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PS blends
Fluid Phase Equilibria 194–197 (2002) 847–858
Solubility of carbon dioxide in PPO and PPO/PS blends Yoshiyuki Sato, Tadao Takikawa, Michiyo Yamane, Shigeki Takishima, Hirokatsu Masuoka∗ Department of Chemical Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan Received 7 April 2001; accepted 10 August 2001
Abstract Solubility of carbon dioxide in poly(2,6-dimethyl-1,4-phenylene ether) (PPO) and PPO+polystyrene (PS) blends (25–50 wt.% PPO) was measured at temperatures of 373.15, 427.15, and 473.15 K and pressures up to 20 MPa. The solubility in the blends increased with increasing PPO concentration. The solubility could be correlated with the extended dual mode sorption (EDMS) model in conjunction with Sanchez and Lacombe equation-of-state. The EDMS model correlation estimated a 100 K glass transition temperature depression of PPO by dissolution of carbon dioxide. While Henry’s constants for carbon dioxide in the blend polymers in molten state could be satisfied by additivity of the Henry’s constant in each pure polymer, the Henry’s constants in the glassy state did not show additivity. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Data; Solubility; Henry’s constant; Carbon dioxide; Polymer blend
1. Introduction Polymeric foams are widely used as heat insulators, food trays, and support materials, because of their many advantageous characteristics such as low thermal conductivity, light weight, and high impact strength. Trichlorofluoromethane (CFC-11) and dichlorodifluoromethane (CFC-12) have been used as physical blowing agents for these types of industrial foaming processes. However, since production of these gases has been prohibited, new environmentally benign alternative blowing agents such as carbon dioxide and nitrogen are being considered. For effective process design, solubility and diffusivity of these gases in polymers are necessary. While a lot of polymer blends are immiscible, some polymer blends can form single-phase solids and melts. Probably the most important and most widely studied single-phase blends are the blends of poly(2,6-dimethyl-1,4-phenylene ether) (PPO) with polystyrene (PS). Molecular compatibility of PPO with PS has been demonstrated over the whole composition range by a number of different techniques ∗
Corresponding author. Tel.: +81-824-24-7721; fax: +81-824-24-7721. E-mail address: [email protected] (H. Masuoka). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 6 8 7 - 2
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[1–3]. Hence, examine of the composition dependence of blend polymers on gas solubility is needed data. While solubility of carbon dioxide in pure PPO or PS was reported by a number of authors [4–14], the solubility in these blends of this work have not been reported. Solubility of carbon dioxide in blend polymers was studied by several researchers [15–17], while concentration dependence of blend polymers on solubility of gas was not clear especially in thermodynamically equilibrium molten state. In this work, solubility of carbon dioxide in PPO and PPO + PS blends was measured at temperatures of 373.15, 427.15, and 473.15 K and pressures up to 20 MPa. Furthermore, Henry’s constants for carbon dioxide in PPO and the blend were examined to investigate the PPO concentration dependence of the solubility.
2. Experimental 2.1. Materials Two phenylene ether polymers were used: low molecular weight poly(2,6-dimethyl-1,4-phenylene ether), PPO(L) and high molecular weight poly(2,6-dimethyl-1,4-phenylene ether), PPO(H). PPO(L) with PS blends (PPO(L) 25–50 wt.%) were also used. All polymers were supplied by Asahi Chemicals Inc. (Kawasaki). Table 1 gives the characteristics of the polymers as reported by the supplier. Carbon dioxide (>99.5% purity) was obtained from Iwatani Industrial Gases Corp. (Hiroshima). All chemicals were used as received. 2.2. Apparatus and methods The solubility of carbon dioxide was obtained with a magnetic suspension balance (MSB) [18]. In this method, the measuring force is transmitted contactlessly via magnetic coupling from the measuring chamber to the microbalance, which is located outside the chamber under ambient atmospheric conditions. The MSB can be used at pressures up to 35 MPa and temperatures up to 523 K. Resolution and accuracy of the microbalance (Mettler AT261, Switzerland) are 0.01 mg and 0.002%, respectively. Details of the apparatus and experimental procedure used in this work have been described in previous publications [11,19]. Density of carbon dioxide needed for buoyancy correction was obtained from the equation-of-state of Span and Wagner [20]. The volume of the sample was obtained from sample mass and specific volume that was calculated from the Tait [21] parameters reported by Zoller and Hoehn [22]. Swelling of the polymer is caused by gas sorption. Since it is difficult to measure the swelling of the Table 1 Polymer properties Tg (K) PPO(H) PPO(L) PPO(L)/PS 50/50 PPO(L)/PS 25/75 PS
479.0 477.1 416.8 394.3 381.4
M¯ n × 10−4
M¯ w × 10−4
2.4 2.2
6.3 4.7
10.6
33.1
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molten polymer, we estimated its value by the Sanchez–Lacombe equation-of-state (S–L EOS) [23,24] and used this to correct for buoyancy. The uncertainties of pressure, temperature, and solubility in this work were estimated to within 4.1 kPa, 0.05 K, and 15%, respectively. 3. Results and discussion 3.1. Solubility Solubility of carbon dioxide in PPO(H) and PPO(L) are shown in Fig. 1 and Tables 2 and 3. In the figure, open and filled symbols denote lower molecular weight PPO (M¯ w = 4.7 × 104 ) and higher one (M¯ w = 6.3 × 104 ), respectively. While the solubilities at 423.15 and 473.15 K in both polymers agreed within the experimental uncertainty, the solubilities at 373.15 K showed somewhat different results. The solubilities extrapolated to zero pressure did not pass the origin at temperatures of 373.15 and 423.15 K. This behavior seems to show that adsorption [25] of carbon dioxide in the microvoids of the polymer occurred. These isotherms were correlated with the extended dual mode sorption (EDMS) model developed by Kamiya et al. [26]. Since glass transition pressures and concentration data were not available, the glass transition was estimated with EDMS model correlation. EDMS model is developed beginning from the following relationships: C = CD + CH
(1)
where CD and CH are concentrations of gas in polymer matrix and in microvoids existing in glassy polymer. CH is expressed with Langmuir adsorption equation as follow: CH =
CH0 bP(1 − C ∗ /Cg ) 1 + bP
(2)
C ∗ = CD + fCH
(3)
Fig. 1. Solubility of carbon dioxide in PPO.
