How the Solute Polydispersity Affects the Cloud-Point and

Nov 1, 1997 - Exxon Research and Engineering Company, Annandale, New Jersey ... Cloud-point and coexistence pressures, sub- and supercritical, are ...
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Ind. Eng. Chem. Res. 1997, 36, 5520-5525

How the Solute Polydispersity Affects the Cloud-Point and Coexistence Pressures in Propylene and Ethylene Solutions of Alternating Poly(ethylene-co-propylene) S. Joon Han,† Christopher J. Gregg,‡ and Maciej Radosz*,§ Exxon Research and Engineering Company, Annandale, New Jersey 08801, The BOC Group, 100 Mountain Avenue, Murray Hill, New Jersey 07974, and Department of Chemical Engineering and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803-7303

Cloud-point and coexistence pressures, sub- and supercritical, are determined experimentally for a series of ethylene and propylene solutions of nearly monodisperse and polydisperse poly(ethylene-co-propylene), referred to as PEP. The cloud-point and coexistence pressures are found to be close for solutions of nearly monodisperse PEP polymers but not for solutions of polydisperse PEP. The SAFT parameters derived from the experimental cloud points for nearly monodisperse solutes alone are found to predict the cloud-point pressures and solubilities for polydisperse PEP as well. Introduction Understanding the phase behavior of polymer solutions in supercritical fluids is key to numerous applications of supercritical fluids in polymer synthesis and processing (Kiran, 1994). Examples of such applications include polymerization (DeSimone et al., 1992, 1994), fractionation (Daneshvar and Gulari, 1992; McHugh and Krukonis, 1994; Pradhan et al., 1994), microparticle formation (Petersen et al., 1986; Tom and Debenedetti, 1994; Mawson et al., 1995), microcellular foams (Aubert and Clough, 1985; Aubert and Sylwester, 1991), microporous fibers (Dixon and Johnston, 1993), and polymer blending (Lele and Shine, 1994). In all these applications, we need the knowledge of phase transitions, for example, the knowledge of temperatures and pressures required for complete miscibility. One common type of such one-to-two fluid-phase transitions can be determined in so-called cloud-point experiments. The cloud-point pressures and temperatures are usually measured for polymer solutions of fixed composition and then correlated with equations of state. Having an equation-of-state model, derived from the cloud-point data, then makes it possible to predict other thermodynamic properties, such as the mutual solubilities (referred to as the phase coexistence data) and polymer partitioning between the phases. This approach is very attractive because the cloud points are relatively easy to measure while the partitioning data are hard to measure and, yet, they are crucial, e.g., to developing the polymer fractionation processes. In the case of a binary mixture containing two monodisperse components, there is no thermodynamic ambiguity. A cloud point in a binary mixture coincides with the corresponding coexistence point, on the basis of the Gibbs phase rule. In the case of polydisperse components, such as polymers, on the other hand, we know that the cloud points do not coincide with the coexistence points and that the discrepancy increases with increasing polydispersity. This has been established for numerous liquid solutions of polymers. A * Author to whom correspondence is addressed. Telephone: 504-388-1750. Fax: 504-388-1476. E-mail: [email protected]. † Exxon Research and Engineering Co. ‡ The BOC Group. § Louisiana State University. S0888-5885(96)00504-0 CCC: $14.00

