Phase Behavior of Telechelic Polyisobutylene (PIB) in Subcritical and

Aug 1, 1994 - Yoann Dini , Mildred Becerra , and John M. Shaw. Journal of Chemical ... Erich A. Müller , Keith E. Gubbins. Industrial & Engineering C...
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Macromolecules 1994, 27, 4912-4980

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Phase Behavior of Telechelic Polyisobutylene (PIB) in Subcritical and Supercritical Fluids. 1. Inter- and Intra-Association Effects for Blank, Monohydroxy, and Dihydroxy PIB(1K) in Ethane, Propane, Dimethyl Ether, Carbon Dioxide, and Chlorodifluoromethane Christopher J. Gregg,+ Fred P.Stein: a n d Maciej Radosz*J Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, and Exxon Research and Engineering Company, Annandale, New Jersey 08801 Received December 14, 1993; Revised Manuscript Received June 10, 1994@

ABSTRACT The cloud-pointpressuresfor nonfunctional (referredto as blank),monohydroxy,and dihydroxy telechelic polyisobutylene were measured in ethane, propane, chlorodifluoromethane, dimethyl ether, and carbon dioxide up to 200 "C and 2000 bar. These amorphous polyisobutylene samples of molecular weight around 1000 are nearly monodisperse and have zero, one, or two terminal hydroxy groups. In nonpolar solvents,the hydroxy groups increasethe cloud-pointpressures. In polar solvents,however,one group increases but two groups decrease the cloud-point pressures. These shifts in pressures are interpreted on the basis of intermolecularand intramolecular association estimated from the statistical associating fluid theory (SAFT). Introduction The phase behavior of supercritical fluid solutions of polymers is easily controlled by varying the system temperature and pressure.14 This behavior is often mapped onto the pressure-temperature coordinates and the resulting curves are referred to as cloud-point curves. These curves can represent the upper critical solution temperature (UCST),lower critical solution temperature (LCST),or upper-lower critical solution temperature (ULCST) type of phase separation. Saeki et al.7-9 and Pattersonlo showed on the basis of Flory theory that, to a first approximation, differences in energetic interactions between the solvent and polymer result in UCST phase separation and that differences in thermal expansion coefficients between the solvent and polymer result in LCST phase separation. Chen and Radosz,ll Chen et d.12and Gregg et al.13 experimentallycharacterized differenttypes of cloud-point curves for supercritical fluid solutions of poly(ethy1enepropylene) in terms of system asymmetry. As the size difference between the polymer and the solvent increased, that is to say as the asymmetry increased, the UCST curve shifted toward higher temperatures while the LCST curve shifted toward lower temperatures until the two curves merged to form a single U-LCST curve. In addition to the measurements, they were able to calculate this asymmetry effect, including the merging of the UCST and the LCST curves, by using the statistical associating fluid theory model (SAFT). The system asymmetry can also be increased effectively by allowing associating polymers to form short-lived, hydrogen-bonded clusters or aggregates. Therefore, the goal of this work is to collect cloud-point data for such associating polymeric systems in solutions with supercritical fluids. The polymers selected for this study are nearly monodisperse, amorphous, end-functionalized polyisobutylenes often referred to as tele~helics.'~J5These samples are of both industrial1G19and academic interest%z because they exhibit unusual thermodynamic and rheo-

* To whom correspondence should be addressed. University. 1 Exxon Research and Engineering Co. t Lehigh

e Abstract published in

Advance ACS Abstracts, July 15, 1994.

0024-929719412227-4972$04.50/0

Table 1. Physical Properties of the Solvents* Mw 1VaQ 1V% solvent (g/mol) T,(K) P, (bar) c (D) cm6l2) (cm9 304.1 73.8 0.00 4.00 26.5 coz 44.0 89.4 1.10 1.97 34.1 373.2 HzS CHClFz 86.5 369.3 48.7 1.48 0.00 105.0 52.7 1.50 1.19 CzHeO 46.1 400.1 33.0 12.9 0.00 0.66 7.9 2.0 Hz 190.4 46.0 0.00 0.00 26.0 CH4 16.0 52.0 305.4 48.8 0.00 0.00 CzHs 30.1 78.0 42.5 0.00 0.00 44.1 369.8 C3H8 a t

dipole moment; Q

polarizability.

= quadrupole moment;

a

average

logical pr0perties,23-~~ they serve as the starting material for block and graft copolymer synthesis, and they are wellcharacterized examples of a larger class of associating polymers. These polymers are also ideal candidates for thermodynamic modeling. They offer a unique way of determing the SAFT association parameters because their cloud-point data can be referenced to data for the corresponding nonassociating polyisobutylene systems. Specifically,this work addresses issues related to the cloudpoint calculation for the telechelic solutions such as (1) the telechelic pure-component parameters, (2) the association parameters, and (3) the binary interaction parameters (hi,).

