- Email: [email protected]
Phase behaviour of the ternary mixture system of poly(l -lactic acid), dichloromethane and carbon dioxide
J. Chem. Thermodynamics 55 (2012) 37–41
Contents lists available at SciVerse ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Phase behaviour of the ternary mixture system of poly(L-lactic acid), dichloromethane and carbon dioxide Jungmin Gwon a, Dong Woo Cho a, Soo Hyeon Kim b, Hun Yong Shin c, Hwayong Kim a,⇑ a
Brain Korea 21 Program in Chemical Engineering, School of Chemical and Biological Engineering, and Institute of Chemical Processes, Seoul National University, 559 Gwanangno, Gwanak-gu, Seoul 151-744, Republic of Korea b Korea Institute of Science and Technology, 39-1 Hawolgok-dong, Seongbuk-gu, Seoul 136-791, Republic of Korea c Department of Chemical and Biological Engineering, Seoul National University of Science and Technology, 172, Gongneung 2-dong, Nowon-gu, Seoul 139-743, Republic of Korea
a r t i c l e
i n f o
Article history: Received 21 March 2012 Received in revised form 24 May 2012 Accepted 9 June 2012 Available online 16 June 2012 Keywords: Supercritical carbon dioxide Poly(L-lactic acid) Polymer–solvent–gas ternary systems The hybrid equation of state for CO2polymer system Biodegradable polymer
a b s t r a c t In this study, the high pressure phase behaviour of poly(L-lactic acid) (M = 312,000), dichloromethane and carbon dioxide ternary mixtures was studied using a variable volume view cell at temperatures ranging from 313.15 K to 363.15 K and pressures of up to 30.0 MPa as functions of temperature and the CO2/ dichloromethane mass ratio at poly(L-lactic acid) weight fractions of 1.0%, 2.5% and 3.0%. The experimental results were correlated with the hybrid equation of state for the CO2-polymer system using the van der Waals one-fluid mixing rule with three adjustable binary interaction parameters. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Poly(L-lactic acid) (PLLA) is a thermoplastic aliphatic polyester derived from renewable resources, such as corn starch, tapioca products or sugarcane. PLLA is a biodegradable polymer which is used in the encapsulation of drugs and in the food industry [1]. Recently, PLLA has been studied to develop an eco-friendly polymer material for the automobile industry. The supercritical fluid (SCF) process was mainly used for the synthesis and development of the PLLA. The SCFs are an attractive alternative to incompressible organic liquid solvents, since they are environmentally friendly, less hazardous, flexible and have liquid-like dissolving power while exhibiting the transport properties of a gas [2]. SCFs are used as solvents in a variety of polymer processes, such as extraction, separations and reaction. Particularly, carbon dioxide (CO2), which is used as a solvent, is easy to remove, simply by reducing the pressure, leaving almost no trace and the CO2 is almost always recovered [3]. However, it cannot dissolve the high molecular weight poly(L-lactic acid) (PLLA) which is used in this work. To dissolve PLLA, we use dichloromethane as a solvent. For a variety of PLLA processes, knowledge of the phase behaviour of the (PLLA + dichlorometh-
ane + CO2) system is important for the determination of the best operating conditions. In this work, we measured the bubble and cloud point pressures for ternary mixtures consisting of (PLLA + dichloromethane + CO2) at temperatures ranging from 313.15 K to 363.15 K and pressures of up to 30.0 MPa and correlated with the hybrid equation of state [4]. This system was also studied by Kalogiannis et al. [5], but under different conditions and they did not correlate the experimental data. 2. Experimental 2.1. Materials PLLA (M 312 000, polydispersity 2.189) was synthesized by the Korea Institute of Science and Technology (KIST) and was used without further purification. Carbon dioxide (0.99999 minimum mole fraction purity) was purchased from Korea Industrial Gases. Dichloromethane (0.998 minimum mole fraction purity) was purchased from Samchun pure chemical Co., Ltd. The properties of pure components are reported in table 1. 2.2. Apparatus and procedure
⇑ Corresponding author. Tel.: +82 2 880 7406; fax: +82 2 888 6695. E-mail address: [email protected] (H. Kim). 0021-9614/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2012.06.011
The phase separation pressure data were obtained with a highpressure apparatus equipped with a variable volume view cell,
38
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41 TABLE 1 The properties of pure components. Material
Molar mass
Poly(L-lactic acid)
312,000
Molecular structure
Polydispersity 2.189
O C
O CH CH3
n Mole fraction purity
Dichloromethane
84.93
0.998
Cl Cl
C H H
Carbon dioxide
44.01
which is described in detail elsewhere [6–8]. The advantage of this apparatus is that the concentration of the material can be kept constant during the experiment. The phase behaviour measurement of the (PLLA + dichloromethane + CO2) system was conducted using the following procedures. A predetermined mass of the polymer was added to the cell with a pair of tweezers to an accuracy of within ±0.001 g and the solvent was inserted into the cell with a syringe to within ±0.001 g. To remove all traces of air and chemicals within it, the cell was initially purged several times with CO2 at room temperature. Then, the cell was filled with a predetermined weight fraction of CO2 to within ±0.01 g using a high-pressure CO2 bomb. When the temperature of the cell reached the desired point, the pressure was increased by a high-pressure generator (High Pressure Equipment Co., model 62-6-10). The mixture was compressed until a single phase was formed and a magnetic stirring bar in the cell was used to agitate it for the purpose of reaching equilibrium quickly and to ensure homogeneity. Once the solution reached a single phase, the pressure was slowly decreased until the phase separation pressure, which is the bubble or cloud point, was reached. After recording the phase separation pressure, the pressure of the mixture was increased again until a single phase was obtained. This procedure was repeated several times until the phase transition pressure converged to within ±0.4 MPa, and the average of the last three pressures was recorded as the experiment result. This solution pressure was determined by measuring the water pressure with a digital pressure transducer (Honeywell International Inc., model TJE / Redlion PAXS0000, accuracy of 0.1%) and indicator (Red lion controls INC., model PAXP0000). The temperature was determined by a PRT type thermometer (HART Scientific, Inc., Model 5622-32SR, accuracy of ±0.045 K) fixed to the surface of the cell and displayed by an indicator (Hart Scientific, Inc., Model 1502). The temperature of the cell was measured to within ± 0.1 K, while the temperature was maintained to within ± 0.1 K. The camera (Veltek international, Inc., Model CVC5520) 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 thermometer was 0.022 K and that of the pressure transducer was 0.01 MPa.
