J. Phys. Chem. 1994, 98, 10634-10639
10634
Phase Behavior of Telechelic Polyisobutylene in Subcritical and Supercritical Fluids. 3. Three-Arm-Star PIB (4K) as a Model Trimer for Monohydroxy and Dihydroxy PIB (1K) in Ethane, Propane, Dimethyl Ether, Carbon Dioxide, and Chlorodifluoromethane Christopher J. Gregg,? Fred P. Stein,? and Maciej Radosz*g$ Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 1801 5, and Exxon Research and Engineering Company, Annandale, New Jersey 08801 Received: March 2, 1994; In Final Form: June 10, 1994@
The cloud-point pressures for a three-arm-star polyisobutylene (4K) in ethane, propane, dimethyl ether, carbon dioxide, and chlorodifluoromethane were measured in a variable volume optical cell up to 200 "C and 2000 bar. These pressures, presented as LCST and U-LCST curves, are found to depend strongly on the size difference and polarity difference between solvent and polymer. The cloud points measured in this work confirm the aggregate size estimated from the statistical associating fluid theory (SAFT) for CH3-PIB-OH (1K) and HO-PIB-OH (1K).
Introduction
Experiment
Understanding the phase behavior of polymer solutions is key to synthesizing and processing of polymers in subcritical and supercritical fluids.' In general, the behavior can be described in terms of system dissimilarities between the solvent and polymer. As the system dissimilarities increase, cloud-point pressures increase and the LCST (lower critical solution temperature) curve shifts to lower temperatures and the UCST (upper critical solution temperature) curve shifts to higher temperatures until the two merge to form a U-LCST (upperlower critical solution temperature) curve. The dissimilarities are characterized in two ways: (1) size difference, referred to as the asymmetry and (2) polarity difference. The asymmetry arises from either increasing the polymer molecular weight,*s3 reducing the solvent molecular eight,^,^ or increasing the polymer aggregate size.6-s An example of the latter is the formation of polymer aggregates via hydrogen bonds. Polarity differences arise from either a polar solvent or polar groups on the polymer chain. One way to increase the asymmetry is to increase the chain length. Another way is to add long-chain b r a n ~ h e s ,e.g. ~ to form star, comb, or H-comb'O shapes. These branchy polymers have received theoretical' 1-13 and industrial a t t e n t i ~ n , ' ~due ,'~ to their rheological proper tie^,^^^^^ but little is known about their phase behavior in supercritical fluids. In this work, the cloudpoint pressures for a three-arm-star polyisobutylene are measured in solutions of propane, ethane, chlorodifluoromethane, dimethyl ether, and carbon dioxide. The experimental data are tabulated for comparison with other polymer systems and for evaluating thermodynamic models that account for branched structure. 18-*1 Equally important, the three-arm-star polyisobutylene is a model trimer aggregate which, when viewed as a collection of aggregated arms in solution, establishes cloud-point boundaries of a known-size, monodisperse aggregate. These boundaries are compared to the cloud-point pressures for CH3-PIB-OH (1K) and HO-PIB-OH (1K) systems,' which allow for gauging the aggregate size of the hydrogen-bonded cluster.