Phase Equilibrium Measurements Solvents and Polymers. Five solvents were selected to study the various degrees of self-association and cross-association between telechelic (R-PIB-R)polymers and solvent molecules:

namely,ethane,propane, chlorodifluoromethane,dimethyl ether, and carbon dioxide. These fluids were purchased from Matheson with a known minimum purity of 99.8% and were used without further purification. Table 1lists the physical property data for the various solvent^.^^^^ Three nearly monodisperse amorphous polymers (Mw/M,,5 1.15)were selected for this study: blank, monohydroxy, and dihydroxy polyisobutylenes. These three samples,synthetically prepared by living carbocationicpolymerization,28have identical backbone structure,essentially the same number of repeat units (degree of polymerization (DP)),and a known functional group location. As schematically illustrated in Figure 1, each sample has an approximate degree of polymerization equal to 20 with 0 1994 American Chemical Society

Phase Behavior of PIB in Supercritical Fluids 4973

Macromolecules, Vol. 27, No. 18, 1994 Cy-PlB-CH, (lk)

Table 2. SAFT Pure Component Parameters (m, e, d/k)

blank PIE

coz CH,-PIB-OH (lk) monohydroxy PIB

HO-PIB-OH (k) I dlhydroxy PIB

Figure 1. Chemical structures for telechelic polyisobutylenes.

Q

Q

Q

TO SAMPLING DEVICE TEMPERATURE SENSOR

FROM LOADING PUMP

Figure 2. Schematic of the variable-volumeoptical cell (Gregg et al.9: (1)main body: (2)front gland nut; (3) Viton O-ring; (4) brass heating block; (5) Viton O-ring; (6) sapphire window; (7) rear gland nut; (8) tube gland; (9) Viton O-ring; (10)moveable piston; (11)Viton O-ring; (12)braas window cap; (13) heating jacket. zero, one, or two hydroxy groups attached directly to ends of the chain. Experiment. The clouid points were measured in a variablevolume optical cell that has been discussed in detail by Gregg et a1.m As shown in Figure 2,the cell is equipped with a sapphire window, moveable piston, feed, sampling, and RTD ports, brass block, and heating jacket. The key components are the window and piston, which allow for visual observation of the phase transitionsand continuouscontrolof the cellvolume and pressure at constant composition. In operation, known amounts of polymer and solvent are loaded into the cell and stirred with a magnetic stir bar. The piston is then moved toward the window to reduce the sample volume and increasepressureto form a homogeneoussolution. After adjusting temperature and establishingequilibrium,the pressure is reduoed at constant temperature by moving the piston away from the window until the solutionturns hazy, as seen througha borescope. At this time the cloud-point pressure is recorded and identified as either bubble point-like or dew point-like,ll depending upon the phase disengagement pattern. Next, a new temperature is establiahed and the procedure repeated 80 as to produce a pressuretemperature isopleth curve.

SAFT Modeling The statistical associating fluid theory (SAFT) model is applicable to small and large, chain, and associating molecules. The SAFT equation of state used in this work, uoo, u o / k ) including the pure-component parameters (m, and extension to mixtures via the van der Waals one-fluid (vdW1) mixing rules, is given by Huang and Radosz.30~31 SAFT applications are illustrated for solution of long-

CZHe C3Hs CHsOCHa CHClF'z CHs-PIB-CHa(1K) CHs-PIB-OH(1K) HO-PIB-OH(1K)

44.0 30.1 44.1 46.1 86.5 1 W 112P 1300'

1.417 1.941 2.696 2.799 3.752 28.41 31.77 36.81

13.59 . 14.46

13.46 11.54 7.33 12.00 12.00 12.00

216.08 194.83 193.03 207.83 162.82 225.00 225.00 225.00

Weight-average molar mass;Mw/MnI 1.15.

chain n-alkanes,13p o l y m e r ~ , ~and ~ J hydrogen-bonding ~*~~ diols.33 Huang and Radosz30 found that the SAFT purecomponent parameters for n-alkanes were strongly correlated to molecular weight, thus making it possible to estimate parameters for polymers with n-alkane-like structure, for example, polyethylene (PE). We use this correlation but correct for the difference in repeat structure between polyisobutylene (PIB) and PE. For instance, the repeat structure of PIB is double in mass (M= 56 g/mol) compared to the analogous repeat structure for the PE (M = 28 g/mol). As a result, for the same molecular weight, a PIB chain will be about 2 times shorter than the corresponding P E chain. Hence, we use an empirical correction: the estimated mpEvalue (the number of SAFT segments) is multiplied by 0.6 to obtain the corresponding ~ P I Bvalue. The other SAFT parameters-molecular volume (uoo) and energy (uo/k)-are similar to those for n-alkanes: 12.00 cm3/mol and 225 K, respectively. This set of parameters allows for good agreement between SAFT and the literature results for propane + CH3-PIB-CH3 (2K): SAFT is used to calculate the slope of the pressuretemperature curves (dP/dT) a t the lower critical end point and is found to be 2.13, which compares with the result from Zeeman et who used experimental data to estimate dP/dT = 2.08. Ideally, all of the association parameters should be determined from independent spectroscopic measurements. However, in this work, the self-associating energy (e) and bond volume ( K ) for CH3-PIB-OH (1K) were determined from spectroscopic data and the cross-association t and K for carbon dioxide, chlorodifluoromethane, and dimethyl ether were determined from equlibrium data. Specifically, the FTIR-measured monomer concentration data of Fulton et al.3sfor alcohol solutions were correlated with SAFT to yield the self-association parameters. The details are provided by Gregg et al.% The cross-association parameters, describing (1)the interactions between the hydroxy gorup and the quadrupole moment of carbon dioxide and (2) the hydrogen bonding between the hydroxy group and chlorodifluoromethaneand dimethyl ether, were determined by fitting the cloud-point data collected in this work. This procedure requires first capturing the solventpolymer interaction by correlating a binary interaction parameter ( k i j ) related to the dispersion forces. For each solvent, the temperature-dependent kij is fitted to the cloud-point pressures for CH3-PIB-CH3(1K). Next, the cross-association e and K are adjusted until SAFT reproduces the experiment cloud-point data for the CH3-PIBOH(1K) solutions. In these solutions the polymer can self-associate as well as cross-associate; thus the selfassociation parameters derived from spectroscopic data are used. This set is also used for HO-PIB-OH(1K) solutions. Table 2 lists the nonassociation and Table 3 lists the association parameters.

