponda to the solubility of the overall polymer (mixtureof pseudocomponentsthat were soluble under the conditions of the experiment).
styrene molecules and the flowing solvent. The state of thermodynamicequilibrium is verified simply by repeating a few experiments a t lower flow rates, but at the same T and P, to make sure that the solubilities do not change. Ethane, C.P., and propane, C.P., were obtained from Matheson Gas Products. Two polystyrene samples, PS3250 and PS48000, were made by Pressure Chemical Co. PS3250 had a weight-average molecular weight (M,) of 3250 and a number-average molecular weight (M,) of 3080 while PS48000had a M, of 47 960 and a Mn of 45 550. The third sample, PS45000, was a bimodal polymer with M , = 45 000, and it was obtained from Scientific Polymer Products, Inc. The GPC trace of the three polymers is shown in Figure 3. The Tgfor PS45000 and PS48000 was determined by differential scanning calorimetry (DSC) to be approximately 61 and 104 OC, respectively. In the presenceof a supercritical diluent, like propane or ethane, Tgis expected to be much lower.
Modeling The solubility data obtained in our experiments are correlated using an equation of state derived from the statistical associating fluid theory (SAFT). Details of the SAFT equation of state have been discussed elsewhere (Huang and h d o s z , 1990; Economou et al., 1992); only the basic equations are shown here. The general expression
Each of the above contributions can be expressed as a function of known quantities and three molecular parameters: (i) the number of segments, m,per molecule, (ii) the segment volume, uoo, per mole of segments, and (iii) the segment energy, uolk. In addition, one adjustable binary interaction parameter, kij, is required to fit the experimental data. The numerical approach used in this work is a block-algebra, simultaneous (BAS) flash algorithm described by Chen et al. (1993).
Results and Discussion The polymer-SCF solutions are treated as multicomponent systemsfor the purpose of our calculationswhereby the polydisperse feed is treated as a mixture of discrete pseudocomponents. Each pseudocomponent-shown as a slice under the molecular weight distribution (MWD) curve in Figure 3-is essentially a narrow fraction of the polymer consisting of a mixture of different chain lengths. Pseudocomponentsare chosen in such a way that they are common to two, or more, polymers-of the same chemical structure-irrespective of their MWD, and hence can be used as a basis for comparison of the properties of the two polymers. Two pseudocomponents are considered equivalent if they elute out of a set of GPC columns in the same time interval, say from time tl to time t 2 . They should both contain the same n-mers but, usually, in different proportions. For this reason, the equivalent pseudocomponents cannot be considered as identical. The differences between a pseudocomponent from one polymer and another from a different polymer may be reduced by decreasing the time interval At = t 2 - tl. In the limit of At going to 0, a pseudocomponent becomes identical to an individual chain.
1986 Ind. Eng. Chem. Res., Vol. 33, No. 8, 1994 1
Propane
0.01
1
- Polystyrene
1
Ethane - Polystyrene
‘I
A
+ 66.5 MPa, l2OC
446.02 MPa, lOOC
MPa, 12OC 46.1 MPa, 12OC
m 56.5 A
0.001 1000
3000
1E-005 5000
7000
9000
lo00
Molecular weight Figure 4. K’ vs MW for PS45000 pseudocomponents in propane.