pertinent reference to the effects of polydispersity on the solution-phase behavior is that of Kiran et al. (1994). One objective of this work is to confirm a hypothesis that the cloud points measured for binary solutions of nearly monodisperse polymers are close to the corresponding coexistence points. When a polymer sample is referred to as monodisperse in this work, it will mean that such a sample is nearly monodisperse and not exactly monodisperse. Another objective is to explore how the increasing solute polydispersity affects the cloud-point and coexistence pressures. Our approach is to measure directly the cloud-point and coexistence pressures in propylene and ethylene solutions of alternating poly(ethylene-co-propylene) of well-controlled polydispersity, from monodisperse to broadly polydisperse, and to model such experimental data using a polymer equation of state derived from the statistical associating fluid theory (SAFT). Specifically, we will fit the cloud-point pressures for the monodisperse PEP and then will attempt to predict the cloud-point and coexistence pressures for a bimodal polydisperse PEP, without any refitting. This should address the question if the monodisperse cloud-point data alone can provide the basis for predicting the behavior of polydisperse systems, at least for the narrow class of systems studied in this work. Experimental Section Apparatus and Operational Procedure. The cloud points and coexistence points were measured in a variable-volume batch cell described by Chen et al. (1993). In brief, a known amount of polymer is charged into a cell and then pressurized with a known amount of solvent. Next, the constant-composition solution is equilibrated by stirring at constant temperature and at some arbitrary but sufficiently high pressure in the onephase region. Upon reaching the state of thermal equilibrium, the pressure is decreased slowly until the onset of turbidity that corresponds to the cloud point is detected; this is recorded as the cloud-point pressure. The next step is to decrease the system pressure to a desired phase coexistence pressure and to continue stirring until the system reaches the state of phase equilibrium. At this state, the phases are allowed to disengage completely without stirring, and samples of both phases are withdrawn for analysis; the amount of © 1997 American Chemical Society

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Figure 1. Simplified scheme of a batch cell for cloud-point and coexistence-point experiments. Table 1. Characterization of Poly(ethylene-co-propylene) sample

Mw

PDI (Mw/Mn)

Tga (°C)

hydrogenation (%)

PEP2.6K PEP2.6K PEP96K PEP96K PEP195K PEP51K

2 600 2 600 96 000 96 000 195 000 51 000

1.1 1.2 1.1 1.8 1.1 14.7

-65 -64 -53 -53 -48 -58

38 98 100 100 94 97

a

Tg’s are determined by differential scanning calorimetry.

Table 2. SAFT Pure-Component Parameters

Figure 2. Chemical structures for an alternating poly(ethyleneco-propylene) and model polydisperse system.

polymer is determined by weighing, and the amount of solvent is determined by measuring its volume at room conditions. The cloud-point and sampling procedures are shown in a simplified way in Figure 1. Since our cell is large enough (17 cm3), that is the volume of gas and the weight of liquid are large enough for accurate measurements, this procedure was tested to be reproducible and accurate. The phase cross-contamination due to diffusion during sampling is avoided using a short sampling time (a few seconds) and maintaining constant pressure (adjusting the piston position). Such a direct sampling of the polymer-rich phase was not attempted, however, when its viscosity was on the high side due to the high molecular weight of the polymer. Materials. The polymer samples used in these experiments were hydrogenated or partly hydrogenated samples of 1,4-polyisoprene (PI). The original PI samples were prepared by anionic polymerization. The hydrogenated PI is identical with, and hence is referred to as, alternating poly(ethylene-co-propylene), or PEP for short. The hydrogenation step has been carried out over palladium on barium sulfate support. The monodisperse PEP samples were blended to give a model polydisperse PEP, as shown in Figure 2. Table 1, on the other hand, gives the polymer characterization data,

compound

molar mass (g/mol)

m (segments)

v°° (cm3/mol)

u°/k (K)

ethylene propylene PEP

28.1 42.1 Mwa

1.464 2.223 0.05096Mwa

18.157 15.648 12.000

212.06 213.90 210.00

a

Mw ) molecular weight of poly(ethylene-co-propylene).