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Table 2 Solubility of carbon dioxide in PPO(H) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling S w (S–L EOS) (vol.%)a
373.15
2.058 4.003 6.095 8.100 10.111 11.965 13.935 15.993 17.933 20.006
0.03525 0.05158 0.06313 0.07050 0.07544 0.07815 0.08050 0.08303 0.08637 0.08802
0.03583 0.05389 0.06887 0.08128 0.09330 0.10601 0.12026 0.13747 0.15604 0.17442
2.0 3.9 5.9 7.9 9.8 12.2 14.0 15.8 17.4 19.0
423.15
1.983 4.105 6.101 8.056 10.061 12.108 14.078 16.098 18.076 20.076
0.01474 0.02577 0.03358 0.03925 0.04596 0.05327 0.05909 0.06366 0.06759 0.07087
0.01508 0.02725 0.03696 0.04548 0.05595 0.06812 0.07960 0.09099 0.10252 0.11434
1.4 2.8 4.2 5.7 7.1 8.5 9.9 11.2 12.5 13.8
473.15
2.179 4.142 6.174 8.085 10.082 12.078 14.063 16.032 18.106 20.208
0.00680 0.01482 0.02277 0.02976 0.03602 0.04213 0.04732 0.05166 0.05625 0.05935
0.00704 0.01585 0.02525 0.03423 0.04312 0.05263 0.06182 0.07073 0.08111 0.09038
1.0 2.2 3.5 4.7 5.9 7.2 8.5 9.7 11.1 12.3
a Sw = (1 + S)vSL (T , P , S)/(vSL (T , P , 0)) × 100, where v SL : specific volume estimated with S–L EOS, S: solubility of CO2 (g gas/g polymer).
where C∗ and CH0 are effective concentration of sorbed solute to plasticize the polymer and hole saturation ∗ constant at C = 0, respectively. In Eq. (2), Cg is a glass transition concentration that is a function of temperature and pressure. The variable f is the ratio of the plasticizing ability of a Langmuir species to that of a sorbed species and was set equal to zero for simplicity in the calculations. The CD is expressed with Henry’s law or Flory–Huggins law in the EDMS model of Kamiya et al. [26]. In this work, we used the Sanchez and Lacombe equation-of-state [23,24] to represent the CD term. The S–L EOS is shown below: 1 2 ˜ ˜ P = −ρ˜ − T ln(1 − ρ) ˜ + 1− ρ˜ (4) r
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Table 3 Solubility of carbon dioxide in PPO(L) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling Sw (S–L EOS) (vol.%)a
373.15
2.125 4.118 6.098 8.051 12.043 16.023 19.964
0.02916 0.04649 0.05902 0.06833 0.08131 0.08616 0.09202
0.02980 0.04904 0.06498 0.07938 0.11084 0.14338 0.18232
2.1 4.1 6.2 8.2 12.8 16.5 19.9
423.15
2.15 4.15 6.04 8.133 12.121 16.077
0.01420 0.02462 0.03211 0.03942 0.05276 0.06369
0.01459 0.02612 0.03540 0.04573 0.06753 0.09072
1.5 2.8 4.1 5.7 8.5 11.1
473.15
2.097 4.155 6.120 8.048 12.122 16.072
0.00849 0.01596 0.02233 0.02817 0.04037 0.04672
0.00877 0.01707 0.02474 0.03237 0.05048 0.06398
1.2 2.4 3.4 4.5 6.9 8.7
a
Same as defined in Table 2.
P P˜ = ∗ , P
ρ˜ =
ρ , ρ∗
T T˜ = ∗ , T
r=
MP∗ RT∗ ρ ∗
(5)
where characteristic parameters, P∗ , ρ ∗ , and T∗ of the S–L EOS for mixture were evaluated from the following mixing rules: P∗ = (6) φi φj Pij∗ i
j
Pij∗ = (1 − kij )(Pi∗ Pj∗ )0.5 φ0T ∗ i i ∗ ∗ T =P ∗ P i i 1 φi0 = r ri0 i
(7) (8)
(9)
φi P ∗ /T ∗ φi0 = i ∗ i ∗ j φj Pj /Tj
(10)
wi /ρi∗ φi = ∗ j wj /ρj
(11)
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Table 4 Characteristic parameters for Sanchez–Lacombe EOS Substance
P∗ (MPa)
ρ ∗ (kg/m3 )
T∗ (K)
Ref.
