Trichloromethane, and Carbon Dioxide Ternary Mixture S - American

Article pubs.acs.org/jced

High-Pressure Phase Behavior of Poly(L‑lactic acid), Trichloromethane, and Carbon Dioxide Ternary Mixture Systems Taehyun Im,† JungMin Gwon,† Soo Hyun Kim,‡ Hun Yong Shin,§ and Hwayong Kim*,† †

School of Chemical and Biological Engineering, and Institute of Chemical Processes, Seoul National University, 559 Gwanangno, Gwanak-gu, Seoul, 151-744, Korea ‡ Korea Institute of Science and Technology, 5, Hwarang-ro 14-gil, Seoul, 136-791, Korea § Department of Chemical and Biological Engineering, Seoul National University of Science and Technology, 232 Gongreung-ro, Nowon-gu, Seoul, 139-743, Korea

ABSTRACT: In this study, the phase behavior of a poly(L-lactic acid) (M = 312 000, polydispersity 2.189)−trichloromethane− carbon dioxide ternary system was measured using a variable volume view cell at pressures up to 34.0 MPa and temperatures between (313.15 K and 363.15) K at an interval of 10 K. Bubble and cloud point pressures were determined as functions of the trichlomethane-to-carbon dioxide ratio, concentration of poly(L-lactic acid) (1.0, 2.0, and 3.0 wt %), and temperature. The hybrid equation of state for the supercritical CO2-polymer system combined with the van der Waals one-fluid mixing rule was used for correlation of the experimental results. The three binary parameters of this system were optimized by the simplex method algorithm.

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INTRODUCTION Poly(L-lactic acid) (PLLA) is a biodegradable polymer obtained from biobased resources, such as sugar cane, corn starch, and tapioca roots. PLLA has applications in a number of fields, including packaging, biomedical devices, apparel, and so on. Commonly, PLLA is produced through lactide ring-opening polymerization with Sn(II)-based catalyst.1 This is not a new polymer, as this environmentally friendly material has existed for many decades. However, it recently gained attention in study for the replacement of petroleum-based thermoplastics in the automobile industry.2 The increase in research on PLLA was stimulated by its increased availability, which was accompanied by an exponential increase in the number of published articles related to PLLA over the past decade.3 Processes involving supercritical fluids (SCFs) were mainly employed for the production and development of PLLA. SCFs are widely used as solvents in many polymer processes, such as reaction, fractionation, separation, and extraction.4 Particularly, CO2 is the most commonly employed SCF, since it is inexpensive, nonflammable, nontoxic, and abundant.5 However, PLLA, which was chosen for analysis in this work, hardly dissolves in CO2. To allow easy dissolution of PLLA, trichloromethane (TCM) is used © 2015 American Chemical Society

as a solvent. TCM is a widely used solvent, and is suitable for many chemical processes. Knowledge of the phase behavior of the PLLA−TCM−CO2 system is important to determine the best operating conditions for PLLA processes. In this work, the cloud and bubble points at which phase transition occurred were measured for the PLLA−TCM−CO2 ternary system in a highpressure apparatus with pressures up to 34.0 MPa and temperatures between (313.15 and 363.15) K at an interval of 10 K. The experimental results were then correlated with the hybrid equation of state6 (hybrid-EOS).

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EXPERIMENTAL SECTION

1. Materials. PLLA was synthesized by the Korea Institute of Science and Technology (KIST) using high purity L-lactide (Purac Biochem BV, Gorinchem, The Netherlands, chiral purity minimum 99 %), without further purification. The molecular weight and polydispersity were determined by GPC. Carbon dioxide (99.999 mol % minimum purity) was supplied by Korea Received: April 5, 2015 Accepted: June 16, 2015 Published: June 24, 2015 2172