Materials. The three-arm-star polyisobutylene (3 x S-PIB) sample used in this work was synthetically prepared by living carbocationic polymerization.22 The process involves the polymerization of isobutylene using a trifunctional tricumyl methyl ether initiator. In essence, the arms of the star are attached in the 1,3,5-positions of the cumene ring. The sample molecular weight and the number of arms were determined by GPC (gel permeation chromatography) and 'H NMR (hydrogen nuclear magnetic resonance) as described by Faust and Kennedy.23The analysis indicated that the polymer has three arms, each arm having a molecular weight of 1367 glmol, a total molecular weight of 4100 glmol, and a polydispersity index (Mw/Md of 1.11. The sample impurities were removed by rinsing the polymer with hexane and then distilling the sample under a vacuum. Ethane (CZH~),propane (C3Hs), chlorodifluoromethane (CHClFz), dimethyl ether (CH30CH3), and carbon dioxide (Cod were purchased from Matheson with a known minimum purity of 99.8+% and were used without further purification. Their properties are given by Gregg et al.' Apparatus and Procedure. The cloud points were measured in a variable volume optical cell which has an upper temperature and pressure limit of 200 "C and 2000 bar. The cell is equipped with a sapphire window, moveable piston, various ports, and a heating jacket. The key components are the window and piston, which allow for visual observation of the phase transition and continuous control of the cell volume and pressure at constant composition. The details are given by Gregg et al." In operation, a known amount of the polymer and solvent is loaded into the cell and stirred with a magnet chip. The piston is then moved toward the window to reduce the sample volume and increase pressure to form a homogeneous solution. After adjusting temperature and establishing equilibrium, the pressure is reduced at constant temperature by moving the piston away from the window until the solution turns hazy, as seen through a borescope. At this time, the cloud-point pressure is recorded and identified as either bubble point-like or dew point-like (Chen and Radosz4) depending upon the phase disengagement pattern. Next, a new temperature is established and the procedure repeated so as to produce a pressure-temperature isopleth curve.
* Corresponding author. t Lehigh University. @
Exxon Research and Engineering Company. Abstract published in Advance ACS Abstracts, September 1, 1994.
0022-365419412098-10634$04.5010
0 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 41, 1994 10635
Phase Behavior of Telechelic Polyisobutylene
TABLE 1: Experimental Cloud-Point Pressures for 3xS-PIB Polyisobutylene (4K)in Propane polymer (wt %) 6.57 6.57 6.57 6.57 6.57 6.57 6.57 6.57
T(fO.1 "C) 150.5 125.0 100.0 95.O 89.5 80.0 55.0 50.0
Phase transition type: VL
P (fl.O bar) 270.8 239.6 202.2 194.2 185.2 171.9 124.4 112.5
typen LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
polymer (wt %) 6.57 6.57 6.57 6.57 6.57 6.57 6.57 6.57
T(fO.1 "C) 43.9 39.0 35.0 25.1 20.0 18.0 15.0 8.3
P (fl.O bar)
99.4 89.6 79.0 56.7 46.1 41.6 33.7 17.2
type" LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
= vapor-liquid; LL = liquid-liquid; BP -= bubble point-like transition; DP dew point-like transition.
TABLE 2: Experimental Cloud-Point Pressures for 3 xS-PIB Polyisobutylene (4K)in Ethane polymer (wt %) 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4
T(fO.l "C) 149.9 130.0 119.2 110.4 98.5 89.4 90.1 79.9 70.0 60.5 50.0 40.0
P (51.0 bar)
656.4 650.4 646.4 642.3 636.6 632.7 633.4 631.3 627.0 621.4 617.9 613.5
type" LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
polymer (wt %) 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4
T(fO.1 "C) 34.5 31.7 25.1 4.5 -3.5 -6.5 - 14.5 -20.5 -30.1 -35.2 -38.7
P ( f l . O bar)
611.8 610.2 608.8 605.9 606.5 607.3 609.8 613.0 621.3 628.0 631.6
type" LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
Phase transition type: VL = vapor-liquid; LL = liquid-liquid; BP = bubble point-like transition; DP = dew point-like transition.
TABLE 3: Experimental Cloud-Point Pressures for 3x S-PIB Polyisobutylene (4K)in Chlorodifluoromethane polymer (wt %) 1.5 1.5 1.5 1.5 1.5 1.5 1.5
T(fO.l "C) 175.5 160.0 150.0 140.1 130.0 128.0 126.0
P (fl.O bar)
575.2 619.4 656.0 727.6 825.3 860.7 900.5
type" LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
polymer (wt %) 1.5 1.5 1.5 1.5 1.5 1.5
T(fO.l "C) 124.0 121.9 120.0 117.1 116.0 115.0
Phase transition type: VL = vapor-liquid; LL = liquid-liquid; BP = bubble point-like transition; DP
P (fl.O bar)
937.4 985.1 1044.7 1139.2 1178.7 1233.2
type" LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
dew point-like transition.