3. Thermodynamic models The experimental data obtained in this study were correlated with the hybrid equation of state for the CO2-polymer system using the van der Waals one-fluid mixing rule including three binary interaction parameters (kij). The reason for the use this equa-
O=C=O
0.999
tion of state is the PLLA pure parameters. The PLLA properties are necessary to correlate the presented equation of state, such as PR-EOS and PCSAFT, etc. However, there are no experimental results available for the properties of the PLLA. The main advantage of this hybrid equation of state is estimated the polymer pure parameters by experimental data. This characteristic of the hybrid equation of state can correlate the experimental data. That is the reason we used the hybrid equation of state. The compressibility factor of the hybrid EOS is defined as follows.
Z ¼ Z PR þ Z assoc þ Z chain :
ð1Þ
In this work, we use the first two terms for pure CO2 and the first and third terms for polymers. The compressibility factor from the PR-EOS [9] is obtained from the following cubic equation.
Z PR ð1 BÞZ 2PR þ ðA 3B2 2BÞZ PR ðAB B2 B3 Þ ¼ 0;
ð2Þ
where
A¼
B¼
aP R2 T 2
;
bP : RT
ð3Þ
ð4Þ
The mixture parameters used in the PR-EOS are determined by the van der Waals one-fluid mixing rule.
a¼
XX xi xj aij ; i
b¼
ð5Þ
j
X xi b i ;
ð6Þ
i
aij ¼
pffiffiffiffiffiffiffiffi ai aj ð1 kij Þ:
ð7Þ
The critical temperature (TC), pressure (PC) and acentric factor (x) of the materials are necessary to calculate the compressibility factor of the PR-EOS. However, PLLA typically does not have a critical constant or acentric factor and there are no experimental results available for the acentric factor of dichloromethane. Therefore, the acentric factor of dichloromethane was estimated using the Lee–Kesler method [10]. The van der Waals energy parameter (ai) of the PR-EOS for the polymer was estimated with the following empirical equation.
ai ¼ a0i expðC i TÞ; 0
ð8Þ
where ai and Ci are adjustable parameters obtained by fitting the experimental results and the excluded volume (bi) parameter of the PR-EOS is determined in the same way.
39
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41 TABLE 2 The parameters of the materials for the hybrid equation of state. Material
TABLE 3 Experimental data for the {PLLA(1) + Dichloromethane(2) + CO2(3)} system.a Mass fractionb
Parameters of macromolecule 3
Poly(L-lactic acid)
a0/(J m ) 16.7237 3
b0/(cm mol
w2 0.681 w3 0.319
1
) 128.170
c 0.00005 m w2 0.623 w3 0.377
5481.26 Critical constants
Dichloromethane Carbon dioxide a
TC/K
PC/MPa
x
510 304.12
6.1 7.374
0.207a 0.225
Estimation with the Lee–Kesler method.
w2 0.590 w3 0.410
The compressibility factor for the associating effect is given by
X 1 1 @X S Z assoc ¼ q ; XS 2 @q S
ð9Þ
where q is the number density of the associating molecules, XS is the mole fraction of the associating molecules not bonded at site S, and the summation is over all binding sites of the associating molecule. The compressibility factor for the chain connectivity of the polymer is given by the following equation. X xi ð1 mi Þ
Z chain ¼
i
g hs ii ðdii Þ
"
f3 ð1 f3 Þ
þ 2
# 2 2 3 dii f2 3dii f2 f3 dii f22 3 dii f22 f3 ; þ þ þ 2 ð1 f3 Þ2 ð1 f3 Þ3 ð1 f3 Þ2 2 ð1 f3 Þ4 ð10Þ
where xi is the mole fraction of polymer i, mi is the number of polymer segments, dii is the effective molecular diameter, f is the reduced density. The parameter mi is obtained from the experimental results. The parameter gii is the radial distribution function for a pair of polymer segments and is given by
g hs ii ðdii Þ ¼
2 1 3dii f2 dii f22 þ þ 2 ; 1 f3 2 ð1 f3 Þ2 2 ð1 f3 Þ3
ð11Þ
w2 0.530 w3 0.470
w2 0.477 w3 0.523
w2 0.691 w3 0.309
w2 0.632 w3 0.368
w2 0.586 w3 0.414
where
fk ¼
pN A X q X i mi dkii : 6
ð12Þ
i
In this work, the polymer parameters (ai0, Ci, bi, mi), the critical constant (TC, PC, x) for the hybrid EOS and the binary interaction parameter kij used in the one-fluid mixing rule were estimated by the regression of the experimental data using the simplex method algorithm, as shown in tables 2 and 4.