Carbon dioxide PS PPO/PS (25/75) PPO/PS (50/50) PPO
720.3 387.0 511.7 432.0 452.0
1580 1108 1118 1136 1173
208.9 + 0.459T − 7.56 × 10−4 T 2 739.9 758.5 748.9 729.5
[27] [10] This worka This worka This worka
a
Parameters were determined in this work using PVT data reported by Zoller and Hoehn [22].
In Eqs. (6)–(11), Ti∗ , Pi∗ , ρi∗ , and ri0 refer to the characteristic parameters of component i in the pure state and kij is a binary interaction parameter determined by fitting the equation to the experimental solubilities. The pure component parameters used are given in Table 4. The parameters for blend polymer were determined as pseudo-pure polymer by fitting PVT data reported by Zoller and Hoehn [22]. In the calculation of the solubilities, it was assumed that the polymer was monodisperse and that it did not dissolve in the vapor phase. Correlation results with the EDMS model are shown by the lines in Fig. 1. The EDMS model satisfactorily represented the solubility data. The EDMS model parameters determined with the correlation are given in Table 5. Glass transition pressure, Pg , was determined from Cg and the equation-of-state and is listed in Table 5 for reference. Estimated glass transition temperature of PPO plasticized by carbon dioxide is shown in Fig. 2. The glass transition temperatures of PPO reported by Handa et al. [28], and Hachisuka et al. [29] are also shown. These literature values were plotted against the solubility predicted with S–L EOS in conjunction with the interaction parameter described below. Depression of the glass transition temperature dependence on the solubility was similar to that reported by Handa et al. [28]. The glass transition temperature almost linearly decreased with the amount of carbon dioxide and was depressed about 100 K from dissolution of 0.1 g CO2 /g polymer. Depression of the glass transition temperature of PPO was 1.2, 1.6, 2.1, and 2.2 times higher than that of polycarbonate, poly(ethylene Table 5 Parameters of extended dual mode sorption model Polymer
Temperature (K)
k12 (–)
CH0 /Cg (–)
Cg (g gas/kg polymer)
b (MPa−1 )
Pg (MPa)
PPO(L)
373.15 423.15 473.15 373.15 423.15 473.15 373.15 423.15 473.15 373.15 423.15 473.15
−0.087 −0.124 −0.179 −0.083 −0.124 −0.179 −0.043 −0.092 −0.148 −0.069 −0.116 −0.182
0.385 2.012 – 0.445 0.419 –
88.55 39.86 – 95.72 45.11 –
0.293 0.022 – 0.498 0.190 –
9.36 7.08 – 10.63 7.94 –
PPO(H)
PPO/PS (25/75)
PPO/PS (50/50)
Y. Sato et al. / Fluid Phase Equilibria 194–197 (2002) 847–858
853
Fig. 2. Glass transition temperature of PPO plasticized by carbon dioxide.
terephthalate), polystyrene, poly(vinyl chloride) at conditions reported by Chiou et al. [30], respectively. The glass transition temperature was compared with that predicted by Chow’s equation [31]: Tg ln = β{(1 − θ ) ln(1 − θ ) + θ ln θ } (12) Tg0 θ=
MP w zMd (1 − w)
(13)
β=
zR MP CPP
(14)
where MP and Md are the molar masses of the polymer repeat unit and the gas, respectively, R is the gas constant, CPP is the heat capacity change associated with the glass transition of the pure polymer, w the weight fraction of the gas, and z is the lattice coordination number that depends on the sizes of the gas molecule and the polymer repeat unit. The calculated glass transition temperatures using C PP = 0.265 J/K reported by Karasz et al. [32] are shown in Fig. 2. We used z = 3 to represent the glass transition temperature, whereas Handa et al. [28] reported a good fit of experimental results was obtained using z = 1. This discrepancy seems to be from the difference of the solubility data source, because Handa et al. used literature data [14] at a temperature of 35 ◦ C to make calculation with Chow’s equation. Solubilities of carbon dioxide in PPO(L)/PS (25–50 wt.% PPO(L)) blends are shown in Fig. 3 and Tables 6 and 7. In the figures, the solubilities in pure PPO and pure PS [11] are also shown. The solubility in PPO was from about 20 to 50% greater than that in PS at fixed temperature and pressure. While the solubility in PPO/PS (25/75) was slightly lower than that in PS at temperature of 373.15 K and above 12 MPa, the solubilities decreased with increasing PS concentration. The PPO/PS (25/75) blend, however, was in a glassy state at 373.15 K and atmospheric pressure as shown in Table 1, the solubilities did not exhibit dual mode sorption behavior. Kamiya et al. [33] found that sorption isotherms depended on the
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Fig. 3. Solubilities of carbon dioxide in PPO(L)/PS (50/50 and 25/75) blends.
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Table 6 Solubility of carbon dioxide in PPO/PS (50/50) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling Sw (S–L EOS) (vol.%)a
373.15
2.147 4.087 6.085 8.108 12.059 16.012 19.789
0.01659 0.02783 0.03708 0.04596 0.05800 0.06376 0.06432
0.01716 0.02982 0.04142 0.05398 0.07744 0.10178 0.12506
1.9 3.3 4.6 6.0 8.6 11.3 13.8
423.15
2.167 4.126 6.091 8.115 12.110 16.059 20.104
0.00997 0.01860 0.02661 0.03409 0.04537 0.05184 0.05398
0.01031 0.01989 0.02953 0.03944 0.05766 0.07354 0.08701
1.3 2.4 3.6 4.8 7.0 8.9 10.5
473.15
2.148 4.148 6.127 8.110 12.117 16.144 20.046
0.00808 0.01507 0.02135 0.02731 0.03721 0.04355 0.04691
0.00837 0.01613 0.02368 0.03146 0.04660 0.05986 0.07112
1.1 2.2 3.2 4.3 6.3 8.0 9.5
a
Same as defined in Table 2.
