Solubility of Subcritical and Supercritical Propylene in the

Article pubs.acs.org/jced

Solubility of Subcritical and Supercritical Propylene in the Semicrystalline Polyethylenes Zhen Yao,‡ Lin-jie Xu,‡ Fang-jun Zhu,‡ Yun-fei Zhang,‡ Changchun Zeng,*,§,∥ and Kun Cao*,†,‡ State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering and ‡Institute of Polymerization and Polymer Engineering, Zhejiang University, Hangzhou 310027, China § High Performance Materials Institute, Florida State University, Tallahassee, Florida 32310, United States ∥ Department of Industrial & Manufacturing Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32310, United States Downloaded by UNIV OF NEBRASKA-LINCOLN on September 15, 2015 | http://pubs.acs.org Publication Date (Web): September 9, 2015 | doi: 10.1021/acs.jced.5b00466

†

ABSTRACT: Solubilities of propylene in high-density polyethylene (HDPE), low-density polyethylene (LDPE), and linear low density polyethylene (LLDPE) were measured using the pressure-decay approach at temperature ranges from (348.15 to 383.15) K and pressures up to 8 MPa. The experimental data were correlated by the Sanchez−Lacombe equation of state (SL EoS) with temperature-dependent binary interaction parameters kij. The SL EoS could predict well the solubilities of propylene in the different semicrystalline polyethylenes (PEs) over a wide range of conditions, including the supercritical state. The discrepancies between the model calculation and the experimental data were within 4 %. Among the above three PEs, HDPE had the lowest propylene solubility due to its high crystallinity and small free volume. Although LDPE and LLDPE had the similar crystallinity, the propylene solubility was higher in the former, suggesting that the propylene solubility in PEs also depends on the chain microstructure.

1. INTRODUCTION In-reactor alloy technology has been increasingly used in the polyolefin industry to produce the high-end products. The solubility of olefins in polyolefins under operating temperature and pressure should be a key parameter for designing the polymerization and subsequent devolatilzation processes.1−6 Previous studies on the solubility of olefins in polyolefins have been primarily conducted at moderate temperatures and pressures. Michaels et al. determined the solubility of ethylene and propylene in different polyethylenes (PEs) at 298.15 K.7 Meshkova et al. measured the solubility of ethylene and propylene in PE and polypropylene (PP) at (295.15 to 343.15) K.2 Yoon et al. reported the solubility of 1-butene, 1-hexene, and 1-octene in linear low density polyethylene (LLDPE) at (343.15 to 358.15) K.8 Using a gas chromatography technique, Sliepcevich et al. obtained the diffusivity and solubility of the olefins in PP at 353.15 K and 0.6 MPa.9 Moore et al. measured the solubility of ethylene, 1-butene, and 1-hexene in different kinds of PEs with a gravimetric method at (303.15 to 363.15) K and 3.5 MPa.10 Sato et al. developed a pressure-decay method to determine the solubility of propylene in different semicrystalline PPs at (323.15 to 348.15) K and 3.0 MPa, and in ethylene−propylene copolymer at (323.15 to 363.15) K and 2.4 MPa.11,12 The solubility of olefins in olefin copolymers had been also measured by Bartke et al. and Yoon et al. at 343.15 K/1.0 MPa and (303.15 to 363.15) K/0.3 MPa, respectively.13,14 Kiparissides et al. reported experimental and theoretical investigation of the solubility and diffusion of © XXXX American Chemical Society

ethylene in semicrystalline PE at temperatures and pressures up to 353.15 K and 6.6 MPa, respectively.15 Nevertheless, experimental data at both high temperature and high pressure approaching the critical states of propylene are still lacking. In our previous work, we investigated the solubility of propylene in semicrystalline polypropylene at temperatures from (348.15 to 383.15) K and pressures up to 8 MPa.16 The purpose of this study was to measure the solubility of subcritical and supercritical propylene in three kinds of polyethylenes: high-density polyethylene (HDPE), low-density polyethylene (LDPE), and linear low-density polyethylene (LLDPE). The experimental data were then correlated by Sanchez−Lacombe equation of state (SL EoS) to determine the relationships between solubility and structure of the above polyethylenes.

