Architectural Effects on the Solution Behavior of Linear and Star

Article pubs.acs.org/IECR

Architectural Effects on the Solution Behavior of Linear and Star Polymers in Propane at High Pressures Yue Wu,*,† Matthew S. Newkirk,† Sean T. Dudek,† Kara Williams,‡ Val Krukonis,‡ and Mark A. McHugh† †

Department of Chemical and Life Science Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, United States ‡ Phasex Corporation, Lawrence, Massachusetts 01843, United States S Supporting Information *

ABSTRACT: A star polymer with a divinylbenzene core and statistically random methacrylate copolymer arms is synthesized with reversible addition−fragmentation−transfer method and fractionated with supercritical carbon dioxide and propane to obtain fractions with low molecular weight polydispersity. The phase behavior and density behavior are experimentally determined in supercritical propane for fractionated star polymers and the corresponding linear copolymer arms at temperatures to 423 K and pressures to 210 MPa. Experimental data are presented on the impact of the number of arms, the backbone composition of the lauryl and methyl methacrylate repeat units in the copolymer arms, and the divinylbenzene core on the polymer−propane solution behavior. The star polymer is significantly more soluble because of its unique structure compared with the solubility of the linear copolymer arms in propane. The resultant phase behavior for the two homopolymers and the copolymer arms in propane are modeled using the perturbed chain statistical associating fluid theory (PC-SAFT). Model calculations are not presented for the phase behavior of the star polymers in propane because the PC-SAFT approach is not applicable for star polymer structures.

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INTRODUCTION Over the past few decades the advent of new chemistries has led to the creation of polymers with unique, well-defined architectures, such as star polymers with a fixed number of branches or, in other words, arms. Star polymers, with low to moderate molecular weight arms, have a globular structure that does not promote chain entanglements. Star polymers can be synthesized from a large range of homopolymer, block, and copolymer arms that can also contain functionilized groups.1 Once the star polymer is synthesized the functional groups can be readily modified to adjust their physical properties for specific applications in the areas of catalysis,1 coatings,2 lubrication,3 membrane formation,4 and drug delivery.5,6 Despite their increasingly mature applications, some fundamental physical properties, such as phase behavior and solution densities, are still lacking, and an accurate prediction of these properties over wide ranges of temperatures and pressures remains a challenge. Previously reported studies on star polymer−solvent solution behavior are typically performed with incompressible liquids at ambient pressure, not at high pressures with supercritical fluids. Star (sPS) and linear polystyrene (lPS) are primarily used in these studies to investigate the impact of multibranching architectural effects on solution behavior. Liquid solvents used for dissolving sPS and lPS include toluene, cyclohexane (CH), and methylcyclohexane (MCH), which, for these polymers, are characterized as a good, theta (Θ), and poor quality solvents, respectively.7 Studies have been performed to determine the upper critical solution temperature (UCST), radius of gyration ⟨Rg2⟩, and second osmotic virial coefficient B22 for sPS−solvent and lPS−solvent solutions at the same molecular weight Mw, at different compositions, and at atmospheric pressure. Given that © 2014 American Chemical Society

star and linear polymers can be readily dissolved in a good solvent such as toluene, the UCST was reported only for each PS in CH and MCH. A 2−4 K decrease in UCST was observed for sPS−CH mixtures relative to that observed for lPS−CH mixtures.8−11 Furthermore, the critical volume fraction of the sPS−CH system is slightly greater than that for the lPS−CH system, indicating that the star morphology suppresses the impact of molecular weight on solubility relative to the effect found with the linear polymer analogue.9 Alessi et al.12 observed a 5−15 K decrease in the UCST for an eight-arm sPS−MCH mixture relative to lPS−MCH mixture with PS of the same molecular weight (Mw = 77 000 or 268 000), although these researchers observed no noticeable difference for the critical volume fraction of these mixtures. Literature studies report that ⟨Rg2⟩ for the star polymer is always smaller than its linear analogue with the same molecular weight.7,13 The compact star structure reduces chain−chain penetration, which is one of the reasons for the greater solubility of star polymers in a poor solvent. ⟨Rg2⟩ decreases with an increase in the number of arms while it increases with an increase in the arm length.7 Molecular simulation studies show that arms are stretched in a star polymer to best accommodate both the intra- and interarm repulsions.14,15 Recently, Wever et al.16 reported experimental evidence that the hydrodynamic radius, Rh, of star polyacrylamide (PAM) increases with an increase in the number of arms, although the ⟨Rg2⟩ decreases simultaneously. The increase in Rh confirms the Received: Revised: Accepted: Published: 10133

March 18, 2014 May 27, 2014 May 30, 2014 May 30, 2014 dx.doi.org/10.1021/ie5011417 | Ind. Eng. Chem. Res. 2014, 53, 10133−10143