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Gregg et al.

Macromolecules, Vol. 27, No. 18, 1994 Table 3. SAFT Association Parameters (e/k,I ( )

self-association"OH---OH system

c/k (K)

K

CHs-PIB-CHs( 1K) CHs-PIB-OH( 1K) HO-PIB-OH( 1K)

2752 2752

0.015 0.01 5

cross-associationb CClFz-H---HO elk (K) K 2064 2064

0.025 0.025

OH---O(CHs)z c/k(K) K 1700 1700

0.010

0.010

OH---O=C=O

elk (IO

K

1320 1320

0.010 0.010

Association parameters determined from spectroscopic data except for K , which is reduced from 0.02 to 0.015 in this work. Association parameters determined by fitting the cloud-point data of CH3-PIB-OH(lK) solutions.

0 SAFT

I

IO

Temperalure C

Figure 3. Binary pressure-temperature diagramsfor CH3-PIB-

CHs(1K)(upper)inethane (CzHe)and propane (C3He)and (lower) in chlorodifluoromethane(CHClF2),dimethyl ether (CHSOCH~), and carbon dioxide (COz). The difference in cloud-point curves shows the effects of asymmetry and polarity. Experimental and Modeling Results Solvent Effect on Cloud Points. Over 200 cloudpoint pressures on 15 isopleth phase-boundary curves measured in this work for CH3-PIB-CH3(1K), CH3-PIBOH(lK), and HO-PIB-OH(1K) in ethane, propane, chlorodifluoromethane,dimethyl ether, and carbon dioxide up to 200 "C and 2000 bar are plotted in pressuretemperature coordinates and are tabulated in Tables I-V in the Supplementary Material (available separately; see Supplementary Material paragraph at the end of this article). In the figures that follow, the experimental data and SAFT curves are referred to as LCST, UCST, or U-LCST and represent the cloud-point phase boundaries. The area above each curve is the one-phase region and the area below the curve is the two-phase region. Furthermore, for a given solvent, the feed compositon from sample to sample is nearly constant. Figure 3 shows the cloud-point pressures and SAFT curvesfor CHrPIB--CH3(lK) in polar and nonpolar fluids. The upper diagram shows the results for ethane and propane solutions,and the lower diagram shows the results for carbon dioxide, chlorodifluoromethane,and dimethyl ether solutions. LCST behavior is observed for CH3-PIB-

CHdlK) in ethane and in propane; SAFT predicts the lower critical end points (LCEP) at -51.6 for ethane and 76.1 O C for propane. The difference in pressures and LCEP between these two curves is a result of an increase in the size asymmetry as propane is replaced with ethane. The lower diagram in Figure 3 (note the change in pressure scale) shows the cloud-point pressures and SAFT curves for CH3-PIB-CH3( 1K) in carbon dioxide, chlorodifluoromethane, and dimethyl ether solutions; these solvents differ in polarity and affinity toward CH3-PIBCH3(1K). For carbon dioxide, the cloud-point pressures are U-LCST with a steep UCST branch near 100 OC and are a t least double those measured for ethane. This is a clear exampleof the different solvating properties of carbon dioxide and ethane. Carbon dioxide has a lower affinity, because of its lower polarizability and higher polarity, toward the polymer backbone than does ethane. Thus higher pressures are required to dissolve CH3-PIB-CH3(1K) in carbon dioxide. Chlorodifluoromethane, on the other hand, is more polarizable than carbon dioxide, resulting in a higher affinity toward the polymer backbone. Thus, the chlorodifluoromethane cloud-point pressures are lower, even though the size asymmetry is greater. The UCST branch for chlorodifluoromethane solutions is more than 50 "C below that measured in carbon dioxide. The methyl groups of dimethyl ether further increase the affinity toward the polymer backbone, even though dimethyl ether is about as polar as chlorodifluoromethane. Therefore, the dimethyl ether cloud-point pressures are much lower and similar to those measured in propane. The dimethyl ether behavior is of the LCST type with no UCST branch observed. Qualitatively, the cloud-point pressure for these nonassociating systems is found to depend upon both the size asymmetry and the solvent polarity. This balance is quantitatively captured by SAFT, as shown in Figure 3. Cloud-Point Pressures for CHrPIB-CHs( lK), CH3PIB-OH( lK), a n d HO-PIB-OH( 1K) in Propane and Ethane. Figures 4 and 5 show the cloud-point pressures for CH3-PIB-CH3(1K), CH3-PIB-OH(lK), and HO-PIBOH(1K) in propane and ethane solutions. In both solvents, CH3-PIB-CH3( 1K) (our base-line system) exhibits LCST behavior, with an LCEP projected onto the vapor pressure curve of the solvent. When one of the end methyl groups is replaced by a hydroxy group, CH~-PIB-CHS(~K) becomes CH3-PIB-OH(lK) and the LCST curve shifts to higher pressures. For propane, the behavior remains LCST but the LCEP shifts by -16.9 O C to 59.2 O C . For ethane, the cloud-point pressures at constant temperature increase by at least 100 bar and become U-LCST. The second hydroxy group further increases the cloudpoint pressures. Propane solutions of HO-PIB-OH(1K) become U-LCST with large deviations from the CH3-PIBCHs(1K)base-line curve at lower temperatures. In ethane, the U-LCST curve for HO-PIB-OH(1K) shifts to even higher pressures. The shift in cloud-point pressures for these two systems is readily explained in terms of intermolecular selfassociation. The addition of a hydroxy group induces the

