Phase Behavior of Poly(d-lactic acid), Dichloromethane, and Carbon

Article pubs.acs.org/jced

Phase Behavior of Poly(D‑lactic acid), Dichloromethane, and Carbon Dioxide Ternary Mixture Systems at High Pressure 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, 39-1 Hawolgok-dong, Seongbuk-gu, Seoul, 136-791 Korea § Department of Chemical and Biological Engineering, Seoul National University of Science and Technology, 172, Gongneung 2-dong, Nowon-gu, Seoul, 139-743 Korea ABSTRACT: The phase behavior of a poly(D-lactic acid) (Mw = 359 000 g/mol, polydispersity 1.7), carbon dioxide, and dichloromethane ternary system was measured by a variablevolume view cell. The experimental temperatures and pressures ranged from 313.15 to 363.15 K, up to 300 bar as various experimental conditions of the CO2/dichloromethane mass ratio and temperature, at poly(D-lactic acid) mass fractions of 1.0, 2.0, and 3.0%. The correlation results were obtained from the hybrid equation of state (Peng−Robinson equation of state + SAFT equation of state) using the van der Waals one-fluid mixing rule for the polymer−CO2−solvent system. The binary interaction parameters were optimized by the simplex method algorithm.

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for many chemical processes.7 Besides, DCM is low in toxicity compare to other chlorohydrocarbon solvents. The phase behavior of the PDLA, DCM, CO2 ternary system is important for the design of the optimized operating conditions for PDLA processes. We experimented with the phase separation pressures for mixtures consisting of PDLA, DCM, CO2 at temperatures and pressures ranging from 313.15 to 363.15 K, up to 300 bar. The experimental data were correlated with the hybrid equation of state.8

INTRODUCTION Poly(D-lactic acid) (PDLA), is biodegradable polymer and thermoplastic aliphatic polyester obtained from renewable resources, such as chips, starch, or tapioca roots, (mostly in Asia), or corn starch (in the United States), or sugar cane (in the rest of the world). The common route to obtain PDLA is the lactide ring-opening polymerization with metal catalysts (typically tin octoate) in the melt, in solution, or as a suspension.1 There are industrial routes to obtain usable PDLA with high molecular weight, such as the food industry and the encapsulation of drugs. Recently, the adoption of PDLA for automotive parts has been studied since PDLA-based automotive parts are environmentally friendly compared to petroleum-based thermoplastics.2 The supercritical fluids (SCFs) commonly require the high pressure equipment, but SCFs are an alternative to organic solvents, since they are less hazardous, environmentally friendly, and can effuse through solids like a gas, and dissolve materials like a liquid.3 SCFs are used in several of polymer processes as a solvent, such as separation, extraction, and reaction processes. Particularly, many SCF processes use carbon dioxide (CO2) as a solvent because the critical temperature (Tc = 304.12 K) of CO2 makes it an ideal solvent for extracting materials that are thermally labile. Also, CO2 is nontoxic, nonflammable, environmentally acceptable, and inexpensive.4 However, the high-molecular weight poly(D-lactic acid) (PDLA) dissolves CO2 above the high pressure (about 1500 bar).5,6 To easily dissolve PDLA, we chose dichloromethane (DCM) as a solvent. DCM is an organic solvent, and volatility is suitable for dissolving in a wide variety of organic compounds © 2014 American Chemical Society

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EXPERIMENTAL SECTION 1. Materials. High purity D-lactide (Purac Biochem BV, Gorinchem, The Netherlands, chiral purity minimum 99%) was used for synthesizing the PDLA. The Korea Institute of Science and Technology (KIST) synthesized the PDLA (Mw 359 000 g/mol, polydispersity 1.7), and it was used without further purification. PDLA molecular weight and polydispersity were determined by GPC. Carbon dioxide (99.999 mol % minimum purity) was purchased from Korea Industrial Gases. DCM (99.8 mol % minimum purity) was purchased from Samchun Pure Chemical Co., Ltd. The properties of the components are reported in Table 1. 2. Apparatus and Procedures. The phase separation pressure, which defines the bubble and cloud points, was obtained with a variable-volume view cell apparatus, which is described in detail elsewhere.9−12 Figure 1 shows a schematic diagram of a typical variable-volume view cell apparatus Received: August 7, 2013 Accepted: June 11, 2014 Published: June 20, 2014 2144