In this work, the choice of pseudocomponents is somewhat arbitrary: the purpose being merely to examine if the multicomponent polymer-solvent system can be treated as a set of independent quasi-binaries, each composed of a pseudocomponent and the solvent. Therefore, the method of selection of pseudocomponents or their molecular weights (MW’s) is not crucial. The results of the experiments, which were carried out at temperatures ranging from 323 to 453 K and pressures up to 67 MPa, are expressed in terms of the solubility, yi, of a pseudocomponent i, and its mass-based partition coefficient, K’i. The partition coefficient is defined as
K’i = yif di
(3)
where yi is the weight fraction of pseudocomponent i in the solvent-rich (extract) phase, and x’i is the weight fraction of the same pseudocomponent in the polymerrich phase, but on a solvent-free basis. A plot of K’ versus MW for PS45000 pseudocomponents in propane at different temperatures (2‘‘) and pressures (P)is shown in Figure 4. For a given MW, K’i increases with T and P. Also, the relationship between log K’ and MW is approximately linear with the slopes of the lines decreasing with increasing T and P. A similar plot for PS45000 pseudocomponents in supercritical ethane is shown in Figure 5. In order to maintain consistency between the two plots, the MW’s of the pseudocomponents are kept the same. Compared to propane, K’s in ethane are roughly 1 order of magnitude lower, and hence less accurate, on an absolute basis, than those in propane. Moreover, under the conditions of the experiments only the three lightest pseudocomponents are extracted by ethane. Therefore, we report the results of the SAFT correlations for the solubilities in propane, but not for those in ethane. The values of the SAFT parameters for PS-propane, which are shown in Table 1,are determined empirically by interpolating between ethylbenzene (Huang and Radosz, 1990) and polystyrene PS90700. The method of interpolation is similar to that for n-alkanes, described in Tables I11 and IV of Huang and Radosz (1990); both m and muooare fitted as linear functions of molecular weight with functional coefficients determined from the known two sets of parameters, one for ethylbenzene and one for PS90700. The ulk is assumed to approach alimiting value of 268.19 at MW = 2000. The parameters show the trend similar to that of n-alkane or polyethylene; m increases
1500
2000
2500
3000
Molecular weight Figure 5. K’ vs MW for PS45000 pseudocomponentain ethane. Table 1. Molecular Parameters Used in SAFT Calculations component MW ethane 30 propane 44 pseudo 1 270 pseudo2 1000 pseudo 3 1950 pseudo4 2850 pseudo 5 4150 pseudo 6 5350 pseudo7 7000 pseudo8 9500 pseudo9 45000
w t fraction
uoo
infeed
(mL/mol) 14.46 13.457 12.6711 12.6293 12.5814 12.5815 12.4915 12.4518 12.4054 12.3483 12.075
0.3437 0.0734 0.0508 0.03 0.0167 0.0111 0.0104 0.0115 0.4524
uo/k 1.941 191.44 2.696 193.03 4.7809 250.47 5.057 257.95 5.4162 268.19 5.7566 268.19 6.2482 268.19 6.7021 268.19 7.3261 268.19 8.2715 268.19 21.697 268.19 m
with molecular weight and uoo decreases with molecular weight but quickly approaches as asymptotic value, as does ulk. None of the pure component parameters is readjusted to fit the solubility data. These are only firstpass, empirical estimates that do not have quantitative physical meaning. The empirical binary parameter, kii, is the only parameter that is adjusted to fit the experimental data. The kij for PS-propane depends on both T and P as follows: kij = 0.363 + 0.00033T (K) - 0.0025P (MPa)
(4)
The results of the calculation for PS45000-propane at various T and P values are shown in Figure 6. Experimental solubilities are denoted by points whereas the SAFT calculated values are represented by curves. Since the quality of fit is good, SAFT is used to predict the composition of the polymer-rich phase, x i , on a weight fraction basis. This is different from the x’j in eq 3 which is defined on a solvent-freebasis. The partition coefficient, Ki, can now be calculated as yilxi. A plot of K versus MW, as predicted by SAFT, is shown in Figure 7. Figure 8 shows a plot of the SAFT-predicted selectivities (KJKj,i < j ) for different pairs of the PS45000 pseudocomponents in propane, as a function of the overall solubility of the polymer in propane. As expected, the selectivity decreases with increasing solubility and depends on the choice of pseudocomponents. No two polymers or polymeric components are exactly alike due to differences in MWD. Therefore, a few experiments were carried out on narrow MWD standards (PS3250 and PS48000) and propane at 393 K and 66.5 MPa in order to determine the effect of polydispersity on
Ind. Eng. Chem. Res., Vol. 33, No. 8,1994 1987
/
0.05
Table 2. Comparison of the Solubility of Equivalent Pseudocomponents from Different Feeds equiv solubility Feed (propane +) pseudocomponent (wt fraction) case1 PS3250 PS3250 0.15 0.01 w e 1 1 PS45000 PS325OE 0.1 0.01 m e I11 PS3250/PS48OOO 30/10 PS3250 0.05 0.01 (w/w)mixture
';i 0.04
* *
0
. CI e
a &
4 0*03 P)
5
0 0.02
- SAFT
3
3 0.01 0 1000
5000
3000
7000
9OOO
Molecular Weight Figure 6. Solubility of PS45000 pseudocomponents in propane: symbols,experimental points; curves, calculated using SAFT. 10
1
M
I
i
- 66.5 MPa, 120C
...3 6 . 5 MPa, 120C
---46.1 MPa, 120C
0.1
._ --..
0.01
..