Phase Behavior of PIB in Supercritical Fluids 4975

Macromolecules, Vol. 27,No.18, 1994 Ann

CHJ-PIB-CH~(1 k)

0 -50

50

0

100

200

150

Temperature (C) Figure 4. Binary pressure-temperature diagram for CsH8 + CHs-PIB-CHs( lK),CHs-PIB-OH(lK), and HO-PIB-OH(1K). Self-associationof polymer molecules due to hydrogen bonding shifts the curves to higher pressure. The curves are calculated by SAFT. The solid data points represent experimental bubble point-liketransitions,and open symbolsrepresent experimental dew point-like transitions. 700

- SAFT

C2Hg + HO-PIB-OH ( l k )

600

-b

500

& 400

E2

3 300 200

+ CHyPIB-CH3 ( I k )

I00 0 -50

0

50

100

150

200

250

300

Temperature (C) Figure 5. Binary pressure-temperature diagram for CzH6 + CHs-PIB-CHs(lK), CHg-PIB-OH(lK), and HO-PIB-OH(1K). Self-associationof polymer molecules due to hydrogen bonding shifts the curves to higher pressure. The curves are calculated by SAFT. The solid data points represent experimental bubble point-liketransitions,and open symbols represent experimental dew point-like transitions. formation of hydrogen-bonded polymer aggregates. As the number of hydroxy groups increases, in this case from one to two, the degree of association and hence average aggregate size increase. This effectively increases the degree of asymmetry. Therefore, the phase boundaries shift to higher pressures in going from CH3-PIB-CH3(1K) through CH3-PIB-OH(lK) to HO-PIB-OH(1K). The aggregate size, defined as the average number of molecules per aggregate and also referred to as the aggregate number (N,),can be estimated through a massaction-type expression that relates the monomer and aggregate stoichiometric concentrations. This approach has been recently used to estimate the average aggregate size from spectroscopic data% and SAFT monomerconcentration predictions33for alcohol solutions. As shown in Table 4 at 100 "C and near the cloud-point pressures,

the average aggregate size for HO-PIB-OH(1K) in ethane is Na = 2.5 (nearly a trimer). By comparison, the average aggregate size for CH3-PIB-OH(lK) is a dimer (Na= 2.0) and, of course, the nonassociating CHa-PIB-CHs( 1K) exists as a monomer (N,,= 1.0). In this example, as the number of hydroxy groups increases, so does the aggregate size and hence asymmetry; zero hydroxy groups correspond to a monomer, one hydroxy group results in a dimer, and two hydroxy groups result in a trimer. The degree of asymmetry is expected to increase with decreasing temperature because hydrogen bonding increases with decreasing temperature. As shown in Table 4, a decrease in temperature from 200 to 100 "C does not change N,, but rather increases the extent of aggregation of CH3-PIB-OH(lK), the mole fraction of polymer molecules involved in hydrogen bonding, in ethane increases from 0.02 to 0.08. Similarly, for HO-PIB-OH(1K) in ethane, the aggregate size increases from Na = 2.2 to N , = 2.5 and the extent of aggregation increases from 0.05 to 0.27. This increase in asymmetry, as the temperature is lowered, explains the increase in cloud-point pressures relative to the blank PIB case, illustrated in Figure 5. The SAFT cloud-point curves are in good agreement with the experimental data for propane and are in qualitative agreement with the experimental data for ethane. However, it must be pointed out that the K determined from the spectroscopic data was reduced from 0.020 to 0.015 for both propane and ethane. This change improved the agreement between SAFT and data for propane solutions of CH3-PIB-OH( 1K). No further adjustment was necessary to predict the cloud points for HO-PIB-OH(1K) in propane and for CH3-PIB-OH(lK) and HO-PIB-OH( 1K) in ethane. Clearly, SAFT captures the associating effects due to the system temperature, solvent type, and number of polymer hydroxy groups. Cloud-PointPressure for CH3-PIB-CH3( lK), CH3PIB-OH(lK), and HO-PIB-OH( 1K) in Chlorodifluoromethane, Dimethyl Ether,and Carbon Dioxide. Figures 6-8 show the pressure-temperature cloud-point data for binary solutions of CH3-PIB-CH3(1K), CH3-PIBOH(lK), or HO-PIB-OH(1K) in chlorodifluoromethane, dimethyl ether, and carbon dioxide. The data points shown in these figures are measured experimentally, and the curves are estimated from SAFT assuming intermolecular association only. As shown in Figure 6 (upper) for chlorodifluoromethane,the CHB-PIB-CH~(~K) solutions exhibit U-LCST behavior, with a steep UCST branch above 50 "C. When one methyl end group is replaced by a hydroxy group, the cloud-point curve shifts to higher pressures and temperatures. In these solutions there are two types of intermolecular association: the self-association of the hydroxy groups and the cross-association between the hydroxy groups on PIB and the hydrogen on chlorodifluoromethane. Provided that both interactions are characterized by the association parameters, the SAFT calculations are in good agreement with the experimental data. For HO-PIB-OH( 1K) solutions, assuming two sites per molecule and assumingintermolecular association only, the predicted cloud-point pressures increase by over 100 bar and the U-LCST branch is shifted by 75 to 125 "C, as shown in the lower part of Figure 6 . However, the experimental cloud-point curves shift to lower pressures. Below 100 "C, the cloud-point pressures for HO-PIBOH(1K) are actually lower than those measured for CH3PIB-CHd 1K). As the temperature approaches and exceeds the solvent critical temperature, around 100 "C,