for example, the extent of hydrogenation from 1H-NMR, the molecular weight from GPC, and the glass transition temperature from DSC. The solvent samples, ethylene (99.9%) and propylene (99.5%), were obtained from Matheson Gas Co. Normal dodecane (purity better than 99.9%, anhydrous), referred to as dodecane in this work, was obtained from Aldrich. All were used without further purification. Computational Approach and Parameters The experimental cloud-point data for the monodisperse polymer samples are correlated using a polymer equation of state derived from the statistical associating fluid theory (SAFT) by Huang and Radosz (1990). SAFT requires three pure-component parameters for nonassociating components and one binary parameter for each pair of components. The pure-component parameters are as follows: the segment volume, v°°, the segment energy, u°/k, and the segment number, m. The values of these parameters used in this work, estimated from the Huang correlations, are given in Table 2. Results A relatively small difference in polydispersity, with all the other properties being the same, can induce a

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Figure 3. Cloud points for PEP96K in propylene: 4.5 wt % (PDI ) 1.1) (2); 4.8 wt % (PDI ) 1.8) (9). The dotted line is the vapor pressure curve for propylene.

Figure 4. Cloud points for 15 wt % of PEP2.6K (PDI ) 1.1) in propylene: (0) 1st run; (4) 2nd run; (3) 3rd run. The dotted line is the vapor-pressure curve for propylene.

measurable effect on the cloud-point pressure. This observation is illustrated in Figure 3, where the cloudpoint pressure is plotted against the temperature for a constant polymer concentration of about 5 wt %. The two sets of LCST-type points shown in Figure 3 are for two propylene solutions of PEP having the same weightaverage molecular weight of about 96 000. One PEP sample, however, has a higher concentration of lights and, as a result, it has a higher polydispersity index (PDI), 1.8 compared to 1.1. This higher PDI causes the cloud-point pressure, shown with squares, to be shifted down by about 70 bar. In order to probe the effects of polydispersity, not only on the cloud-point pressures but also on the solubilities, let us first explore a binary solution of a monodisperse solute. An example of a phase diagram for such as solution is shown in Figure 4 in terms of the cloud-point pressure plotted versus temperature. The polymer in this case is PEP2.6K (PDI ) 1.1), about 15 wt %, and the solvent is propylene. In this experiment, after the first series of cloud-point measurements (squares), a sample of the solvent-rich phase is extracted and analyzed. Next, fresh propylene is added (same amount

Figure 5. Cloud points (9) and coexistence points (0) for PEP2.6K (PDI ) 1.1) in propylene at 150 °C and 28.9 bar and 36.0 wt % of PEP2.6K (PDI ) 1.1) in the feed.

as that withdrawn with the first sample), the system is reequilibrated, and another series of cloud points (triangles pointing up) and another sampling are done. This is repeated again (triangles pointing down). A substantial amount, a total of about 16 wt % of the initial polymer, is extracted this way from the cell. The samples of polymer extracted from the upper phase are analyzed for MW and MWD, and the results are also shown in Figure 4. The results shown in Figure 4 can be summarized as follows. The extract molecular weight is only slightly lower than that of the initial polymer, and the final polymer molecular weight is about the same as that of the initial polymer (a difference of about 200 is within the accuracy range of GPC). Normally, an extract obtained from a polydisperse polymer has a much lower molecular weight than that of the parent polymer. This finding suggests that our polymer, while not truly monodisperse, adequately approximates a monodisperse solute. Also, as expected, the cloud-point pressure does not change upon repeated sampling. This PEP sample, which approximates a monodisperse solute, is used to generate a series of cloud-point and coexistence-phase composition data shown in Figure 5, where the pressure is plotted versus the polymer weight percent. The filled squares indicate the cloud points, and the open squares indicate the coexistence points. The cloud points nearly coincide with the coexistence points in this case, which usually is not the case for polydisperse polymeric solutes. This further confirms our hypothesis that, if PDI is low enough, as it is 1.1 in our case, the solution will behave as a binary solution and the cloud-point pressures will be close to the coexistence pressures, except perhaps for very low solubilities that may be very sensitive to low-concentration impurities, which have not been studied in this work. The next series of cloud-point and coexistence data, also plotted in one figure (Figure 6), is different in two ways from the set shown in Figure 5. One obvious difference is that the solvent is ethylene instead of propylene; ethylene is a weaker solvent that requires higher cloud-point pressures and is much more selective in extracting the lights. A more subtle difference is that the PEP sample used to prepare Figure 6 has a

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Figure 6. Cloud points (9) and coexistence points (0) for PEP2.6K (PDI ) 1.2) in ethylene at 150 °C and 3.4 wt % of PEP2.6K (PDI ) 1.2) in the feed. The pressure-composition phase boundary (solid curve) is calculated from SAFT.