Industrial & Engineering Chemistry Research

Article

poly(lauryl methacrylate-co-methyl methacrylate) (LMAMMA50 where 50 represents the mole percent MA) arms in supercritical propane. The originality and benefits of this study are 2-fold: (1) experimental results are presented with a selfsynthesized high molecular weight star polymer with poly(lauryl methacrylate-co-methyl methacrylate) arms, which complements previous studies that almost exclusively investigated polystyrene star polymers and (2) a detailed comparison is presented for solubility studies for star and linear polymer in propane, a poor quality supercritical fluid solvent for the investigated polymers, which offers a means to quantify solubility differences with the same solvent at different operating pressures and temperatures. The choice of supercritical propane rather than other supercritical fluids is based on several preliminary experiments to ensure the pressure to obtain a single phase is high enough to significantly magnify polymer architectural effects but still within the operating range of the high-pressure apparatus used in this study. In the present study, the star polymer is first fractionated to recover “free” LMA-MMA50 arms from the parent solution and to obtain star polymer fractions with low molecular weight polydispersity indices. Experiments are performed with the “free” LMA-MMA50 arms and the star polymers to elucidate the impact of the star morphology and molecular weight on the phase behavior in supercritical propane. Companion solubility experiments are performed with poly(lauryl methacrylate) (PLMA), poly(methyl methacrylate) (PMMA), and LMAMMA35 to demonstrate the impact of LMA on the phase behavior in supercritical propane. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) and the copolymer PC-SAFT EoS are used to model the resultant solution behavior for the homopolymers and copolymers in propane. No attempt is made to model the phase behavior of the LMA-MMAx star polymer in propane because SAFT-based equations do not account for the unique morphological characteristics of a star polymer.

molecular simulation results that arm stretching increases with an increase in the number of arms.7 A star polymer exhibits a larger free volume relative to its linear analogue because of the larger number of end groups and the stretching of the arms. In the same contribution by Wever et al.,16 the rheological properties are also compared for linear and star PAM with different arms. Wever et al. found that the viscosity and thickening efficiency increase with an increase in number of arms at equal molecular weight. The differences between the second osmotic coefficient B22 for a star polymer−solvent solution and the corresponding linear polymer−solvent solution depends on solvent quality. Consider, for example, the results of Striolo et al.7 who reported B22 valuse for sPS solution and lPS solution in toluene (good solvent), CH (Θ solvent), and MCH (poor solvent) at temperatures from 283 to 333 K. B22 for sPS solution is always positive regardless of solvent quality, indicating a good solubility in all three solvents. Conversely, B22 for lPS in toluene is positive and larger than B22 for sPS in toluene, while B22 for lPS becomes negative in CH (Θ solvent) and MCH (poor solvent). In a recent study, Xiong et al.17 obtained the Flory−Huggins interaction parameter χ for three-arm, star polybutadiene (PB)−tetrahydrofuran (THF) solutions from vapor pressure measurements and compared χ for the star polybutadiene (PB)−tetrahydrofuran (THF) solutions to those of linear PB−THF solutions. They concluded that the free volume of the star PB is larger than the free volume of the linear PB at 328 K (55 °C), whereas this relationship reverses at 298 K (25 °C). Xiong et al.17 ruled out end group effects when explaining the differences in star and linear polymer solubility and concluded that the observed solubilities are a strong function of the differences in the number of inter- and intrasegmental contacts for a star versus a linear polymer. The previously described solution behavior studies demonstrate the effect of branching on the solubility of a star polymer in a liquid solvent that, regardless of whether it was a Θ or poor quality solvent, can still have a sufficiently high solvent strength to mask or obscure the potential differences in the solution behavior of these related polymers. For example, Okumoto et al.13 reported “no substantial difference appears in the Θ temperature” between a four-arm sPS−CH mixture and the lPS−CH mixture. In the present study the differences in star and linear polymer solubility are examined in a highly compressible, supercritical fluid solvent to magnify the impact of polymer architecture on solubility. To the best of our knowledge, there are only a modest number of reported studies on the high-pressure phase behavior of multibranched polymer−SCF mixtures. The bulk of these recently published studies utilized low molecular weight hyperbranched polymers (Mw < 35 000) rather than star polymers.18−23 However, in one study, Gregg et al.24 reported cloud-point data for a three-arm, low molecular weight polyisobutylene (Mw = 4100) in different SCF solvents, although the authors did not investigate the impact of increasing the number of arms on the phase behavior. The purpose of the present study is to extend the understandings of solubility differences between star polymers and linear polymers in a poor solvent and the effect of arm number on star polymer solubility. This study also extends the current solution behavior database to 200 MPa for potential high-pressure applications of star polymers. In the present study, the solution behavior is reported for high molecular weight (Mw ∼ 100 000 to 900 000) star polymer with

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EXPERIMENTAL SECTION

Materials. Figure 1 shows a schematic diagram of the synthesis of the star polymers and the LMA-MMAx copolymer arms using reversible addition−fragmentation−transfer (RAFT) method.25 The star polymers are donated by Afton Chemical Corporation and are fractionated prior to use. One

Figure 1. Schematic diagram of the synthesis and structure of the star polymer and the methyl methacrylate (A) and lauryl methacrylate (B) repeat groups in the copolymer arms used in this study. 10134

dx.doi.org/10.1021/ie5011417 | Ind. Eng. Chem. Res. 2014, 53, 10133−10143


Article

star polymer sample is expected to have an average of 6 LMAMMA50 copolymer arms, and the other star polymer sample is expected to have an average of 20 LMA-MMA50 copolymer arms. The PLMA used in this study was synthesized using standard emulsion polymerization techniques and used as received.26 PMMA (Mw =15 000) and propane (98 wt % purity) are purchased from Sigma-Aldrich and used as received. Polymer Characterization. Table 1 shows polymer characterization data obtained with gel permeation chromatogTable 1. Characterization Data for PLMA, PMMA, LMAMMA35, LMA-MMA50, and Parent Star Polymersa sample

Mw (× 10−3)

Mw/Mn

LMA/MMA mole ratio

PLMA PMMA LMA-MMA35 LMA-MMA50 star polymer (6-arm) star polymer (20-arm)