TABLE 4: Experimental Cloud-Point Pressures for 3x S-PIB Polyisobutylene (4K)in Dimethyl Ether polymer (wt %) 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35
T(f0.1 "C) 150.5 136.7 130.0 118.8 110.0 99.5 94.0 78.0 70.0 59.4 55.5 49.6 39.0
Phase transition type: VL
P ( f l . O bar)
212.0 192.0 181.1 161.9 147.0 129.4 120.4 93.4 89.1 79.5 77.1 75.7 84.3
type" LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
vapor-liquid; LL = liquid-liquid; BP
Cloud Points for Three-Arm-Star Polyisobutylene Solutions The cloud-point pressures measured for the 3xS-PIB (4K) are reported in Table 1 for propane, in Table 2 for ethane, in Table 3 for chlorodifluoromethane, and in Table for dimethyl ether, These data are presented in pressure temperature coordinates as phase boundary (cloud-point) curves and represent the miscibility limit. ~ ~ ~ the i ~area~above l l the~ curve , is a one-phase region and the area below the curve is a twophase region. In the text to follow, these boundaries are discussed with respect to the asymmetry and polarity and are compared to the cloud-point curves for the hydrogen-bonding CH3-PIB-OH (1K) and HO-PIB-OH (1K) systems.
polymer (wt %) 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35 6.35
T(fO.l "C) 36.0 30.1 24.2 19.7 14.9 10.0
9.7 9.0 7.8 7.4 7.3 7.1 6.1
P ( f l . O bar)
91.1 117.1 148.9 191.8 261.1 387.2 421.7 456.3 506.9 529.8 545.9 592.9 652.0
type LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP) LL(DP)
bubble point-like transition; DP E dew point-like transition.
Asymmetry and Polarity Effects. Shown in Figure 1 are the cloud-point pressures for propane and ethane solutions containing the 3 x S-PIB (4K). In propane solutions of 6.57 wt % 3 x S-PIB (4K), the cloud points exhibit LCST behavior with an LCEP (lower critical end point) at 8.3 "C; at t h i s temperature, the polymer is soluble and a homogeneous solution at 17.2 bar. AS usual, the LCST cloud-point pressures increase as the temperature increases. For example, at 150 "C, the cloud-point pressure is 270J3 bar. By contrast, higher pressures are required to dissolve the 3 xSPIB in ethane. The cloud points are U-LCST, and below 150 "C, for 10.4 wt % 3 x S-PIB (4K), a minimum pressure of 605.9 bar is required to form a homogeneous solution. These
Gregg et al.
10636 J. Phys. Chem., Vol. 98, No. 41, 1994 1,000 803
1,400 800
I
\ I
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/
i
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1,000
2 3
800
c 600 n v)
t
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O
"T(cY
'"
A AA A
400
-50
CHClF2 + ~xS-PIB
C2Hg + ~xS-PIB
0
50
100
150
200
Temperature (C)
Figure 1. Pressure-temperature cloud-pointcurves for 3 x S-PIB (4K) in ethane (10.4 wt % 3xS-PIB) and propane (6.57 wt % 3xS-PIB). Propane solutions exhibit LCST behavior with LCEP at 8.3 "C, while ethane solutions exhibit U-LCST behavior. The open symbols represent dew point-like transitions, and the line represents the vapor pressure curve for propane. pressures are nearly 2.5 times greater than those measured in propane. For example, at 150 "C the cloud-point pressures are 656.4 bar for ethane and 270.8 bar for propane, and the difference increases with decreasing temperatures. This pressure difference is due to the increase in the asymmetry, as propane is replaced by ethane. Moreover, the magnitude change in pressure is similar to that found for the linear 1K and 11K PIB solutions; the pressure ratio between ethane and propane for CH3-PIB-CH3 (lK)7 and CH3-PIB-CH3 (llK)8 was found to be 2.5 and 2.4, respectively. Figure 2 shows the cloud-point pressures for the 3xS-PIB (4K) solutions in chlorodifluoromethane and dimethyl ether. Both systems exhibit U-LCST behavior. For dimethyl ether solutions of 6.35 wt % 3xS-PIB (4K), the UCST branch occurs at about 7 "C. In chlorodifluoromethane solutions of 1.5 wt % 3xS-PIB (4K), the UCST branch is above 100 "C. From a practical point of view, these