w2 0.537 w3 0.463
w2 0.486 w3 0.514
4. Results and discussion Table 3 shows the cloud and bubble points for the (PLLA + Dichloromethane + CO2) system at T = (313.15, 323.15, 333.15, 343.15, 353.15, and 363.15) K with pressures ranging from 4.247 to 30.222 MPa. Figures 1–3 present the P-T isopleths of the cloud and bubble points at mass fractions of PLLA = 1.0%, 2.5%, and 3.0% in (dichloromethane + CO2), respectively. Kalogiannis et al. studied the same system for different molar mass of PLLA, which are significantly lower than our values. Figures 1–3 present the phase behaviour of (PLLA + dichloromethane + CO2). The L–V transition, which defines the bubble point, occurs in the low temperature region. Beyond a certain temperature, the volumes of the solvent increases, since it is close to the critical point, while the
w2 0.670 w3 0.330
w2 0.628 w3 0.372
T/K
P/MPa
Transitionc
Polymer mass fraction (w1) = 1% 363.15 8.019 353.15 7.185 343.15 6.44 333.15 5.624 323.15 4.868 313.15 4.247 363.15 9.935 353.15 7.238 343.15 6.489 333.15 5.713 323.15 4.890 313.15 4.248 363.15 13.886 353.15 10.333 343.15 7.009 333.15 6.281 323.15 4.240 313.15 4.495 363.15 22.881 353.15 19.315 343.15 16.001 333.15 11.780 323.15 7.556 313.15 5.115 363.15 29.933 353.15 26.142 343.15 22.442 333.15 17.877 323.15 13.613 313.15 8.637
BP BP BP BP BP BP BP BP BP BP BP BP CP CP CP CP BP BP CP CP CP CP CP BP CP CP CP CP CP CP
Polymer mass fraction (w1) = 2.5% 363.15 6.576 353.15 6.123 343.15 5.290 333.15 4.709 323.15 4.098 313.15 3.496 363.15 10.607 353.15 7.894 343.15 6.997 333.15 6.104 323.15 5.289 313.15 4.506 363.15 15.478 353.15 11.827 343.15 8.109 333.15 6.499 323.15 5.627 313.15 4.776 363.15 23.127 353.15 19.468 343.15 15.550 333.15 11.337 323.15 6.484 313.15 5.366 363.15 30.222 353.15 26.452 343.15 22.483 333.15 18.322 323.15 13.897 313.15 8.962
BP BP BP BP BP BP CP BP BP BP BP BP CP CP BP BP BP BP CP CP CP CP CP BP CP CP CP CP CP CP
Polymer mass fraction (w1) = 3% 363.15 11.095 353.15 7.800 343.15 6.950 333.15 6.113 323.15 5.232 313.15 4.510 363.15 11.575 353.15 7.970 343.15 7.029 333.15 6.171
CP BP BP BP BP BP CP BP BP BP (continued on next page)
40
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41
350
TABLE 3 (continued)
w2 0.586 w3 0.414
w2 0.536 w3 0.464
w2 0.517 w3 0.483
T/K
P/MPa
Transition
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
5.485 4.719 18.045 14.376 10.533 6.942 6.019 5.142 23.473 19.718 15.828 11.761 7.302 5.203 25.656 21.992 18.239 14.075 9.667 5.340
BP BP CP CP CP BP BP BP CP CP CP CP CP BP CP CP CP CP CP BP
c
300 250
Pressure (bar)
Mass fraction
b
200 150 100 50 0 310
320
330
340
350
360
370
Temperature (K)
a
Standard uncertainties u are u(T) = ±0.0815 K, u(P) = ±0.00698 MPa, and u(w) = ±0.0016 g. b w1 (PLLA), w2 (dichloromethane) and w3 (CO2) are mass fractions; w2 and w3 are calculated on a polymer-free basis. c BP: bubble-point, CP: cloud point.
FIGURE 2. Calculation results using the hybrid equation of state for {PLLA (mass fraction = 2.5%) + dichloromethane + CO2} system. Mass fraction CO2 in the mixed solvent on a polymer-free basis: j, 0.514; 4, 0.463; ., 0.414; s, 0.368; d, 0.309.