Figure 7. Cloud points for PEP195K in propylene: 0.8 wt % (2), 5.0 wt % (4). Cloud points for PEP2.6K (PDI ) 1.2) in propylene: 0.9 wt % (9); 4.3 wt % (0). The pressure-temperature phase boundaries (solid curves) are calculated from SAFT. The dotted line is the vapor pressure curve for propylene.

somewhat higher PDI (1.2 compared to 1.1) and, by the way, it is also more saturated. Primarily as a result of the higher PDI (the degree of saturation with hydrogen is probably less relevant in this case), the coexistence pressure is measurably lower than the corresponding cloud-point pressure this time; the polymer solubility is higher than the cloud-point concentration at the same pressure. Since the experimental polymer-rich phase compositions have not been measured for this system, the cloudpoint curve is calculated from SAFT. In this calculation, the available experimental points are used to fit a binary parameter kij for PEP2.6K and ethylene, which is then used to calculate the whole cloud-point curve. The binary parameter kij from the correlation of the experimental cloud points is also used to calculate a pair of constant-composition, PEP2.6K + propylene, PT curves in Figure 7. The other pair of constant-composition PT curves shown in Figure 7, for a much larger PEP195K, also in propylene, is calculated using an

Figure 8. Cloud points for model polydisperse PEP51K (1), PEP195K (PDI ) 1.1) (2), and PEP2.6K (PDI ) 1.2) (9), all in propylene at 150 °C. The pressure-composition phase boundaries (solid curves) are calculated from SAFT. The diamond (() is the cloud point for a PEP51K + dodecane, 5 wt % solution in propylene. The open square (0) is the coexistence solubility of PEP51K in propylene at 150 °C and for a 5 wt % PEP51K feed.

empirical value of kij fitted to the experimental cloudpoint data for PEP195K (shown as triangles). We will need these kij values to simulate the polydispersity effects discussed below, but let us note for now that, as expected, the PEP195K pressures are much higher, and their sensitivity to a change in polymer concentration, in this narrow range at least, is lower, compared to those measured and calculated for PEP2.6K. Furthermore, increasing pressure with increasing polymer concentration suggests that these cloud-point transitions are of the dewpoint type. Let us also note that all the curves in Figure 7 are of the LCST type; the cloud-point pressure increases with increasing temperature. The SAFT parameters derived from correlating the binary cloud points shown in Figure 7 for the two monodisperse solutes, 0.022 for PEP195K and 0.010 for PEP2.6K, are used without further readjustment to predict other data. Examples of such predicted data at 150 °C, along with a few experimental points shown in Figure 8, are as follows: pressure versus composition curves for the two monodisperse systems, PEP195K + propylene and PEP2.6K + propylene, and a pressure versus composition curve for a “polydisperse” system, PEP51K + propylene. The PEP51K sample was prepared by blending 3 parts of PEP2.6K and 1 part of PEP195K, by weight. PEP51K is therefore bimodal and has a weight-average molecular weight of about 51 000 and a PDI of about 14.7. All these SAFT predictions, including the one for the bimodal PEP51K, are in reasonable agreement with the experimental cloud-point pressures shown in Figure 8. Furthermore, these predictions reveal that, at low solute concentrations, on the dew-point side, the PEP51K curve is closer to the PEP195K curve. This is expected because the dew-point pressure is more sensitive to the presence of a large component (PEP195K) than it is to the presence of a small component (PEP2.6K); it is the large component that is likely to precipitate first at the onset of a dew-point transition. On the other hand, the PEP51K curve becomes closer to the PEP2.6K curve at higher solute concentrations, on the bubble-point side. This is also expected because the bubble pressure is