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Macromolecules, Vol. 27, No. 18, 1994

Gregg et al.

Table 4. SAFT Predicted & M a t e Size (N.) for CHS-PIB-OH(1K) and HO-PIB-OH( 1K) C& solvent C3Ha solvent system comp (mol frac) tempa ("C) Nab estc N, ext CHs-PIB-CHs( 1K) all comp all temp 1.0 1.0 1.0 1.0 CHs-PIB-OH( 1K) 0.002-0.006 100.0 2.0 0.08 0.002-0.006 200.0 2.0 0.02 HO-PIB-OH( 1K) 0.002-0.006 40.0 4.3 0.61 0.002-0.006 100.0 2.5 0.27 2.3 0.20 0.002-0.006 200.0 2.2 0.05 Aggregate size calculatedat pressures 1.05times the mixture critical pressure. * N , = average aggregate size. ext = extent of aggregation on a solvent-free basis. defined as 1.0 - monomer mole fraction.

6oo

500

fi

I c Interrrtocuting HO-PIE-OH ( I k )

300

e 5 400

CH3OCH)

HOPIE-OH (1 k)

5 200 *O0

I , , CHCIF + CH3PIEZH

100

0

(Ik)

, -,

5wt 1I

8 E

Q

SAFT

I00

0

50

0

100

I k CHCIF 2 + CHjPlBZH

400

J

(1k1

-

0

SAFT

co2

c: 100

250

Figure 7. Binary pressure-temperature diagram for CHaOCHa + CH3-PIB-CHs(lK), CHa-PIB-OH(lK), and HO-PIB-OH(1K). Self-associationof polymer molecules shifts the curve to higher pressure and intramolecular association shifts the curve to lower pressure. The curves are calculated by SAFT assuming only intermolecular association.

1

50

200

150

Temperature C

150

200

250

1,600

CH3-PIB.OH(lk)

CHrPIBCH3 ( I k )

Temp.ntun (C)

Figure 6. Binary pressure-temperature diagrams for CHCAF, + CHs-PIB-CH3(1K), CHs-PIB-OH(lK), and HO-PIB-OH(1K). (Upper) Self-association of polymer molecules shifts the curve to higher pressure and (lower)intramolecular association shifts the curve to lower presusre. The curves are calculated by SAFT assuming only intermolecular association. the cloud-pointpressures for HO-PIB-OH(1K) are slightly above those for CH3-PIB-CH3(1K). Shown in Figure 7 are the experimental cloud points and SAFT curves for CH3-PIB-CH3(1K), CH3-PIB-OH(lK),and HO-PIB-OH(1K) in dimethyl ether. Dimethyl ether solutions of CHs-PIB-CH3(1K) exhibit LCST behavior with an LCEP a t 117.0 "C. When one of the end methyl groups is replaced with a hydroxy group, the LCST curve shifts to higher pressure by over 40 7% ,and the LCEP decreases by 21.7 to 95.1 "C. This trend is accurately captured by SAFT. The addition of a second hydroxy group shifts the experimental cloud-point data to lower pressures, toward those measured for CH3-PIB-CHs(lK). This behavior is similar to that found in the chlorodifluoromethane solutions. As for chlorodifluoromethane, assuming two sites per molecule and assuming intermolecular association only, SAFT predicts that the cloudpoint pressures for HO-PIB-OH(1K) increase and that the LCEP shifts to lower temperatures. The predicted LCEP is 80.1 "C, but the experimental value is 115.0 "C.

eb ,200 E

P

800

/

HO-PIB-OH (1k)

Inter-associating HO-PIB-OH ( l k )

400

-

SAFT

,

0 0

50

100

150

200

250

300

Temperature C

Figure 8. Binarypressure-temperature diagramfor Cot + C& PIB-CHs(lK),CHs-PIB+H(lK), and HO-PIB-OH(1K). &Ifassociation of polymer molecules shifts the curve to higher pressure and intramolecularassociation shifts the curve to lower pressure. The curves are calculated by SAFT assuming only intermolecular association.

To illustrate that these unusual shifts (the decrease in cloud-point pressure upon adding the second hydroxy group) are not limited to hydrogen-bonding solvents, the cloud points for CH3-PIB-CH3(1K), CHs-PIB-OH(lK), and HO-PIB-OH( 1K) were measured in carbon dioxide and are shown in Figure 8. The U-LCSTbehavior of CH3-

Phase Behavior of PIB in Supercritical Fluids 4977

Macromolecules, Vol. 27, No. 18, 1994 CH. + P r o p y k y s b h l m

I

400

-z

300

e 9

z?? 200

0.