steep branches represent the minimum temperature for miscibility; at least two phases exist below this temperature. The difference between the cloud-point curves for these two systems is likely due to the difference in solvent polarizability and affinity toward the polymer and not polarity, because both solvents have similar dipole moments. The methyl groups of the dimethyl ether increase the solvent's affinity toward the polymer, which lowers the cloud-point pressures with respect to chlorodifluoromethane solutions. A striking example of the polarity effect is shown in the inset of Figure 2, which illustrates the cloud-point pressures for 3 x SPIB (4K) solutions in propane (6.57 wt % 3xS-PIB) and dimethyl ether (6.35 wt % 3xS-PIB). These two solvents are nearly identical in size but differ in polarity: propane is nonpolar, and dimethyl ether is polar. At 150 "C, where the polarity effect is small, the cloud-point pressure in dimethyl ether solution is 58.8 bar lower than that measured in propane. However, as the temperature is lowered, the polarity of dimethyl ether increases as Up,which increases the dissimilarity between the solvent and polymer. At 8 "C, the cloud-point pressure in dimethyl ether solution is 490 bar greater than that measured for propane. This order-of-magnitude increase in pressure is due to the unfavorable polar-nonpolar interactions between the
0 ' -50
+ ~xS-PIB
I
I
I
I
0
50
100
150
200
Temperature (C) Figure 2. Pressure-temperature cloud-pointcurves for 3 xS-PIB (4K) in chlorodifluoromethane (1.5 wt % 3xS-PIB) and dimethyl ether (6.35 wt % 3 xS-PIB). Chlorodifluoromethaneand dimethyl ether solutions exhibit U-LCST behavior with UCST branches above 100 and 7 "C, respectively. The open symbols represent dew point-like transitions. The inset shows the polarity effect on the cloud-point curves for 3xSPIB in propane and dimethyl ether. solvent and polymer. These unfavorable interactions promote polymer-polymer interactions,' 1,25.26 which in turn result in the observed U-LCST phase behavior shown in the inset in Figure 2. In carbon dioxide solutions of approximately 2 wt % 3xSPIB (4K), the cloud points exceed the maximum operating pressure and temperature of the cell. That is, the UCST branch exists above 200 "C and 2000 bar.
Model Trimer Aggregate for Hydrogen-Bonding CH3-PIB-OH (1K) and HO-PIB-OH (1K) The 3 x S-PIB (4K) simulates a model trimer aggregate when viewed as a collection of aggregated arms. Here, one arm of the star represents either a CH3-PIB-OH (1K) or a HO-PIBOH (1K) that has hydrogen bonded with two other arms. In Figures 3-7, the cloud-point curves for CH3-PIB-CH3 (1K) and 3 xS-PIB (4K) establish a known-size aggregate boundary. The CH3-PIB-CH3 (1K) represents a monomer (aggregate of size = 1) and sets the low-asymmetry boundary. The 3 x S-PIB (4K) represents a trimer (aggregate of size = 3) and sets the highasymmetry boundary. These curves of known-aggregate size are compared with, and used to gauge the degree of asymmetry for, CH3-PIB-OH (1K) and HO-PIB-OH (1K) in nonpolar and polar solvents. Nonpolar Solvents. Figure 3 shows the cloud-point curves for CH3-PIB-CH3 (lK), CH3-PIB-OH (lK), HO-PIB-OH (lK), and 3 x S-PIB (4K) in propane solutions. The experimental data (symbols) and SAW calculations (lines) for the R-PIB-R (1K) are taken from Gregg et al.? and the 3xS-PIB(4K) data are from this work. As shown, the CH3-PIB-CH3 (1K) and the 3 x S-PIB (4K) boundaries, hereinafter referred to as monomer and trimer, exhibit LCST behavior with LCEP at 74.5 and 8.3 "C, respectively. If one of the end methyl groups of the monomer is replaced by a hydroxy group, then the sample becomes CH3-PIB-OH (1K) and can hydrogen bond to form aggregates. As a result, the cloud-point curve and LCEP for CH3-PIB-OH (1K) are shifted to lower temperatures (toward
Phase Behavior of Telechelic Polyisobutylene
J. Phys. Chem., Vol. 98, No. 41, 1994 10637 400
400 Trlmer (3xSPlB)
\\.