DOI: 10.1021/acs.jced.5b00319 J. Chem. Eng. Data 2015, 60, 2172−2177

Journal of Chemical & Engineering Data

Article

Table 1. Properties of the Materials

Table 3. Optimized Binary Interaction Parameters and AADPs

Table 2. Pure Parameters of the Components for the HybridEOS polymer parameters 5

a0/(kg·m /s2) 13.4540 b0/(m3/mol) 0.00000011485 c 0.00125 m 2296.32 critical constants

poly(L-lactic acid)

material

PC (MPa)

trichloromethane carbon dioxide a

5.500a 7.374a

TC (K) 536.50a 304.12a

k12

k13

k23

AADP/%

1.0 % 2.0 % 3.0 %

0.01876 0.01536 0.03372

0.98520 0.44170 0.22947

0.05284 0.06242 0.12828

2.94 3.69 2.73

the phase transition pressure, which defines the cloud and bubble points. A schematic diagram of a conventional variable volume view cell (VVVC) apparatus is presented in Figure 1. The phase behavior data of the PLLA−TCM−CO2 ternary system was obtained using the same procedures and apparatus as described in a previous paper.7 The thermometer and pressure transducer were calibrated by the Korea Testing Laboratory (KTL), the national calibration laboratory of the Republic of Korea. The uncertainty of the thermometer was 0.062 K, while that of the pressure transducer was 0.001 MPa. 3. Thermodynamic Model. To correlate the experimental data measured herein, the hybrid-EOS combined with the van der Waals one-fluid mixing rule, including three binary interaction parameters (kij), was employed. The properties of PLLA are essential for correlation of the presented equation of state, such as the Peng−Robinson equation of state (PR-EOS) and PCSAFT, but no experimental data on PLLA are available. The hybrid-EOS, on the other hand, does not require information on the properties of the polymer other than the molecular weight, and can estimate the pure parameters of the polymer through experimental data. The experimental data can therefore be correlated through the above-mentioned advantages of the hybrid-EOS. This is why the hybrid-EOS for the CO2− polymer system was chosen in this work. The following equation can be used to express the compressibility factor of the hybrid-EOS:

Figure 1. Schematic diagram of the variable volume view cell (VVVC) apparatus: 1, camera; 2, light source; 3, borescope; 4, thermocouple; 5, magnetic stirrer; 6, air bath; 7, view cell; 8, digital thermometer; 9, digital pressure indicator; 10, digital pressure transducer; 11, pressure gauge; 12, hand pump; 13, monitor.

material

weight fraction of PLLA

ω 0.229b 0.225a

Reference12. bReference13.

Z = Z PR + Zassoc + Zchain

Industrial Gases. TCM (99.9 mol % minimum purity) was obtained from Sigma-Aldrich. Table 1 shows the properties of PLLA, TCM, and CO2. 2. Apparatus and Procedures. A variable volume view cell apparatus, which is described elsewhere,7−10 was used to obtain

(1)

In this study, ZPR and Zassoc were used for TCM and pure CO2, and ZPR and Zchain were used for polymers. Equation 2 can be used to obtain the compressibility factor through PR-EOS:11 2173



Article

Table 4. Experimental Data for the PLLA(1) + Trichloromethane(2) + CO2(3) Systema polymer weight fractionb (w1) = 1.0 wt % weight fraction

b

T/K

P/MPa

w2 70.0 wt % w3 30.0 wt %

w2 64.6 wt w3 35.4 wt

w2 59.4 wt w3 40.6 wt

w2 55.3 wt w3 44.7 wt

w2 50.0 wt w3 50.0 wt

363.15 8.766 353.15 8.072 343.15 7.125 333.15 6.497 323.15 5.642 313.15 4.820 % 363.15 10.742 % 353.15 8.755 343.15 7.732 333.15 6.845 323.15 6.154 313.15 5.321 % 363.15 19.151 % 353.15 15.752 343.15 12.090 333.15 8.500 323.15 6.741 313.15 5.845 % 363.15 24.684 % 353.15 20.829 343.15 17.251 333.15 13.413 323.15 9.750 313.15 6.122 % 363.15 29.635 % 353.15 26.033 343.15 22.588 333.15 18.551 323.15 13.865 313.15 9.262 polymer weight fraction (w1) = 2.0 wt %

polymer weight fraction (w1) = 2.0 wt % transition

c

BP BP BP BP BP BP CP BP BP BP BP BP CP CP CP CP BP BP CP CP CP CP CP BP CP CP CP CP CP CP

w2 69.7 wt % w3 30.3 wt %

363.15 353.15 343.15 333.15 323.15 313.15 363.15 353.15 343.15 333.15 323.15 313.15 363.15 353.15 343.15 333.15 323.15

9.163 8.296 7.560 6.634 5.865 5.118 12.946 10.021 7.754 6.892 6.105 5.250 18.815 15.388 11.600 7.655 6.603