350 300
350
Pressure (bar)
250
300
Pressure (bar)
250 200
200 150
150
100
100
50
50
0 310
0
310
320
330
340
350
360
370
Temperature (K) 320
330
340
350
360
370
Temperature (K) FIGURE 1. Calculation results using the hybrid equation of state for {PLLA (mass fraction = 1%) + dichloromethane + CO2} system. Mass fraction CO2 in the mixed solvent on a polymer-free basis: j, 0.523; 4, 0.471; ., 0.410; s, 0.371; d, 0.319.
polymer, which is not yet approaching its hypothetical critical point, does not expand. This difference in ‘‘free volume’’ leads to an L–L transition, which observes the cloud point. At a constant CO2 mass fraction, while the bubble point (L–V transition) is slightly increased, the cloud point (the L–L transition) is dramatically increased. This phenomenon occurs regardless of the mass ratio of PLLA. Moreover, figure 4 presents the effect of the dichloromethane mass ratio, which demonstrates that dichloromethane is a good solvent, but CO2 is not. The above observations are in agreement with the characteristics of the LCST behaviour of polymer–solvent–gas systems described by Bungert et al. [11]. Figures 1–3 show the comparisons between the experimental results and the correlation data that were obtained with the hybrid EOS model. The objective function (OBF) and the absolute average deviation of pressure (AADP) percent for the correlation were defined as follows.
FIGURE 3. Calculation results using the hybrid equation of state for {PLLA (mass fraction = 3%) + dichloromethane + CO2} system. Mass fraction CO2 in the mixed solvent on a polymer-free basis: j, 0.483; 4, 0.465; ., 0.414; s, 0.372; d, 0.330.
OBF ¼
cal N exp X P i P i ; Pexp i i¼1
AADPð%Þ ¼
ð13Þ
PN exp exp Pcal i¼1 ðP i i Þ=P i N
100;
ð14Þ
where N is the number of experimental data points and Pexp and Pcal are the experimental and calculated pressures, respectively. The binary interaction parameter kij and the AADP (%) for the (PLLA + dichloromethane + CO2) system are summarized in table 4. When the L–V transition region is replaced with the L–L transition region, the correlation data show a relatively distinct difference (3.0 MPa) between the correlation data and experimental results, especially at a mass ratio of CO2 of about 0.42. This reason for this is the dramatic increment of pressure when the L–V transition replaces the L–L transition. At this region, this equation of state has difficulty to follow the experimental data. The more the PLLA weight fraction increases, the more the AADP (%) decreases (wt 1.0% = 5.52, wt 2.5% = 5.08 and wt 3.0% = 4.90).
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41
350
ature and CO2/dichloromethane mass ratio. As the weight fraction of PLLA increased, the phase separation pressure increased and the L–L transition appeared more quickly. However, increasing the mass ratio of dichloromethane caused a decrease in the bubble or cloud point. The reason for this is the increment of the solvent polarity, leading to a shift of the L–V and L–L transitions to lower pressures at constant temperature. The experimental results were correlated with the hybrid equation of state using the van der Waals one-fluid mixing rule with three binary interaction parameters, kij. The correlated pressure data improved with increasing PLLA weight fraction. [AADP(%) = 5.52 (wt 1.0%), 5.08 (wt 2.5%) and 4.90(wt 3.0%)]
300 250
Pressure (bar)
41
200 150 100 50
Acknowledgments
0 0.45
0.50
0.55
0.60
0.65
0.70
0.75
Weight fraction of Dichloromethane FIGURE 4. Effect of dichloromethane weight fraction in a mixed solvent on bubble and cloud point pressures of PLLA (mass fraction = 2.5%) at various temperatures: d, 363.15 K; s, 353.15 K; ., 343.15 K; 4, 333.15 K; j, 323.15 K; h, 313.15 K.
TABLE 4 Calculation results with the hybrid equation of state. Mass fraction of PLLA (%)
k12
k13
k23
AADP (%)
1.0 2.5 3.0
0.01564 0.04015 0.01216
0.28982 0.07223 0.02530
0.10077 0.10924 0.00132
5.78 5.07 4.89
5. Conclusions We measured the pressure-temperature (P-T) isopleths for ternary mixtures of (poly(L-lactic acid) + dichloromethane + CO2) at temperatures ranging from 313.15 K to 363.15 K and pressures of up to 30.0 MPa. The L–V (bubble point) or L–L (cloud point) transitions occurred, depending on the weight fraction of PLLA, temper-
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2010-C1AAA001-2010-0028939). References [1] N. Elvassore, A. Bertucco, P. Caliceti, Industrial & Engineering Chemistry Research 40 (2001) 795–800. [2] P. Subra, P. Jestin, Powder Technology 103 (1999) 2–9. [3] Supercritical fluid extraction, http://en.wikipedia.org/wiki/ Supercritical_fluid_extraction. [4] H.Y. Shin, J. Wu, Industrial & Engineering Chemistry Research 49 (2010) 7678– 7684. [5] C.G. Kalogiannis, C.G. Panayiotou, Journal of Chemical & Engineering Data 50 (2005) 1442–1447. [6] J. Shin, Y.-W. Lee, H. Kim, W. Bae, Journal of Chemical & Engineering Data 51 (2006) 1571–1575. [7] S. Kwon, W. Bae, H. Kim, Journal of Chemical & Engineering Data 50 (2005) 1560–1563. [8] W. Bae, S. Kwon, H.-S. Byun, H. Kim, The Journal of Supercritical Fluids 30 (2004) 127–137. [9] D.-Y. Peng, D.B. Robinson, Industrial & Engineering Chemistry Fundamentals 15 (1976) 59–64. [10] B.I. Lee, M.G. Kesler, AIChE Journal 21 (1975) 510–527. [11] B. Bungert, G. Sadowski, W. Arlt, Industrial & Engineering Chemistry Research 37 (1998) 3208–3220.