300 HOPIB-OH
300
h
h
Bf
5 9
f 200 8
200
c v)
2
CL
CL
100
100
0 -50
0
0
50
150
100
Temperature (C) Figure 3. Pressure-temperature cloud-point curves for -7 wt % CH3PIB-CH3 (lK), -7 wt % CH3-PIB-OH (lK), 6.88 wt % HO-PIB-OH (lK), and 6.57 wt % 3xS-PIB (4K) in propane. 3xS-PIB data were measured in this work; R-PIB-R (1K) data and SAFT curves were taken from Gregg et aL7 The data and curves shift toward the trimer (3xSPIB) as hydroxy groups are added, a result of an increase in asymmetry. 800
100
50
0
200
150
200
Temperature (C) Figure 5. Pressure-temperature cloud-point curves for -7 wt % CH3PIB-CH3 (lK), 6.88 wt % HO-PIB-OH (lK), and 6.57 wt % 3 x S PIB(4K) in propane. SAFT-calculated aggregate sizes for HO-PIBOH (1K) at the cloud point confirm the increase in asymmetry as the temperature is lowered, resulting in a steep UCST branch of the U-LCST curve at approximately 20 "C.
I
Trlmer (3xSPIB)
1,200 600 -
5500
1,000
-
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em 800
9
f 400 8
f 300
-
e!
-
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400 -
200 -
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lntem8wclatlngHOPIB-OH
200
'
0 -50
0
50
100
I50
200
Temperature (C)
-50
0
Exprlmentel HOPIB-OH
I
I
I
1
50
100
150
200
250
Temperature (C)
Figure 4. Pressure-temperature cloud-point curves for 13.1 wt % CH3-
Figure 6. Pressure-temperature cloud-point curves for 4.58 wt % CH3-
PIB-CH3 (lK), 13.4 wt % CH3-PIB-OH (lK), 10.4 wt % HO-PIB-OH (lK), and 10.4 wt % 3xS-PIB (4K) in ethane. 3xS-PIB data were measured in this work; R-PIB-R (1K) data and SAFT curves were taken from Gregg et aL7 The data and curves shift toward the trimer (3 xSPIB) as hydroxy groups are added, a result of increased asymmetry.
PIB-CH3 (lK), 4.41 wt % CH3-PIB-OH (lK), 4.60 wt % HO-PIB-OH (lK), and 1.5 wt % 3xS-PIB (4K) in chlorodifluoromethane. 3 x S PIB data were measured in this work; R-PIB-R (1K) data and SAFT curves were taken from Gregg et al.7 The data and curve shift toward the trimer (3 x S PIB) boundary when one hydroxy group is added, but shift away from the trimer aggregate boundary (3xS-PIB) when the second hydroxy group is added.
the trimer). Likewise for HO-PIB-OH (lK),the cloud-point pressures shift even closer to the trimer boundary, and the phase behavior becomes U-LCST. In fact, below 50 "C the cloudpoint pressures for HO-PIB-OH (1K)are much higher than those measured for 3 x S-PIB (4K). Ethane solutions of CH3-PIB-OH (1K)and HO-PlB-OH (1K) exhibit simiIar shifts in cloud-point pressures. As shown in Figure 4,the cloud-point pressures for CH3-PIB-OH (1K)shift toward those for the trimer and the behavior resembles U-LCST. The cloud-point pressures for HO-PIB-OH (1K)shift still further
toward those for the trimer, and the behavior is U-LCST. By projecting the cloud-point curve for HO-PIB-OH (1K)to lower temperatures, it is estimated that HO-PIB-OH (1K) and 3 x S PIB (4K)intersect near 70 "C and 627 bar. The monomer and trimer boundaries measured in ethane are at higher pressures than, and differ in type from, those measured in propane, a result of the increased asymmetry. This increased asymmetry also affects the magnitude of shifts due to hydrogen
10638 J. Phys. Chem., Vol. 98, No. 41, 1994 400
Gregg et al. To facilitate these plots, the SAFT equation of state is used to calculate the X,, given X,. SAFT was used in this way in earlier work by Gregg et aL6s7 and was found to be in good agreement with the data by Fulton et al.27 Because the procedure and model parameters are identical to those used in the earlier work, they are not repeated here. Furthermore, the details and uses of SAFT are not discussed either but can be reviewed in the literature (Huang and R a d o s ~ ; ~Gregg ~ , * ~ et a1.2.3,6-8).