BP BP BP BP BP BP CP CP BP BP BP BP CP CP CP CP BP

P/MPa

transitionc

w2 70.0 wt % w3 30.0 wt %

363.15 353.15 343.15 333.15 323.15 313.15 363.15 353.15 343.15 333.15 323.15 313.15 363.15 353.15 343.15 333.15 323.15 313.15 363.15 353.15 343.15 333.15 323.15 313.15 363.15 353.15 343.15 333.15 323.15 313.15

8.860 8.171 7.292 6.555 5.853 4.922 13.066 9.631 8.128 7.235 6.381 5.512 19.452 15.948 12.253 8.599 6.841 5.920 26.101 22.478 18.685 14.711 10.472 6.145 33.955 30.098 26.102 22.151 18.088 13.524

BP BP BP BP BP BP CP CP CP BP BP BP CP CP CP CP BP BP CP CP CP CP CP CP CP CP CP CP CP CP

w2 55.2 wt % w3 44.8 wt %

w2 50.0 wt % w3 50.0 wt %

a Standard uncertainties u are u(T) = ± 0.0848 K, u(P) = ± 0.00630 MPa, and u(w) = ± 0.0020 g.14,15 bw1 (PLLA), w2 (trichloromethane), and w3 (CO2) are weight fractions; w2 and w3 are obtained on a polymer-free basis. cBP: bubble-point, CP: cloud point.

3 2 Z PR − (1 − B)Z PR + (A − 3B2 − 2B)Z PR

B= (2)

bP RT

(4)

For mixtures, parameters of the PR-EOS can be obtained from the van der Waals one-fluid mixing rule.

where A=

BP CP CP CP CP CP BP CP CP CP CP CP CP

T/K

w2 60.0 wt % w3 40.0 wt %

transitionc

transitionc

weight fractionb

w2 65.0 wt % w3 35.0 wt %

P/MPa

− (AB − B2 − B3) = 0

P/MPa

313.15 5.688 363.15 25.085 353.15 21.601 343.15 17.740 333.15 13.741 323.15 9.554 313.15 5.815 w2 50.0 wt % 363.15 32.688 w3 50.0 wt % 353.15 29.322 343.15 25.566 333.15 21.408 323.15 17.100 313.15 12.464 polymer weight fraction (w1) = 3.0 wt %

T/K

w2 59.9 wt % w3 40.1 wt %

T/K

w2 55.0 wt % w3 45.0 wt %

weight fractionb

w2 64.3 wt % w3 35.7 wt %

weight fraction

b

aP R2T 2

a= (3)

∑ ∑ xixjaij i

2174

j

(5) DOI: 10.1021/acs.jced.5b00319 J. Chem. Eng. Data 2015, 60, 2172−2177

Journal of Chemical & Engineering Data b=

∑ xibi

(6)

i

aij =

Article

aiaj (1 − kij)

(7)

Although the critical constants (PC, TC) and acentric factor (ω) of the pure materials are essential for determination of the compressibility factor of the PR-EOS, it is very difficult to obtain information about PLLA regarding the critical pressure, temperature, or acentric factor. In addition, these values are not readily available in the literature. The solvent parameters are shown in Table 2. The van der Waals energy parameter (ai) and the excluded volume parameter (bi) of the PR-EOS were estimated with the following empirical equation:

ai = ai0 exp(CiT )

(8)

ai0

where and Ci stand for adjustable parameters determined by fitting the experimental data, and the bi is obtained by the same method. The compressibility factor due to the association is calculated from the following equation: ⎛ 1 1 ⎞ ∂X S Zassoc = ρ ∑ ⎜ S − ⎟ ⎝X 2 ⎠ ∂ρ S

Figure 2. Correlation results using the hybrid-EOS for PLLA (weight fraction = 1.0 %) + trichloromethane + CO2 system. Weight fractions of CO2 in the mixed solvent on a polymer-free basis: ■, 0.500; △, 0.447; ▼, 0.406; ○, 0.354; ●, 0.300; solid lines, the calculations with the hybrid-EOS.