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Figure 9. Gel permeation chromatography (GPC) trace of model polydisperse PEP51K and its extract corresponding to the 0 point in Figure 8.

likely to scale with the average molecular weight rather than with that of one of the components. Figure 8 also shows two additional experimental points, meant as two perturbations on the PEP51K experiment, illustrating further the effects of polydispersity. In one experiment discussed above, the PEP51K feed was blended with normal dodecane (1 part of dodecane per 4 parts of PEP51K, by weight, which amounts to about 20 wt % of dodecane on a solventfree basis). Dodecane is to simulate a very light end, equivalent to, say, a straight-chain 3-mer (a PEP repeating unit has four carbons in the backbone and a methyl branch). The addition of 20 wt % of dodecane causes the PEP51K cloud-point pressure to be shifted down by about 20 bar. This shift, shown with a diamond in Figure 8, relative to the PEP51K curve, can be viewed as a result either of the cosolvent effect of dodecane (which is a much better solvent for PEP than propylene) or of the lower average molecular weight of

the new solute (its average molecular weight is now less than 51 000 after addition of dodecane). In another experiment, a coexistence-phase composition experiment, the PEP51K + propylene solution was equilibrated and allowed to phase disengage at 150 °C and 356 bar. Next, a small sample of the upper, propylene-rich phase was withdrawn and analyzed for polymer concentration and MWD; the polymer-rich phase was not sampled this time. This coexistence point is shown as an open square in Figure 8. It is clear that, as expected, this point is far removed from the PEP51K cloud point. The reason for this discrepancy, between the cloud-point and coexistence pressures, is that the polymer partitioning between the phases is not uniform for polydisperse feeds; the polymer fraction that is present in the solvent-rich phase primarily contains the lights and not the bulk polymer. This is vividly illustrated in Figure 9 where two GPC traces are compared. The upper one is for the bulk PEP51K, and the

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Acknowledgment We are grateful to Dr. Lewis Fetters for providing us with some PEP samples and to Dr. T. C. Chung for providing us with PI samples that we hydrogenated in this work. A preliminary account of this work was presented at the Annual Meeting of the American Institute of Chemical Engineers in San Francisco, 1994. Supporting Information Available: Tables of experimental data collected in this work (7 pages). Ordering information is given on any current masthead page. Literature Cited

Figure 10. Solubility of model polydisperse PEP51K in propylene at 150 °C as a function of pressure predicted by SAFT. 0 is the coexistence point shown in Figure 8.

lower one is for the propylene extract obtained in the coexistence experiment. The extract GPC trace has the PEP2.6K peak only, which means that the extract does not contain PEP195 at all. Such good selectivity, by the way, is only possible for bimodal feeds containing vastly differing components. While taking many polymer solubility data is outside of the scope of this work, one can easily calculate such data from a realistic equation of state, for example, one derived from the cloud-point data. This is especially useful at very low solubility levels because such data are very difficult to measure accurately (large samples are needed). An example of a calculated solubility versus pressure curve (solid curve) is shown in Figure 10. This curve seems to be approximately consistent with the experimental coexistence point shown as the open square in Figure 10. Unfortunately, we do not have more data, especially at lower pressures, to judge the accuracy of the solubility predictions in general. The basis for realistic solubility predictions is a realistic polymer characterization, discrete or continuous, that quantitatively takes into account its polydispersity. This calls for equation-of-state parameters derived, for example, from experimental cloud-point data, obtained for monodisperse polymers. Such parameters can, in principle, be used for predicting the solubilities of polydisperse feeds, as is shown in the example in Figure 10. By contrast, the equation-of-state parameters derived from experimental cloud-point data obtained for a solution containing a polydisperse polymer usually lead to wrong solubility predictions, especially if the polydisperse polymer is treated as one pseudocomponent in calculations.