sample history in CO2 glassy poly(vinyl benzoate) system. In spite of the glassy state, the first sorption isotherm did not show adsorption in microvoid space and linearly increased with pressure. The isotherms agreed with those extrapolated from higher pressures above the glass transition concentration. In this work, since we wanted to discuss the blend concentration dependence on the solubility, a sample which had not been exposed to carbon dioxide was used. The solubilities were correlated with S–L EOS. The interaction parameters, k12 , determined from fitting the solubility are given in Table 5 and were found to be inversely proportional to absolute temperature. 3.2. Henry’s constant Henry’s constant were obtained from the experimental solubility data to examine concentration dependence on the solubility. Henry’s constant, KP (kg MPa/cm3 (STP)), was defined as follows: fg KP = lim (15) s→0 s where fg is fugacity of gas and s is solubility of gas in polymer (cm3 (STP)/kg polymer). Henry’s constant was evaluated by using the S–L EOS with optimized kij to exclude the Langmuir adsorption term.
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Table 7 Solubility of carbon dioxide in PPO/PS (25/75) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling S w (S–L EOS) (vol.%)a
373.15
2.127 4.107 6.051 8.095 11.887 15.965 20.110
0.01332 0.02451 0.03468 0.04377 0.05472 0.05773 0.05547
0.01375 0.02618 0.03849 0.05096 0.07147 0.08939 0.10470
1.4 2.7 4.0 5.3 7.4 9.2 10.8
423.15
2.113 4.125 6.023 8.047 12.023 15.995 20.013
0.00967 0.01831 0.02585 0.03303 0.04421 0.05056 0.05363
0.00997 0.01950 0.02846 0.03779 0.05518 0.06989 0.08334
1.1 2.2 3.2 4.3 6.2 7.9 9.3
473.15
2.219 4.113 6.111 8.088 12.092 16.065 20.060
0.00663 0.01327 0.01980 0.02574 0.03596 0.04303 0.04794
0.00685 0.01413 0.02179 0.02933 0.04427 0.05765 0.07046
0.9 1.8 2.7 3.7 5.5 7.1 8.7
a
Same as defined in Table 2.
Concentration dependence on Henry’s constants for carbon dioxide in PPO, PS, and their blends is shown in Fig. 4. At temperatures of 423.15 and 473.15 K, Henry’s constants in the blend polymers satisfied additivity of that in each pure polymer. Henry’s constants at temperature of 373.15 K, however, deviated from additivity. This behavior was very similar to that observed for PPO/PS blend specific volumes [22]; while specific volume of the blends at atmospheric pressure exhibited volume additivity of pure polymer in the molten state, that in glassy state deviated from volume additivity. Masi et al. [15] observed similar additivity of Henry’s constants for carbon dioxide in glassy polycarbonate/copolyester blend. They represented concentration dependence on Henry’s constant based on Flory–Huggins theory as follows: 1 1 1 ln (16) = φ20 ln + φ30 ln + φ20 φ30 χ23 KP1b KP12 KP13 where φ20 + φ30 = 1, and φ i 0 give the blend volume fraction of i on a component 1 (gas) free basis. This relation predicts that ln(1/KP1b ) will be a linear function of the blend volume fraction when χ23 = 0. For miscible blends of high molecular weight polymers, χ23 must be negative. Hence, only departures below the linear tie line connection ln(1/KP ) in pure polymers can be expected, whereas the Henry’s constant in molten state were found to be linear functions of the composition.
Y. Sato et al. / Fluid Phase Equilibria 194–197 (2002) 847–858
857
Fig. 4. Concentration dependence on Henry’s constants for carbon dioxide in PPO, PS, and their blends.
4. Conclusion The solubility of carbon dioxide in PPO and PPO/PS blends increased with increasing pressure and decreasing temperature. The solubility in PPO was from 20 to 50% greater than that in PS at similar conditions of temperature and pressure. The solubilities could be correlated with the EDMS model in conjunction with Sanchez and Lacombe equation-of-state. According to the estimations, a 100 K glass transition temperature depression was caused by dissolution of carbon dioxide into PPO. Interaction parameters of the S–L EOS determined from fitting the solubility were found to be inversely proportional to absolute temperature. PPO concentration dependence on Henry’s constant for carbon dioxide in the blends were studied. The Henry’s constants in the molten state appeared to be additive for that of each pure polymer, while the Henry’s constants in the glassy state deviated below from additivity. Acknowledgements The authors wish to acknowledge Asahi Chemical Industry Co. Ltd. (Kawasaki) for supplying the PPO and PPO/PS blends, and Mr. A. Sorakubo for his assistance with experiments. This work was supported through a “Metrological Study of Thermophysical Properties of Liquids and High Temperature Melts” program of Japan Space Utilization Promotion Center contracted under the New Energy and Industrial Technology Development Organization as a part of “Research and Development for Establishment and Utilization of a Technical Infrastructure for Japanese Industry”. References [1] J. Stoelting, F.E. Karasz, W.J. MacKnight, Polym. Eng. Sci. 10 (1970) 133–138. [2] A.R. Schultz, B.M. Bendron, J. Appl. Polym. Sci. 16 (1972) 461–471.