80 15 45 130 173 peak, 35 peak 626 peak, 31 peak

2.0 1.6 1.2 2.0 − −

100/0 0/100 65/35 50/50 50/50 50/50

Figure 2. Schematic diagram of high-pressure fractionation system used in this study.

performed using a variable-volume view cell shown in Figure 3 and described in detail elsewhere.27,28 The system pressure is measured with a transducer (Viatran Corporation, Model 245; 0−345 MPa, accurate to ±0.35 MPa) and the temperature is measured with a type-k thermocouple (Omega Corporation, accurate to ±0.1 K). Figure 3B shows the linear variable differential transformer (LVDT, Schaevitz Corporation, Model 1000 HR) coupled to the piston in the view cell. The internal volume of the cell is calibrated, as described in detail elsewhere,28,29 with propane and n-decane using highly accurate density data.30 Phase equilibrium data are determined for mixtures with polymer at 5.0 ± 0.5 wt % in propane. The mixture in the cell is projected on a video monitor using a camera (Olympus Corporation, Model STC-N63CJ) connected to a borescope (Olympus Corporation, Model F100-024-000-55) placed against a sapphire window secured at one end of the cell. The mixture is isothermally compressed to a single phase, and the pressure is then decreased incrementally and held constant for approximately 10 min. If the mixture remains clear, the pressure is decreased further until the mixture begins to get hazy (Phazy). The pressure is further decreased, stepwise, until the mixture becomes so opaque that the piston is not visible (Popaque). The cloud-point pressure is the midpoint between Phazy and Popaque. The difference between these two pressures, ΔP, along with the cloud-point pressures are reported in the Supporting Information. Generally, ΔP is less than 2% of the cloud-point pressures for the linear copolymer−propane mixtures and 2−10% of the pressures for the star polymer− propane mixtures. Isothermal density data are obtained in the single-phase region of the polymer−propane mixtures from the cloud-point pressure to ∼210 MPa at random pressures to minimize any potential experimental artifacts in the measurements. The standard uncertainties for the density data U are U(T) = 0.20 K and U(P) = 0.07 MPa below 56 and 0.35 MPa from 56 to 275 MPa. The estimated accumulated (combined) experimental uncertainty Uc is Uc(ρ) = 0.75% · ρ (at k = 2 for an interval having a confidence level of approximately 95%) where ρ is a density data point.

a

PMMA molecular weight information is obtained from the supplier (Sigma-Aldrich).

raphy (GPC, columns calibrated with lPS standards and tetrahydrofuran as the eluent at a flow rate of 1.0 mL/min at ∼313 K (40 °C)) and 1H nuclear magnetic resonance (NMR) spectroscopy (500 MHz Bruker Advance III spectrometer with a 5 mm probe in CDCl3 solutions at 303 K). Table 1 lists molecular weight and molecular weight distribution data for PLMA, LMA-MMA35 and LMA-MMA50, and the parent 6-arm and 20-arm star polymers. The GPC chromatogram for the parent 6-arm star polymer has a polymer peak centered at ∼173 000 and an LMA-MMA50 free arm peak at ∼35 000. Similarly, the GPC chromatogram for the parent 20-arm star polymer has a polymer peak centered at ∼626 000 and an LMA-MMA50 free arm peak centered at ∼31 000. Detailed GPC chromagrams for the parent star polymers are shown in Figure S1a,b in the Supporting Information. Figure S2 in the Supporting Information shows the GPC chromagram of PMMA used in the study. NMR data listed in Table 1 show that the LMA/MMA mole ratios are 1.86 (65/35), 1.0, and 1.0 for the LMA-MMA35 copolymer, LMA-MMA50 copolymer, and the arms on each of the star polymers, respectively. In addition, differential scanning calorimetry (DSC, Q1000 DSC, TA Instruments) data obtained in this study confirm that all of the homopolymers, copolymers, and parent star polymers are amorphous. Fractionation. Figure 2 shows the schematic diagram of the fractionation system, which is described in detail elsewhere.27 Typically 10 to 20 g of polymer are charged to a column interspersed with stainless steel packing. Propane is pressurized (diaphram compressor, Newport Scientific Inc., Model 4613421-2) to ∼70 MPa and charged to a surge tank. The propane is then throttled through an in-line pressure regulator to obtain the desired operating pressure, to within ±0.5 MPa, delivered to a preheat column, and to the polymer column maintained at a fixed temperature, to within ±1.0 K. The SCF solvent, loaded with extract, exits the column and is throttled to atmospheric pressure, which causes the extract to precipitate into a preweighed, side arm beaker. Phase Equilibrium and Density Determination. Highpressure phase behavior and density measurements are

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RESULTS AND DISCUSSION Fractionation. Preliminary solubility experiments using supercritical propane, not presented here, are used to determine the pressure−temperature (P−T) conditions needed 10135



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Figure 3. Schematic diagram of (A) the high-presssure variable-volume view cell and (B) the coupling of the LVDT to the piston.

ether) dendrimer that is not seen with the higher-generation dendrimers. Phase Behavior. Figure 4 shows the phase behavior for ∼5 wt % PLMA (Mw = 80 000), LMA-MMA35 (Mw = 45 000),

to dissolve the two parent LMA-MMA50 star polymers. Table 2 shows the fractionation results for the 6-arm and 20-arm parent Table 2. Operating Conditions for the Fractionation of Two Parent LMA-MMA50 Star Polymers Using Supercritical Propane at ∼400 K Mw/Mn

Tmelt (K)

no. of arms

28

1.5

none

−

37.6

162

1.4

343

6

F5

44.8

194

1.5

344

7

F6

38.3

604

2.4

none

20

F7

41.4

883

2.2

none

30

sample

pressure (MPa)