2. EXPERIMENTAL SECTION 2.1. Materials. Propylene (mass purity > 0.999) was supplied by Foshan Kodi Gas Chemical Industry Co. (Guangzhou, China). Helium (mass purity > 0.9999) was purchased from Hangzhou Jingong Special Products Co. (Hangzhou, China). The selected polyethylenes were all in pellet form from the following sources: HDPE (T60-800), Tianjin Petrochemcial Co. (Tianjin, China); LDPE (2426), CNOOC-Shell JV Petrochemicals; and LLDPE (DFDA7042), Received: June 5, 2015 Accepted: August 28, 2015

A

DOI: 10.1021/acs.jced.5b00466 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Sinopec Qilu Petrochemcial Co. (Zibo, China). All three PEs were used as received. The weight-average and number-average molecular weights of the PEs were determined by gel permeation chromatography (PL-GPC220, Polymer Lab, U.S.A.) at 423.15 K with 1,2,4-trichlorobenzene as solvent. Mass fraction crystallinity (Xc) and melting temperature (Tm) of the PEs were obtained by a differential scanning calorimeter (Q200, TA Instruments) in a nitrogen atmosphere at ambient pressure. The crystallinity Xc could be calculated using the following equation:

Downloaded by UNIV OF NEBRASKA-LINCOLN on September 15, 2015 | http://pubs.acs.org Publication Date (Web): September 9, 2015 | doi: 10.1021/acs.jced.5b00466

Xc = ΔH /ΔHm0·100 %

The solubility of propylene in the sample (S) was calculated using the following equation: S=

where ΔH is the crystallization enthalpy of the sample and ΔHm0 is the crystallization enthalpy of the same type of polymer with 100 % crystallinity, which is 293 J·g−1 for polyethylene.17 The density values were measured by the pycnometry at room temperature and atmospheric pressure. Table 1 summarized the basic characteristics of the given polyethylenes used in this work.

Mw

Tm/K

Xc/%

density/(kg·m−3)

HDPE LDPE LLDPE

15800 18500 27500

62900 76100 89800

405 386 397

61 46 45

0.937 0.924 0.925

(2)

3. RESULTS AND DISCUSSION 3.1. Thermodynamic Model. SL EoS, a lattice fluid based thermodynamic model commonly used for fluid phase equilibria of small molecule in polymer,21 was used to correlate the solubility of propylene in the amorphous regions of polyethylene. The SL EoS takes the following form:

Table 1. Summary of the Properties of the Polyethylenes Used in the Study Mn

mp(1 − Xc)

where V1 is the volume between V-5 and V-7; V2 is the volume behind V-7. ρ1 is the density of propylene before pressure decay; ρ2 is the density of the propylene after solubility equilibrium. Both ρ1 and ρ2 are calculated by Benedict−Webb− Rubin (BWR) equation of state.18 Vp, mp, and Xc are the volume, mass, and crystallinity of the polymer sample, respectively. Note that Vp should change after the dissolution of propylene in the polymers.19,20 In this work, this had been properly taken into account when calculating this value using SL EoS.

(1)

sample

V1ρ1 − (V1 + V2 − Vp)ρ2

⎡ ⎛ 1⎞ ⎤ ρ 2̃ + P ̃ + T̃ ⎢ln(1 − ρ ̃) + ⎜1 − ⎟ρ ̃⎥ = 0 ⎝ ⎣ r⎠ ⎦

(3)

where T̃ = (T/T*), P̃ = (P/P*), ρ̃ = (ρ/ρ*), T, P, and ρ are the absolute temperature, system pressure, and density, respectively. T*, P*, and ρ* are the three characteristic parameters whose values for each of the polymer and propylene are listed

2.2. Solubility Measurement Apparatus and Experimental Procedure. All samples were dried in a vacuum oven for 24 h before being used. The solubility was measured by a pressure-decay method utilizing a custom-built high-pressure system, as shown in Figure 1. The system and experimental procedure were previously discussed in detail.16

Table 2. SL EoS Parameters for Propylene and the Polyethylenes Used in the Study sample

T*/K

P*/MPa

ρ*/(kg·m−3)

reference

propylene HDPE LDPE LLDPE

346 650 628 667

379.0 425.0 420.8 437.0

0.755 0.905 0.905 0.900

19 19 20 19

in Table 2. The number of lattice sites occupied by a molecule, r, is r=

M w P* RT *ρ*

(4)

Here, R and Mw are the universal gas constant and the polymer molecular weight, respectively. For mixtures such as the propylene−polymer mixtures studied herein, appropriate mixing rules were necessary, which are shown in the following:

P* =

P* ∑ ∑ ϕϕ i j ij i

j

T * = P* ∑ (ϕi°Ti*/Pi*) i

1/r =

Figure 1. Schematic diagram of experimental apparatus for solubility measurement by pressure-decay method. 1, helium capsule; 2, propylene capsule; 3, 4, 5, filter; 6, high pressure supply pump; 7, high pressure container A; 8, high pressure container B; 9, pressure sensor; 10, constant temperature drying oven; V-1, V-2, V-3, V-4, V-5, V-6, V-7, high pressure pin valve.