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Solubility of carbon dioxide in PPO and PPO/PS blends Yoshiyuki Sato, Tadao Takikawa, Michiyo Yamane, Shigeki Takishima, Hirokatsu Masuoka∗ Department of Chemical Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan Received 7 April 2001; accepted 10 August 2001
Abstract Solubility of carbon dioxide in poly(2,6-dimethyl-1,4-phenylene ether) (PPO) and PPO+polystyrene (PS) blends (25–50 wt.% PPO) was measured at temperatures of 373.15, 427.15, and 473.15 K and pressures up to 20 MPa. The solubility in the blends increased with increasing PPO concentration. The solubility could be correlated with the extended dual mode sorption (EDMS) model in conjunction with Sanchez and Lacombe equation-of-state. The EDMS model correlation estimated a 100 K glass transition temperature depression of PPO by dissolution of carbon dioxide. While Henry’s constants for carbon dioxide in the blend polymers in molten state could be satisfied by additivity of the Henry’s constant in each pure polymer, the Henry’s constants in the glassy state did not show additivity. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Data; Solubility; Henry’s constant; Carbon dioxide; Polymer blend
1. Introduction Polymeric foams are widely used as heat insulators, food trays, and support materials, because of their many advantageous characteristics such as low thermal conductivity, light weight, and high impact strength. Trichlorofluoromethane (CFC-11) and dichlorodifluoromethane (CFC-12) have been used as physical blowing agents for these types of industrial foaming processes. However, since production of these gases has been prohibited, new environmentally benign alternative blowing agents such as carbon dioxide and nitrogen are being considered. For effective process design, solubility and diffusivity of these gases in polymers are necessary. While a lot of polymer blends are immiscible, some polymer blends can form single-phase solids and melts. Probably the most important and most widely studied single-phase blends are the blends of poly(2,6-dimethyl-1,4-phenylene ether) (PPO) with polystyrene (PS). Molecular compatibility of PPO with PS has been demonstrated over the whole composition range by a number of different techniques ∗
Corresponding author. Tel.: +81-824-24-7721; fax: +81-824-24-7721. E-mail address: [email protected] (H. Masuoka). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 6 8 7 - 2
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[1–3]. Hence, examine of the composition dependence of blend polymers on gas solubility is needed data. While solubility of carbon dioxide in pure PPO or PS was reported by a number of authors [4–14], the solubility in these blends of this work have not been reported. Solubility of carbon dioxide in blend polymers was studied by several researchers [15–17], while concentration dependence of blend polymers on solubility of gas was not clear especially in thermodynamically equilibrium molten state. In this work, solubility of carbon dioxide in PPO and PPO + PS blends was measured at temperatures of 373.15, 427.15, and 473.15 K and pressures up to 20 MPa. Furthermore, Henry’s constants for carbon dioxide in PPO and the blend were examined to investigate the PPO concentration dependence of the solubility.
2. Experimental 2.1. Materials Two phenylene ether polymers were used: low molecular weight poly(2,6-dimethyl-1,4-phenylene ether), PPO(L) and high molecular weight poly(2,6-dimethyl-1,4-phenylene ether), PPO(H). PPO(L) with PS blends (PPO(L) 25–50 wt.%) were also used. All polymers were supplied by Asahi Chemicals Inc. (Kawasaki). Table 1 gives the characteristics of the polymers as reported by the supplier. Carbon dioxide (>99.5% purity) was obtained from Iwatani Industrial Gases Corp. (Hiroshima). All chemicals were used as received. 2.2. Apparatus and methods The solubility of carbon dioxide was obtained with a magnetic suspension balance (MSB) [18]. In this method, the measuring force is transmitted contactlessly via magnetic coupling from the measuring chamber to the microbalance, which is located outside the chamber under ambient atmospheric conditions. The MSB can be used at pressures up to 35 MPa and temperatures up to 523 K. Resolution and accuracy of the microbalance (Mettler AT261, Switzerland) are 0.01 mg and 0.002%, respectively. Details of the apparatus and experimental procedure used in this work have been described in previous publications [11,19]. Density of carbon dioxide needed for buoyancy correction was obtained from the equation-of-state of Span and Wagner [20]. The volume of the sample was obtained from sample mass and specific volume that was calculated from the Tait [21] parameters reported by Zoller and Hoehn [22]. Swelling of the polymer is caused by gas sorption. Since it is difficult to measure the swelling of the Table 1 Polymer properties Tg (K) PPO(H) PPO(L) PPO(L)/PS 50/50 PPO(L)/PS 25/75 PS
479.0 477.1 416.8 394.3 381.4
M¯ n × 10−4
M¯ w × 10−4
2.4 2.2
6.3 4.7
10.6
33.1
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molten polymer, we estimated its value by the Sanchez–Lacombe equation-of-state (S–L EOS) [23,24] and used this to correct for buoyancy. The uncertainties of pressure, temperature, and solubility in this work were estimated to within 4.1 kPa, 0.05 K, and 15%, respectively. 3. Results and discussion 3.1. Solubility Solubility of carbon dioxide in PPO(H) and PPO(L) are shown in Fig. 1 and Tables 2 and 3. In the figure, open and filled symbols denote lower molecular weight PPO (M¯ w = 4.7 × 104 ) and higher one (M¯ w = 6.3 × 104 ), respectively. While the solubilities at 423.15 and 473.15 K in both polymers agreed within the experimental uncertainty, the solubilities at 373.15 K showed somewhat different results. The solubilities extrapolated to zero pressure did not pass the origin at temperatures of 373.15 and 423.15 K. This behavior seems to show that adsorption [25] of carbon dioxide in the microvoids of the polymer occurred. These isotherms were correlated with the extended dual mode sorption (EDMS) model developed by Kamiya et al. [26]. Since glass transition pressures and concentration data were not available, the glass transition was estimated with EDMS model correlation. EDMS model is developed beginning from the following relationships: C = CD + CH
(1)
where CD and CH are concentrations of gas in polymer matrix and in microvoids existing in glassy polymer. CH is expressed with Langmuir adsorption equation as follow: CH =
CH0 bP(1 − C ∗ /Cg ) 1 + bP
(2)
C ∗ = CD + fCH
(3)
Fig. 1. Solubility of carbon dioxide in PPO.