100

0

0

0.2

0.4

0.6

0.8

1

Solute Concentration (mol-fr)

Figure 9. Binary pressure-composition (2' = 40 "C) data for nonane and propylcyclohexane in CH4 (uppertwo data seta) and heptane and methylcyclohexanein HzS (lowertwo data seta).In HzS, the ring and chain structures have nearly coinciding phase envelopes,but in CHI positive excess molar volumes (inset) give rise to large differences in phase envelopes.

PIB-OH(1K) is shifted 50 OC toward high temperatures relative to the base-line system. Although carbon dioxide has no specific site for hydrogen bonding, it does possess a quadrupole moment which can interact with hydrogenbonding groups.3w1 The SAFT-calculated cloud-point curve for CH3-PIB-OH(lK) is in agreement with the experimental results. As for chlorodifluoromethane and dimethyl ether solutions, the SAFT-predicted cloud-point curve for HO-PIB-OH(1K) shifts in the opposite direction to the experimental results. Experimentally, the HOPIB-OH(1K) cloud-point curve is below that of the baseline system.

Intermolecular and Intramolecular Association In polar solvents, such as those discussed above, the addition of one terminal hydroxy group shifts the cloud points to higher pressures but the addition of two terminal groups either (1) does not shift or (2) lowers the cloud points relative to the base-line system. This can be explained by hypothesizing two competing types of association: intermolecular and intramolecular. While only intermolecular association can occur in the CH3PIB-OH(1K) solutions, both types of association can occur in the HO-PIB-OH(1K) solutions. Furthermore, nonpolar solvents are likely to promote the intermolecular association, whereas polar solvents are likely to promote the intramolecular association. This hypothesis can be justified with the following three examples: (1)the phase behavior of n-alkanes and cycloalkanes in nonpolar and polar fluids, (2) the end-to-end probability of intramolecular hydrogen bonding (end-to-end probability) and polarity effects on chain dimensions, and (3) the phase behavior of associating ring compounds. Phase Behavior for n-Alkanes and Cycloalkanes in Nonpolar and Polar Fluids. Figure 9 shows the overlaid pressure-concentration diagram4u5 for binary systems of nonane in methane (CHI) and propylcyclohexane in methane (CHI) at 40.5 "C and for heptane in hydrogen sulfide (HzS) and methylcyclohexane in hydrogen sulfide (H2S) at -40 O C . The curves are grouped by solvent polarity and solute carbon number; the upper two curves are for a nonpolar system with a Cg solute, and the lower two curves are for a polar system with a C7 solute.

As can be seen for methane, the difference in phaseboundary pressures between nonane (Cg chain) and propylcyclohexane (Cg ring) near the mixture critical pointis over 100 bar; the chain structure is more readily miscible (requires lower pressures) than the ring structure. In contrast, the phase-boundary pressures for heptane (C7 chain) and methylcyclohexane (C7 ring) in hydrogen sulfide essentially coincide over the entire composition range. The same trend is observed for hexane and cyclohexane in hydr0gen,4~1~~ pentane and cyclopentane in carbon d i ~ x i d ehexane , ~ ~ ~and ~ methylcyclopentane in methane, and heptane and methylcyclohexane in methane.18 All of these examples suggest that the chain and ring structures have like miscibility in polar but unlike miscibility in nonpolar solvents. The inset of Figure 9 shows the excess molar volumes for cyclohexane and hexane in hydrogen; positive values are found for the ring and negative values are found for the chain in The positive values for the ring are a plausible explanation for the phase-boundary difference between the chain and ring systems in nonpolar solvents: higher pressures are required to overcome the larger entropy of mixing. Although similar excess volume data are not available for chains and rings in polar solutions, it is possible that the corresponding excess molar volumes are nearly equal in magnitude and sign, thus leading to similar phase-boundary pressures. These observations of macroscopic behavior do not explain the microscopic driving forces behind intramolecular association of HO-PIB-OH( 1K). They simply illustrate the differences, or lack of difference, in phaseboundary pressures and excessvolumes of mixing for polar and nonpolar solutions of chains and corresponding rings. The useful conclusion here is that, if a ring is formed in a polar solution, the phase boundary would not differ from that of the analogous chain. Intramolecular Hydrogen Bonding (End-to-End Probability) and Chain Dimensions for Polymers. It is known that ring structures become more thermodynamically stable as the number of ring members (ringsize) increase, as indicated by heat of combustion data for ~ycloalkanes.5~ These data indicate that the bond strain within a ring diminishes to zero as the carbon number exceeds 14. This means that HO-PIB-OH(1K) is long enough to form stable rings through intramolecular hydrogen bonds. The statistics of random, flexible chains with attractive ends56 should indicate if such intramolecular hydrogen bonding for HO-PIB-OH(1K) is realistically probable. The probability of two ends interacting is a function of both site-site energy and chain length, given by

where PO a DPa (degree of polymerization, the chain length) and UILT is the site-site energy. Figure 10 illustrates this probability for various chain lengths and temperatures. As shown on the left, the probability to form an intramolecular hydrogen bond increases sharply with decreasing chain length and increasing site energy. For a chain of DP = 20, a value similar to that for HOPIB-OH(lK), and 0 "C, the intramolecular probability ranges from 12.5 to 84.9% for hydrogen-bonding energies between 2000 and 4000 cal/mol. For a chain of DP = 20, the intramolecular probability at 100O C decreases to 5.1 % from 44.096, as the hydrogen-bonding energy decreases from 4000 to 2000 cal/mol, as shown on the right of Figure 10.