Mw (× 10−3)

F3

20.7

F4

comments free copolymer arms from 6-arm parent star polymer from 6-arm parent star polymer from 20-arm parent star polymer from 20-arm parent star polymer

Figure 4. Cloud-point curves for ∼5 wt % PLMA (Mw = 80 000) (○), LMA-MMA35 (Mw = 45 000) (◊), LMA-MMA50 (Mw = 28 000) (Δ), and LMA-MMA50 (Mw = 130 000) (□) in propane obtained in this study and PLMA (Mw = 250 000) (●) in propane from Liu et al.32 Solid lines are used to guide the eye.

star polymers. Detailed GPC chromagrams for the fractions are found in Figure S1 in the Supporting Information. Fraction F3 consists of free LMA-MMA50 copolymer arms. Fractions F4 and F5 are star polymers from the 6-arm parent star polymer, and fractions F6 and F7 are star polymers from the 20-arm parent star polymer. The polydispersity indicies Mw/Mn are less than 2.4 for all the fractions. Table 2 lists the estimated number of arms for each polymer fraction based on a straightforward calculation that divides the apparent Mw of the star polymer by the Mw of the free arms. As previously reported in the literature,16 Rh increases with an increase in number of arms; hence, the apparent Mw determined by GPC must also increase as the number of arms increases. All of the star polymer fractions exhibit a single peak in the GPC chromatogram, verifying that the free arms have already been extracted from the parent star polymer. 1H NMR data also confirm the LMAto-MMA mole ratio is 1.0 for each fractionated polymer sample. Interestingly, fractions F4 and F5 each exhibit a melting transition at ∼343 K; however, fractions F6 and F7 do not exhibit a melting transition. Because linear LMA-MMA50 copolymers are amorphous, the crystallization transitions exhibited by fractions F4 and F5 are directly related to the DVB core of these star polymers, which have a modest number of arms. The DVB core does not crystallize for fractions F6 and F7, which have a large number of arms. The apparent lack of a melting transition for these two high-Mw star polymer fractions is similar to the behavior observed by Hay et al.,31 who report a melting transition for a less-than-third generation poly(benzyl

LMA-MMA50 (Mw = 28 000), and LMA-MMA50 (Mw = 130 000) in propane. Detailed cloud-point data are found in Table 3. Figure 4 also shows the cloud-point curve for 5.2 wt % PLMA (Mw = 250 000) in propane from Liu et al.32 for comparison to the data in the present study. The cloud-point pressures from Liu et al.32 are only slightly higher than those exhibited by the PLMA (Mw = 80 000)−propane system, suggesting that the effect of Mw has already reached a point of saturation on the phase behavior for this binary mixture. Polymer backbone architecture has a more significant effect on the phase behavior for the polar polymer−nonpolar solvent, binary mixture considered here than does polymer Mw. Consider first the phase behavior of the LMA-MMA x copolymer−propane mixtures. The cloud-point curves for PLMA, LMA-MMA35 (Mw = 45 000), and LMA-MMA50 (Mw = 28 000) shift to higher pressures as MMA is incorporated randomly into the backbone of the polymer. Note also that the shift to higher pressures is opposite to that expected based on polymer Mw, indicating that polymer−solvent interactions have a larger effect on the conditions needed to dissolve these polymers than does molecular weight. The polarity of the ester group, per unit molar volume, is reduced in LMA, with a nonpolar dodecane tail, relative to MMA, with a short methyl tail. In fact, PMMA, with an Mw of only 15 000, does not dissolve in propane even to temperatures to 473 K and pressures to 200 MPa verifying that MMA-rich copolymers are 10136



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Table 3. P−T Trace of the Cloud-Point Curves for ∼5 wt % PLMA (Mw = 80 000) in Propane and LMA-MA35 (Mw = 45 000) and LMA-MA50 (Mw = 28 000 and 130 000) in Propanea PLMA (Mw = 80 000) T (K)

P (MPa)

ΔP (MPa)

294.3 3.3 0.3 308.1 7.2 0.3 326.4 11.5 0.2 354.6 17.1 0.2 376.2 20.7 0.3 398.9 24.0 0.3 422.7 27.0 0.2 452.8 28.9 0.3 472.8 30.1 0.3 520.2 33.2 0.2 LMA-MMA50 (Mw = 28 000)

LMA-MMA35 (Mw = 45 000) T (K)

P (MPa)

ΔP (MPa)

308.8 326.2 342.2 351.8 374.0 401.2 421.9 447.9

17.5 20.8 23.5 25.0 28.2 31.6 33.7 35.9

0.3 0.3 0.3 0.2 0.1 0.2 0.2 0.1

Figure 5. Cloud-point curves for ∼5 wt % F4 (□), F5 (○), F6 (Δ), and F7 (◊) in propane and for ∼5 wt % LMA-MMA50 (Mw = 28 000) (▲) and LMA-MMA50 (Mw = 130 000) (■) (upper right corner) in propane. Solid lines are used to guide the eye. The dashed line represents a solid−liquid phase boundary.