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Table 2 Solubility of carbon dioxide in PPO(H) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling S w (S–L EOS) (vol.%)a
373.15
2.058 4.003 6.095 8.100 10.111 11.965 13.935 15.993 17.933 20.006
0.03525 0.05158 0.06313 0.07050 0.07544 0.07815 0.08050 0.08303 0.08637 0.08802
0.03583 0.05389 0.06887 0.08128 0.09330 0.10601 0.12026 0.13747 0.15604 0.17442
2.0 3.9 5.9 7.9 9.8 12.2 14.0 15.8 17.4 19.0
423.15
1.983 4.105 6.101 8.056 10.061 12.108 14.078 16.098 18.076 20.076
0.01474 0.02577 0.03358 0.03925 0.04596 0.05327 0.05909 0.06366 0.06759 0.07087
0.01508 0.02725 0.03696 0.04548 0.05595 0.06812 0.07960 0.09099 0.10252 0.11434
1.4 2.8 4.2 5.7 7.1 8.5 9.9 11.2 12.5 13.8
473.15
2.179 4.142 6.174 8.085 10.082 12.078 14.063 16.032 18.106 20.208
0.00680 0.01482 0.02277 0.02976 0.03602 0.04213 0.04732 0.05166 0.05625 0.05935
0.00704 0.01585 0.02525 0.03423 0.04312 0.05263 0.06182 0.07073 0.08111 0.09038
1.0 2.2 3.5 4.7 5.9 7.2 8.5 9.7 11.1 12.3
a Sw = (1 + S)vSL (T , P , S)/(vSL (T , P , 0)) × 100, where v SL : specific volume estimated with S–L EOS, S: solubility of CO2 (g gas/g polymer).
where C∗ and CH0 are effective concentration of sorbed solute to plasticize the polymer and hole saturation ∗ constant at C = 0, respectively. In Eq. (2), Cg is a glass transition concentration that is a function of temperature and pressure. The variable f is the ratio of the plasticizing ability of a Langmuir species to that of a sorbed species and was set equal to zero for simplicity in the calculations. The CD is expressed with Henry’s law or Flory–Huggins law in the EDMS model of Kamiya et al. [26]. In this work, we used the Sanchez and Lacombe equation-of-state [23,24] to represent the CD term. The S–L EOS is shown below: 1 2 ˜ ˜ P = −ρ˜ − T ln(1 − ρ) ˜ + 1− ρ˜ (4) r
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Table 3 Solubility of carbon dioxide in PPO(L) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling Sw (S–L EOS) (vol.%)a
373.15
2.125 4.118 6.098 8.051 12.043 16.023 19.964
0.02916 0.04649 0.05902 0.06833 0.08131 0.08616 0.09202
0.02980 0.04904 0.06498 0.07938 0.11084 0.14338 0.18232
2.1 4.1 6.2 8.2 12.8 16.5 19.9
423.15
2.15 4.15 6.04 8.133 12.121 16.077
0.01420 0.02462 0.03211 0.03942 0.05276 0.06369
0.01459 0.02612 0.03540 0.04573 0.06753 0.09072
1.5 2.8 4.1 5.7 8.5 11.1
473.15
2.097 4.155 6.120 8.048 12.122 16.072
0.00849 0.01596 0.02233 0.02817 0.04037 0.04672
0.00877 0.01707 0.02474 0.03237 0.05048 0.06398
1.2 2.4 3.4 4.5 6.9 8.7
a
Same as defined in Table 2.
P P˜ = ∗ , P
ρ˜ =
ρ , ρ∗
T T˜ = ∗ , T
r=
MP∗ RT∗ ρ ∗
(5)
where characteristic parameters, P∗ , ρ ∗ , and T∗ of the S–L EOS for mixture were evaluated from the following mixing rules: P∗ = (6) φi φj Pij∗ i
j
Pij∗ = (1 − kij )(Pi∗ Pj∗ )0.5 φ0T ∗ i i ∗ ∗ T =P ∗ P i i 1 φi0 = r ri0 i
(7) (8)
(9)
φi P ∗ /T ∗ φi0 = i ∗ i ∗ j φj Pj /Tj
(10)
wi /ρi∗ φi = ∗ j wj /ρj
(11)
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Table 4 Characteristic parameters for Sanchez–Lacombe EOS Substance
P∗ (MPa)
ρ ∗ (kg/m3 )
T∗ (K)
Ref.
Carbon dioxide PS PPO/PS (25/75) PPO/PS (50/50) PPO
720.3 387.0 511.7 432.0 452.0
1580 1108 1118 1136 1173
208.9 + 0.459T − 7.56 × 10−4 T 2 739.9 758.5 748.9 729.5
[27] [10] This worka This worka This worka
a
Parameters were determined in this work using PVT data reported by Zoller and Hoehn [22].