Macromolecules, Vol. 27, No. 18, 1994

4978 Gregg et al. 1

100,

T 8 0.OC

-E

I

100

DP = 20

75

m

f

25

L-3

I

U=2000 cal

0

50

0

150

100

I

Ue2000 cal

-I O

200

0

50

Chain Length (Degree of Polymerization)

150

100

200

Temperature (C)

Figure 10. Random walk calculations indicate that intramolecular association (end-bend probability) of the HO-PIB-OH(1K) hydroxy groups increases with decreasing chain length and decreasing system temperatures. 2,500

2,500

2,000

;-1,500

U

n

2,000

CF4

U

+ Decalin

d,500

8

01

c

5

?Rg0

i

t 1.000

:1,000 CHFj

0

CF4 +Tetralin

500

+ Tetralin

500

0

0 0

50

100

150

200

250

300

350

Temperature ( C )

-50

0

I

1

,

50

100

160

200

I

I

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300

Temperature (C)

Figure 11. Binary pressure-temperature diagrams for (right) CFr + n-dodecane (n-CltH~),decen, and tetralin and (left) CHF3 + n-decane (n-CloHzz) and tetralin. In nonpolar solvents the r-r interactions promote self-association and shift the U-LCSTcurve to high temperatures, in contrast, in polar solvents dipole-r interaction causes the U-LCSTcurve to shift to lower temperatures. Although these end-to-end calculations are strictly valid only for long flexible chains, they qualitatively suggest that the probability of intramolecular hydrogen bonding not only increases with decreasing temperature but also increases with decreases distance between the sites. This distance is known to vary from solvent to solvent and to depend upon the radius of gyration. The radius of gyration is a measure of chain size and is found to be smaller in a 8 solvent than in a good solvent. For example, for polyisoprene in 1,4-dio~ane~~-a polar 8 solvent-the radius of gyration is given by 0.0309Mo.505, and in cyclohexane-a nonpolar good s ~ l v e n t . ~ ~ J ~ - t h e radius of gyration is given by 0.0248Mo.545.Using these two expressions, the radius of gyration for polyisoprene samples having molecular weights of 103and 106 is ~ 1 7 . 5 and 37.5 % less in 1,4-dioxane than in cyclohexane solutions. Mel'nichenkom and T s ~ n a s h i m a 5 ~found 9 ~ ~ that the polymer chain dimensions decrease as the solvent polarity is increased. The polar fluids cause a polymer chain to condense and coil, which effectively reduces the radius of gyration and hence the characteristic chain length. For polar solutions of CHa-PIB-OH(lK), this change in length has little or no effect on hydrogen bonding. The polar head group, exposedtothe polar medium, intermolecularly associates with head groups on other coils. However, for polar solutions of HO-PIB-OH( lK), the reduced radius of gyration physically brings the associating end groups closer together. The polar head groups are still available

for intermolecular association (inter-association)but can now associate intramolecularly (intra-association)as well. The increasedproximity of the two groups,as was discussed and illustrated in Figure 10, is expected to increase the degree of such intramolecular association. This explains the lack of a shift in cloud-point pressures for chlorodifluoromethane, dimethyl ether, and carbon dioxide solutions of HO-PIB-OH(1K). The end groups intra-associate, which reduces or even caps off all sites for inter-association. The resulting system would have a degree of asymmetry similar to that for CHs-PIB-CH3(1K) and, with all things being equal, would have similar cloud-point pressures. This aggregate formation alone, however, cannot explain the lowering of the cloud-point pressures as is shown in Figure 6 for HO-PIB-OH(1K) solutions in chlorodifluoromethane. One additional example is needed to explain this behavior. Phase Behavior of Associating Rings: Equilibria of Decane, Decalin, and Tetralin in Tetrafluoromethane and Trifluoromethane. The shifts in phaseboundary pressures for the binary systems containing decalin (CIoH18) and tetralin (C1oHd in polar trifluoromethane (CHF3) are similar to those shifts for CH3PIB-CHs(1K) and HO-PIB-OH(1K) in chlorodifluoromethane. Let us first consider the phaae-boundary curvesG1shown on the left-hand side of Figure 11. Solutions of dodecane (n-ClzHza) in nonpolar tetrafluoromethane (used here to approximate the phase-boundary curve for n-decane) are U-LCST with a UCST branch near 150 "C.