Aubert, J. H.; Clough, R. L. Low-Density, Microcellular Polystyrene Foams. Polymer 1985, 26, 2047. Aubert, J. H.; Sylwester, A. P. Microcelluar Foam? Here’s How! CHEMTECH 1991, 21, 234. Chen S.-J.; Randelman, R. E.; Seldomridge, R. L.; Radosz, M. Mass Spectrometer Composition Probe for Batch Cell Studies of Supercritical Fluid Phase Equilibria. J. Chem. Eng. Data 1993, 38, 211. Daneshvar, M.; Gulari, E. Supercritical-Fluid Fractionation of Poly(ethylene glycols). J. Supercrit. Fluids 1992, 5, 143. DeSimone, J. M.; Guan, Z.; Elsbernd, C. S. Synthesis of Fluoropolymers in Supercritical Carbon Dioxide. Science 1992, 257, 945. DeSimone, J. M.; Maury, E. E.; Menceloglu, Y. Z.; McClain, J. B.; Romack, T. J.; Combes, J. R. Dispersion Polymerizations in Supercritical Carbon Dioxide. Science 1994, 265, 356. Dixon, D. J.; Johnston, K. P. Formation of Microporous Polymer Fibers and Oriented Fibrils by Precipitation with a Compressed Fluid Antisolvent. J. Appl. Polym. Sci. 1993, 50, 1929. Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res. 1990, 29, 2284. Kiran, E. Polymer Formation, Modifications and Processing in or with Supercritical Fluids. In Supercritical Fluids; Kiran, E., Levelt Sengers, J. M. H., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994. Kiran, E.; Xiong, Y.; Zhung, W. Effect of Polydispersity on the Demixing Pressures of Polyethylene in Near- or Supercritical Alkanes. J. Supercrit. Fluids 1994, 7, 283. Lele, A. K.; Shine, A. Effect of RESS Dynamics on Polymer Morphology. Ind. Eng. Chem. Res. 1994, 33 (6), 1476. Mawson, S.; Johnston, K. P.; Combes, J. R.; DeSimone, J. M. Formation of Poly(1,1,2,2-tetrahydroperfluorodecyl acrylate) Submicron Fibers and Particles from Supercritical Carbon Dioxide Solutions. Macromolecules 1995, 28, 3182. McHugh, M. A.; Krukonis, V. J. Polymer Fractionation Process. Supercritical Fluid Extraction, 2nd ed.; ButterworthHeinemann: Boston, 1994; p 192. Petersen, R. C.; Matson, D. W.; Smith, R. D. Rapid Precipitation of Low Vapor Pressure Solids from Supercritical Fluid Solutions: The Formation of Thin Films and Powders. J. Am. Chem. Soc. 1986, 108, 2100. Pradhan, D.; Chen, C.-K.; Radosz, M. Fractionation of Polystyrene with Supercritical Propane and Ethane: Characterization, Semibatch Solubility Experiments, and SAFT Simulations. Ind. Eng. Chem. Res. 1994, 33, 1984. Tom, J. W.; Debenedetti, P. G. Precipitation of Poly(L-lactic acid) and Composite Poly(L-lactic acid)-Pyrene Particles by Rapid Expansion of Supercritical Solutions. J. Supercrit. Fluids 1994, 7, 9.

Conclusions Cloud-point and coexistence pressures are found to be close for binary solutions of nearly monodisperse PEP polymers but not for solutions of polydisperse solutions. The SAFT parameters derived from the experimental cloud points for monodisperse polymeric solutes are found to predict cloud-point pressures and solubilities for polydisperse solutes as well.

Resubmitted for review August 19, 1997 Accepted August 25, 1997X IE960504Z

Abstract published in Advance ACS Abstracts, November 1, 1997. X