In Eqs. (6)–(11), Ti∗ , Pi∗ , ρi∗ , and ri0 refer to the characteristic parameters of component i in the pure state and kij is a binary interaction parameter determined by fitting the equation to the experimental solubilities. The pure component parameters used are given in Table 4. The parameters for blend polymer were determined as pseudo-pure polymer by fitting PVT data reported by Zoller and Hoehn [22]. In the calculation of the solubilities, it was assumed that the polymer was monodisperse and that it did not dissolve in the vapor phase. Correlation results with the EDMS model are shown by the lines in Fig. 1. The EDMS model satisfactorily represented the solubility data. The EDMS model parameters determined with the correlation are given in Table 5. Glass transition pressure, Pg , was determined from Cg and the equation-of-state and is listed in Table 5 for reference. Estimated glass transition temperature of PPO plasticized by carbon dioxide is shown in Fig. 2. The glass transition temperatures of PPO reported by Handa et al. [28], and Hachisuka et al. [29] are also shown. These literature values were plotted against the solubility predicted with S–L EOS in conjunction with the interaction parameter described below. Depression of the glass transition temperature dependence on the solubility was similar to that reported by Handa et al. [28]. The glass transition temperature almost linearly decreased with the amount of carbon dioxide and was depressed about 100 K from dissolution of 0.1 g CO2 /g polymer. Depression of the glass transition temperature of PPO was 1.2, 1.6, 2.1, and 2.2 times higher than that of polycarbonate, poly(ethylene Table 5 Parameters of extended dual mode sorption model Polymer
Temperature (K)
k12 (–)
CH0 /Cg (–)
Cg (g gas/kg polymer)
b (MPa−1 )
Pg (MPa)
PPO(L)
373.15 423.15 473.15 373.15 423.15 473.15 373.15 423.15 473.15 373.15 423.15 473.15
−0.087 −0.124 −0.179 −0.083 −0.124 −0.179 −0.043 −0.092 −0.148 −0.069 −0.116 −0.182
0.385 2.012 – 0.445 0.419 –
88.55 39.86 – 95.72 45.11 –
0.293 0.022 – 0.498 0.190 –
9.36 7.08 – 10.63 7.94 –
PPO(H)
PPO/PS (25/75)
PPO/PS (50/50)
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853
Fig. 2. Glass transition temperature of PPO plasticized by carbon dioxide.
terephthalate), polystyrene, poly(vinyl chloride) at conditions reported by Chiou et al. [30], respectively. The glass transition temperature was compared with that predicted by Chow’s equation [31]: Tg ln = β{(1 − θ ) ln(1 − θ ) + θ ln θ } (12) Tg0 θ=
MP w zMd (1 − w)
(13)
β=
zR MP CPP
(14)
where MP and Md are the molar masses of the polymer repeat unit and the gas, respectively, R is the gas constant, CPP is the heat capacity change associated with the glass transition of the pure polymer, w the weight fraction of the gas, and z is the lattice coordination number that depends on the sizes of the gas molecule and the polymer repeat unit. The calculated glass transition temperatures using C PP = 0.265 J/K reported by Karasz et al. [32] are shown in Fig. 2. We used z = 3 to represent the glass transition temperature, whereas Handa et al. [28] reported a good fit of experimental results was obtained using z = 1. This discrepancy seems to be from the difference of the solubility data source, because Handa et al. used literature data [14] at a temperature of 35 ◦ C to make calculation with Chow’s equation. Solubilities of carbon dioxide in PPO(L)/PS (25–50 wt.% PPO(L)) blends are shown in Fig. 3 and Tables 6 and 7. In the figures, the solubilities in pure PPO and pure PS [11] are also shown. The solubility in PPO was from about 20 to 50% greater than that in PS at fixed temperature and pressure. While the solubility in PPO/PS (25/75) was slightly lower than that in PS at temperature of 373.15 K and above 12 MPa, the solubilities decreased with increasing PS concentration. The PPO/PS (25/75) blend, however, was in a glassy state at 373.15 K and atmospheric pressure as shown in Table 1, the solubilities did not exhibit dual mode sorption behavior. Kamiya et al. [33] found that sorption isotherms depended on the
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Fig. 3. Solubilities of carbon dioxide in PPO(L)/PS (50/50 and 25/75) blends.
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Table 6 Solubility of carbon dioxide in PPO/PS (50/50) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling Sw (S–L EOS) (vol.%)a
373.15
2.147 4.087 6.085 8.108 12.059 16.012 19.789
0.01659 0.02783 0.03708 0.04596 0.05800 0.06376 0.06432
0.01716 0.02982 0.04142 0.05398 0.07744 0.10178 0.12506
1.9 3.3 4.6 6.0 8.6 11.3 13.8
423.15
2.167 4.126 6.091 8.115 12.110 16.059 20.104
0.00997 0.01860 0.02661 0.03409 0.04537 0.05184 0.05398
0.01031 0.01989 0.02953 0.03944 0.05766 0.07354 0.08701
1.3 2.4 3.6 4.8 7.0 8.9 10.5
473.15
2.148 4.148 6.127 8.110 12.117 16.144 20.046
0.00808 0.01507 0.02135 0.02731 0.03721 0.04355 0.04691
0.00837 0.01613 0.02368 0.03146 0.04660 0.05986 0.07112
1.1 2.2 3.2 4.3 6.3 8.0 9.5
a
Same as defined in Table 2.