∑ (ϕi°/ri) i

(5)

(6) (7)

and Pij* = (1 − κij) Pi*P*j B

(8) DOI: 10.1021/acs.jced.5b00466 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

ϕi = (wi /ρi*)/∑ (wj /ρj*) (9)

j

ϕi° = (ϕiTi*/Pi*)/∑ (ϕjT *j /P*j ) j

(10)

where ϕi is the volume fraction of component i, kij is the binary interaction parameter introduced to account for the deviation of Pij* from the geometric mean. At equilibrium the chemical potentials of propylene (i = 1) in the vapor phase (G) and polymer phase (P) are equal. Assuming no dissolution of polymer into the vapor phase and at equilibrium, it follows that ⎛ r 0T *P* ⎞ = ln ϕ1 + ⎜1 − 10 1 2 ⎟ϕ2 RT r2 T2*P1* ⎠ ⎝ 0 r1 ρT1*ϕ2[P1* + P2* − 2(1 − k12)(P1*P2*)0.5 ] + P1*ρ*T


μ1P

⎡ ρT * ⎞ ⎛ Pρ*T1* ⎛ ρ* ρ⎞ + r10⎢ − 1 + +⎜ − 1⎟ln⎜1 − ⎟ ρ* ⎠ ⎝ ρ ⎠ ⎝ P1*ρT ⎣ ρ*T +

1 ⎛ ρ ⎞⎤ ln⎜ ⎟⎥ r10 ⎝ ρ* ⎠⎦

⎡ ρ T* ⎞ ⎛ ρ ⎞ Pρ *T1* ⎛ ρ1* 1 = r10⎢ − 1 + 1 + ⎜⎜ − 1⎟⎟ln⎜⎜1 − 1 ⎟⎟ ⎢⎣ ρ1*T ρ1* ⎠ P1*ρ1T ⎝ ρ1 ⎠ ⎝ +

⎤ μ1G 1 ⎛ ρ1 ⎞⎥ ⎜ ⎟ ln = ⎜ ⎟ r10 ⎝ ρ1* ⎠⎥⎦ RT

(11)

The calculation of binary interactive parameter kij is a recursive process. For a particular kij, one can solve eqs 3 and 11 together to obtain ρ and ϕi. Vp and S*(calculated solubility) can be then calculated from ρ and ϕi, respectively. On the other hand, S (measured solubility) should also be obtained from eq 2. By minimizing the difference between S* and S, optimal values for kij can be obtained. 3.2. Solubility of Propylene in the Polyethylenes. The solubilities of propylene in polyethylenes at various temperatures and pressures were shown in Figure 2 and Table 3. Two temperatures [(348.15 and 358.15) K] were below, while the other two [(368.15 and 383.15) K] were above the critical temperature of propylene (365.57 K). Pressure employed for subcritical temperature measurements was limited by the propylene vapor pressure. The solubility was expressed in grams of propylene per gram of amorphous polyethylene. In all polyethylenes studied herein, the solubility of propylene decreased as the temperature increased. At subcritical temperature, the propylene solubility in HDPE (Figure 2a) increased almost linearly with increasing pressure. The similar linear dependency was also observed at temperatures higher than the propylene’s critical temperature, but only at low to moderate pressure. At higher pressure, the solubility was less dependent on the pressure and appeared to gradually approach to a similar limiting value at both temperatures. At higher pressure the increase will also raise the pressure surrounding the polymer, forcing the chains closer together again. This hinders the expansion of the free volume, leading to a decrease in solubility as the free volume decreases.22 When measuring the propylene solubility in LDPE at 368.15 K, the polymer pellets started to melt when the pressure was

Figure 2. Solubility of propylene in the polyethylenes at different temperatures and pressures: (a) HDPE; (b) LDPE; (c) LLDPE.

over 4.5 MPa, which made determining the PVT properties of the samples extremely difficult. Similar situations occurred for LLDPE when measurements were conducted at 368.15 K and the pressure was over 5.2 MPa. As had been reported in the literatures23,24 the dissolved dense gases could significantly decrease the polymer melting point. These results were shown in Figure 2b (LDPE) and 2c (LLDPE), both demonstrating a linear pressure dependence at each temperature. C



Article

Table 3. Solubilities of Propylene in the Polyethylenes at Different Temperatures and Pressures


HDPE T/K

P/MPa

348.15

1.06 1.43 1.60 1.86 1.89 2.34 2.44 2.69 2.81

358.15

368.15

383.15

LDPE

solubility (g-gas/g-amorph.polymer)