A
300 h
kJ e
Experimental HO-PIB-OH
a 5 200
A
fn v)
2
A
L
A
100
0 -50
0
50
100
150
200
Temperature (C) Figure 7. Pressure-temperature cloud-pointcurves for -6 wt % CH3PIB-CH, (lK), 5.72 wt % CH3-PIB-OH (lK), 9.75 wt % HO-PIB-OH (lK), and 6.35 wt % 3x S-PIB (4K) in dimethyl ether. 3 x S-PIB data were measured in this work; R-PIB-R (1K) data and SAFT curves were taken from Gregg et al.' The data and curve shift toward the trimer aggregate (3xS PIB) boundary when one hydroxy group is added, but shift away from the trimer aggregate boundary (3 x S-PIB) when the second hydroxy group is added.
bonding. As can be seen by comparing Figures 3 and 4, larger pressure shifts per hydroxy group are found in ethane solutions. In both propane and ethane, as the number of hydroxy groups on the PIB increases, the cloud points shift to higher pressures because the polymer self-associates through intermolecular interactions and forms hydrogen-bondedclusters. These clusters increase the effective degree of asymmetry and, hence, the cloud-point pressures. Furthermore, because the CH3-PIB-OH (1K) curve is bounded by the monomer and trimer curves, the degree of asymmetry for this system is expected to lie between that for the monomer and trimer systems. On the other hand, the HO-PIB-OH (1K) cloud-point pressures exceed those measured for the trimer below 60 "C, which suggests that the HO-PIB-OH (1K) asymmetry exceeds that for the trimer system. Aggregate Size Calculations. To illustrate further that hydrogen bonding increases the asymmetry and the cloud-point pressures, the aggregate size for HO-PIB-OH (1K) in solution is estimated. The procedure is based upon a postulated massaction-type principle, an approach recently used by Fulton et al.,27which describes the aggregation process:
where X, is the monomer mole fraction, X, is the aggregate mole fraction, and n is the number of monomers that hydrogen bond to form the aggregate, which is referred to as the aggregate size. Inherent to this approach is the assumption that only an aggregate of uniform size exists. From this stoichiometry, an equilibrium constant can be defined and rewritten in terms of total solute mole fraction (Xt), monomer mole fraction (Xm), and aggregate size (n): ln(X,-X,)
= n ln(X,)
+ ln(nK,)
(2)
Plots of ln(X,-X,) versus ln(X,) result in lines with slopes equal to n and intercepts equal to nK,.