(9)

where ρ stands for the molecular number density of the associating molecules, XS stands for the mole fraction of the associating molecules not bonded at site S, and the total includes all binding sites of the associating molecule. The compressibility factor due to the effect of polymer chain connectivity is obtained from the following equation: Zchain =

∑ i

+

ζ3 xi(1 − mi) ⎡ 3 diiζ2 ⎢ + 2 hs 2 (1 − ζ3)2 gii (dii) ⎣ (1 − ζ3) 3diiζ2ζ3

(1 − ζ3)3

+

dii2ζ22 (1 − ζ3)2

+

2 2 3 dii ζ2 ζ3 ⎤ ⎥ 2 (1 − ζ3)4 ⎦

(10)

where xi is the mole fraction of polymer i, mi is the number of PLLA segments, dii is the effective molecular diameter, and ζ is the reduced density. The parameter mi is obtained through optimization of the experimental data. Equation 11 demonstrates the radial distribution function, gii, for a pair of PLLA segments: giihs(dii) =


⎡ dii ⎤2 3d ζ2 ζ22 1 + ii + 2 ⎢ ⎥ ⎣ 2 ⎦ (1 − ζ3)3 1 − ζ3 2 (1 − ζ3)2 (11)

where

πNA ζk = ρ ∑ Ximidiik 6 i

ternary system at the PLLA weight fractions of (1.0, 2.0, and 3.0) % are displayed in Figures 2 to 4, respectively. Depending on the temperature conditions and PLLA composition, the L−V phase transition, which defines the bubble point, or the L−L phase transition, which defines the cloud point, may occur. In the lowtemperature region, the L−V phase transition occurred. However, beyond a certain temperature, the L−V transition was replaced by an L−L transition. The phase separation pressure was slightly increased at the bubble points compared with the cloud points. The effects of the CO2 weight fraction under various conditions are shown in Figures 5 and 6. In Figures 5 and 6, as the CO2 weight fraction increased, the phase transition pressure also increased at constant temperature (353.15 K) and PLLA weight fraction (1.0 wt %), respectively. These phenomena show that TCM is a good solvent, but CO2 acts as an antisolvent. This tendency was observed throughout this study. Figures 2 to 4 show the comparison of the

(12)

In this study, the simplex method algorithm was adopted for optimization of the parameters (ai0, bi, Ci, mi) and the critical constant (PC, TC, ω) of the polymer for the hybrid-EOS and the binary interaction parameter (kij) used in the one-fluid mixing rule, as shown in Tables 2 and 3.

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RESULT AND DISCUSSION The experiments were conducted for temperatures between (313.15 K and 363.15) K at an interval of 10 K and pressures up to 34.0 MPa. In addition, investigation was carried out on three different PLLA compositions: weight fractions of PLLA = (1.0, 2.0, and 3.0) %. Table 4 shows the phase separation data for the PLLA−TCM−CO2 ternary system. The phase behavior of this 2175



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Figure 6. Effect of CO2 weight fraction in constant PLLA weight fraction (w1 = 1.0 wt %) on the phase separation pressure at temperatures between (313.15 and 363.15) K at an interval of 10 K: □, 313.15 K; ■, 323.15 K; △, 333.15 K; ▼, 343.15 K; ○, 353.15 K; ●, 363.15 K.

it was concluded that the hybrid-EOS used in this study is suitable for the CO2−polymer−solvent system.

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CONCLUSION We measured the phase behavior of a poly(L-lactic acid)− trichloromethane−CO2 ternary system at temperatures between (313.15 to 363.15) K at an interval of 10 K, and pressures up to 34.0 MPa. The phase transition pressures were dependent on the temperature, weight fraction of PLLA, and CO2/TCM weight ratio. As the weight fraction of PLLA increased, the L−L transition occurred and the phase separation pressure increased more quickly. However, the increment of the TCM weight fraction caused a decrease in the cloud or bubble point. The experimental data were correlated with the hybrid-EOS combined with the van der Waals one-fluid mixing rule with three adjustable binary interaction parameters, kij. The correlation results indicate an AADP (%) of about 2.73 to 3.69 (1.0 wt % = 2.93, 2.0 wt % = 3.69, and 3.0 wt % = 2.73).

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Figure 5. Effect of CO2 weight fraction in constant temperature (T = 353.15 K) on the phase separation pressure at various PLLA weight fraction: ×, 3.0 %; +, 2.0 %; ○, 1.0 %.

*Tel.: +82-2-880-7406. Fax: +82-2-888-6695. E-mail: [email protected].

experimental data and the correlation results, which were calculated by the hybrid-EOS mentioned above. The simplex method algorithm was used for the regression of the three binary interaction parameters and the PLLA parameters. The objective function (OBF) and the absolute average deviation of pressure (AADP) percent for the correlation were given by N

OBF =

∑ i=1

− Pical Piexp

Funding

This work was supported by the Korea government (MEST) (NRF-2012M1A2A2671789). Notes

The authors declare no competing financial interest.