Phase Behavior of PIB in Supercritical Fluids 4979

Macromolecules, Vol. 27,No. 18, 1994

500

-

400

f

300

1

CHCIF2

";/

CHCIF2 CH3P:BCH) ( I k ) Selfdssociation

t

No association

I

il

P

200 Cross- and Intra~ssociation Crossdssociation

100 Only

-

F:T

,

association, are shifted to much higher temperatures (from 125 to 175 "C). Conversely, the cloud-point curve for a strict solvent-polymer cross-associating system, that is, assuming no polymer-polymer self-association, is shifted to much lower temperatures and pressures and becomes LCST with an end point at 62.8 "C. For the intramolecular ring, we hypothesize that, when the hydroxy groups hydrogen bond to form the ring, they are sterically hindered to the point that ring-ring aggregates are unlikely but solvent-ring aggregates are still possible. Hence, the self-association parameters for the hydroxy groups are set equal to zero. The cross-associating K is reduced by a third but t is the same as that for CH3PIB-OH(1K). This hypothesis results in SAFT predictions that are in qualitative agreement with the experimental HO-PIB-OH(1K) data, as shown in Figure 12.

0 0

50

100

150

200

250

Temperature (C) Figure 12. SAFT-predicted cloud-point pressures for CHClF2 + HO-PIB-OH(1K) with various associating schemes: (1)no association,all associationparameters set equal to zero; (2) strict self-association,cross-association parameters set equal to zero; (3) strict cross-association,self-associationparameters set equal to zero; (4) cross-association,self-associationparametersset equal to zero and adjusted, lowered cross-association. The phase boundary curve for decalin (a saturated ring structure) is shifted 50 "C to temperatures higher than those for dodecane (a chain structure) because of the difference in solute structure. The phase boundary curve for tetralin is shifted 40 "C relative to that of decalin. The explanation for this behavior is that the ?r electrons of tetralin from short-range sites that induce some degree of clustering, which increases the asymmetry and hence leads to an increase in phase-boundary pressures. Shown on the right-hand side of Figure 11are the phaseboundary pressures for n-decane (n-CloH22) and tetralin in polar solutions of trifluoromethane (CHF3). Contrary to the behavior in nonpolar tetrafluoromethane, the phase boundary for tetralin does not shift to higher temperatures relative to n-decane. In fact, as the temperature increases above 60 "C, the curve is initially lower than, then intersects and remains slightly above, the phase boundary for n-decane. Below 60 "C, tetralin probably cross-associates with trifluoromethane. The ?r electrons interact with the hydrogen on the CHF3, which leads to a tetralin phase boundary below that of n-decane. This is similar to CH3PIB-CH3( 1K) and HO-PIB-OH(1K) in chlorodifluoromethane, where HO-PIB-OH( 1K) cloud points are lower than those for CH~-PIB-CHB(~K) at low temperatures. The explanation is that the hydroxy groups of the intramolecular HO-PIB-OH(lK), monomer rings weakly cross-associate with the solvent molecules. How To Account for Intra-Association. The intraassociation and cross-association can be accounted for indirectly by varing site-site interactions and association parameters. Figure 12 shows the SAFT-predicted cloudpoint curves for HO-PIB-OH(1K) in chlorodifluoromethane for various association schemes: (1)a nonassociating system, (2) a strict self-associating system, (3) a strict cross-associating system, and finally (4) a cross- and intra-associating system. The cloud points for the nonassociating system, with all of the associating parameters set equal to zero, are U-LCST with the UCST branch above 50 "C. This is very close to the experimental points for CH3-PIB-CH3(1K). The cloud points for a strict polymer-polymer self-associatingsystem, that is, assuming no cross-associationbetween solvent-polymer and no intra-

Conclusions The cloud-point pressures for CH3-PIB-CH3(1K),CH3PIB-OH(lK), and HO-PIB-OH(1K) in nonpolar and polar solvents have two distinct trends as the number of hydroxy groups increases. In ethane and propane solutions, the cloud-point pressures increase for both CH3PIB-OH(1K) and HO-PIB-OH(1K) relative to the baseline nonassociating CHs-PIB-CH3(1K) system. This increase is a result of polymer aggregation due to selfassociation which increases the system asymmetry and, hence, shifts the cloud points to higher pressures. In polar solvents such as chlorodifluoromethane, dimethyl ether, and carbon dioxide, the CH3-PIB-OH(lK) cloud-point pressures are consistently higher than those measured for CHS-PIB-CH3(1K), while the cloud-point pressures for HO-PIB-OH(1K) and CHs-PIB-CH3( 1K) essentially coincide. The cloud-point shift to higher pressures for CH3-PIB-OH(lK) is explained by selfassociation of the intermolecular type. On the other hand, the cloud point shift to lower pressures for HO-PIB-OH(1K)is explained by intramolecular association that leads to ring formation. The SAFT model quantitatively captures the intermolecular association of CH3-PIB-OH(lK) and HO-PIBOH(1K) in all the solutions studied in this work. Furthermore, SAFT captures the intramolecular association, for example, for HO-PIB-OH(1K) in chlorodifluoromethane, by postulating cross-associating, intramolecular-ring structures in solution. Acknowledgment. We thank Professor Rudolf Faust of the Department of Chemistry, University of Massachusetts Lowell, for the synthesis and characterization of the polyisobutylene samples used in this work. We also thank S.-j.Chen for stimulating discussions on the physical properties of telechelic polymers. Supplementary Material Available: The experimental data-cloud-point pressure, system temperature and concentration, and phase transition type-collected in this work for binary systems of CH3-PIB-CHs(lK), CHa-PIB-OH(lK), and HOPIB-OH(1K) in propane, ethane, chlorodifluoromethane, dimethyl ether, and carbon dioxide are provided as Supplementary Material (7 pages). Ordering information is given on any current masthead page.

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