LMA-MMA50 (Mw = 130 000)

T (K)

P (MPa)

ΔP (MPa)

T (K)

P (MPa)

ΔP (MPa)

294.3 309.2 322.3 336.0 350.0 375.1 402.2 423.4 439.0 462.8

35.4 34.9 35.4 37.3 38.3 39.5 40.6 41.4 42.0 42.5

0.6 0.5 0.5 0.5 0.3 0.6 0.5 0.2 0.3 0.2

376.9 387.6 395.5 418.4 438.5 450.4 472.7

218.5 160.2 138.0 119.4 120.7 121.1 123.4

1.0 0.9 0.8 0.8 0.8 0.8 0.6

Table 4. P−T Trace of the Cloud-Point Curves for ∼5 wt % Fractionated Star Polymers, F4, F5, F6, and F7 in Propanea F4 (Mw = 162 000) T (K) 343.0 349.7 374.4 398.8 423.2 444.1

a The cloud-point pressure P is the midpoint between a slightly hazy and a completely opaque solution, and ΔP is the pressure range between these two conditions.

harder to dissolve in nonpolar propane compared to LMA-rich copolymers. Figure 4 also shows the cloud-point curve for LMA-MMA50 (Mw = 130 000) in propane obtained in this study. In this instance the curve exhibits a sharp increase in pressure at temperatures less than ∼400 K. It is likely that the cloud-point curves for the other LMA-MMAx copolymers also exhibit sharp increases in pressure at temperatures less than than 300 K, which is outside the range for the apparatus used in this study. As the copolymer molecular weight increases, the size asymmetry with propane increases and the number of propane−MMA interactions per unit volume also increases. Hence, the cloud-point curve shifts to higher pressures, due primarily to a size disparity, and to higher temperatures, due primarily to a mismatch in energetics.33 Figure 5 shows the cloud-point curves in propane for fractionated LMA-MMA50 star polymers F4, F5, F6, and F7. The cloud-point curves for the LMA-MMA50 (Mw = 28 000)− propane and LMA-MMA50 (Mw = 130 000)−propane systems are also included in Figure 5 for a direct comparison of the phase behavior for polymers with different structural architecture. Detailed cloud-point data are listed in Table 4 for the star polymer−propane systems. Solidification boundaries are found at ∼343 K for the lower Mw F4 and F5 star polymers, but not for the higher Mw F6 and F7 star polymers, in agreement with DSC results. The increase in cloud-point pressures with decreasing temperature for the F6−propane and F7−propane curves is due to the increase in dipole−dipole interactions between polymer molecules that scale with inverse

P (MPa)

F5 (Mw = 194 000)

ΔP (MPa)

solidification 39.6 0.9 40.0 0.8 40.6 0.6 41.1 0.5 41.4 0.5 F6 (Mw = 604 000)

T (K) 344.0 352.1 374.3 399.8 422.7 443.5

P (MPa)

ΔP (MPa)

solidification 42.6 1.0 42.3 0.8 42.1 0.6 42.1 0.6 42.3 0.6 F7 (Mw = 883 000)

T (K)

P (MPa)

ΔP (MPa)

T (K)

P (MPa)

ΔP (MPa)

309.4 325.6 349.9 361.2 374.0 392.0 406.4 422.6 444.6

56.0 51.7 46.9 45.7 45.2 44.7 44.2 44.5 44.9

5.0 4.8 4.2 3.1 3.0 2.4 1.8 2.1 1.9

306.2 325.0 349.7 374.4 401.4 422.7 442.8

62.9 56.6 51.1 48.1 48.0 47.8 48.0

5.4 4.8 4.6 2.2 2.4 2.7 2.6

a

The cloud-point pressure P is the midpoint between a slightly hazy and a completely opaque solution, and ΔP is the pressure range between these two conditions.

temperature and that dominate polymer−propane dispersion interactions. The cloud-point curves for the F4−propane and F5−propane systems are also expected to exhibit negative P−T slopes at low temperatures, although this behavior is masked by the solid−liquid transition for these two star polymers. An interesting observation stems from the comparison of the cloud-point curves for star polymers and linear LMA-MMAx copolymers in propane. As shown in Figure 5, the cloud-point pressures for LMA-MMA50 (Mw = 28 000) in propane at temperature exceeding 350 K are very close to the pressures exhibited by the F4 star polymer (Mw = 162 000)−propane system. The ordering of these two curves is a bit surprising given that the LMA-to-MMA ratio is the same for both the F4 copolymer arms and the linear LMA-MMA50 (Mw = 28 000) copolymer. This trend is even more exacerbated when comparing the P−T trace of the cloud-point curves of any these high Mw star polymers with the curve for linear LMAMMA50 (Mw = 130 000), which appears at ∼50 MPa higher pressures. These trends are consistent with previously reported 10137



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Figure 6. Densities in the single-phase region for the (a) 5.2 wt % F4−propane system, (b) 4.8 wt % PLMA−propane, and (c) 4.2 wt % LMAMMA50 (Mw = 28 000)−propane at ∼375 K (○) and ∼424 K (□). The dashed line represents the liquid−liquid phase boundary, and the solid lines are to guide the eye.