Shown in Figure 5 are the SAFT-calculated cloud-point curves for CH3-PIB-CH3 (1K) and HO-PIB-OH (lK), taken from Gregg et a1.: along with the trimer data measured in this work. In addition to the curves, the calculated aggregate size is indicated. For example, the aggregate size for the trimer is n = 3 and that for the monomer n = 1, both of which are independent of temperature. However, for the hydrogenbonding HO-PIB-OH (lK), a decrease in temperature increases the aggregate size. At 100 "C, the aggregate size of HO-PIBOH (1K) is slightly larger than a dimer (2.3) and results in cloudpoint pressures that are bounded by those pressures measured for the monomer and trimer. At 20 "C, where the cloud-point pressure for HO-PIB-OH (1K) is greater than that for 3xSPIB (4K), the calculated aggregate size of HO-PIB-OH (1K) is 8.2. Thus, the higher cloud-point pressures for HO-PIB-OH ( 1K) are due to the increase in asymmetry over that of the trimer system. Although not shown, analogous behavior is observed in ethane solutions. As shown in Figure 4, the SAFT-predicted cloud-point curve for HO-PIB-OH (1K) crosses over that measured for the trimer at 100 "C. At this temperature and pressure the calculated aggregate size for HO-PIB-OH (1K) is 2.5, close to that of the trimer. Polar Solvents. Figures 6 and 7 show the cloud-point curves for the CH3-PIB-CH3 (lK), CH3-PIB-OH (lK), HO-PIB-OH (lK), and the trimer in chlorodifluoromethane and dimethyl ether, respectively. The experimental data (symbols) and SAFT calculations (curves) for the R-PIB-R (1K) are taken from Gregg et al.,7 and the trimer data are from this work. As shown in Figure 6 for chlorodifluoromethanesolutions, the monomer and trimer are both U-LCST with UCST branches near 60 and 115 "C, respectively. The cloud-point pressures measured for CH3PIB-OH (1K) are shifted away from the monomer boundary toward the trimer. Specifically, the UCST branch shifts +10 "C and is a result of the increased asymmetry even though chlorodifluoromethane can cross-associate with the CH3-PIBOH (1K) hydroxy groups. The experimental data show that the second hydroxy group shifts the cloud-point curve away from the trimer boundary and below the monomer boundary. As it was discussed by Gregg et aL7 this suggests that the asymmetry decreases as a result of intramolecular association. That is, the hydroxy groups on the same molecule self-associate to form a monomer (n = 1). On the other hand, if only intermolecular association of the hydroxy groups is allowed, the cloud-point curve (estimated from SAFT) shifts toward the trimer curve, as shown in Figure 6. Like the behavior in chlorodifluoromethane solutions, dimethyl ether solutions of CH3-PIB-OH (1K) and HO-PIB-OH (1K) exhibit similar shifts in cloud-point pressures. Figure 7 shows that the monomer boundary is LCST and the trimer boundary is U-LCST. These boundaries are closer together than those for chlorodifluoromethane because of the higher affinity of dimethyl ether toward the polymer. The LCEP of the monomer boundary is at 115.0 "C, and the UCST branch for the trimer boundary is near 6 "C. The cloud-point pressures for CH3-PIB-OH (1K) shift away from the monomer boundary
Phase Behavior of Telechelic Polyisobutylene toward the trimer boundary. The curve remains LCST, with a LCEP predicted at 95.1 "C (Gregg et al.'). The second hydroxy group on HO-PIB-OH (1K) does not significantly increase the cloud-point pressures relative to the monomer. Again, this is due to intramolecular association. The hypothetical cloud-point curve for intermolecularly associating HO-PIB-OH (1K) is shown to be close to the trimer boundary, as shown in Figure 7. Conclusions The cloud-point pressures and phase-behavior type for the three-arm-star PIB in subcritical and supercritical solutions are related to the size and polarity differences between the solvent and polymer. As these differences increase, so does the cloudpoint pressures and the probability of U-LCST phase separation. The three-ann-star PIB represents a model trimer aggregate, and the CH3-PIB-CH3 (1K) represents a model monomer. Their phase boundaries are used as benchmarks of known aggregate size to evaluate the aggregate size, and hence the effective asymmetry, of CH3-PIB-OH (1K) and HO-PIB-OH (1K). CH3PIB-OH (1K) hydrogen bonds to form clusters that increase the asymmetry and thus increase the cloud-point pressures. HOPIB-OH (1K) hydrogen bonds intramolecularly to form monomer aggregates in polar solvent, which lowers the size asymmetry and thus lowers the cloud-point pressures. Acknowledgment. The authors wish to thank Professor Rudolf Faust of the Department of Chemistry, University of Massachusetts in Lowell, for the synthesis and characterization of the three-arm-star polyisobutylene sample. References and Notes (1) Radosz, M. In Supercritical Fluids-Fundamentals for Applications; Kiran, E., Levelt-Sengers, J. M. H., Eds.; Kluver: Amsterdam, 1994; pp 61 9-627. (2) Gregg, C. J.; Chen, S-j.; Stein, F. P.; Radosz, M. Fluid Phase Equilib. 1993, 83, 375.
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