dx.doi.org/10.1021/je400715b | J. Chem. Eng. Data 2014, 59, 2144−2149

Journal of Chemical & Engineering Data

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atmospheric pressure. The total amount of components (PDLA + DCM + CO2) was about 8 g per one experiment. The pressure was increased up until a single phase was formed by a high-pressure generator (High Pressure Equipment Co., model 62-6-10) when the temperature reached the predetermined experiment point. A magnetic stirring bar in the cell helped to ensure homogeneity and to reach equilibrium quickly. After reaching a single phase of the solution, the pressure was decreased until the phase transition was reached, upon which a cloud or bubble point can be observed. The pressure was recorded as the phase separation pressure, and then the pressure of VVVC cell was increased until a single phase was reached again. This step was repeated until the standard deviation of separation pressure converged to within ±0.4 bar, and the average of the last three separation pressures was recorded as the final experimental result of that condition. This pressure was indirectly measured by the water with a digital pressure transducer (Honeywell International Inc., model TJE, accuracy of 0.1%) and indicator (Red Lion Controls Inc., model PAXP0000). The VVVC cell temperature was measured by a PRT thermometer (Hart Scientific, Inc., model 5622-32SR, accuracy of ±0.045 K) fixed to the surface, and displayed by an indicator (Hart Scientific, Inc., model 1502). The VVVC cell temperature was measured to within ±0.1 K, and the condition was maintained to within ±0.1 K during measurement of the phase separation pressure. A camera (Veltek international, Inc., model CVC5520) was used to observe the inside of the cell through a borescope (Olympus Corp., model R100-038-00-50) toward the sapphire window. The pressure transducer and thermometer were calibrated by the Korea Testing Laboratory (KTL), the national calibration laboratory. The uncertainty of the pressure transducer was 0.1 bar, and that of the thermometer was 0.062 K. 3. Thermodynamic Model. The hybrid equation of state was used in the correlation of the experimental results in this study. To correlate the data, the van der Waals one-fluid mixing rule including binary interaction parameters (kij) was chosen as the equation of state. The main advantage of the hybrid equation of state is that it is relatively simple in comparison with the presented polymer system equation of state, such as PCSAFT, etc., and does not require properties of the polymer other than the molecular weight. We concluded that this equation of state is suitable for the PDLA + DCM + CO2 ternary system, because there are no properties in experimental data available for the pure polymer properties of PDLA. The compressibility factor of the hybrid equation of state is defined as follows:

Table 1. Properties of Materials

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

Table 2. Parameters for the Hybrid Equation of State material

parameters of macromolecule ai0/(J·m3) b0/(cm3/mol) C m critical constants

poly(D-lactic acid)

a

11.5497 118.902 0.001 62 3660.04

material

TC (K)

PC (bar)

ω

dichloromethane carbon dioxide

510.0a 304.12a

61.0a 73.74a

0.199b 0.225a

Reference 14. bReference 15.

Z = Z PR + Zassoc + Zchain

(1)

The first and third terms are used for polymers, and the first two terms are used for pure CO2 and DCM. The compressibility factor from the Peng−Robinson equation of state (PR-EOS)13 is calculated by the following cubic equation:

(VVVC). The advantage of this apparatus is that the phase separation can be observed through a sapphire window, and the overall composition in the view cell can be maintained during the experiment. The experiment of the PDLA + DCM + CO2 ternary system was performed with the following procedures. First, a predetermined weight of the PCL was inserted into the VVVC cell with tweezers to within ±0.001 g, and the DCM was added to the VVVC cell with a syringe to an accuracy of within ±0.001 g. The cell was slowly purged three times with CO2 (about 0.05 g) at room temperature to remove all traces of air within the cell. Then, the predetermined weight of CO2 was fed in the VVVC cell with a high-pressure CO2 bomb to within ±0.01 g, which is about 140 bar. This step was progressed at

2 Z PR − (1 − B)Z PR + (A − 3B2 − 2B)Z PR − (AB − B2 − B3) = 0

(2)

where A= 2145

aP R2T 2

(3) dx.doi.org/10.1021/je400715b | J. Chem. Eng. Data 2014, 59, 2144−2149


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Table 3. Phase Separation Pressure for the PDLA(1) + Dichloromethane(2) + CO2(3) Systema polymer mass fraction (w1) = 2%

polymer mass fraction (w1) = 1% mass fraction

b

w2 0.690 w3 0.310

T (K) 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 polymer mass fraction

w2 0.655 w3 0.345

w2 0.592 w3 0.408

w2 0.526 w3 0.474

w2 0.485 w3 0.515

P (bar)

transition

76.40 69.54 61.53 53.69 46.36 39.33 84.48 75.62 67.74 59.39 51.34 43.03 151.39 113.80 75.67 65.46 56.48 47.94 238.78 201.98 161.99 122.22 78.23 54.66 300.38 262.26 221.72 181.31 135.51 89.42 (w1) = 2%