JCT 12-172
Contents lists available at SciVerse ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Phase behaviour of the ternary mixture system of poly(L-lactic acid), dichloromethane and carbon dioxide Jungmin Gwon a, Dong Woo Cho a, Soo Hyeon Kim b, Hun Yong Shin c, Hwayong Kim a,⇑ a
Brain Korea 21 Program in Chemical Engineering, School of Chemical and Biological Engineering, and Institute of Chemical Processes, Seoul National University, 559 Gwanangno, Gwanak-gu, Seoul 151-744, Republic of Korea b Korea Institute of Science and Technology, 39-1 Hawolgok-dong, Seongbuk-gu, Seoul 136-791, Republic of Korea c Department of Chemical and Biological Engineering, Seoul National University of Science and Technology, 172, Gongneung 2-dong, Nowon-gu, Seoul 139-743, Republic of Korea
a r t i c l e
i n f o
Article history: Received 21 March 2012 Received in revised form 24 May 2012 Accepted 9 June 2012 Available online 16 June 2012 Keywords: Supercritical carbon dioxide Poly(L-lactic acid) Polymer–solvent–gas ternary systems The hybrid equation of state for CO2polymer system Biodegradable polymer
a b s t r a c t In this study, the high pressure phase behaviour of poly(L-lactic acid) (M = 312,000), dichloromethane and carbon dioxide ternary mixtures was studied using a variable volume view cell at temperatures ranging from 313.15 K to 363.15 K and pressures of up to 30.0 MPa as functions of temperature and the CO2/ dichloromethane mass ratio at poly(L-lactic acid) weight fractions of 1.0%, 2.5% and 3.0%. The experimental results were correlated with the hybrid equation of state for the CO2-polymer system using the van der Waals one-fluid mixing rule with three adjustable binary interaction parameters. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Poly(L-lactic acid) (PLLA) is a thermoplastic aliphatic polyester derived from renewable resources, such as corn starch, tapioca products or sugarcane. PLLA is a biodegradable polymer which is used in the encapsulation of drugs and in the food industry [1]. Recently, PLLA has been studied to develop an eco-friendly polymer material for the automobile industry. The supercritical fluid (SCF) process was mainly used for the synthesis and development of the PLLA. The SCFs are an attractive alternative to incompressible organic liquid solvents, since they are environmentally friendly, less hazardous, flexible and have liquid-like dissolving power while exhibiting the transport properties of a gas [2]. SCFs are used as solvents in a variety of polymer processes, such as extraction, separations and reaction. Particularly, carbon dioxide (CO2), which is used as a solvent, is easy to remove, simply by reducing the pressure, leaving almost no trace and the CO2 is almost always recovered [3]. However, it cannot dissolve the high molecular weight poly(L-lactic acid) (PLLA) which is used in this work. To dissolve PLLA, we use dichloromethane as a solvent. For a variety of PLLA processes, knowledge of the phase behaviour of the (PLLA + dichlorometh-
ane + CO2) system is important for the determination of the best operating conditions. In this work, we measured the bubble and cloud point pressures for ternary mixtures consisting of (PLLA + dichloromethane + CO2) at temperatures ranging from 313.15 K to 363.15 K and pressures of up to 30.0 MPa and correlated with the hybrid equation of state [4]. This system was also studied by Kalogiannis et al. [5], but under different conditions and they did not correlate the experimental data. 2. Experimental 2.1. Materials PLLA (M 312 000, polydispersity 2.189) was synthesized by the Korea Institute of Science and Technology (KIST) and was used without further purification. Carbon dioxide (0.99999 minimum mole fraction purity) was purchased from Korea Industrial Gases. Dichloromethane (0.998 minimum mole fraction purity) was purchased from Samchun pure chemical Co., Ltd. The properties of pure components are reported in table 1. 2.2. Apparatus and procedure
⇑ Corresponding author. Tel.: +82 2 880 7406; fax: +82 2 888 6695. E-mail address: [email protected] (H. Kim). 0021-9614/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2012.06.011
The phase separation pressure data were obtained with a highpressure apparatus equipped with a variable volume view cell,
38
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41 TABLE 1 The properties of pure components. Material
Molar mass
Poly(L-lactic acid)
312,000
Molecular structure
Polydispersity 2.189
O C
O CH CH3
n Mole fraction purity
Dichloromethane
84.93
0.998
Cl Cl
C H H
Carbon dioxide
44.01
which is described in detail elsewhere [6–8]. The advantage of this apparatus is that the concentration of the material can be kept constant during the experiment. The phase behaviour measurement of the (PLLA + dichloromethane + CO2) system was conducted using the following procedures. A predetermined mass of the polymer was added to the cell with a pair of tweezers to an accuracy of within ±0.001 g and the solvent was inserted into the cell with a syringe to within ±0.001 g. To remove all traces of air and chemicals within it, the cell was initially purged several times with CO2 at room temperature. Then, the cell was filled with a predetermined weight fraction of CO2 to within ±0.01 g using a high-pressure CO2 bomb. When the temperature of the cell reached the desired point, the pressure was increased by a high-pressure generator (High Pressure Equipment Co., model 62-6-10). The mixture was compressed until a single phase was formed and a magnetic stirring bar in the cell was used to agitate it for the purpose of reaching equilibrium quickly and to ensure homogeneity. Once the solution reached a single phase, the pressure was slowly decreased until the phase separation pressure, which is the bubble or cloud point, was reached. After recording the phase separation pressure, the pressure of the mixture was increased again until a single phase was obtained. This procedure was repeated several times until the phase transition pressure converged to within ±0.4 MPa, and the average of the last three pressures was recorded as the experiment result. This solution pressure was determined by measuring the water pressure with a digital pressure transducer (Honeywell International Inc., model TJE / Redlion PAXS0000, accuracy of 0.1%) and indicator (Red lion controls INC., model PAXP0000). The temperature was determined by a PRT type thermometer (HART Scientific, Inc., Model 5622-32SR, accuracy of ±0.045 K) fixed to the surface of the cell and displayed by an indicator (Hart Scientific, Inc., Model 1502). The temperature of the cell was measured to within ± 0.1 K, while the temperature was maintained to within ± 0.1 K. The camera (Veltek international, Inc., Model CVC5520) 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 thermometer was 0.022 K and that of the pressure transducer was 0.01 MPa.