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Piexp

(13)

AADP/% =

N

·100

REFERENCES

(1) Auras, R. A.; Lim, L.-T.; Selke, S. E. M.; Tsuji, H. Poly(lactic acid): Synthesis, Structures, Properties, Processing, and Applications; Wiley: New York, 2011. (2) Gwon, J.; Cho, D. W.; Kim, S. H.; Shin, H. Y.; Kim, H. Phase Behaviour of the Ternary Mixture System of Poly(L-lactic acid), Dichloromethane, and Carbon Dioxide. J. Chem. Thermodyn. 2012, 55, 37−41. (3) Gwon, J.; Kim, S. H.; Shin, H. Y.; Kim, H. Phase Behavior of Poly(D-lactic acid), Dichloromethane, and Carbon Dioxide Ternary Mixture Systems at High Pressure. J. Chem. Eng. Data 2014, 59, 2144− 2149.

N

∑i = 1 |(Piexp − Pical)/Piexp|

AUTHOR INFORMATION

Corresponding Author

(14)

where N is the number of experimental data points, and Pexp and Pcal are the experimental and calculated pressures, respectively. Table 3 shows the binary interaction parameters kij and the AADP (%) for the PLLA, TCM, and CO2 ternary system. The results showed an AADP (%) of about 2.73% to 3.69 % (1.0 wt % = 2.93, 2.0 wt % = 3.69, and 3.0 wt % = 2.73). From these results, 2176



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(4) Kalogiannis, C. G.; Panayiotou, C. G. Bubble and Cloud Points of the Systems Poly(E-caprolactone) + Carbon Dioxide + Dichloromethane or Chloroform. Supercritical fluid extraction. J. Chem. Eng. Data 2006, 51, 107−111. (5) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice, 2nd ed.; Butterworth-Heinemann: Woburn, MA, 1994. (6) Shin, H. Y.; Wu, J. Equation of State for the Phase Behavior of Carbon Dioxide−Polymer Systems. Ind. Eng. Chem. Res. 2010, 49, 7678−7684. (7) Gwon, J.; Cho, D. W.; Kim, S. H.; Shin, H. Y.; Kim, H. Phase Behaviour of the Ternary Mixture System of Poly(L-lactic acid), Dichloromethane and Carbon Dioxide. J. Chem. Thermodyn. 2012, 55, 37−41. (8) Bae, W.; Kwon, S.; Byun, H.-S.; Kim, H. Phase Behavior of the Poly(vinyl pyrrolidone) + N-Vinyl-2-pyrrolidone + Carbon Dioxide System. J. Supercrit. Fluids 2004, 30, 127−137. (9) Shin, H. Y.; Wu, J. Equation of State for the Phase Behavior of Carbon Dioxide−Polymer Systems. Ind. Eng. Chem. Res. 2010, 49, 7678−7684. (10) Gwon, J.; Cho, D. W.; Bae, W.; Kim, H. High-Pressure Phase Behavior of Carbon Dioxide + Tetrahydrofurfuryl Acrylate and Carbon Dioxide + Tetrahydrofurfuryl Methacrylate Binary Mixture Systems. J. Chem. Eng. Data 2011, 56, 3463−3467. (11) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (12) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P.: The Properties of Gases and Liquids, 5th ed.; McGraw-Hill Book Company: New York, 2000. (13) Liessmann, G.; Schmidt, W.; Reiffarth, S. Data Compilation of the Saechsische Olefinwerke Boehlen; DETHERM: Frankfurt, 1995. (14) Analytical Methods Committee Uncertainty of Measurement: Implications of Its Use in Analytical Science. Analyst 1995, 120, 2303− 2308. (15) Chirico, R. D.; Frenkel, M.; Diky, V. V.; Marsh, K. N.; Wilhoit, R. C. ThermoMLAn XML-Based Approach for Storage and Exchange of Experimental and Critically Evaluated Thermophysical and Thermochemical Property Data. 2. Uncertainties. J. Chem. Eng. Data 2003, 48, 1344−1359.

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Trichloromethane, and Carbon Dioxide Ternary Mixture S - American

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