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

c

w2 0.545 w3 0.455

w2 0.487 w3 0.513

w2 0.638 w3 0.362

w2 0.576 w3 0.424

P (bar)

transitionc

w2 0.692 w3 0.308

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

77.98 69.95 62.64 54.50 47.00 40.24 86.11 76.78 67.70 59.52 51.58 43.69 139.99 103.72 73.66 64.14 55.29

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

w2 0.503 w3 0.397

B=

bP RT

w2 0.554 w3 0.446

w2 0.501 w3 0.499

b= (4)

j

∑ xibi

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

T (K)

P (bar)

transitionc

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

78.74 70.61 63.23 55.39 47.70 41.22 107.79 78.61 69.28 60.39 51.65 43.77 184.29 147.81 83.20 69.24 59.19 49 229.97 193.28 154.37 113.45 69.14 52.20 264.96 228.99 189.57 148.87 105.10 56.65

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

(6)

i

aij =

aiaj (1 − kij)

(7)

To calculate the compressibility factor of the PR-EOS, the critical constants (TC, PC) and acentric factor (ω) of the materials are necessary. Table 2 shows the solvent parameters for this equation of state. However, the polymer commonly

∑ ∑ xixjaij i

47.47 202.54 166.68 127.64 86.86 59.90 51.13 292.71 254.87 215.21 173.48 128.1 81.40 (w1) = 3%

a Standard uncertainties u are u(T) = ±0.0815 K, u(P) = ±0.0698 bar, and u(w) = ±0.0016 g.16,17 bw1 (PDLA), w2 (dichloromethane), and w3 (CO2) are mass fractions; w2 and w3 are calculated on a polymerfree basis. cBP: bubble-point, CP: cloud point

The mixture parameters of the PR-EOS are calculated by the van der Waals one-fluid mixing rule. a=

transitionc

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 polymer mass fraction

w2 0.693 w3 0.307

T (K)

P (bar)

T (K)

mass fractionb

mass fractionb

w2 0.656 w3 0.344

mass fraction

b

(5) 2146



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does not have critical properties and an acentric factor. The van der Waals energy (ai) and the excluded volume (bi) parameters of the PR-EOS for the PDLA were calculated by the following emprical equation: ai = ai0 exp(CT )

(8)

ai0

where and C are adjustable parameters obtained from the experimental data, and the excluded volume (bi) parameter is determined in the same way. The compressibility factor for the associating effect is obtained from the following equation: ⎛ 1 1 ⎞ ∂X S Zassoc = ρ ∑ ⎜ S − ⎟ ⎝X 2 ⎠ ∂ρ S

(9)

where ρ is the number density of the associating molecules. And the XS parameter is the mole fraction of the associating molecules not bonded at site S, and the total is all binding sites of the associating molecule. The compressibility factor for the chain connectivity of the PCL is defined as follows. Zchain =

∑ i

xi(1 − mi) giihs(dii)

Figure 2. Correlation results using the hybrid EOS for PDLA (mass fraction = 1.0%) + DCM + CO2 system. Mass fractions of CO2 in the solvent on a polymer-free basis: ■, 0.515; Δ, 0.474; ▼, 0.408; ○, 0.345; ●, 0.310.

×

⎡ ζ3 3diiζ2ζ3 dii2ζ22 3 diiζ2 ⎢ + + + 2 2 3 2 (1 − ζ3) (1 − ζ3) (1 − ζ3)2 ⎣ (1 − ζ3) +

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 PCL segments, dii is the effective molecular diameter, and ζ is the reduced density. The parameter mi is optimized by the experimental data. The parameter gii is the radial distribution function for a pair of PCL segments and is defined as follows. giihs(dii) =

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

(11)

where ζk =

πNA ρ ∑ Ximidiik 6 i

Figure 3. Correlation results using the hybrid EOS for PDLA (mass fraction = 2%) + DCM + CO2 system. Mass fractions of CO2 in the solvent on a polymer-free basis: ■, 0.513; Δ, 0.455; ▼, 0.397; ○, 0.344; ●, 0.308.

(12)

(ai0,

The polymer parameters Ci, bi, mi) were optimized by the experimental data using the simplex method, as shown in Table 2.