Polymer solubility is also examined in supercritical CO2 for PLMA and PMMA, the linear LMA-MMAx copolymers, and the star polymer fractions. As expected, none of these methacrylate-rich homopolymers, copolymers, and star polymers dissolve in CO2 at temperatures to 448 K and pressures to 200 MPa.34 This observation also agrees with the results reported by Liu et al.,32 who were not able to dissolve PLMA (Mw = 250 000) in CO2 without a cosolvent. Density Determination. Polymer density plays an important role in polymer processing35 and viscosity determination.36 In modeling studies, density data over a wide range of temperatures and pressures provide a database for testing contemporary EoS28,29 and for deriving EoS parameters.37 In this study, mixture densities are determined for fractionated star polymer−propane mixtures with ∼5.0 wt % F4, F5, F6, and F7, and for 4.8 wt % PLMA−propane and 4.2 wt % LMA-MMA50 (Mw = 28 000)−propane mixtures at 373 and 423 K and pressures to 200 MPa. Figure 6 shows examples of the variation of density with pressure for the F4−propane, PLMA−propane, and LMA-MMA50−propane mixtures. Detailed density data are found in Table 5.

trends for the UCST behavior of star and linear polystyrene at atmosphere pressure, which showed the star polymer was more soluble than its linear analogue in a poor solvent.7,9,10 The results obtained in the present study also support the argument that the star morphology suppresses the impact of molecular weight on solubility relative to the Mw effect found when comparing the behavior with the linear polymer analogue.9 The free volume of a star polymer is expected to be higher than that for a linear polymer because the arms are tethered to a core resulting in constrained conformations and there is an increase in chain ends from the multiple arms of a star polymer. This conformation argument is also proposed by Forni et al.,14,15 who calculated the molecular shape of star polymers using offlattice Monte Carlo simulations. These researchers concluded that the arms of the star polymer stretch to best accommodate both intra- and interarm repulsions. Wever et al.16 also report that the arms adapt a more stretched conformation with an increase in number of arms in a star polymer. The increased free volume of the LMA-MMA50 star polymer relative to its copolymer analogue apparently has a more dominant effect on the phase behavior than the MMA−propane energetic mismatch that is magnified with the large number of MMA groups within the star polymer. The radius of gyration of the star polymer is smaller than its linear analogue,14,16 which also reduces the cloud-point pressure for a star polymer−solvent solution compared to that of the analogue linear polymer− solvent solution. Figure 5 shows a significant difference in cloud-point pressures and miscibility regions when a weak, supercritical fluid solvent, such as propane, is used. As mentioned previously in the introduction, such a large disparity in miscibility region between a linear and star polymer is not observed with a liquid solvent.

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EQUATION OF STATE MODELING Equations and Parameters. In this study, the PCSAFT38−40 and the copolymer PC-SAFT41 equations are used to predict the high-pressure solution behavior for the PMMA−propane, PLMA−propane, and LMA-MMAx−propane mixtures. Although the copolymer PC-SAFT EoS with branching effects has been used to model hyperbranchedsolvent phase behavior,18 no attempt is made to use this approach for the LMA-MMA50 star polymer−propane systems because SAFT-based equations do not account for the unique 10138



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Table 5. Density Data in the Single-Phase Region for ∼5 wt % Star Polymers (F4, F5, F6, and F7), PLMA, and Copolymer LMA-MMA50 (Mw = 28 000) Each in Propane 5.2 wt % F4 in propane 375.7 ± 0.1 K P (MPa) 42.9 48.5 55.4 62.7 69.4 83.4 104.1 124.4 138.8 152.8 173.2 189.5 208.4

density (kg/m3)

P (MPa)

500 43.8 509 48.9 519 55.5 528 62.3 536 70.0 550 83.2 569 103.9 584 125.0 595 138.5 603 153.7 615 173.9 624 188.5 634 207.6 4.9 wt % F6 in propane 373.9 ± 0.1 K

P (MPa) 50.1 55.6 62.3 69.5 83.6 103.8 123.3 139.3 153.0 173.0 188.1 208.4

5.0 wt % F5 in propane 424.4 ± 0.1 K

density (kg/m3)

376.1 ± 0.1 K

density (kg/m3)

P (MPa)

461 471 482 493 503 519 540 558 569 579 592 601 611

45.0 48.4 55.8 62.7 69.6 83.0 103.4 123.9 139.5 153.7 173.0 187.4 207.6

422.6 ± 0.1 K P (MPa)

519 49.4 527 55.5 536 62.4 544 69.8 558 84.0 577 102.9 592 124.1 603 139.0 612 153.2 624 173.4 633 186.9 643 207.7 4.8 wt % PLMA in propane 374.7 ± 0.1 K

density (kg/m3)

424.6 ± 0.1 K density (kg/m3)

P (MPa)

501 45.0 506 48.7 516 55.2 525 61.9 533 69.2 547 82.7 565 104.1 581 124.4 591 138.7 600 152.9 611 172.9 618 187.6 629 207.1 5.0 wt % F7 in propane 374.8 ± 0.1 K

461 468 480 490 499 515 536 553 564 574 586 595 605 422.2 ± 0.1 K

density (kg/m3)

P (MPa)

density (kg/m3)

P (MPa)

density (kg/m3)

480 490 501 512 528 547 566 578 588 601 610 621

55.5 63.9 70.8 83.0 103.7 125.0 139.1 152.6 173.7 190.0 207.5

522 533 541 554 574 590 599 607 621 630 639

55.9 62.8 69.6 83.2 104.3 125.0 138.9 152.9 172.6 190.6 208.0

487 498 507 523 546 564 575 584 597 608 618

4.2 wt % LMA-MMA50 (Mw = 28 000) in propane

423.8 ± 0.1 K

376.6 ± 0.1 K

424.9 ± 0.1 K

P (MPa)

density (kg/m3)

P (MPa)

density (kg/m3)

P (MPa)

density (kg/m3)

P (MPa)

density (kg/m3)