P/MPa

0.0362 0.0515 0.0606 0.0677 0.0700 0.0890 0.0976 0.1078 0.1157

± ± ± ± ± ± ± ± ±

0.44 0.32 0.16 0.49 0.28 0.48 0.23 0.36 0.28

% % % % % % % % %

1.03 1.38 1.60 1.73 1.82 2.01 2.32 2.67 2.84 3.13 3.43 4.02

0.0314 0.0409 0.0512 0.0546 0.0584 0.0647 0.0775 0.0891 0.0977 0.1094 0.1117 0.1397

± ± ± ± ± ± ± ± ± ± ± ±

0.42 0.24 0.25 0.22 0.43 0.19 0.26 0.16 0.32 0.38 0.27 0.39

% % % % % % % % % % % %

1.27 2.15 2.40 2.58 2.93 3.52 3.90 4.69 5.18 5.61 6.12 6.54 7.18 7.23 7.50 8.17 1.32 1.53 1.99 2.22 2.94 2.97 3.39 3.69 4.52 4.84 4.98 5.66 5.98 6.10

0.0331 0.0572 0.0628 0.0681 0.0813 0.0998 0.1161 0.1328 0.1495 0.1563 0.1591 0.1623 0.1692 0.1648 0.1688 0.1686 0.0289 0.0330 0.0451 0.0498 0.0690 0.0728 0.0781 0.0880 0.1145 0.1193 0.1209 0.1413 0.1482 0.1445

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.34 0.33 0.23 0.28 0.25 0.41 0.48 0.43 0.16 0.13 0.35 0.24 0.39 0.21 0.17 0.29 0.42 0.46 0.23 0.15 0.31 0.15 0.34 0.28 0.11 0.28 0.47 0.26 0.36 0.41

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

0.91 1.04 1.11 1.21 1.33 1.63 1.93 2.07 2.12 2.22 2.44 2.61 2.88 2.93 2.98 1.05 1.17 1.34 1.62 1.75 2.12 2.33 2.51 2.58 2.81 3.26 3.37 3.67 3.77 1.04 1.27 1.65 1.97 2.11 2.33 2.72 3.08 3.36 3.69

LLDPE


P/MPa

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.98 1.20 1.36 1.77 1.96 2.23 2.43 2.75 3.04

0.0312 0.0411 0.0479 0.0602 0.0648 0.0842 0.0911 0.1086 0.1184

± ± ± ± ± ± ± ± ±

0.41 0.28 0.38 0.44 0.18 0.48 0.34 0.26 0.36

% % % % % % % % %

0.95 1.04 1.18 1.64 1.97 2.12 2.36 2.67 3.11 3.22 3.66

0.0273 0.0333 0.0350 0.0506 0.0638 0.0650 0.0751 0.0871 0.1028 0.1119 0.1257

± ± ± ± ± ± ± ± ± ± ±

0.45 0.41 0.22 0.35 0.39 0.28 0.23 0.39 0.31 0.42 0.28

% % % % % % % % % % %

0.99 1.20 1.55 1.93 2.10 2.18 2.47 2.52 2.71 2.81 3.03 3.54 3.98 4.21 4.55

0.0270 0.0316 0.0408 0.0519 0.0592 0.0579 0.0659 0.0732 0.0823 0.0842 0.0855 0.1086 0.1194 0.1290 0.1386

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.33 0.29 0.45 0.45 0.36 0.31 0.39 0.38 0.47 0.48 0.34 0.24 0.42 0.46 0.32

% % % % % % % % % % % % % % %

0.0369 0.0421 0.0447 0.0482 0.0557 0.0686 0.0829 0.0916 0.0929 0.0999 0.1087 0.1156 0.1377 0.1448 0.1445 0.0367 0.0426 0.0481 0.0601 0.0659 0.0805 0.0912 0.0970 0.1000 0.1048 0.1381 0.1413 0.1597 0.1535 0.0319 0.0404 0.0501 0.0656 0.0722 0.0748 0.0895 0.1111 0.1214 0.1401

D

0.47 0.33 0.37 0.23 0.36 0.35 0.25 0.45 0.19 0.28 0.38 0.39 0.44 0.44 0.21 0.41 0.39 0.22 0.47 0.25 0.26 0.43 0.45 0.36 0.39 0.35 0.28 0.47 0.38 0.25 0.34 0.49 0.39 0.36 0.41 0.48 0.34 0.23 0.28