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pressure which defines the cloud and bubble points. This tendency shows the whole range of temperature in this study. Figures 2−4 present the comparison of the experimental results and the correlation results. As mentioned, the hybrid EOS is suitable for the polymer system in that there are no pure polymer properties except for the molecular weight. The correlation results were calculated by the hybrid EOS model. The critical constants (TC, PC) and the acentric factor (ω) of DCM and CO2 are necessary for the hybrid EOS correlation. The simplex method was used for the regression of the PDLA polymer parameters and the three binary interaction parameters. The objective function (OBF) and the absolute average deviation of pressure (AADP) percent for the calculation results were given by

RESULTS AND DISCUSSION Table 3 shows the phase separation pressure for the PDLA + DCM + CO2 system with pressures up to 300 bar and temperatures ranging from 313.15 to 363.15 K. Figures 2−4 present the phase behavior of this system. These figures show the phase separation pressure (the cloud and bubble points) at the PDLA mass fractions of 1.0, 2.0, and 3.0%, respectively. The bubble point, which is the L−V phase transition, occurs in the relatively low-temperature region with a low CO2 mass fraction. Beyond a certain temperature or increment in the CO2 mass fraction, the cloud points occur, which is the L−L phase transition. At the cloud points, the phase separation pressure is dramatically increased compared with the bubble points. Figures 5 and 6 show the effect of the CO2 mass fraction at various conditions, which indicates that CO2 is an antisolvent, but DCM is a good solvent. Figure 5 shows that the CO2/ DCM mass ratio is a major factor of the phase separation

N

OBF =

∑ i=1

2147

Piexp − Pical Piexp

(13)



Article

Figure 4. Correlation results using the hybrid EOS for PDLA (mass fraction = 3.0%) + DCM + CO2 system. Mass fractions of CO2 in the solvent on a polymer-free basis: ■, 0.499; Δ, 0.446; ▼, 0.424; ○, 0.362; ●, 0.307.

Figure 6. Effect of CO2 weight fraction in constant PDLA mass fraction (w = 2.0%) on the phase separation pressure at various temperature: □, 313.15 K; ■, 323.15 K; Δ, 333.15 K; ▼, 343.15 K; ○, 353.15 K; ●, 363.15 K.

Table 4. Correlation Results with the Hybrid Equations of State mass fraction of PDLA (%)

k12

k13

k23

AADP (%)

1.0 2.0 3.0

0.0059 0.0062 0.0068

0.6206 0.6168 0.6197

0.1416 0.2546 0.3863

4.5 3.9 3.4

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CONCLUSION We examined the phase behavior of a poly(D-lactic acid) + dichloromethane + CO2 ternary system at pressures of up to 300 bar and temperatures ranging from 313.15 to 363.15 K. The phase transition pressures (bubble and cloud points) depend on the CO2/DCM mass ratio, the mass fraction of PDLA, and temperature. We conclude that the main factor of phase separation pressure is the CO2 mass fraction. As the mass fraction of CO2 increased, the phase transition pressure increased, and the cloud point (L−L transition) appeared quickly. However, the increment of the DCM mass ratio caused a decrease in the phase separation pressure. The main reason for this phenomenon is the increment of solvent polarity. That effect led to a move of the transition to lower pressures during the constant temperature. The experimental data were correlated with the hybrid EOS using the van der Waals one-fluid mixing rule with binary interaction parameters, kij. The hybrid equation of state produced reasonable correlation data (AADP(%) = 4.5 (wt % 1.0), 3.9 (wt % 2.0) and 3.4 (wt % 3.0)).

Figure 5. Effect of CO2 weight fraction in constant temperature (T = 343.15 K) on the phase separation pressure at various PDLA mass fraction: ▼, 3.0%; ○, 2.0%; ●, 1.0%. N

AADP(%) =

∑i = 1 |(Piexp − Pical)/Piexp| N

× 100

(14)

where Pexp and Pcal are the experimental and calculated pressures, respectively, and N is the number of experimental data points. The three binary interaction parameters kij and the AADP (%) for PDLA + DCM + CO2 system are summarized in Table 4. The binary interaction parameters were converged about specific value (k12 = 0.006, k13 = 0.62), and the k23 parameter was increased according to PDLA weight fraction. The reason for this phenomenon is that DCM acted as a cosolvent to easily dissolve high-molecular weight PDLA. Thus, the k23 parameter was affected by increments of polymer weight fraction. The results indicate an AADP (%) of about 3−4% (wt % 1.0 = 4.5, wt % 2.0 = 3.9 and wt % 3.0 = 3.4), from which we conclude that these equations of state are suitable for the PDLA + DCM + CO2 system.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-2-880-7406. Fax: +82-2-888-6695. E-mail: [email protected] (H.K.). Funding

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

The authors declare no competing financial interest. 2148



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Phase Behavior of Poly(d-lactic acid), Dichloromethane, and Carbon

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