24.4 28.0 31.4 35.0 42.0 48.9 56.0 63.0 69.8 84.3 105.6 125.6 143.3 176.0 213.7

477 485 492 498 510 520 529 537 545 558 575 588 599 616 634

28.8 31.4 35.1 42.0 49.3 55.7 62.5 70.8 84.4 106.1 125.1 139.6 175.3 210.3

439 447 455 472 485 495 504 514 529 549 564 573 595 613

48.4 55.9 63.3 69.7 83.9 105.3 125.6 140.6 152.8 172.5 188.9 208.0

516 527 536 545 560 580 596 607 616 630 639 648

48.2 56.2 62.6 69.6 83.4 104.2 124.7 138.8 153.5 174.5 206.1

474 489 499 510 527 550 568 580 590 604 624

bonds with propane; therefore, the association term is not used in this study. The PC-SAFT EoS is described with the following equations.

morphological characteristics of a highly structured, star polymer. These equations are only briefly described here because details are found elsewhere.18,38,41 The PC-SAFT EoS is composed of an expansion of the residual molar Helmholtz free energy,a ̃res , containing terms for hard-chain interactions,a ̃hc , dispersion interactions,a disp ̃ . ̃ , and chemical associations,a assoc None of the polymers self-associate nor do they form hydrogen

a ̃res = a ̃hc + a disp ̃ hs a ̃hc = ma ̅ ̃ −

∑ xi(mi − 1) ln giihs(σii) i

10139

(1)

(2)



∑ ximi

m̅ =

gijhs

Table 6. PC-SAFT Parameters for LMA, MMA, and Propane and the Binary Interaction Parameters between LMA and Propane (kLMA−propane) Obtained from the Literature.38,42 The Binary Interaction Parameters between MMA and Propane (kMMA−propane) Are Obtained by Fitting LMAMMAx−Propane Phase Behavior Data Obtained in This Study

(3)

i

a ̃hs =

Article

⎤ ⎛ζ 3 ⎞ ζ2 3 1 ⎡⎢ 3ζ1ζ2 2 ⎥ ⎜ ⎟ ln(1 ) + + − ζ − ζ 0 3 2 ⎥⎦ ζ0 ⎢⎣ (1 − ζ3) ζ3(1 − ζ3)2 ⎝ ζ3 ⎠ (4)

⎛ didj ⎞ 3ζ ⎛ didj ⎞2 2ζ 2 1 2 2 ⎜ ⎟ ⎟⎟ = + ⎜⎜ 3 (1 − ζ3) ⎜⎝ di + dj ⎟⎠ (1 − ζ3)2 ⎝ di + dj ⎠ (1 − ζ3)

ζn =

π ρ ∑ ximidi n 6 i

(6)

mi =

(7)

miα =

n = 0, 1, 2, 3

⎡ ε ⎞⎤ ⎛ di = σi⎢1 − 0.12 exp⎜ −3 i ⎟⎥ ⎝ kT ⎠⎦ ⎣ a disp ̃

(5)

LMA MMA propane

σij = εij =

j

1 (σi + σj) 2

(8)

(10)

α

3.8964 3.6000 3.6184

254.05 245.00 208.11

−0.09 −0.12 −

∑ miα

(12)

wiαM w,copoly (m /M w )iα

(13)

π ρ ∑ ximi ∑ ziαdiα n 6 i α

ziα =

miα mi

n = 0, 1, 2, 3 (14)

(15)

i

j

α

β

⎛ εiαjβ ⎞2 3 ⎟ σ I2(η , m̅ ) ∑ ∑ xixjmimj ∑ ∑ ziαziβ ⎜ ⎝ kT ⎠ iαjβ i

j

α

β

(16)

where miα is the segment number of type α in copolymer i, obtained from pure-component parameter (m/Mw)iα, and wiα and Mw,copol represent the mass fraction of the repeat unit α and the molecular weight of the copolymer, respectively. The interaction parameter between MMA and propane, kMMA−propane = −0.12, is obtained by fitting LMA-MMAx−propane mixture data, and kLMA‑MMA is assumed to be zero. Solution Behavior Predictions. Figure 7 shows a comparison of the cloud-point curves calculated with PCSAFT EoS for the PLMA−propane system and the copolymer PC-SAFT EoS for the LMA-MMAx−propane systems. Not

Figure 7. Comparison of cloud-point curves obtained in this study (symbols) with calculated curves (lines) using the PC-SAFT EoS for ∼5 wt % PLMA (Mw = 80 000) in propane (○) and using the copolymer PC-SAFT EoS for ∼5 wt % LMA-MMA35 (Mw = 45 000) (◊), LMA-MMA50 (Mw = 28 000) (Δ), and LMA-MMA50 (Mw = 130 000) (□) in propane.

∑ xi(mi − 1) ∑ ∑ Biαiβ ln gihsαiβ (diαiβ) i

0.0268 0.0262 0.0454

−1 ⎛ 20η − 27η2 + 12η3 − 2η 4 ⎞ 8η − 2η 2 + (1 − ) − πρm̅ ⎜1 + m̅ m ⎟ ̅ (1 − η)4 [(1 − η)(2 − η)]2 ⎝ ⎠