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %




Article

Table 3. continued HDPE T/K

P/MPa


6.92 7.30 7.82 8.08

LDPE

solubility (g-gas/g-amorph.polymer) 0.1551 0.1603 0.1686 0.1692

± ± ± ±

0.38 0.38 0.46 0.31

P/MPa

LLDPE


P/MPa


% % % %

Under the same pressure and temperature, LDPE had the highest propylene solubility among the three PEs, while HPDE had the lowest propylene solubility. This might be attributed to the difference in crystallinity between the PEs. As previously discussed, higher crystallinity would lead to lower solubility as the solvent is unable to penetrate the crystal lamellae. Additionally, the crystalline polymer phase hinders the solvent permeation and swelling of amorphous polymer phase. Of the three PEs studied here, HDPE had the highest crystallinity and hence the lowest solubility. Despite the similar density and crystallinity between the LDPE and LLDPE listed in Table 1, the propylene solubility was higher in the former than the latter, suggesting the chain microstructure also plays an important role. The LLDPE molecules are primarily linear chains with short branches, while LDPE has significantly greater amount of branched chains that are longer. These long branched chains have been reported to increase the gas solubility in PEs.25,26 Moreover, the larger amount of end alkyl groups in LLPE can also increase the solubility in olefins, as Nath et al. discovered in their study.27,28 3.3. Data Correlation with SL EoS. The experimental results were correlated by the SL EoOS with temperaturedependent binary interaction parameters kij. The results predicted from the model using the optimized kij were also shown in Figure 2 as the lines. The SL EoS simulated well the solubility of propylene in polyolefins over a wide range of conditions, even for those above critical temperatures and pressures. Table 4 showed a quantitative comparison between the experimental data and the calculated results. The deviations were within 4 %.

used to correlate k12 and temperature for propylene/HDPE. The regression results in the three systems were listed as follows and also graphically depicted in Figure 3:

Table 4. Optimized Binary Interaction Parameters kij for SL EoS and Correlation Accuracy

Figure 3. Interaction parameter k12 of propylene as a function of temperature for different polyethylenes.

HDPE

LDPE

LLDPE

a

T/K

binary interaction parameter kij

AAD correlation error (%)

348.15 358.15 368.15 383.15 348.15 358.15 368.15 348.15 358.15 368.15

0.026 0.025 0.023 0.018 0.023 0.020 0.016 0.025 0.021 0.017

2.64 3.67 2.41 2.73 2.41 3.58 3.36 3.32 2.22 3.57

HDPE k12 = −5.20 ·10−6T 2 + 3.58 ·10−3T − 0.589 (R2 = 1.000)

(12)

LDPE k12 = −3.50 ·10−4T + 0.145

(R2 = 0.993) (13)

LLDPE k12 = −4.00·10−4T + 0.164

(R2 = 1.000) (14)

Based on temperature-dependent interactive parameter k12, the solubility of propylene in the semicrystalline polyethylenes under other conditions can also be calculated by the SL EoS.

4. CONCLUSIONS The solubility of propylene in several semicrystalline polyethylenes, e.g., HDPE, LDPE, and LLDPE, have been measured over a wide range of temperatures and pressures using a pressure-decay method. For the three PEs studied, we found that the propylene solubility increased as the pressure increased and the temperature decreased. Under the same condition, the solubility of propylene in the three PEs followed the order LDPE > LLDPE > HDPE. The lowest propylene solubility in HDPE may be due to the highest crystallinity and smallest free volume in the polymer. Furthermore, the microstructure also plays a role, which can be seen from the higher propylene solubility in LDPE than that in LLDPE with similar crystallinity due to the longer chain branch and higher terminal alkyl moiety content. Moreover, the measured solubility data were correlated by SL EoS with temperature dependent binary

AAD = 1/no∑no i=1|((Sexp − S*)/S*)|i·100.

The binary interaction parameter k12 of the SL EoS is strongly dependent on temperature. The k12 appears to be a linear function of temperature for propylene/LDPE and LLDPE but shows a nonlinear temperature dependency for HDPE. Thus, linear regression should be performed for the former two systems, while a second-order regression can be E



Article

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interactive parameters, which provided good correlations for the propylene solubility over a wide range of conditions that covered both below and above the critical temperatures and pressures. The temperature dependency of the interactive parameter kij was correlated and could be used to calculate the solubility of propylene in the semicrystalline polyethylenes under the other conditions.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].


Funding

This study was supported by the National Natural Science Foundation of China through NSFC Project No. 51173166, 863 Program of China (No. 2012AA040306), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20110101110030). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors sincerely thank Jian Yang for constructive discussion.

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REFERENCES

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Solubility of Subcritical and Supercritical Propylene in the

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