0.001 lo00
3000
7000
5000
9000
Molecular weight Figure 7. K vs MW for PS45000 pseudocomponents in propane, from SAFT.
the same elution time interval as PS3250 through the same set of GPC columns), some lights (low-MW chains), and some heavies (high-MW chains). The concentration of PS3250E was 30 wt % on a solvent-free basis. For case 111, we prepared a 30/70 (w/w) mixture of PS3250 with PS48000 and loaded it into the extraction cell. Propane was passed through the three feeds under similar conditions of temperature and pressure. The solubility of the equivalent slices in the above three experiments is shown in Table 2. The differences in solubility between cases I and I1 can be attributed to two factors: (i) the inherent difference in the composition of the monodisperse polymer and the equivalent pseudocomponent and (ii) the dependence of the solubility of PS3250E on the presence of other species in solution. Comparison of case I, which is treated as a binary, to case I11 suggests that the solubility of a pseudocomponent does depend on the overall composition of the polymer solution (or MWD of the polymer). This is to be expected because it can be mathematically shown that the solubility of a component in multicomponent systems (e.g., ternary in case 111)will depend on the feed composition, whereas the solubility in binary systems (e.g., in c s e I) will not. Comparison of case I1 (30wt % PS3250E in feed) and case I11 (30wt % PS3250 in the feed) suggests that the presence of lights in case I1enhances the solubility of PS3250E in propane, which means that lights may act like cosolvents.
Conclusions Solubility and the partition coefficients of polystyrene pseudocomponents are measured in supercritical propane and ethane a t temperatures ranging from 323 to 453 K and pressures up to 67 MPa. In the range of MW studied, log K'i is found to decrease approximately linearly with MW. Under the conditions of the experiments, the solubility and partition coefficients increase with temperature and with pressure. Correlation of the solubility data for PS45000 pseudocomponents in propane with SAFT enables us to calculate the composition of both phases, the partition coefficients, Ki, and selectivities. Comparison of the solubility of a monodisperse polystyrene in propane with that of its equivalent pseudocomponent from either a polydisperse polystyrene or a mixture of two monodisperse polystyrenes suggests a dependence of solubility on MWD. Literature Cited
1
2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Overall Solubility (Weight Fraction) Figure 8. Selectivity of PS45000 pseudocomponents in propane (from SAFT). K4150 refera to the pseudocomponent with MW = 4150, etc.
solubility. Three specific cases were examined. In case I, the extraction cell was loaded only with PS3250. In case 11,the extraction cell was loaded with PS45000, which consisted of the equivalent slice PS3250E (this slice has
Chen, C. K.; Duran, M. A.; Radosz, M. Two-Phase Equilibria in Polymer Solutions. Block-Algebra,SimultaneousFlash Algorithm Coupled with SAFT Equation of State, Applied to Single-Stage SupercriticalAntisolventFractionation of Polyethylene. Znd. Eng. Chem. Res. 1993,32,3123. Cygnarowicz, M. L.; Seider, W. D. In Supercritical Fluid Technology: Reviews in Modern Theory and Applications; Bruno, T. J., Ely, J. F., Eds.; CRC Press: Boston, 1991; pp 383-403. Daneshvar, M.; Gulari, E. Supercritical-Fluid Fractionation of Poly(ethylene glycols). J. Supercrit. Fluids 1992, 5, 143-150. Eckert, C. A.; Ekart, M. P.; Knutaon, B. L.; Payne, K. P.; Tomasko, D. L.; Liotta, C. L.; Foster, N. R. Supercritical Fluid Fractionation of a Nonionic Surfactant. Znd. Eng. Chem. Res. 1992,3I, 11051110.
1988 Ind. Eng. Chem. Res., Vol. 33, No. 8, 1994 Economou, I. G.; Gregg, C. J.; Radosz, M. Solubilities of Solid Polynuclear Aromatics (PNA's) in Supercritical Ethylene and Ethane from Statistical AssociatingFluid Theory (SAFT):Toward Separating PNA's by Size and Structure. Znd. Eng. Chem. Res. 1992,31,2620. Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules. Znd. Eng. Chem. Res. 1990,29, 2284; SAFT parameters for polystyrene obtained from PVT data were unpublished data. Kumar, S. K.; Suter, U. W.; Reid, R. C. Fractionation of Polymers with Supercritical Fluids. Fluid Phase Equilib. 1986, 29, 373383. Kumar, S. K.; Chhabria, S. P.; Reid, R. C.; Suter, U. W. Solubility of Polystyrene in Supercritical Fluids. Macromolecules 1987,20, 2550-2557.
McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice, 2nd ed.; Butterworths: Boston, MA, 1994. Westwood, S. A., Ed. Supercritical Fluid Extraction and its Use in Chromatographic Sample Preparation; Blackie Academic & Professional: New York, 1993.
Received for reuiew December 14, 1993 Revised manuscript received May 10, 1994 Accepted May 24, 1994O
* Abstractpublished in Advance ACSAbstracts, June 15,1994.