where a ̃hs is the residual Helmholtz free energy for hard-sphere fluid interactions, xi the mole fraction of component i, mi the number of segments of component i, ghs the hard-sphere fluid radial distribution function, and di the temperature-dependent segment diameter for component i, which is a function of the temperature-independent segment diameter σi and the interaction energy εi. I1 and I2 in eq 8 are calculated from a power series in density.38 ρ, k, and η are total number density of molecules, Boltzmann’s constant, and reduced fluid density that is equal to ζ3, respectively. For a nonassociating binary mixture, three parameters, m, σ, and ε/k, are needed for each pure component and a binary interaction parameter, kij, is needed to model mixture behavior. For polymers, m/Mw is usually used instead of m, in which Mw is the molecular weight of the polymer. In this study, the solution behavior of the PMMA− propane and PLMA−propane mixtures is modeled with the PC-SAFT EoS. Pure component parameters for propane, PMMA, and PLMA and the binary interaction parameter between LMA and propane, kLMA−propane, are taken directly from literature sources.38,42 These parameters are shown in Table 6 along with kMMA−propane, which is obtained by fitting LMA-MMAx−propane phase behavior data obtained in this study. The solution behavior of LMA-MMAx−propane mixtures is modeled with the copolymer PC-SAFT EoS, which accounts for the fraction of each segment type, ziα and ziβ, and the bonding fraction between segments Biαiβ in copolymer i.41 The hard-chain interaction and dispersion residual Helmholtz freeenergy terms are now given as hs a ̃hc = ma ̅ ̃ −

ksegment−propane

⎛ εiαjβ ⎞ 3 ⎟σ a disp ̃ = −2πρI1(η , m̅ ) ∑ ∑ xixjmimj ∑ ∑ ziαziβ ⎜ ⎝ kT ⎠ iαjβ

(9)

εiεj (1 − kij)

ε/k (K)

ζn = 2

i

σ (Å)

α

⎛ εij ⎞ = −2πρI1(η , m̅ ) ∑ ∑ xixjmimj⎜ ⎟σij 3 ⎝ kT ⎠ i j ⎛ εij ⎞ 3 −πρmC ̅ 1I2(η , m̅ ) ∑ ∑ xixjmimj⎜⎝ kT ⎟⎠ σij

m/Mw

β

(11) 10140



Article

Figure 8. Comparison of single-phase density data obtained in this study (symbols) and calculated densities (lines) using (a) the PC-SAFT EoS for 4.8 wt % PLMA in propane and (b) the copolymer PC-SAFT EoS for 4.2 wt % LMA-MMA50 (Mw = 28 000) in propane at ∼375 K (○) and ∼424 K (□). Dashed line represents the liquid−liquid phase boundary.

■

CONCLUSION The solubility behavior in supercritical propane is very different between the LMA-MMA50 star polymer and the respective “free” linear LMA-MMA50 copolymer arms. In propane, the liquid−liquid phase transition shifts more than 50 MPa to lower pressures for the star polymer compared with that of the linear copolymer, indicating the enhanced solubility of the star polymers because of its discrete branched structure. The enhanced solubility, relative to a random coil, makes the star polymer an attractive additive for a variety of industrial applications. It is also found that the LMA and MMA content in the backbone of these methacrylate copolymers has a significant effect on the temperatures and pressures needed to dissolve the copolymer in propane. Phase transition pressures increase as the number of MMA repeat units increases in the copolymer backbone. Further studies are in progress to ascertain the impact of LMA and MMA content in the copolymer arms on the phase behavior of the LMA-MMA star polymer.

shown are the calculated curves for the PMMA−propane system because these curves are located at temperatures and pressures significantly higher than those on the axes of the graph. The PMMA−propane calculations confirm the experimental observation that PMMA, with Mw of 15 000, can not be dissolved in propane at temperatures to 473 K and pressures to 200 MPa. The calculated cloud-point curves in Figure 7 are in good agreement with experimental results for the PLMA− propane, LMA-MMA35 (Mw = 45 000)−propane, and LMAMMA50 (Mw = 28 000)−propane mixtures. Larger deviations appear for LMA-MMA50 (Mw = 130 000)−propane calculated curve; however, even these calculations capture the trend exhibited by the experimental data. As mentioned previously, the interaction parameter between MMA and propane, kMMA−propane = −0.12, is optimized by fitting the LMA-MMAx phase behavior data obtained in this study. If kMMA−propane is set to zero, the mean absolute percent difference (MAPD) between calculated and experimental cloud-point data increases from 5.2 to 29.6%, and if kMMA−propane is set to −0.20, the MAPD increases to 18.1%. Figure 8 shows a typical comparison between experimental and calculated single-phase densities for the 4.8 wt % PLMA− propane and 4.2 wt % LMA-MMA50 (Mw = 28 000)−propane mixtures. The PC-SAFT predictions tend to overestimate slightly the density data. MAPD values are 1.76% and 1.29% between experimental and calculated densities for PLMA− propane and LMA-MMA50 (Mw = 28 000)−propane mixtures, respectively. To the best of our knowledge, no one has reported modeling solution behavior data for linear copolymer LMA-MMAx using the copolymer PC-SAFT EoS. The present work is the first to demonstrate that the copolymer PC-SAFT EoS gives reasonable predictions of the phase behavior and densities for LMA-MMAx copolymer−propane mixtures at temperatures to 423 K and pressures to 210 MPa by fitting only one parameter, kMMA−propane, the MMA−propane interaction parameter, to the experimental data obtained in this study. Further, no one has reported values for kMMA−propane because of the difficulty in dissolving pure PMMA in propane. In the present study, we are the first to report a value for kMMA−propane by fitting the copolymer PC-SAFT EoS to the experimental phase behavior data obtained in this study. This value of kMMA−propane can then be used for future predictions of the behavior of other linear, branched, and star polymers in propane, which contain MMA segments.

■

ASSOCIATED CONTENT

S Supporting Information *

GPC chromagrams of the parent and fractionated star polymer samples and PMMA. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1-804-822-7136. Dept. Chemical and Life Science Engineering, Virginia Commonwealth University, 601 West Main St., Richmond, VA 23284. Notes

The authors declare no competing financial interest.

■

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Architectural Effects on the Solution Behavior of Linear and Star

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