3. Thermodynamic models The experimental data obtained in this study were correlated with the hybrid equation of state for the CO2-polymer system using the van der Waals one-fluid mixing rule including three binary interaction parameters (kij). The reason for the use this equa-
O=C=O
0.999
tion of state is the PLLA pure parameters. The PLLA properties are necessary to correlate the presented equation of state, such as PR-EOS and PCSAFT, etc. However, there are no experimental results available for the properties of the PLLA. The main advantage of this hybrid equation of state is estimated the polymer pure parameters by experimental data. This characteristic of the hybrid equation of state can correlate the experimental data. That is the reason we used the hybrid equation of state. The compressibility factor of the hybrid EOS is defined as follows.
Z ¼ Z PR þ Z assoc þ Z chain :
ð1Þ
In this work, we use the first two terms for pure CO2 and the first and third terms for polymers. The compressibility factor from the PR-EOS [9] is obtained from the following cubic equation.
Z PR ð1 BÞZ 2PR þ ðA 3B2 2BÞZ PR ðAB B2 B3 Þ ¼ 0;
ð2Þ
where
A¼
B¼
aP R2 T 2
;
bP : RT
ð3Þ
ð4Þ
The mixture parameters used in the PR-EOS are determined by the van der Waals one-fluid mixing rule.
a¼
XX xi xj aij ; i
b¼
ð5Þ
j
X xi b i ;
ð6Þ
i
aij ¼
pffiffiffiffiffiffiffiffi ai aj ð1 kij Þ:
ð7Þ
The critical temperature (TC), pressure (PC) and acentric factor (x) of the materials are necessary to calculate the compressibility factor of the PR-EOS. However, PLLA typically does not have a critical constant or acentric factor and there are no experimental results available for the acentric factor of dichloromethane. Therefore, the acentric factor of dichloromethane was estimated using the Lee–Kesler method [10]. The van der Waals energy parameter (ai) of the PR-EOS for the polymer was estimated with the following empirical equation.
ai ¼ a0i expðC i TÞ; 0
ð8Þ
where ai and Ci are adjustable parameters obtained by fitting the experimental results and the excluded volume (bi) parameter of the PR-EOS is determined in the same way.
39
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41 TABLE 2 The parameters of the materials for the hybrid equation of state. Material
TABLE 3 Experimental data for the {PLLA(1) + Dichloromethane(2) + CO2(3)} system.a Mass fractionb
Parameters of macromolecule 3
Poly(L-lactic acid)
a0/(J m ) 16.7237 3
b0/(cm mol
w2 0.681 w3 0.319
1
) 128.170
c 0.00005 m w2 0.623 w3 0.377
5481.26 Critical constants
Dichloromethane Carbon dioxide a
TC/K
PC/MPa
x
510 304.12
6.1 7.374
0.207a 0.225
Estimation with the Lee–Kesler method.
w2 0.590 w3 0.410
The compressibility factor for the associating effect is given by
X 1 1 @X S Z assoc ¼ q ; XS 2 @q S
ð9Þ
where q is the number density of the associating molecules, XS is the mole fraction of the associating molecules not bonded at site S, and the summation is over all binding sites of the associating molecule. The compressibility factor for the chain connectivity of the polymer is given by the following equation. X xi ð1 mi Þ
Z chain ¼
i
g hs ii ðdii Þ
"
f3 ð1 f3 Þ
þ 2
# 2 2 3 dii f2 3dii f2 f3 dii f22 3 dii f22 f3 ; þ þ þ 2 ð1 f3 Þ2 ð1 f3 Þ3 ð1 f3 Þ2 2 ð1 f3 Þ4 ð10Þ
where xi is the mole fraction of polymer i, mi is the number of polymer segments, dii is the effective molecular diameter, f is the reduced density. The parameter mi is obtained from the experimental results. The parameter gii is the radial distribution function for a pair of polymer segments and is given by
g hs ii ðdii Þ ¼
2 1 3dii f2 dii f22 þ þ 2 ; 1 f3 2 ð1 f3 Þ2 2 ð1 f3 Þ3
ð11Þ
w2 0.530 w3 0.470
w2 0.477 w3 0.523
w2 0.691 w3 0.309
w2 0.632 w3 0.368
w2 0.586 w3 0.414
where
fk ¼
pN A X q X i mi dkii : 6
ð12Þ
i
In this work, the polymer parameters (ai0, Ci, bi, mi), the critical constant (TC, PC, x) for the hybrid EOS and the binary interaction parameter kij used in the one-fluid mixing rule were estimated by the regression of the experimental data using the simplex method algorithm, as shown in tables 2 and 4.