sample history in CO2 glassy poly(vinyl benzoate) system. In spite of the glassy state, the first sorption isotherm did not show adsorption in microvoid space and linearly increased with pressure. The isotherms agreed with those extrapolated from higher pressures above the glass transition concentration. In this work, since we wanted to discuss the blend concentration dependence on the solubility, a sample which had not been exposed to carbon dioxide was used. The solubilities were correlated with S–L EOS. The interaction parameters, k12 , determined from fitting the solubility are given in Table 5 and were found to be inversely proportional to absolute temperature. 3.2. Henry’s constant Henry’s constant were obtained from the experimental solubility data to examine concentration dependence on the solubility. Henry’s constant, KP (kg MPa/cm3 (STP)), was defined as follows: fg KP = lim (15) s→0 s where fg is fugacity of gas and s is solubility of gas in polymer (cm3 (STP)/kg polymer). Henry’s constant was evaluated by using the S–L EOS with optimized kij to exclude the Langmuir adsorption term.
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Table 7 Solubility of carbon dioxide in PPO/PS (25/75) Temperature (K)
Pressure (MPa)
Solubility without swelling correction (g gas/g polymer)
Solubility with swelling correction (g gas/g polymer)
Swelling S w (S–L EOS) (vol.%)a
373.15
2.127 4.107 6.051 8.095 11.887 15.965 20.110
0.01332 0.02451 0.03468 0.04377 0.05472 0.05773 0.05547
0.01375 0.02618 0.03849 0.05096 0.07147 0.08939 0.10470
1.4 2.7 4.0 5.3 7.4 9.2 10.8
423.15
2.113 4.125 6.023 8.047 12.023 15.995 20.013
0.00967 0.01831 0.02585 0.03303 0.04421 0.05056 0.05363
0.00997 0.01950 0.02846 0.03779 0.05518 0.06989 0.08334
1.1 2.2 3.2 4.3 6.2 7.9 9.3
473.15
2.219 4.113 6.111 8.088 12.092 16.065 20.060
0.00663 0.01327 0.01980 0.02574 0.03596 0.04303 0.04794
0.00685 0.01413 0.02179 0.02933 0.04427 0.05765 0.07046
0.9 1.8 2.7 3.7 5.5 7.1 8.7
a
Same as defined in Table 2.
Concentration dependence on Henry’s constants for carbon dioxide in PPO, PS, and their blends is shown in Fig. 4. At temperatures of 423.15 and 473.15 K, Henry’s constants in the blend polymers satisfied additivity of that in each pure polymer. Henry’s constants at temperature of 373.15 K, however, deviated from additivity. This behavior was very similar to that observed for PPO/PS blend specific volumes [22]; while specific volume of the blends at atmospheric pressure exhibited volume additivity of pure polymer in the molten state, that in glassy state deviated from volume additivity. Masi et al. [15] observed similar additivity of Henry’s constants for carbon dioxide in glassy polycarbonate/copolyester blend. They represented concentration dependence on Henry’s constant based on Flory–Huggins theory as follows: 1 1 1 ln (16) = φ20 ln + φ30 ln + φ20 φ30 χ23 KP1b KP12 KP13 where φ20 + φ30 = 1, and φ i 0 give the blend volume fraction of i on a component 1 (gas) free basis. This relation predicts that ln(1/KP1b ) will be a linear function of the blend volume fraction when χ23 = 0. For miscible blends of high molecular weight polymers, χ23 must be negative. Hence, only departures below the linear tie line connection ln(1/KP ) in pure polymers can be expected, whereas the Henry’s constant in molten state were found to be linear functions of the composition.
Y. Sato et al. / Fluid Phase Equilibria 194–197 (2002) 847–858
857
Fig. 4. Concentration dependence on Henry’s constants for carbon dioxide in PPO, PS, and their blends.
4. Conclusion The solubility of carbon dioxide in PPO and PPO/PS blends increased with increasing pressure and decreasing temperature. The solubility in PPO was from 20 to 50% greater than that in PS at similar conditions of temperature and pressure. The solubilities could be correlated with the EDMS model in conjunction with Sanchez and Lacombe equation-of-state. According to the estimations, a 100 K glass transition temperature depression was caused by dissolution of carbon dioxide into PPO. Interaction parameters of the S–L EOS determined from fitting the solubility were found to be inversely proportional to absolute temperature. PPO concentration dependence on Henry’s constant for carbon dioxide in the blends were studied. The Henry’s constants in the molten state appeared to be additive for that of each pure polymer, while the Henry’s constants in the glassy state deviated below from additivity. Acknowledgements The authors wish to acknowledge Asahi Chemical Industry Co. Ltd. (Kawasaki) for supplying the PPO and PPO/PS blends, and Mr. A. Sorakubo for his assistance with experiments. This work was supported through a “Metrological Study of Thermophysical Properties of Liquids and High Temperature Melts” program of Japan Space Utilization Promotion Center contracted under the New Energy and Industrial Technology Development Organization as a part of “Research and Development for Establishment and Utilization of a Technical Infrastructure for Japanese Industry”. References [1] J. Stoelting, F.E. Karasz, W.J. MacKnight, Polym. Eng. Sci. 10 (1970) 133–138. [2] A.R. Schultz, B.M. Bendron, J. Appl. Polym. Sci. 16 (1972) 461–471.
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