w2 0.537 w3 0.463
w2 0.486 w3 0.514
4. Results and discussion Table 3 shows the cloud and bubble points for the (PLLA + Dichloromethane + CO2) system at T = (313.15, 323.15, 333.15, 343.15, 353.15, and 363.15) K with pressures ranging from 4.247 to 30.222 MPa. Figures 1–3 present the P-T isopleths of the cloud and bubble points at mass fractions of PLLA = 1.0%, 2.5%, and 3.0% in (dichloromethane + CO2), respectively. Kalogiannis et al. studied the same system for different molar mass of PLLA, which are significantly lower than our values. Figures 1–3 present the phase behaviour of (PLLA + dichloromethane + CO2). The L–V transition, which defines the bubble point, occurs in the low temperature region. Beyond a certain temperature, the volumes of the solvent increases, since it is close to the critical point, while the
w2 0.670 w3 0.330
w2 0.628 w3 0.372
T/K
P/MPa
Transitionc
Polymer mass fraction (w1) = 1% 363.15 8.019 353.15 7.185 343.15 6.44 333.15 5.624 323.15 4.868 313.15 4.247 363.15 9.935 353.15 7.238 343.15 6.489 333.15 5.713 323.15 4.890 313.15 4.248 363.15 13.886 353.15 10.333 343.15 7.009 333.15 6.281 323.15 4.240 313.15 4.495 363.15 22.881 353.15 19.315 343.15 16.001 333.15 11.780 323.15 7.556 313.15 5.115 363.15 29.933 353.15 26.142 343.15 22.442 333.15 17.877 323.15 13.613 313.15 8.637
BP BP BP BP BP BP BP BP BP BP BP BP CP CP CP CP BP BP CP CP CP CP CP BP CP CP CP CP CP CP
Polymer mass fraction (w1) = 2.5% 363.15 6.576 353.15 6.123 343.15 5.290 333.15 4.709 323.15 4.098 313.15 3.496 363.15 10.607 353.15 7.894 343.15 6.997 333.15 6.104 323.15 5.289 313.15 4.506 363.15 15.478 353.15 11.827 343.15 8.109 333.15 6.499 323.15 5.627 313.15 4.776 363.15 23.127 353.15 19.468 343.15 15.550 333.15 11.337 323.15 6.484 313.15 5.366 363.15 30.222 353.15 26.452 343.15 22.483 333.15 18.322 323.15 13.897 313.15 8.962
BP BP BP BP BP BP CP BP BP BP BP BP CP CP BP BP BP BP CP CP CP CP CP BP CP CP CP CP CP CP
Polymer mass fraction (w1) = 3% 363.15 11.095 353.15 7.800 343.15 6.950 333.15 6.113 323.15 5.232 313.15 4.510 363.15 11.575 353.15 7.970 343.15 7.029 333.15 6.171
CP BP BP BP BP BP CP BP BP BP (continued on next page)
40
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41
350
TABLE 3 (continued)
w2 0.586 w3 0.414
w2 0.536 w3 0.464
w2 0.517 w3 0.483
T/K
P/MPa
Transition
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
5.485 4.719 18.045 14.376 10.533 6.942 6.019 5.142 23.473 19.718 15.828 11.761 7.302 5.203 25.656 21.992 18.239 14.075 9.667 5.340
BP BP CP CP CP BP BP BP CP CP CP CP CP BP CP CP CP CP CP BP
c
300 250
Pressure (bar)
Mass fraction
b
200 150 100 50 0 310
320
330
340
350
360
370
Temperature (K)
a
Standard uncertainties u are u(T) = ±0.0815 K, u(P) = ±0.00698 MPa, and u(w) = ±0.0016 g. b w1 (PLLA), w2 (dichloromethane) and w3 (CO2) are mass fractions; w2 and w3 are calculated on a polymer-free basis. c BP: bubble-point, CP: cloud point.
FIGURE 2. Calculation results using the hybrid equation of state for {PLLA (mass fraction = 2.5%) + dichloromethane + CO2} system. Mass fraction CO2 in the mixed solvent on a polymer-free basis: j, 0.514; 4, 0.463; ., 0.414; s, 0.368; d, 0.309.
350 300
350
Pressure (bar)
250
300
Pressure (bar)
250 200
200 150
150
100
100
50
50
0 310
0
310
320
330
340
350
360
370
Temperature (K) 320
330
340
350
360
370
Temperature (K) FIGURE 1. Calculation results using the hybrid equation of state for {PLLA (mass fraction = 1%) + dichloromethane + CO2} system. Mass fraction CO2 in the mixed solvent on a polymer-free basis: j, 0.523; 4, 0.471; ., 0.410; s, 0.371; d, 0.319.
polymer, which is not yet approaching its hypothetical critical point, does not expand. This difference in ‘‘free volume’’ leads to an L–L transition, which observes the cloud point. At a constant CO2 mass fraction, while the bubble point (L–V transition) is slightly increased, the cloud point (the L–L transition) is dramatically increased. This phenomenon occurs regardless of the mass ratio of PLLA. Moreover, figure 4 presents the effect of the dichloromethane mass ratio, which demonstrates that dichloromethane is a good solvent, but CO2 is not. The above observations are in agreement with the characteristics of the LCST behaviour of polymer–solvent–gas systems described by Bungert et al. [11]. Figures 1–3 show the comparisons between the experimental results and the correlation data that were obtained with the hybrid EOS model. The objective function (OBF) and the absolute average deviation of pressure (AADP) percent for the correlation were defined as follows.
FIGURE 3. Calculation results using the hybrid equation of state for {PLLA (mass fraction = 3%) + dichloromethane + CO2} system. Mass fraction CO2 in the mixed solvent on a polymer-free basis: j, 0.483; 4, 0.465; ., 0.414; s, 0.372; d, 0.330.
OBF ¼
cal N exp X P i P i ; Pexp i i¼1
AADPð%Þ ¼
ð13Þ
PN exp exp Pcal i¼1 ðP i i Þ=P i N
100;
ð14Þ
where N is the number of experimental data points and Pexp and Pcal are the experimental and calculated pressures, respectively. The binary interaction parameter kij and the AADP (%) for the (PLLA + dichloromethane + CO2) system are summarized in table 4. When the L–V transition region is replaced with the L–L transition region, the correlation data show a relatively distinct difference (3.0 MPa) between the correlation data and experimental results, especially at a mass ratio of CO2 of about 0.42. This reason for this is the dramatic increment of pressure when the L–V transition replaces the L–L transition. At this region, this equation of state has difficulty to follow the experimental data. The more the PLLA weight fraction increases, the more the AADP (%) decreases (wt 1.0% = 5.52, wt 2.5% = 5.08 and wt 3.0% = 4.90).
J. Gwon et al. / J. Chem. Thermodynamics 55 (2012) 37–41
350
ature and CO2/dichloromethane mass ratio. As the weight fraction of PLLA increased, the phase separation pressure increased and the L–L transition appeared more quickly. However, increasing the mass ratio of dichloromethane caused a decrease in the bubble or cloud point. The reason for this is the increment of the solvent polarity, leading to a shift of the L–V and L–L transitions to lower pressures at constant temperature. The experimental results were correlated with the hybrid equation of state using the van der Waals one-fluid mixing rule with three binary interaction parameters, kij. The correlated pressure data improved with increasing PLLA weight fraction. [AADP(%) = 5.52 (wt 1.0%), 5.08 (wt 2.5%) and 4.90(wt 3.0%)]
300 250
Pressure (bar)
41
200 150 100 50
Acknowledgments
0 0.45
0.50
0.55
0.60
0.65
0.70
0.75
Weight fraction of Dichloromethane FIGURE 4. Effect of dichloromethane weight fraction in a mixed solvent on bubble and cloud point pressures of PLLA (mass fraction = 2.5%) at various temperatures: d, 363.15 K; s, 353.15 K; ., 343.15 K; 4, 333.15 K; j, 323.15 K; h, 313.15 K.
TABLE 4 Calculation results with the hybrid equation of state. Mass fraction of PLLA (%)
k12
k13
k23
AADP (%)
1.0 2.5 3.0
0.01564 0.04015 0.01216
0.28982 0.07223 0.02530
0.10077 0.10924 0.00132
5.78 5.07 4.89
5. Conclusions We measured the pressure-temperature (P-T) isopleths for ternary mixtures of (poly(L-lactic acid) + dichloromethane + CO2) at temperatures ranging from 313.15 K to 363.15 K and pressures of up to 30.0 MPa. The L–V (bubble point) or L–L (cloud point) transitions occurred, depending on the weight fraction of PLLA, temper-
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2010-C1AAA001-2010-0028939). References [1] N. Elvassore, A. Bertucco, P. Caliceti, Industrial & Engineering Chemistry Research 40 (2001) 795–800. [2] P. Subra, P. Jestin, Powder Technology 103 (1999) 2–9. [3] Supercritical fluid extraction, http://en.wikipedia.org/wiki/ Supercritical_fluid_extraction. [4] H.Y. Shin, J. Wu, Industrial & Engineering Chemistry Research 49 (2010) 7678– 7684. [5] C.G. Kalogiannis, C.G. Panayiotou, Journal of Chemical & Engineering Data 50 (2005) 1442–1447. [6] J. Shin, Y.-W. Lee, H. Kim, W. Bae, Journal of Chemical & Engineering Data 51 (2006) 1571–1575. [7] S. Kwon, W. Bae, H. Kim, Journal of Chemical & Engineering Data 50 (2005) 1560–1563. [8] W. Bae, S. Kwon, H.-S. Byun, H. Kim, The Journal of Supercritical Fluids 30 (2004) 127–137. [9] D.-Y. Peng, D.B. Robinson, Industrial & Engineering Chemistry Fundamentals 15 (1976) 59–64. [10] B.I. Lee, M.G. Kesler, AIChE Journal 21 (1975) 510–527. [11] B. Bungert, G. Sadowski, W. Arlt, Industrial & Engineering Chemistry Research 37 (1998) 3208–3220.
JCT 12-172